Wikipedia talk:WikiProject Mathematics/Archive/2012

Jan 2012

Galilean transformations

Could we add something about Galilean transformations as a Lie group? For example, the Euclidean transformations, Euc(n,R) can be embedded as a Lie subgroup of GL(n+1,R), if I remember correctly, by

$(X,t)\mapsto \left[{\begin{array}{c|c}1&0\\\hline t&X\end{array}}\right],$

where X is a special orthogonal transformation and t is a translation. Could (or should) we add something similar for Galilean transformations? — Fly by Night (talk) 16:11, 23 December 2011 (UTC)

There is something on this topic in the Representation theory of the Galilean group article. But in a notation similar to yours, there is an embedding to GL(n+2, ℝ) :

$(X,\mathbf {v} ,\mathbf {t} ,t_{0})\mapsto \left[{\begin{array}{c|c|c}1&0&0\\\hline t_{0}&1&0\\\hline \mathbf {t} &\mathbf {v} &X\end{array}}\right],$

where X is a special orthogonal transformation, v is a relative velocity, t and t₀ are spacial and temporal translations. Incnis Mrsi (talk) 19:25, 1 January 2012 (UTC)

Many EoM links still broken

Not long ago, there was a discussion about links to Springer's Encyclopedia of Mathematics now being broken due to a restructuring of that website. I just noticed that many of the links are still broken. Is someone making a systematic effort to repair these, or are we supposed to do it on an ad hoc basis? Sławomir Biały (talk) 14:12, 30 December 2011 (UTC)

a working patch would be to replace the line "contribution-url=http://www.encyclopediaofmath.org/index.php?title={{{id|{{{urlname|Main_Page}}}}}}" with something like "contribution-url=http://www.encyclopediaofmath.org/index.php/{{{title|{{{urlname|Main_Page}}}}}}" (to make it work, "title" should be replaced with a regexp which substitutes underscore for a space, I do not know how to do it)

another solution would be to make a bot replace the id with the title in all the pages that link to the template.

Sasha (talk) 15:18, 30 December 2011 (UTC)

Yes, I was thinking that some sort of automated mass edit would be the way to do it. I lack the skill myself. Sławomir Biały (talk) 00:08, 31 December 2011 (UTC)

Automated edits wouldn't work if you're linking to a specific version of an article, which is something you'd need to do if you're using the EoM as a reference instead of an external link. (I know there are objections to it being used as a ref. but it's being done.) It would at least help avoid having people land on EoM's main page when they click the link, but there would need to be a lot of manual checking and corrections.--RDBury (talk) 03:41, 31 December 2011 (UTC)

Whatever is done, I assume it's possible to update all of the old links so they at least link somewhere. At the moment, they all seem to give 404 errors, which doesn't work for references or external links. Sławomir Biały (talk) 11:48, 2 January 2012 (UTC)

Superior intellects and infinitesimal knowledge

An incident is being discussed here. Tkuvho (talk) 13:41, 3 January 2012 (UTC)

Resolved Brad7777 (talk) 17:11, 4 January 2012 (UTC)

Thanks, 'Here I am, superior to Newton, Leibniz and Cauchy'. That's my one a day essential of something no vitamin pill contains :) Dmcq (talk) 18:20, 4 January 2012 (UTC)

page Philip Ehrlich proposed for deletion

The page is being proposed for deletion even though there are suitable secondary sources there. Tkuvho (talk) 10:39, 4 January 2012 (UTC)

See WP:BLPPROD (the 'policy' link in the PROD template): "the BLP deletion template may be removed only after the biography contains a reliable source that supports at least one statement made about the person in the article" (my emphasis). The one source is a review of one of his works, not about him. The other link is to his department home page, so not a reliable source.--JohnBlackburne^words_deeds 10:50, 4 January 2012 (UTC)

The link is not to his personal homepage, it's to his department's index of him. This is a reliable source for his academic affiliation. I'd say that your being a bit heavy-handed with BLP prod. There may be good reasons to delete the article, but this surely isn't one of them. Sławomir Biały (talk) 11:35, 4 January 2012 (UTC)

Steven G. Krantz

How many things wrong can be found here: Steven G. Krantz? Main thing I can see is that it seems to have been written (or at least contributed to) by himself. Also see some weasel words: "Krantz is widely considered to be a charismatic and galvanizing teacher. Many students consider him to be the best mathematics teacher that they have ever had." What do we do with pages like this? --Matt Westwood 19:00, 6 January 2012 (UTC)

The article is very detailed, but it does have a lot of flowery phrases and weasel words that need to be attributed to a source. Moreover, much of it lacks sources. Whatever we do, let's try not to be gentle with the new editor User:Sgkrantz. Steven Krantz actually is a very well respected mathematician and brilliant expositor. He would definitely be an asset to the project. Sławomir Biały (talk) 10:39, 7 January 2012 (UTC)

I have done a general tidy up to try to remove peacock terms, weasel words, repetition, self-promotion and a story about a 20-year old dispute with Mandelbrot. I haven't addressed the sourcing issue, apart from tagging a couple of the most obvious unsourced facts e.g. Erdős number. User:Sgkrantz is not exactly a new editor - the account was opened in June 2010 and the editor has been sporadically active since then, but has only ever edited the Steven G. Krantz page as far as I can tell. If User:Sgkrantz is indeed Steven G. Krantz then there is obviously a COI issue here. More work needs to be done on the article, but I'll let someone else take it from here. Gandalf61 (talk) 12:35, 7 January 2012 (UTC)

Template:mvar

I have just learned of {{mvar}} through its installation on Quaternion. It applies {{math}} and additionally surrounds its argument in HTML <var> tags.

Is this a good idea? I recall the discussion Wikipedia talk:Manual of Style/Text formatting/Archive 2#Variable markup where consensus was that manually applying <var> was undesirable. It seems to me that {{mvar}} really isn't any better. Ozob (talk) 23:07, 6 January 2012 (UTC)

Reviewing that discussion, my impression is that the consensus was more along the lines that a guideline recommending the use of a manually inserted <var> is undesirable, but that individual editors have some freedom. It was also apparent that the semantic markup value in HTML was pretty much a lost cause in the math context, but that font formatting is necessary. The implementation of {{mvar}} is not important (i.e. whether it uses <var> or '' to italicize), as this can be changed in principle in the template. The question then becomes whether use of {{mvar|x}} in place of {{math|''x''}} is to be discouraged - i.e. whether the template {{mvar}} should be deprecated. I see no urgency in doing so. Its only real value is a shorthand for italic-serif. Its use does show up the continued shortcomings of the HTML output of <math>, and the inconvenience of formatting both italic and serif in-line, resulting in the (IMO unfortunate) de facto use of sans-serif for math. — Quondum^t_c 05:32, 7 January 2012 (UTC)

{{mvar}} is better than <var>, as a wikicode level (i.e. higher than HTML) tag which may be eventually customized. The same reason for which CSS is "better" than physical formatting, <span> better than <font> etc. Concerning the HTML output of <math>, the most annoying shortcoming IMHO is a space after unary minus: $-x$, compared to −x. Sometimes this puts a formula to the edge of unlegibility, like in $[x,y]=xy-(-1)^{|x||y|}yx$ . Sadly, I do not know much about TeX math typesetting. Could we remove that space and, possibly, also add half-spaces ( ) to some positions, like [x, y] ? Incnis Mrsi (talk) 10:58, 8 January 2012 (UTC)

Template:Mactutor once again

Hello colleagues,

{{MacTutor/sandbox}} now implements a suggestion of Daniele Tampieri: O'Connor & Robertson are downgraded to editors, and there are author fields (last, first, last2, ...) It seems to work on the examples that I have checked. I suggest to replace {{MacTutor}} with this version.

Please criticise this suggestion (and the implementation) before it's too late.

Sasha (talk) 23:37, 30 December 2011 (UTC)

Many of the articles, e.g. the one on Gauss, actually were written by O'Connor & Robertson, so changing the template would cause these cites to be inaccurate. Maybe make the template default to them as authors unless another author is given.--RDBury (talk) 03:31, 31 December 2011 (UTC)

you are quite right, but my template skills are very poor (I did not succeed to do this). If yours are better, could you help (or at least explain how to do it)? Sasha (talk) 04:14, 31 December 2011 (UTC)

I'll try to look at the template code this weekend, even if I'm not so skilled in programming: as a matter of fact, RDBury is right when he says that most of the biographies are authored by O'Connor & Robertson. I also would like to praise Sasha's work, since he was able to construct an almost perfectly working (in my opinion) alternative template. Daniele.tampieri (talk) 06:50, 31 December 2011 (UTC)

Unfortunately I was not able to modify the {{MacTutor/sandbox}} yesterday: I'll try to do it this week but I'll probably succeed from next Saturday on, i.e. during next weekend. However, I tried some working solutions that resulted flawed by following shortcomings

1. I was able to introduce O'Connor & Robertson names as a default (i.e. when no other names are specified) in the first two author-related fields, but I was not able to conditionally remove them from the editor fields: is the wiki markup able to deal with flow-control statements? However, this could be considered a minor problem, since adopting one of those solutions would imply the two coordinators of the MacTutor project appearing both as authors and as editors, an situation which is commonly encountered in the proceedings of scientific conferences or collections of scientific papers.
2. This one is worst, and it is still related to the possibility of using flow-control statements in the wiki markup. I was not able to conditionally control the correctness of the author-link field. As an example, if I use the same pattern used to solve (partially) the author fields problem, then when an author-link is not specified since the author doesn't have a dedicated wikipedia entry, a link to O'Connor and/or Robertson wikipedia entries would be placed instead, and this would be damn wrong.

I hope to have a look to the wiki markup syntax rules and solve this issues. Daniele.tampieri (talk) 09:51, 2 January 2012 (UTC)

Conditional statements are available. See Help:Magic words. --Salix (talk): 10:36, 2 January 2012 (UTC)

Thank you very much Richard (aka Salix alba): I'll give a look to 'em and work on a new solution. :-D Daniele.tampieri (talk) 12:11, 2 January 2012 (UTC)

Hi everybody: today I succeeded in modifying the template in order to make it able to perform the format shown here, while leaving intact all its standard features and formats: this means that if there is not a guest author name to provide, the template will show the citation in the same way the actual one does, otherwise it will show the provided authors names, linked to their Wikipedia pages if possible/desired, and will credit O'Connor and Robertson for their work as editors. Everyone can check the template structure looking to the Template:MacTutor/sandbox page, and can see a comparison with the actual template in its testcase page (including many extra cases). Please Enjoy! :-D Daniele.tampieri (talk) 21:37, 6 January 2012 (UTC)

looks perfect on the examples which I checked. Sasha (talk) 01:10, 8 January 2012 (UTC)

Ok, if there's anyone interested in the discussion in the template page, please contribute: otherwise tomorrow we'll place the {{edit protected}} template and start other standard procedures, just to use the supplementary flexibility of the new template version (obviously keeping all standard features). Daniele.tampieri (talk) 20:45, 8 January 2012 (UTC)

Templated {{MacTutor}} has been updated and its documentation have been changed accordingly: please check the template and report/correct any new issue. Daniele.tampieri (talk) 09:08, 10 January 2012 (UTC)

Two new articles up

Hi: I recently moved Double centralizer theorem and a related article on balanced modules into the mainspace. Feel free to take a look if you have spare time. Thanks! Rschwieb (talk) 21:41, 8 January 2012 (UTC)

please check that my copyediting did not introduce mistakes. Also, are the indices in the section "Polynomial identity rings" correct? Sasha (talk) 22:44, 8 January 2012 (UTC)

I tried to spot differences with "diff" but I wasn't sure I spotted them, it looked like entire paragraphs were shifted. After reading it all again though everything looks OK. (If it was an expression that needed changed, do you remember which you changed?) There was a subscript typo in the PI ring section yep, I corrected it. Thanks for taking a look! Rschwieb (talk) 03:27, 9 January 2012 (UTC)

I probably would have made a single article instead of two stubby ones, especially since 'Balanced module' has somewhat questionable notability. It may be just me though.--RDBury (talk) 13:50, 9 January 2012 (UTC)

If you search mathsci.net with "double centralizer property" instead of "balanced module" you get four times as many hits, but it makes for a poor article title. The two topics are of course related, but are not really intertwined, so they don't really make a good single article, especially if one intends to offer examples. Both stubby? I think double centralizer theorem is about an ideal length... Rschwieb (talk) 00:43, 10 January 2012 (UTC)

This also brings me to another question, since I made one of the articles to satisfy a requested mathematics article entry. Does the requested articles page ever get cleared of bluelinks? I had thought a bot was doing it, but it seems to me the bluelinks stay pretty much the same over time. Rschwieb (talk) 00:51, 10 January 2012 (UTC)

Real algebraic geometry and Selman Akbulut

There is a dispute on Talk:Real algebraic geometry#Edits by user:Estater need to be reverted which needs the intervention of other people. The subject of the dispute is edits unambiguously aimed to promote Selman Akbulut's work. Tentative to revert these edits has led to an edit war, which, for the moment, is won by the supporters of Akbulut (most probably Akbulut himself, with several login names). For non specialist people, I precise that Real algebraic geometry is a stub, almost reduced to an historical "guideline", which, before the edits, provided a good idea of the history of the area. D.Lazard (talk) 12:47, 9 January 2012 (UTC)

Too bad a goodwill effort on one math page gets rewarded by an accusation of causing fight or conspiracy on another gossip page. Shouldn't the wiki editors be discussing the mathematical merits of entries and intelligently evaluate their worth with experts, and then insert further edits (e.g. take them out or expand if necessary), as opposed yakety-yak about peoples reputation? generate conspiracy theories as to whose supporters doing which edits. If you behave like this how can you expect to extend the pool of wiki editors? Remarksen (talk) 22.20, 11 January 2012 (UTC)

Too bad this is an encyclopedia and not a goodwill diary. Brad7777 (talk) 23:17, 12 January 2012 (UTC)

Additive synthesis

More of a signal processing than a mathematical article you may think; and you should be right. But this is a needy article with a hefty chunk of mathematical notation, in need of: restructuring, rewriting, and admin attention, I hope in that order (but don't count on it - it has been briefly protected after heavy edit-warring). I'd regard it as a personal favour if people could weigh in and make it all make some sense. The page protection expires in the next few seconds ... Charles Matthews (talk) 19:03, 12 January 2012 (UTC)

Egorov's Theorem

I'd like to add another article about the other Egorov's Theorem which I mention on the talk page of Egorov's Theorem and a disambiguation page (because the two theorems are really not related). Any guidance or input on how to do this? Holmansf (talk) 23:33, 13 January 2012 (UTC)

Sokhotskii-Plemelj formula

Hello colleagues,

following a suggestion of Pym1507, I have added placed a "propose move" template at Talk:Sokhatsky–Weierstrass_theorem#Requested_move. Please comment.

Sasha (talk) 23:34, 13 January 2012 (UTC)

Glossary of areas of mathematics

So i have created the page Glossary of areas of mathematics which at the moment is more of a list with few annotations. i think it has potential and would compliment Areas of mathematics in the same way Outline of mathematics compliments mathematics. It would be useful to see thoughts on this page, and for any help completing it. Ultimately, should it be kept? (btw few entries may not be relevant but i figured it is easy to delete them) Brad7777 (talk) 13:27, 26 December 2011 (UTC)

It seems like a content fork where there already are several competing versions. 'Areas of mathematics' already has a merge tag and the 'Outline of mathematics' article has caused some controversy here as well (see e.g. Wikipedia talk:WikiProject Mathematics/Archive 45#Topic outlines).--RDBury (talk) 14:10, 26 December 2011 (UTC)

I have added computer algebra in both Glossary of areas of mathematics and Areas of mathematics. This area has several other names (mainly "symbolic computation" and "algebraic computation") which have not the same initial letter. Should this area appear 3 times in the glossary? D.Lazard (talk) 14:56, 26 December 2011 (UTC)

I think so; an annotation saying "see computer algebra" next to symbolic computation and algebraic computation would probably be ideal, with an annotation next to computer algebra including the fact that it has several other names such as symbolic computation and algebraic computation. Brad7777 (talk) 15:15, 26 December 2011 (UTC)

I'm not convinced that it's worth developing this article. I'd rather see the time spent on improving Outline of mathematics. Jowa fan (talk) 07:45, 31 December 2011 (UTC)

Isn't the page mathematics an outline of mathematics? i.e, an improved version of outline of mathematics? I think its important to note that Glossary of areas of mathematics can be completed objectively as opposed to outline of mathematics and does exactly what outline of mathematics was trying to do: provide the possiblity of gaining information on mathematics on the macro scale. In essence, the page is like a category, linking all pages relevent and most importantly it is easy to navigate. The beauty of course of outline of mathematics is that it isnt just focused on areas of mathematics, but the lists it contains are unavoidably biased (although the sections are split very efficiently). outline of mathematics would not be needed if the category system of mathematics was made to be more efficient to navigate through (think more along the lines of the sections of the page outline of mathematics) .

Look at

Mathematics

Mathematics by country

Fields of mathematics

Mathematics-related lists

Mathematicians

Works about mathematics

Mathematics and art

Mathematical classification systems

Mathematical concepts

Mathematical constants

Mathematics and culture

Eponyms in mathematics

Mathematical examples

History of mathematics

Mathematical notation

Mathematical science occupations

Outlines of mathematics and logic

Philosophy of mathematics

Mathematical projects

Mathematical proofs

Pseudomathematics

Set index articles on mathematics

Mathematical terminology

Mathematical theorems

Mathematical tools

Mathematics stubs

Who would click on for example Category:mathematical comparisons?? or Category:mathematical examples? or Category:mathematical tables? Category:mathematics-related lists? these are apart of the outline of mathematics? Brad7777 (talk) 14:52, 14 January 2012 (UTC)

Category:Indexes of mathematics topics

Of the 12 pages already in this category,

• 5 are called "Index of ..."
• 7 are called "List of ..."

Just to clarify, an index is just a list that is in alphabetical order? If so, should all the articles in this category called "list of ..." that are in alphabetical order be renamed to "index of ..."? And what are thoughts about the renaming of Category:Indexes of mathematics topics to Category:Mathematics-related indexes to include all the relevant indexes, as im assuming there will be more from the 230 pages currently in Category:Mathematics-related lists. Brad7777 (talk) 20:18, 14 January 2012 (UTC)

GA nomination for Catenary

Last month I put Catenary up for GA and have put a lot of work into it since in response to the reviewer's comments. If interested, see Talk:Catenary/GA1 for the discussion, especially if you'd like to help resolve the outstanding issues. For some reason this isn't showing up on the current activity page.--RDBury (talk) 14:57, 16 January 2012 (UTC)

More specifically, if someone would like to take a look at the lead section and do what needs to be done I'd appreciate it. This is my first time with the GA process so I'm not really sure what's expected with it.--RDBury (talk) 15:17, 19 January 2012 (UTC)

Because of the hatnote, I would suggest to move from the history section to the lead the mention of the other names of catenary. May be also mention that "chainette" is the French name of the catenary, which means "small chain". D.Lazard (talk) 15:50, 19 January 2012 (UTC)

I moved the alternate names to the lead, good idea btw. Not sure that chainette being the French name is needed since it's already listed as an alternate English name.--RDBury (talk) 01:28, 20 January 2012 (UTC)

I have suggested to insert the French origin of "chainette" only because this name could be strange for a non French speaker. D.Lazard (talk) 10:33, 20 January 2012 (UTC)

The Method

The page The Method used to be a disambiguation page, one of the meanings being The Method of Mechanical Theorems of Archimedes. An editor redirected it to Method acting, claiming that the other meanings are rarely used. Tkuvho (talk) 13:08, 19 January 2012 (UTC)

It now redirects to The Method (disambiguation) which is probably a more appropriate title.--RDBury (talk) 14:27, 19 January 2012 (UTC)

Why The Method (disambiguation) is different of Method, which is also a disambiguation page? I suggest to merge them with the name of Method. — D.Lazard (talk) 15:30, 19 January 2012 (UTC)

I guess they could be merged and a redirect done. I'd keep the contents in separate sections though as The Method normally refers to something different from just Method. Dmcq (talk) 15:45, 19 January 2012 (UTC)

Tricomplex number at AfD

The article Tricomplex number has been nominated for deletion.  --Lambiam 00:57, 22 January 2012 (UTC)

Serious problems with entailment

It appears that the lead example involving John, being a bachelor, and being a man, is actually an example not of logical inconsequence as written, but of tautological inconsequence. That is, if Γ = {“John is a bachelor”}, S1 = “John is a bachelor” and S2 = “John is a man,” then S2 is not a tautological consequence of Γ. S2 is still, however, a logical consequence of Γ. And this is only the beginning of the article. It appears there is severe confusion between the concepts of logical consequence (which currently redirects to entailment) and tautological consequence. This article needs to be thoroughly reviewed. Hanlon1755 (talk) 01:05, 22 January 2012 (UTC)

Of course "John is a man" is not, under the usual translation into first-order logic, any sort of consequence of "John is a bachelor". In this case the article is correct about that point. — Carl (CBM · talk) 01:27, 22 January 2012 (UTC)

Please centralize discussion at Talk:Entailment#Lead example mistakenly refers to logical consequence when it should refer to tautological consequence? — Arthur Rubin (talk) 01:43, 22 January 2012 (UTC)

Cosine 404

Hi all,

I'm worried that an article about Sine exists, but not one for Cosine. There is an ongoing discussion at Talk:Trigonometric functions, and a draft for this article is available within my userspace.

Here are some excerpts from the discussion:

This user was for the move:

Sine can be treated independently [of the other trigonometric functions] and it's clearly useful to do so... it seems foolhardy to suggest you delete an article that's accessed 1000+ times a day, has hundreds of internal inbound links, and exists on 34 other language Wikipedias, just because you think people need to simultaneously learn cosine, tangent, cotangent, secant, and cosecant. If someone wants to know about sine, let them learn about sine.

Try reading this article with the goal of finding a definition of "sine". First, you have to get to the second sentence of the second paragraph. And then you have to decipher a 443 word sentence. It's absolutely shockingly bad at defining sine, yet you want the hundreds of references to sine to redirect here?

All the same arguments apply equally for cosine. Cosine, although conceptually very similar to sine, has its own properties, some of which are trivial, and others are trivial for sine but more complex for cosine (e.g. fixed point). I really hope I don't have to argue this point further, and I hope no one else has to deal with deletionist trolls when it comes to basic mathematics articles.
— User:Pengo

This user was against the move:

In fact I'd get rid of the sine article and redirect to this article. It already has accumulated ridiculous cruft compared to this article. There is no sine topic, the topic is the trigonometrical functions. Sine is just one of those functions. A name is not the same as a topic.
— User:Dmcq

You may discuss here as well, but please check the simultaneous discussion at Talk:Trigonometric functions and in my userspace before you say something someone else has already said.

Thanks,

The Doctahedron, 21:22, 7 January 2012 (UTC)

At first glance i was for the creation of cosine, but having a look at [[sine] and trigonometric functions first off it would be important to note that the definitions are not hard to find at all (for anybody who can use a contents!) Try looking at "1.Right-angled triangle definitions" followed by "1.1 Sine, cosine and tangent". The user is not forced to look at the reciprocal trigonometric functions at all, they are under "1.2 Reciprocal functions". However, comparison of the contents reveals that sine contains an "inverse" section, which trigonometric functions ideally needs. It also contains a section on "quadrants", "continued fractions" and an "etymology" section which are also needed. Sine also goes into more detail regarding complex analysis, which i also think trigonometric functions needs. I would vote that sine is merged into trigonometric functions with trigonometric functions being expanded. Perhaps also include a section that explains the relation between sine and cosine (in terms of the translation), because this is only done formally on trigonometric functions Brad7777 (talk) 22:23, 7 January 2012 (UTC)

A clear problem with the proposed "Cosine" article is that it defines the cosine as the ratio of the hypotenuse to the adjacent side of an angle in a right triangle, and then immediately purports to "prove" that the cosine is the derivative of the sine by differentiating a power series. That bit needs to go, I think. (There are more elementary proofs of this. First show that $\sin x/x\to 1$ as $x\to 0$ using geometrical arguments, then apply the angle sum formula. See any standard textbook on calculus. Whether such an argument should be added, I have no opinion.) Sławomir Biały (talk) 23:09, 7 January 2012 (UTC)

Exactly. It "proves" that the derivative of sine is cosine by differentiating the Taylor series of sine. But to find the Taylor series of sine you need to differentiate sine indefinitely. To do that you need to know that the derivative of sine is cosine and that the derivative of cosine is minus sine. So to "prove" that derivative of sine is cosine he assumes that the derivative of sine is cosine. Moreover, after differentiating the Taylor series for sine, he finds that it is the Taylor series for cosine. But how does he know that that is the Taylor series for cosine? To find the Taylor series for cosine he needs to be able to differentiate cosine indefinitely. — Fly by Night (talk) 01:13, 8 January 2012 (UTC)

In analysis, the sine and cosine are sometimes defined by the power series. This makes the proof legitimate, but trivial. However, if we mix the two approaches, then we get this absurdity. As you say, using the geometrical definition of the sine and cosine, the Taylor series becomes a consequence of the differentiation rules rather than vice versa. Sławomir Biały (talk) 11:08, 8 January 2012 (UTC)

I guess this is a question of how people view what Wikipedia is in aid of. I view articles as being about topics rather than terms, that Wikipedia is an encyclopaedia rather than a dictionary or index. So sin an cosine might have separate entries in a dictionary but they don't have separate chapters in maths books. Perhaps we need a separate class of articles in Wikipedia which correspond more with terms that are looked up and we'd know to just put the bare basics in them?, then we'd combine the functions of an encyclopaedia and a technical dictionary. For instance MathWorld which started off as a dictionary has a separate article about each function in Mathematica so it has articles not just about sine and cosine but things like the Bessel functions of the first kind. Encyclopaedia Britannica has a small page which points to various topics which cover sine in some detail. Dmcq (talk) 01:23, 8 January 2012 (UTC)

Wikipedia is not a dictionary. — Fly by Night (talk) 01:28, 8 January 2012 (UTC)

I'm open to improvements

Please remember that Wikipedia is not paper. I am open to suggestions as to how to improve the Cosine article. You may also edit my article as necessary, as long as you refrain from vandalism, trolling etc.

Thanks for your feedback!

The Doctahedron, 22:55, 19 January 2012 (UTC)

Hi. In case you didn't know, I'm really interested in continuing this discussion. Please contribute to the discussion so that we can reach a consensus as to whether this article should be mainspaced. Cheers, The Doctahedron, 02:36, 25 January 2012 (UTC)

Negative idea

i have came up with a theorem and this may sound crazy but stick with me. i would like to ask you all what you think the definition is of the word "negitive". to me, negitive is more than the absence but the inverted space. by this i believe that a simple problem, for example, -1*-1=1, may not be true because 1 can be described as a "ditto" number. anything times 1 is itself so for example, if x*1, it = x. but if we have a problem like x*-1 then then it gets rid of that number and ends up with zero. i would like to hear back about this idea. p.s. this is a 14 year old. — Preceding unsigned comment added by 50.39.254.225 (talk) 04:35, 11 January 2012 (UTC)

Facts like −1×−1 = 1 are unavoidable consequences of the desired properties of addition and multiplication.

0 + x = x

0×y + x×y = (0 + x)×y = x×y

0×y + x×y − x×y = x×y − x×y

0×y + 0 = 0

0×y = 0

(1 + −1)×y = 0

1×y + −1×y = 0

y + −1×y = 0

−1×y + y = 0

−1×y + y + −y = 0 + −y = −y

−1×y = −y

Taking y to be −1, we get

(1 + −1)×−1 = 0

1×−1 + −1×−1 = 0

−1 + −−1 = 0 = −1 + 1

−−1 + −1 + −−1 = −−1 + −1 + 1

0 + −−1 = 0 + 1

−−1 = 1

−1×−1 = −−1 = 1

So I hope you see that this is unavoidable, unless we discard one of: the additive identity, multiplicative identity, additive inverse, commutative law, associative law, distributive law or the properties of equality. JRSpriggs (talk) 06:40, 11 January 2012 (UTC)

Words like "negative" can be kind of confusing. In normal English it often has a very different meaning from the way it is used in maths. In English it often means "the absence of", but in other contexts like maths it might mean something like "the opposite of", which is a very different concept. There are thousands of words like this, especially ones used in maths, that have such incompatible meanings. — Quondum^☏✎ 07:05, 11 January 2012 (UTC)

I think JRSpriggs and Quondum have explained the situation very clearly. Remember that in math, the rules in place have been developed for a long time and they've done a very good job of making sense internally as well as explaining the real world, via science. Perhaps this will help you: what do you think x times 0 should be, if x times -1 is already 0?

You might also take a look at this page, or a forum like math.stackexchange, where people have asked questions similar to yours. They are very helpful over there. Leonxlin (talk) 02:01, 24 January 2012 (UTC)

Baker's theorem on linear forms in logarithms

Coincidentally, I happened to run across Baker's theorem and Linear forms in logarithms within a few days of each other. They look very closely related to me — do they really warrant being two separate articles, or should they be merged? —David Eppstein (talk) 02:35, 16 January 2012 (UTC)

I support merging: The only thing which is in Linear forms in logarithms and not in Baker's theorem is Baker-Wùstholz bound, which is much better than Baker (1977) bound, given in the other page (exponent reduced from 200n to n+2). Thus merging could consist in creating a new section "Explicit bounds" in Baker's theorem and moving the two bounds, with harmonized notation, in this new section. I have no opinion if it is worthwhile to keep Baker's 1977 bound and do not know if there are better, more recent bounds to add. This could be decided after merging. — D.Lazard (talk) 11:56, 16 January 2012 (UTC)

'Linear forms in logarithms' was actually created first and is the more general subject; it appears that the only reason it's still a stub is it hasn't been worked on much. So I would think the merge should really be from 'Baker's theorem' to 'Linear forms in logarithms'. Perhaps 'Linear forms in logarithms' is not the most descriptive name for the subject, but that's what Baker is calling it in the references cited.--RDBury (talk) 14:10, 16 January 2012 (UTC)

I agree that they should be merged, but under Linear forms in logarithms, with a redirect from Baker's theorem. The reason is that there are now many other results that are called linear forms in logarithms, but they were not proven by Baker. For example, there is a large literature devoted to the theory of linear forms in elliptic logarithms, so this topic certainly merits a section on the main linear forms in logarithms page. It would also merit cross-links with the page on elliptic curves. JosephSilverman (talk) 20:55, 26 January 2012 (UTC)

Authors of books on hyperreals

Category:Authors of books on hyperreals is being discussed here Tkuvho (talk) 15:29, 25 January 2012 (UTC)

Proposed Category:Mathematical comparisons for deletion

Brad7777 (talk) 18:58, 14 January 2012 (UTC)

Is a comparison of mathematical software, a mathematical comparison? Brad7777 (talk) 12:55, 16 January 2012 (UTC)

Still open to votes

The current votes:

Nominator's rationale: It contains 1 category and only 2 pages. It is useless Brad7777 (talk) 18:52, 14 January 2012 (UTC)

• keep falls under the "part of a large overall accepted sub-categorization scheme" exception of WP:SMALLCAT as one of the subject-specific subcategories of Category:Comparisons.--JohnBlackburne^words_deeds 19:16, 14 January 2012 (UTC)

  I don't think that's the case here, actually. The "accepted sub-categorization scheme" exception applies to cases where every or almost every element of a set (ideally, a finite set) is expected to have a category – e.g., Category:Flags by country. In the case of Category:Comparisons, there is no fixed or defined population of topics that would form the basis of a scheme of {Topic} comparisons categories. That being said, mathematics is a subject with a significant and broad scope, so I don't think it's correct to dismiss the category entirely. Also, if there is no consensus to keep it, it would need to be upmerged rather than deleted. -- Black Falcon ^(talk) 19:51, 14 January 2012 (UTC)

• Weak keep. I found one more article to add, bringing the total to three in the category itself and seven more in its subcategory. That seems enough to head off arguments based purely on numerics (as the nominator's is). —David Eppstein (talk) 02:47, 16 January 2012 (UTC)
  • Comment I would not say "comparisons of mathematical software" is a "mathematical comparison", but more of a "technological comparison", so i don't think it strictly belongs there... This would leave only 3 articles (should ideally have 10+). However i think this would not matter if the category under discussion was renamed to Category:Mathematics-related comparisons? Brad7777 (talk) 12:44, 16 January 2012 (UTC)
• Delete. But keep the sub category Comparison of mathematical software‎ as a subcategory of Mathematics and Comparisons. I agree that there is nothing mathematical in these comparisons. Among the three other pages:
  • One (Comparison of topologies) is the study of a specific partial ordering and would better be named Partial ordering of the topologies of a set. It has nothing to do here.
  • One,(Comparison of general and generalized linear models) is a stub for which it is difficult to know what is really compared. If, as one could expect, the models are associated to software implementing them, the page may be put in the category Comparisons of mathematical software‎
  • The last one (Comparison of vector algebra and geometric algebra) is a comparison of two mathematical theories, and is the only page which really corresponds to the name of the category.

I may add that "mathematical comparison of algorithms" could contain interesting pages comparing the complexity and the practical efficiency of various mathematical algorithms. But for most algorithms, such a comparison would be original research and thus has not (yet) its place in Wikipedia. — D.Lazard (talk) 14:41, 16 January 2012 (UTC)

• Delete as rather vaguely ambiguous. At the very least rename. Any equation is a mathematical comparison, just for one example. See Comparison, and Comparison (mathematics) in particular. - jc37 19:46, 27 January 2012 (UTC)

Park test

Park test is a new article by a new user that is a mess. It definitely needs a look over from an expert from Mathematics or Statistics. I will also leave a note on the Statistics project page. Thanks. Safiel (talk) 16:32, 27 January 2012 (UTC)

New contributor needs help

Hello. User:Ab konst would like to contribute a new section at L'Hôpital's rule, but is having a little trouble getting the concepts across in English. Specifically, some undefined notions of "conversion" and "comparability" are involved, and a connection to Hardy fields. I'm unable to help (I don't know what the user is referring to) but I'm hoping someone else can. The subject matter is probably very straightforward to an analyst. See Talk:L'Hôpital's rule#Conversion. Thanks, Rschwieb (talk) 16:37, 27 January 2012 (UTC)

Apparently "conversion" means "finding the converse of" and "comparability" is similar to "~" as used in asymptotics; Hardy fields are a bit more arcane. In any case, it might be easier to just point to a reference rather than try to communicate the concepts in a second language. Another idea would be to add the material to the Russian article and request a translation.--RDBury (talk) 18:34, 27 January 2012 (UTC)

Homogeneous redirects

Currently 'Homogeneous', 'Homogenous', 'Inhomogeneous', 'Homogeneous (mathematics)', 'Heterogenous', 'Homogenisation', 'Homogeneous equation', etc. redirect to Homogeneity and heterogeneity which, for the most part, concerns itself with the chemical definition of the terms, though there is an odd mathematical dab section within the article. Most of the mathematical meanings of Homogeneous have nothing to do with chemistry and there are several other cases where the meaning intended in the article has nothing to do with the chemical meaning. So I'm thinking that many of these redirects, and in particular the mathematical ones, should link to Homogeneity (disambiguation) instead and the the articles that link to them should be matched to the article with the intended meaning. I'm going to go ahead and start with the most obvious misplaced redirects, and if there are no objections or better suggestions merge the dab section of 'Homogeneity and heterogeneity' into the actual dab page.--RDBury (talk) 23:02, 26 January 2012 (UTC)

Comments on Homogeneity (disambiguation):

• I suggest to remove the qualification in algebra for homogeneous polynomial, which is useless and non homogeneous :-) with the other items.
• Homogenization is an operation which exists for polynomials, related to the relation between affine and projective space. Thus an item Homogenization of a polynomial should be added
• For this reason, Homogenization (mathematics) should be renamed Asymptotic homogenization

D.Lazard (talk) 09:01, 27 January 2012 (UTC)

I have implemented my suggestions. D.Lazard (talk) 15:49, 27 January 2012 (UTC)

Also homogeneous equation was a redirect to homogeneity and heterogeneity which has nothing to do with equations. I have redirected it instead to homogeneous linear equation, and put a see also there to homogeneous differential equation. There seem to be some more math articles listed at [[1]], if anyone wants to fix these. Sławomir Biały (talk) 13:47, 29 January 2012 (UTC)

Graph isomorphism problem

We seem to have a little edit war going on (again) in Graph isomorphism problem. Can I find an uninvolved admin here to semiprotect it, or would RFPP be a better choice? —David Eppstein (talk) 23:19, 27 January 2012 (UTC)

Solved. Hopefully... —Ruud 14:18, 29 January 2012 (UTC)

The edit war is solved, the G.I.P. is still open (and probably will be for a while to come).--RDBury (talk) 19:39, 29 January 2012 (UTC)

Training = belief ?

I just linked to the Percentage page from the Sourdough page. The How to banner at the top of Percentage struck me, particularly the phrasing, "The purpose of Wikipedia is to present facts, not to train", with the emphasis, "present facts, not ... train". The implication that training is not presenting facts seems odd. If one doesn't have facts, then one has non-facts. Non-facts might include beliefs. It just struck me as unusual any training would consist of Belief. The connection to Mathematics project was the banner on Percentage, and I don't have available time to debate, although if anyone has any clarity on the above implication, which I distill to training = belief ?, your thoughts would be appreciated. Gzuufy (talk) 21:33, 27 January 2012 (UTC)

I think it's simply referring to Wikipedia:Wikipedia is not a textbook. The mathematical idiom, as it appears in journals and textbooks, is much more explanatory/pedagogical/psychological than an encyclopedia is supposed to be. The Percentage article has a bit of this flavor --- hence the notice at the top. Mgnbar (talk) 22:04, 27 January 2012 (UTC)

This is largely a matter of wording: the percentage article is largely written in the mode of an instruction manual ("this is what you should do") which is very different in style (if not necessarily in content) from a typical encyclopedic presentation. Similarly, the collection of Example Problems, which undoubtedly make this article more helpful for some readers, are not something that really belong in an encyclopedia. --Joel B. Lewis (talk) 01:11, 28 January 2012 (UTC)

(ec)The Howto template is often used to cover any issue relating to the whole "Wikipedia is not a manual, guidebook, textbook, or scientific journal" section but it's phrased to cover only part of it, hence the confusion. In this case the tag is probably referring to the "Example problems" section in the article since it should be trimmed by at least half, otherwise the article looks ok. Maybe Template:Textbook would have been more appropriate but now it would be better to just fix the article and move on.--RDBury (talk) 01:32, 28 January 2012 (UTC)

Thank you for all your replies. A related issue is that deleting the Example problems section essentially loses information in the Hall of obscure records, while moving the article to, was it Wikiversity or Wikibooks, as the banner also says, does not necessarily entail such a loss. Gzuufy (talk) 20:02, 28 January 2012 (UTC)

The article doesn't need to be moved, it just needs to be trimmed and copy edited. I'll take a whack at it since no one else seems to be working on it.--RDBury (talk) 23:50, 28 January 2012 (UTC)

"The mathematical idiom, as it appears in journals and textbooks, is much more explanatory/pedagogical/psychological than an encyclopedia is supposed to be." It's that word "supposed" that gets me. Ever since the first encyclopedia was published, it has been cast in stone that "all encyclopedias must be in this format". We have a brand new medium here, so why are we constrained to sticking to the same format that may or may not be appropriate for printed paper? --Matt Westwood 00:10, 29 January 2012 (UTC)

I think one should try and do the one thing well rather than many things badly. There's other people who do things like this well, there's no need to set up competition. Anyway you're welcome to try and improve the Wikiversity where you can see how that sort of thing has gone with the wiki model. Or perhaps Wikibooks might be what you're looking for. Dmcq (talk) 01:35, 29 January 2012 (UTC)

All very well, but this site seems to be doing one thing badly. Yes, there are plenty of wiki maths sites out there which are far superior to this one. The trouble with wikipedia is it's shackled to some tediously bureaucratic rules and a thrice-damned bunch of deletionist lawyers. --Matt Westwood 19:50, 29 January 2012 (UTC)

I really don't know which sites you're talking about. We're immensely superior to MathWorld and somewhat superior to PlanetMath. Springer might compete in the sense that their worst articles are a lot better than our worst articles, but I still think we're more useful overall. --Trovatore (talk) 00:50, 31 January 2012 (UTC)

Filtrator on AfD

Hi folks, Wikipedia:Articles for deletion/Filtrator could use some input. Sławomir Biały (talk) 19:30, 30 January 2012 (UTC)

Theorems in abstract algebra

I have created Category:Theorems in abstract algebra, please help fill it. Many articles can be found in Category:Theorems in algebra and Category:Abstract algebra. Thanks Brad7777 (talk) 14:58, 31 January 2012 (UTC)

How do you tell what is to remain in Category:Theorems in algebra ? Rschwieb (talk) 15:09, 31 January 2012 (UTC)

If the theorem is from another branch of algebra in which it is not worth making its own category, or you are not sure where it would go, I would leave it in there. Brad7777 (talk) 18:46, 31 January 2012 (UTC)

Feb 2012

Use of "we"

I see that many of our math-related articles use the word "we", some of them quite often (i.e. "we find that...", "we can use [blank] to prove that...", if we take...", ect. Generally speaking, this is an unencyclopedic method of phrasing, and I usually don't to hesitste to change it in the rare cases that I find it elsewhere on Wikipedia. But as it seems to be so ubiquitous in math articles, I figured I had better check here before making multiple changes. Joefromrandb (talk) 00:12, 31 January 2012 (UTC)

Yes, these uses should be changed. CRGreathouse (t | c) 00:39, 31 January 2012 (UTC)

The WP:MOSMATH discourages the use of "we" but does not forbid it. At the same time "we" is very common and appropriate in professional mathematics, so it will appear in our articles by inertia and habit. IMO there's nothing wrong in general with rephrasing sentences to avoid "we" as long as adequate care is taken to rephrase the sentences in a reasonable way. — Carl (CBM · talk) 00:40, 31 January 2012 (UTC)

"We" should generally be avoided. Even in professional mathematics, it is abused. However, I say "generally" because every so often something comes along that resists any attempt to state clearly without it. Sławomir Biały (talk) 01:25, 31 January 2012 (UTC)

As MOS:FIRSTPERSON states, this form of "we" may be acceptable but rephrasing to avoid it is generally better (and in my experience not usually difficult or awkward). —David Eppstein (talk) 01:35, 31 January 2012 (UTC)

Thanks for the responses, all. I'm sure there will be occasions where "we" is quasi-necessary. In any case, I only intend to change it in instances where its removal is simple and doesn't require the intervention of a math expert, which I certainly am not. (Although I am fascinated by the things I'm learning in some of these articles!) Joefromrandb (talk) 01:40, 31 January 2012 (UTC)

The use of "we" is probably easier for the reader than rewriting, if the rewriting is into the passive voice. -- 202.124.75.209 (talk) 10:16, 31 January 2012 (UTC)

I think 'we' can be a bit annoying sometimes as in 'we can see' when a person can't and will have a lot of work seeing. I'll quote a bit from Mathematical jokes I like about this. "A mathematics professor is giving a lecture to his students and writing equations on a blackboard. He says, "At this point, it is obvious that this equation can be derived from that one." He pauses, then turns his back on the class and spends an hour filling the entire blackboard with more work. Finally he turns and announces triumphantly, "Yes, I was correct; it is obvious!" Dmcq (talk) 10:21, 31 January 2012 (UTC)

While the actual usage of the "royal we" in science and philosophy is perfectly fine, I suppose it is an important question of whether or not it should be allowed in the wiki format. The most awkward/annoying trope to me is the use of "one" as in "one sees that", "following one's instinct leads one to conclude that..." etc... Rschwieb (talk) 17:40, 31 January 2012 (UTC)

I agree. The word "one" just substitutes one bad pronoun for another. Sławomir Biały (talk) 20:04, 31 January 2012 (UTC)

What's wrong with "It follows that" or "it can be seen that" and so on? Otherwise, I suppose "we" is okay, as long as it's not used in the context "... and we're done". --Matt Westwood 20:02, 31 January 2012 (UTC)

To some extent we is a way of avoiding the passive voice. That's fine in journals. In an encyclopedia, I think passive is better than we, as a general rule. I agree with Sławek that a hard ban is probably undesirable. --Trovatore (talk) 21:16, 31 January 2012 (UTC)

Sentences containing the phrases "note that", "it follows that", "it can be seen that" etc are almost always made clearer and tighter without losing any meaning by deleting the phrase. —David Eppstein (talk) 22:19, 31 January 2012 (UTC)

That's true. The less trivial uses would be along the lines of we employ the same technique to..., which can be mechanically rephrased as the same technique is employed... (there's NOTHING inherently wrong with passive, people! It's fine!) or perhaps better in this case the same technique yields.... --Trovatore (talk) 22:27, 31 January 2012 (UTC)

The last example (the same technique yields...) is a nice example where not even the passive voice is needed. I'd suggest that a good guideline is that whenever "we", passive voice, and unnecessary helper phrases ("note that...", "we see that..." etc.) occur, an editor should seek a natural, encyclopedic rephrasing, and should feel free to make a change if the rephrasing is no clumsier but has substantially the same meaning. Note the criterion: clumsiness (or even wordiness). — Quondum^☏✎ 04:39, 1 February 2012 (UTC)

That seems reasonable a priori — my only concern is that too many editors are already too squeamish about the passive voice, for no particularly good reason. It's true that sometimes active voice is a little peppier, but some people turn it into a shibboleth, and in any case we don't necessarily need pep in encyclopedic math articles. So I don't necessarily want to encourage that. --Trovatore (talk) 04:48, 1 February 2012 (UTC)

Good point. Passive voice is more common in technical writing than in general prose, and for good reason. I too prefer it to dummy subject role placeholders e.g. "we", "it", "one". — Quondum^☏✎ 07:45, 1 February 2012 (UTC)

Algebraic structure

Algebraic structure is an abomination. Is there a good tag for this sort of situation? Rschwieb (talk) 15:10, 31 January 2012 (UTC)

I don't think we have an {{abomination}} tag, but the Expert-subject tag might be what you are looking for. If you add {{expert-subject|mathematics}} to an article then the article name is automatically added to the relevant sub-list at Wikipedia:Pages needing attention/Mathematics and also appears on Wikipedia:WikiProject Mathematics/Current activity. Gandalf61 (talk) 15:46, 31 January 2012 (UTC)

I suggest {{Multiple issues}} with, at least, the items "expert", "technical" and "wikify". "Technical", because it is difficult to read the page without knowing universal algebra. Need to "Wikify" is clear, even if it can only be done by an expert. Another reason for which an "expert" is needed is that the difference between "algebraic structure" and "non algebraic structure" is not made clear. In my opinion the difference is that an algebraic structure is defined by a formula of first order logic, that is the axioms may involve quantifiers only on elements and not on subsets. Thus ordered field is an algebraic structure, but R is not, as its definition involves an axiom with a quantifier on subsets. D.Lazard (talk) 16:44, 31 January 2012 (UTC)

The m.i. tag has been added (not by me). I also bumped the class from B down to Start.--RDBury (talk) 18:41, 31 January 2012 (UTC)

It's a classic Wikipedia mathematics article: largely correct, but written in such a way as to remove all danger of actually informing the reader of anything. The only thing that could make it better is more passive voice.</sarcasm> Seriously, though, it needs a rewrite, and a good discussion of one main example. -- 202.124.72.242 (talk) 11:13, 1 February 2012 (UTC)

Right now, it's organized into "axioms all identities" "not all axioms identities" and an "examples" section, which brings the repetition to a head. I can't appreciate this scheme at all. This article definitely should be accessable to laypeople, so we need to find a better framework. Three tasks I recommend:

1) The intro right now is not terrible, but it should at least be looked at, and the following (longer) section should contain a solid description of what makes an algebraic object an algebraic object (ala D.Lazard's comments above)

2) Next section could be full of examples, wlinks and blurbs, using the scheme of "no operations" "one operation" "two operations" "composite systems" and "even more structures".

3) The category theory section does not do either category theory or universal algebra justice, so we need an expert to sum up how they are related to the article title.

I'll begin work on #2, but #1 and #3 are best explained by someone other than me :) And I'm now realizing this would be a good time to transfer my comments to the talk page itself. I hope to see you all there. Rschwieb (talk) 14:06, 1 February 2012 (UTC)

UPDATE: Quondum alerted me to the existence of Outline_of_algebraic_structures, which largely duplicates the atrocities of Algebraic structure. My feeling is that Algebraic structure should aim to be a readable introduction to the topic, and the outline (which I imagine is limited in its usefulness) can remain as is. Any problematic issues about duplicate articles that I'm overlooking? Rschwieb (talk) 16:34, 1 February 2012 (UTC)

First, I'm having trouble imagining where you'd draw the line between 'Algebraic structure' and Algebra. 'Algebra' should already be a readable introduction to the topic and I'm not sure what 'Algebraic structure' would have in it that shouldn't be in 'Algebra'. Second, 'Outline of algebraic structures' would seem to fall under the jurisdiction of Wikipedia:WikiProject Outlines, the aims of which I tend to agree with but since certain of its proponents have antagonized members of this project in the past, don't expect too much enthusiasm here for articles with names which start with "Outline of ...".--RDBury (talk) 17:37, 1 February 2012 (UTC)

Comment about the line to be drawn between 'Algebraic structure' and Algebra: Algebra has several subtopics, the only one which interest us here is "abstract algebra", which is the study of specific algebraic structures (like groups) and is not concerned with a definition of what is an algebraic structure. On the other hand, universal algebra is the study of algebraic structures as mathematical objects. This leaves the place to a general definition of what is (and what is not) an algebraic structure, which should be the object of Algebraic structure. Note that a general definition is not easy, as 'totally ordered fields' and 'graded algebras' are clearly algebraic structures which are not immediate to define as such in the universal algebra framework. D.Lazard (talk) 18:21, 1 February 2012 (UTC)

Comparing "algebra" to "algebraic structure" is like comparing "language" to "nouns". The article should contain a description of what is meant, and several examples organized in a basic way. Right now, I find the organization of structures to be bizarre, even though it might be correct from a universal algebra standpoint. Any chance you will try your hand at the first few paragraphs of the article, Dr. Lazard? Rschwieb (talk) 18:37, 1 February 2012 (UTC)

Proofs related to the Digamma function is on AfD

See Wikipedia:Articles for deletion/Proofs related to the Digamma function. Sławomir Biały (talk) 12:18, 1 February 2012 (UTC)

You should probably notify User:HenningThielemann and anyone else who has contributed significantly to the article. —Mark Dominus (talk) 16:46, 1 February 2012 (UTC)

Never mind, I did it. —Mark Dominus (talk) 18:11, 1 February 2012 (UTC)

Dirichlet integer translation from french

Can somebody translate fr:Entier_de_Dirichlet from french into english please? Brad7777 (talk) 14:15, 1 February 2012 (UTC)

As far as I realized, it is a quadratic integer ring for d = 5. I made once some use of this ring during mediations and programming related to Penrose tilings. Will you be satisfied if I add a section to aforementioned article and make Dirichlet integer a redirect instead of a stub? Incnis Mrsi (talk) 15:15, 1 February 2012 (UTC)

I'd like to point out that the footnote in the first sentence says the following: "While the mathematical content of this article is a usual part of the field of number theory, the term "Dirichlet integer" is not in common usage. The set of these integers is usually denoted O_Q[√5] and they are often not given any name.". I, for one, have never heard this term and the only source for it given in the (quite detailed) French article is a blog. There's discussion on the talk page of the French article and on their Math WikiProject concerning the problems with this title. So, if we are to translate this, I think we should first come up with a better name. RobHar (talk) 15:59, 1 February 2012 (UTC)

I have just read this French page. I have not the time to translate it myself, but I like the page and I support the idea of the translation. Some more comments:

• Firstly, although Dirichlet integers could be an example in Quadratic integer, I do not support Incnis Mrsi's suggestion: the example would be around 10 times longer than the remaining of the page!
• Secondly: The French page consists in explaining, on a specific important example, most of the theory of quadratic integers. This example is especially important, as it underlies the properties of the golden ratio and the proof of Fermat's last theorem for n=5. The article is easy to understand and shows very well to which problems the number theorists of XIXth century were faced to prove Fermat's last theorem and what were the solutions. It is thus very useful for a non experimented user to understand the notion of quadratic integer. In other word, it is a counter example of the assertion of the sarcastic IP user in #algebraic structure.
• On the other hand, the title is wp:original research, and although there is no original research in the content, the page may be viewed as an original synthesis (but not in the sense of wp:original synthesis, as it does not advances any position). In any case, I support the translation per WP:IAR.
• For the title, my above comment suggests Quadratic integer (example) or Quadratic integer (detailed example)

D.Lazard (talk) 16:53, 1 February 2012 (UTC)

Actually, only a small part of fr:Entier de Dirichlet is dedicated to D = 5. There is much algebra applicable to other quadratic fields IMHO, but I do not attempt to translate the things not clear enough to me. Incnis Mrsi (talk) 17:40, 3 February 2012 (UTC)

There is a very long discussion about it here : fr:Projet:Mathématiques/Le_Thé/Archives_4#Nom_Dirichlet.

You may read theses sources (in English! :-) ):

K. Ireland M. Rosen A Classical Introduction to Modern Number Theory p 13

P. Ribenboim Fermat's Last Theorem for Amateurs Springer 2000 p 49-56

H. M. Stark An Introduction to Number Theory MIT Press 1978 and [2]

French wikipedians decided thas this article is quite borderline, but on the right side. It's an introduction to quadratic integers, but the title is a problem: Q(√5) was proposed, but rejected. --El Caro (talk) 17:10, 1 February 2012 (UTC)

Here's a (somewhat tongue-in-cheek, but maybe real) suggestion for a title: The ring of quadratic integers of discriminant five. This is what the article would be about and it avoids using mathematical notation (which was the opposition to titles such "Q(√5)" that were suggested on French wiki). RobHar (talk) 18:08, 1 February 2012 (UTC)

I'm not really seeing the problem with 'Dirichlet integer'. We already have articles on Gaussian integer and Eisenstein integer and 'Dirichlet integer', even if not the most common name, would be better than O_Q[√5]. I can't resist adding to the OP, learn to read mathematical French! It's much easier than learning regular French since there are a limited number of grammatical constructions and practically every other word is a cognate.--RDBury (talk) 15:34, 2 February 2012 (UTC)

"Gaussian integer" and "Eisenstein integer" are extremely common terms for these objects. Are you saying that if I write a blog post and call the ring of integers of the 7th cyclotomic field the "Lamé integers", then we can create an article here called that? RobHar (talk) 16:13, 2 February 2012 (UTC)

Yes, that's exactly what I'm saying. Actually I missed the part in the above discussion that the name is based on a single blog post, so I though there was at least one reliable source for the name even if it wasn't the most common one in use. So there was an error on my part but I don't see the need to make a sarcastic comment about it.--RDBury (talk) 06:43, 3 February 2012 (UTC)

That wasn't a sarcastic comment, that was an actual question. And since you answered yes, it was apparently a relevant question to ask. I do however completely disagree that we should be proliferating random designations of objects and there must be a guideline that supports my position. RobHar (talk) 14:35, 3 February 2012 (UTC)

Actually I was being facetious when I answered yes; I thought not supporting random names for things was implicit. Sorry for the misunderstanding; it sometimes causes confusion when text communication does not convey the intended tone of voice.--RDBury (talk) 15:54, 3 February 2012 (UTC)

Incidentally and off topic, since this this discussion is still warm while I desperately click on interwikis trying to find in any language an article about the space of continuous functions with compact support, it is amazing how being named after a mathematician helps to get an article in Wikipedia : just look at the list of examples in Function space#Functional analysis. There are 18 examples, none has been wikified with a red link, but only 6 have an article. By a happy coincidence, these are the 5 named after a person (and additionnally one with a short name, that is Lp space) ! Quite a number of fundamental articles are lacking, in my opinion : there is hardly a deep logic in having a separate article about Schwartz space but relegating the space of smooth functions with compact support (this is not even a redirect !) as a paragraph in the article about distributions. French Tourist (talk) 17:00, 5 February 2012 (UTC)

Meanwhile, I expanded the article. Please, check for possible mistakes. Incnis Mrsi (talk) 17:40, 3 February 2012 (UTC)

Integral value transformation

Integral value transformation is quite a badly written article, to say the least. Is it worth doing something with? Michael Hardy (talk) 02:39, 3 February 2012 (UTC)

I'd say it's worth deleting. A quick Google search for the title gives a bunch of badly written papers, all by the same small set of authors, which to me seem to fall into the category of pseudo-science. (Given any two sequences, it's possible to concoct a function sending one to the other. This usually isn't meaningful). I haven't found any secondary sources or anything else that helps the topic satisfy WP:GNG. Jowa fan (talk) 05:59, 3 February 2012 (UTC)

It's been deleted as copyvio of http://arxiv.org/ftp/arxiv/papers/1201/1201.4329.pdf. PamD 15:51, 3 February 2012 (UTC)

Additional opinions requested on Definite bilinear form

Debate at Talk:Definite bilinear form#Definite bilinear forms: symmetric only?. The question is whether the definition of definiteness is restricted to symmetric bilinear forms. Curiously, many but not all authors appear to restrict the definition to the symmetric case, although the restriction appears to be unnecessary and cumbersome. Also, the Properties seciton of the article needs checking and expansion (a few minutes by someone familar with the topic, particularly relating to eigenvalues and related properties). — Quondum^☏✎ 10:09, 3 February 2012 (UTC)

Mathworld's entry seems to support Quondum's position (that there is no real reason to restrict the definition.) Rschwieb (talk) 16:38, 3 February 2012 (UTC)

Smooth completion

AfD for Smooth completion may be found here. Tkuvho (talk) 19:44, 4 February 2012 (UTC)

Article moves and redirect bypasses by Jheald

[3] despite [4]. Suggestions? Incnis Mrsi (talk) 18:37, 5 February 2012 (UTC)

I noted what you wrote, but you were wrong. If an article gets renamed, it is only sensible to rename the "See also" sections and the {{main}} links that point to it.

The previous article title -- Rotation representation (mathematics) -- was rubbish. The new title Rotation formalisms in three dimensions may not be perfect, but it gives a much better idea of what the article's about. Jheald (talk) 18:47, 5 February 2012 (UTC) And if you're going to raise my edits for wider discussion, it's courteous to notify me of the fact. Jheald (talk) 18:47, 5 February 2012 (UTC)

I think his change is probably in good faith, however there probably should be some discussion before the page rename. If you bothered asking for the reasoning it would be helpful to provide a link to that discussion too. A link to your declaration of an edit's uselessness alone is not very helpful. It also doesn't substantiate uncooperativeness, so a link to that would be good too. Rschwieb (talk) 19:07, 5 February 2012 (UTC)

How amusing. I referred to WP:NOTBROKEN, an official Wikipedia guideline, and Jheald's edits are build on a personal taste − but it's me who was wrong. The title of Rotation representation (mathematics), an extensively linked article, was convenient to Wikipedia's editors for many years − but, according to Jheald, it is "rubbish". And he changed it, twice in a hour, without consulting anybody. This is an established article, not a kind of godforsaken stub. Incnis Mrsi (talk) 19:11, 5 February 2012 (UTC)

The old namewas indeed bad. "Representation" has a very specific meaning in the mathematics of symmetry operations such as rotations, a meaning that the old title did not refer to. Avoiding that word in this context is a good idea. So although I agree with Jheald that the new name may not be perfect (it's a bit long and clunky) it's a distinct improvement over the old. —David Eppstein (talk) 19:29, 5 February 2012 (UTC)

FWIW there's now a topic open at Talk:Rotation formalisms in three dimensions#Title if anyone has any good ideas. Jheald (talk) 19:38, 5 February 2012 (UTC)

More links to digi-area.com

Another user (see Wikipedia talk:WikiProject Mathematics/Archive/2011/Sep#Digiarea links) has added a bunch more links to digi-area.com; the most recent one was added to Polar coordinate system. The purpose of the site/product is provide people with pre-made formulas that can be used in TeX or Mathematica. I think this falls under WP:ELNO and I'm going to undo the changes, assuming there are no valid objections, but I was wondering if requesting some help from XLinkBot would be appropriate at this point.--RDBury (talk) 12:08, 6 February 2012 (UTC)

I had a look and the site seemed to provide no additional material about the topic so yes I agree with the removal. It does also just seem to be there as an advertisement. Dmcq (talk) 12:21, 6 February 2012 (UTC)

The topic has no copyable formulas in the formats (MathML, TeX, Mathematica input, Maple input). So, this is really additional material about the topic. If user interested in the topic, then he/she may want to have the copyable formulas. — Preceding unsigned comment added by SandraShklyaeva (talk • contribs) 12:36, 6 February 2012 (UTC)

The DG Library is free and unique resource of copyable formulas for differential geometry objects and its applications. So, the link has practical advantage for the user. I think that free and useful resource can not be an advertisement anyway. — Preceding unsigned comment added by SandraShklyaeva (talk • contribs) 12:43, 6 February 2012 (UTC)

I hope you have good luck with the DG Library site, but I agree that these links are not a good fit for our articles on Wikipedia. It is not hard to simply type a formula, and I can't see why someone would want to search for a website just so they can copy one. Moreover, the formula on the website may not be the exact formula that is desired, and the actual pages being linked to seem to have little content and no explanations [5]. Thus I do not see a strong benefit to including links to these formulas in our articles. — Carl (CBM · talk) 12:55, 6 February 2012 (UTC)

I agree with the removal, per Carl's reasoning. Sławomir Biały (talk) 12:56, 6 February 2012 (UTC)

Formulas of differential geometry objects not always simple and it is not easy to write formulas by hand. For example: Inverse Cassinian Cylindrical. It is just a waste of time. Moreover, most people do not make calculations in differential geometry by hand, because the calculation is very massive. People use different CAS's, so it will be useful to get already prepared formulas for theirs work. — Preceding unsigned comment added by SandraShklyaeva (talk • contribs) 13:21, 6 February 2012 (UTC)

More massive category changes

Brad7777 (talk · contribs · deleted contribs · logs · filter log · block user · block log) has returned, making thousands of changes to categorization of mathematics articles without any discussion. I thought we had a discussion here in which the overall tone was that Brad should stop what he is doing since many of his notions were somewhat controversial. At the time, I checked through the hundred or so mathematics category edits, and reverted the ones that didn't make any sense. But now he's using hotcat, and has done over a thousand such edits. He seems to be single-handedly attempting to redo all of the categories for mathematics articles based on his own personal opinion of what belongs in which category. This is disruptive and a waste of community resources to check all of this damage. What should be done about this? Sławomir Biały (talk) 01:24, 5 February 2012 (UTC)

He should stop, undo all his changes, and find something else to do with his time. There's no shortage of things to do to improve the encyclopaedia, starting e.g. here.--JohnBlackburne^words_deeds 01:47, 5 February 2012 (UTC)

I would support a topic ban on any changes to mathematical categories or to the categories of mathematics articles for this user. Many of his changes make sense, but many more are misguided or badly informed, and politely asking him to behave has had little or no effect. I think I already suggested this the last time around, but I think Wikipedia:Requests for comment/User conduct might be the appropriate next step. —David Eppstein (talk) 02:23, 5 February 2012 (UTC)

Let me know when the petition comes around so I can sign in all caps. Rschwieb (talk) 02:33, 5 February 2012 (UTC)

You must have really strong opinions against my edits, which one\s in particular do you think are non-constructive? Brad7777 (talk) 21:35, 5 February 2012 (UTC)

To my humble opinion, it would be much better to start with specific issues. It is hard to disagree that the categorization has place for improvement. So changes are welcome, though perhaps more discussion would be helpful too.

this and this (compare the timing) are a counterexample to David's statement. Sasha (talk) 03:46, 5 February 2012 (UTC)

ANY kind of large-scale changes made against consensus are disruptive. I would support a permanent ban. -- 202.124.74.138 (talk) 10:20, 5 February 2012 (UTC)

I hadn't noticed that. I had seen the removal of the cycle so origami was under paper folding but not vice versa and I had been wondering what to do about it because it was just causing trouble when trying to find things. I think I'll just go and reinstate the cycle and leave the various bits of the mathematics of origami in the paper folding category except for the top article mathematics of paper folding. Dmcq (talk) 12:41, 5 February 2012 (UTC)

I've got round the problem by putting some text at the top of the origami category referring to the paper folding category for mathematical aspects of origami. Dmcq (talk) 13:33, 5 February 2012 (UTC)

Nice one Brad7777 (talk) 21:31, 5 February 2012 (UTC)

One of the problems with this user seems to be a slight communication impairment. Not providing any rationale for his edits and either denying there is a problem when issues are raised at his talk page or acknowledging them but doing nothing with them. A possible remedy would be to have him post a description of the changes he is going to make on this talk page and link to that description from each of his edit summaries (he would have to stop using HotCat as this tool does not always allow you to write an edit summary). —Ruud 13:10, 5 February 2012 (UTC)

HotCat has two modes. In single change mode you cannot make your own edit summary. But in batch mode (+⁺) the user gets to usual page edit interface and can add his/her own changes, to a page itself as well as to the edit summary (where HotCat propose its format), even if only 1 change was made to categories. Incnis Mrsi (talk) 14:41, 5 February 2012 (UTC)

I assumed the edit summaries Hotcat gave were sufficient. I did not realize there was somewhere saying it wasnt. I will improve on this Brad7777 (talk) 21:27, 5 February 2012 (UTC)

Colleagues,

there is a long discussion here and also on Brad7777's talk page, but so far very little of it is constructive. I found three specific issues raised (origami, subharmonic functions, and manifolds), all the rest was between unconstructive and personal attacks.

It is a truism that every change is potentially against consensus. The earlier we start discussing content (in this case, the structure of the categories), the earlier the consensus that was mentioned so often could appear.

Sasha (talk) 14:36, 5 February 2012 (UTC)

One specific change I object to is the fact that Category:Projective geometry no longer contains either Pascal's theorem, or Desargues' theorem, or Pappus' theorem, or Brianchon's theorem. These are tucked away in a "theorems in projective geometry" category, but that makes it very inconvenient to someone who is not already intimately familiar with Brad7777's tucking away philosophy. Tkuvho (talk) 17:12, 5 February 2012 (UTC)

I would say it helps diffuse both Category:Projective geometry and category Category:Theorems in geometry (both with ~100 articles in them without this category). It may be slightly different to how the category was before, but it isn't difficult to find them and it would remain that way as more pages are added to Category:Projective geometry in the future. Perhaps the examples you have given should be in both Category:Projective geometry and Category:Theorems in projective geometry, but then who decides on which are the most important? Brad7777 (talk) 18:33, 5 February 2012 (UTC)

"....but so far very little of it is constructive". Let's summarise ... multiple users have begged Brad7777 to stop these wholesale changes to categories according to his whim ... 2 users seem to think that it is OK that he should continue (Sasha and Brad7777 ). And let's not forget that categories are meant to be useful to users of Wikipedia, most of whom won't be telepathic enough to follow the peculiar structure that bhas now been set up. Melcombe (talk) 20:41, 5 February 2012 (UTC)

What do you find peculiar about the edits I have made Melcombe? I agree that "categories are meant to be useful to users of Wikipedia" so which of my edits do you think have gone against that? Brad7777 (talk) 21:23, 5 February 2012 (UTC)

The problem is you are making so many so quickly without explanation that it's impossible for others to keep up. But checking through changes today what is the point of this unexplained edit? (the third one I checked).--JohnBlackburne^words_deeds 21:43, 5 February 2012 (UTC)

I am opposed to this intentional de-alphabetization of categories. It is good to de-alphabetize a single main topic for each category (often the one with the same name as the category) but beyond that it just makes things messy for no good reason. —David Eppstein (talk) 21:46, 5 February 2012 (UTC)

I add a space to articles with the same name. The stars on the categories of topological combinatorics, are because this page is noteworthy in the history of these categories. (I think its worth doing as they are also overcrowded). Looking again, I think Category:topology should be removed completely. Im not sure what you mean when you say "it's impossible for others to keep up"? Brad7777 (talk) 22:00, 5 February 2012 (UTC)

The proper way to highlight eponymous articles is with a space, not an asterisk. It's especially confusing to use both - why are some above the star and some below and in Category:topology? But the main problem is it should not have been moved – categories are not meant for sorting articles by how 'noteworthy' you think they are. It's not clear anyone else does, given that the article is still a stub after three years. If you really think it is noteworthy then improve the article. As for keeping up when you're changing categories it's often necessary to look at the category you've moved the page from and to to understand the change; it takes far longer than normal to understand what the change does, especially as you do not explain your edits in edit summaries and are making changes much more rapidly than most editors.--JohnBlackburne^words_deeds 22:19, 5 February 2012 (UTC)

I have seen it in many other categories, and do think its worth doing to seperate the main article from others of importance, but I'll avoid doing it. (It is one way to get them noticed for improvement). Ill add more detail to my edit summaries, is there somewhere that mentions what is suficient? Brad7777 (talk) 22:37, 5 February 2012 (UTC)

Was that the third one you checked with the intention of finding a mistake you think i would have made? Brad7777 (talk) 22:04, 5 February 2012 (UTC)

Break

I would like to ask specifically, that Brad please stop adding categories to redirect pages like paracompactness, compactness (topology), and probably more. This is just one reason I think Brad should stop doing any more category edits. It is going to take hours if not days to clean up his mess. Sławomir Biały (talk) 15:37, 6 February 2012 (UTC)

Only one more Connectedness (topology), and I have stopped, I created a discussion about it below. (I could undo those particular edits in under 3minutes). Are you assuming I have made a mess, or do you have any examples? Brad7777 (talk) 16:38, 6 February 2012 (UTC)

You should refrain from this or any further category edits. I am willing to consider the possibility that you are right about all this, but please consider the fact that a number of editors here feel that you have indeed made a mess. Tkuvho (talk) 16:46, 6 February 2012 (UTC)

It doesn't matter if they have a "feeling" I have made a mess. Wikipedia is not a soapbox, it is supposed to be an encyclopedia written from a neutral point of view (so my view must also be accounted for), free so that anybody can edit, free of personal attacks and free of worry about making mistakes. It would be nice to see some justification of all this mess I have created in terms of the edits I have done. I understand the point of the sceptical criticism (I use constructively) but what is with all the pessimism and totalitarian rules? All my edits have been in good faith. So for those reasons I will continue editing. Brad7777 (talk) 17:48, 6 February 2012 (UTC)

Similarly all of this criticism has been in good faith. You ask in this comment to see some justifications of the claim that you are making a mess, but the "mess" you are making is transpiring a bit too quickly to give you a thoughtful in depth justification. People are trying to say: "Something is telling me there might be a problem with these edits, but maybe there isn't. In the meantime, could you just chill for a bit so that we can look over the edits more carefully and figure out if there is or is not a problem." Your answer is: "Nah, I'm just going to keep going." So, people's reaction has been to simply bring up random examples that have disturbed them. This is not surprising. And know that if you continue and people take it a step further, your ban will also be done in good faith. RobHar (talk) 18:31, 6 February 2012 (UTC)

Yes, please do continue editing. But not categories. This encyclopaedia is run by consensus and there is a clear consensus you should leave categories alone. You have been given many examples of the problems you are causing, both here and on your talk page. No-one is going to review all of your category edits as there are too many of them and it takes too long. But those that have been reviewed show a continued pattern of problems, with the lack of care, the lack of good rationale and the broad disregard of standards and practices they exhibit. So take a break from categories and find something else to work on. There is no shortage of things to do that will actually improve the encyclopaedia.--JohnBlackburne^words_deeds 18:39, 6 February 2012 (UTC)

I concur: please stop editing categories Brad, in particular, unsorting articles within their categories. This is wasting effort and not improving the encyclopedia. Geometry guy 23:20, 6 February 2012 (UTC)

I'm not going to unsort any articles within their categories Brad7777 (talk) 14:41, 7 February 2012 (UTC)

Ditto. Rschwieb (talk) 14:03, 7 February 2012 (UTC)

Given this, are you going to undo the unsorting (which you have made to date) of articles within categories, or rely upon others to clean up? Geometry guy 01:03, 8 February 2012 (UTC)

I have cleaned up Brad7777 (talk) 19:09, 8 February 2012 (UTC)

"Picture perfect"

User:Baroc has been adding photographs of mathematicians to our biographies (e.g. Colin McLarty and Robert Phelps), and deserves our thanks!

 Kiefer.Wolfowitz 14:27, 8 February 2012 (UTC)

Request for comments on Euler's Formula Proofs

I am currently having an argument about whether a "by calculus" proof of Euler's formula should appear in the article of the same subject. I'd like some additional opinions on the subject, and so if you're interested I'd appreciate it if you could go to the talk page there and comment. Thanks. Holmansf (talk) 23:59, 8 February 2012 (UTC)

Mikhail Gromov

The page Mikhail Gromov went through several transformations and is currently redirected to his full name including the little-used middle name. The problem seems to be that there is an aviator of the same first and last name. I think a case can be made in favor of keeping the page at "Mikhail Gromov" with a hat sending the reader to the aviator. Tkuvho (talk) 12:29, 25 January 2012 (UTC)

Could someone comment whether it is reasonable to move Mikhail Leonidovich Gromov to Mikhail Gromov assorted with a hat concerning the aviator? Tkuvho (talk) 13:55, 9 February 2012 (UTC)

Category:Topology

This category currently has 214 articles in it, any suggestions for diffusing it? Brad7777 (talk) 22:23, 5 February 2012 (UTC)

NO. Ozob (talk) 22:33, 5 February 2012 (UTC)

I have a suggestion, what about moving the relevant lemmas into Category:theorems in topology? Brad7777 (talk) 22:40, 5 February 2012 (UTC)

Also a suggestion regarding Category:Topological spaces (see relevant section below) Brad7777 (talk) 13:47, 6 February 2012 (UTC)

Fiber bundle

Currently, the article fiber bundle is in the following categories:

• Category:Fiber bundles
• Category:Differential topology
• Category:Algebraic topology
• Homotopy theory

Whilst the category Category:Fiber bundles is in:

• Category:Topology
• Category:Differential geometry

First, does Category:Fiber bundles need to be a subcat of Category:Topology? Should it be made subcat of Category:Algebraic topology and Category:Homotopy theory instead, or aswell? In which case, secondly, does the article Fiber bundle need to be in any other category except Category:Fiber bundles? Any other comments? Brad7777 (talk) 22:55, 5 February 2012 (UTC)

Topological space

Currently this article is in the categories Category:Topological spaces and Category:General topology, whilst Category:Topological spaces is a subcat of Category:General topology. The topological space should be removed from Category:General topology, because this is overcategorization is it not? I also suggest Category:Topological spaces should be a subcat of Category:Topology aswell, as this could help defuse the category Category:Topology, any objections? Brad7777 (talk) 23:05, 5 February 2012 (UTC)

The overriding reason for categorization is as an aid in finding things, not a separate project to produce a Linnaean tree of knowledge. the business about overcategorization and cycles are guidelines to avoid decreasing the usefulness of categories by overfilling them with details. However if there is a major topic which is relevant it can be included if it doesn't imply dragging in a lot of other things. Also a cycle is fine if some people think the tree should go one way and other think it should go another. They are good guidelines but if something would look wrong to you if you followed them then don't do it. Dmcq (talk) 12:39, 6 February 2012 (UTC)

To me, it would look right having Category:Topological spaces as a subcat of Category:Topology. I would also expect all the articles which are directly in Category:Topology which are on topological spaces to be categorized in there instead. This is because I think the value of Category:Topology is in it being a content category. Brad7777 (talk) 12:57, 6 February 2012 (UTC)

Although I always objected to overcategorization (you even can see my diagram File:Categorization to 2 axes.svg about intersecting category hierarchies), a particular case of topological space is important enough to be included both to Category:Topology and Category:General topology, as a fundamental notion. There are several other articles which have to be (re)moved from "Topology" to subcategories. Incnis Mrsi (talk) 17:15, 6 February 2012 (UTC)

Category:Theorems in geometric topology

Opinions on the creation of this category? Category:Theorems in topology contains 49 articles. Category:Geometric topology contains 123 articles. Category:Theorems in geometric topology would possibly hold 13 articles and is likely to grow. Geometric topology already could do with diffusing, and is also likely to grow in the future. So i think this category will help. Articles for consideration:Grushko theorem, Rokhlin's theorem, Annulus theorem, Side-approximation theorem, Sphere theorem (3-manifolds), Bing's recognition theorem, Double suspension theorem, Blaschke selection theorem, Moise's theorem, Loop theorem, Gordon–Luecke theorem, Cyclic surgery theorem, Fary–Milnor theorem Brad7777 (talk) 00:25, 6 February 2012 (UTC)

What's wrong with leaving Category:Geometric topology as it is? Sławomir Biały (talk) 15:29, 6 February 2012 (UTC)

100+ articles which is likely to grow, hence it would be a good idea to create a few categories to help prevent it becoming over populated. Any objections to the creation of the Category:Theorems in geometrical topology? Brad7777 (talk) 16:52, 6 February 2012 (UTC)

I imagine that when a clearly orthogonal categorization scheme emerges, it is reasonable to follow it even if the number of articles doesn't seem to entirely justfy it. In this instance, "Theorems in [some category]" seems to be an orthogonal categorization scheme (i.e. it makes sense for any mathematical field), so if there are more than a few articles in the category that would be classified as a theorem, it would be reasonable to create the subcategory of theorems. — Quondum^☏✎ 17:50, 6 February 2012 (UTC)

Manifold and Classification of manifolds

Are these two articles overcategorized? They only need to be in one category: Category:Manifolds surely? Brad7777 (talk) 00:39, 6 February 2012 (UTC)

Manifolds are one of the most fundamental objects of study in topology, differential geometry, and especially geometric topology. I definitely don't think this is overcategorization. Our categorization system should satisfy the "least surprise" principle: that if a user expects to see an article in a category, then it should be there. This is clearly such a case. Sławomir Biały (talk) 15:28, 6 February 2012 (UTC)

That is why I do not think they would be surprised that Category:Manifolds currently is a sub cat of the same categories as manifold, in which they could quite easily find it. Hence I think its overcategorization. Articles should be placed in the most specific categories,(in this case one with the same name). I would think they are not needed in all the parent categories aswell. Brad7777 (talk) 16:47, 6 February 2012 (UTC)

On your user page, you have "Categorisation is not a transitive relation" yet many of your edits are in exact opposition to this as is your above statement. I think that there are times that it makes sense to have an article in both a category and one of its subcategories. For example, while it makes sense to have Fundamental theorem of algebra in the category "theorems in algebra", it also makes sense to list it in "algebra" (or perhaps "abstract algebra") since it is the "fundamental theorem" of that subject! Your edit removed it from "abstract algebra" AND "theorems in algebra" and placed it in "theorems in complex analysis", which seems like a twice-wrong re-categorization! RobHar (talk) 17:21, 6 February 2012 (UTC)

Er... Reading the article suggests (to my untrained ear) that the theorem was named before "algebra" came to mean abstract algebra. It seems a better name would have been Fundamental theorem of complex analysis, as it deals with exactly that, and does not have general applicability across all algebras. — Quondum^☏✎ 18:00, 6 February 2012 (UTC)

I don't really know how to start replying to this. A major topic in "abstract algebra" (if not the whole point of it) is studying solutions of polynomial equations, so I'd say that the first theorem that said that every polynomial (over Q or R) has a root in C is a pretty fundamental theorem in the subject. It showed for the first time that there exist algebraically closed fields. It's generalized to Kronecker's theorem which is pretty fundamental. I would not say that it "deals with" complex analysis. A common proof uses complex analysis and in fact many other theorems that are more suitably called the Fundamental theorem of that subject. For example, Cauchy's integral theorem is surely a much more suitable candidate for this name. There's so much more to say, but I'll stop here. RobHar (talk) 18:23, 6 February 2012 (UTC)

Is that not algebraic geometry? I think my rationale was more along the lines that there wasnt a category Category:Theorems in complex geometry at the time, that was the next best thing. It is problematic though Brad7777 (talk) 18:39, 6 February 2012 (UTC)

There is, a problem in the categorization of manifolds, but surely not a problem of overcategorization. Analytic manifold, analytic variety, complex manifold are close and strongly related notions. One may add complex variety which redirects to algebraic variety, when analytic variety would be better suited. I have not found any category more specific than Category: Mathematics which contains all these pages. D.Lazard (talk) 17:52, 6 February 2012 (UTC)

Would they somehow fit into Category:Mathematical structures? You should really be able to find them through Category:Mathematical concepts. Brad7777 (talk) 22:31, 6 February 2012 (UTC)

Category:Properties of topological spaces

At the moment this category seems to be being abused. Many of the articles are on "topological spaces with properties". Strictly, this is like placing articles on triangles in a category called "properties of triangles" while there is a category called "triangles". What are your thoughts on categorizing redirected pages to this category instead where possible. For example, Connectedness (topology), categorized into Category:Properties of topological spaces, instead of Connected space being categorized into there? This would be a more proper use of the categories. It would require that the redirects are more specific where possible, but would reveal which articles do not have a section on the property they have when they could do with one (especially because of this category). I would also suggest that articles which don't have a relevant redirect to them are left in there, although these tend to be mainly stub articles. Comments? Brad7777 (talk) 13:45, 6 February 2012 (UTC)

I don't see the abuse you talk about. "Connected space" is defined as "topological space with the property of being connected". One could argue that the article should be moved from Connected space to Connectedness (topology), but frankly, I don't see the benefit in that. And whether the article is named Connected space or Connectedness (topology), it certainly should be categorized into Category:Properties of topological spaces. — Tobias Bergemann (talk) 14:11, 6 February 2012 (UTC)

You are saying a "topological space with the property of X" belongs to Category:Properties of topological spaces, but you cannot see the logic in having the section on X (being the property of a topological space) in this category? I don't see why this wouldn't a better substitute? I guess one of the points im raising is that a redirect from for example Connectedness (topology) to the connected space is not useful when there is not a clear section on what you have just been redirected from, (given that this could have came from any page). When there is a clear section, it allows articles in categories like Category:Properties of topological spaces or Category:Structures on manifolds to be more relevant. It also allows articles like compact space to be categorized in Category:topological spaces instead of Category:Properties of topological spaces, promoting the proper use of categories. (It is a topological space, not a property of a topological space). The issue about the article being moved to the more specific category in these types of categories perhaps needs its own discussion. Brad7777 (talk) 14:36, 6 February 2012 (UTC)

I think "compact space" is a fine article for the properties category, because it is our article on compactness of topological spaces. For example compactness redirects there. In general our article on property XXX will be called "XXX space" instead of "Property XXX of a topological space" but describing "compact space" as "is a topological space, not a property of a topological space" seems to be confused. — Carl (CBM · talk) 14:57, 6 February 2012 (UTC)

Are you saying compactness and compact space are both properties of topological spaces? Yes I am confused Brad7777 (talk) 15:11, 6 February 2012 (UTC)

I see, you are treating wikipedia as some kind of quantum system? The property having both a wave and particle like form? Brad7777 (talk) 15:17, 6 February 2012 (UTC)

This is more of an English usage thing. "Compactness" is the property possessed by "compact topological spaces". There is not some particular space which is the "compact space", which is what it implies to put the "Topological spaces" category on that article. Instead a compact space is a space which is compact, i.e. one which exhibits compactness. Our article begins, "In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, ...". — Carl (CBM · talk) 16:05, 6 February 2012 (UTC)

What Carl is saying is spot on. RobHar (talk) 17:21, 6 February 2012 (UTC)

It may help to compare e.g. Arens–Fort space, which is a particular topological space, with paracompact space, which is about the property of paracompactness. I would put the former in the "Topological spaces" category and the latter in the "Topological properties" category. — Carl (CBM · talk) 17:45, 6 February 2012 (UTC)

I see what you saying, but I guess this is where the vagueness of the name Category:Topological spaces plays, because to me this category should contain all topological spaces, (A Compact space is a certain type of topological space) whilst Category:Properties of topological spaces suggest articles on or about the properties of topological spaces. The article Compact space does mention a property, but it could be improved by having a unique section on compactness as a property of topological spaces. (In this case the redirect to that section only needs to be included in this catgeory). I think in the case of paracompact space, paracompactness is better suited for Category:Properties of topological spaces with paracompact space in Category:Topological spaces. I would also add a tag to Arens-Fort space saying "paracompact spaces". Brad7777 (talk) 18:25, 6 February 2012 (UTC)

It's useful to have a category that describes individual, specific topological spaces. Category:Topological spaces is that category. And whatever that category is named, compact space does not belong to it because many different spaces are compact. What you are advocating would eliminate any meaningful distinction between Category:Topological spaces and Category:Topology, because everything in topology is in some sense about topological spaces. This seems destructive to me. Far too many of your edits seem motivated by a sense of ideological purity of the Wikipedia category system and/or a shallow syntactic analysis of article and category names rather than out of any actual understanding of the mathematics the categories are trying to describe, and this is a case in point. —David Eppstein (talk) 18:29, 6 February 2012 (UTC)

What you are describing seems better suited for an article, more specifically a type of list. See WP:DEFINING. I also think many general users of wikipedia would use syntactic analysis to find articles and categories they require so do think it is worth taking into account. Brad7777 (talk) 18:57, 6 February 2012 (UTC)

As I understand it:

• Category:Topological spaces is for specific spaces, ones that would have a definite article in front, such as the long line.
• * Category:Properties of topological spaces is for properties that an arbitrary space may or may not have. This includes articles that are eponymous with a property, e.g. paracompact space for paracompactness. A sign that an article belongs here instead of the former category is that the indefinite article is used, e.g. a paracompact space.

If there are no large objections, I will go about fixing the category tree to reflect this. — Carl (CBM · talk) 18:47, 6 February 2012 (UTC)

The idea of the category Category:Topological spaces as you want would be better suited for a list, see WP:DEFINING. Brad7777 (talk) 19:08, 6 February 2012 (UTC)

How is "it is a specific topological space" (in opposition to "it is a class of topological spaces" or "it is a number" or "it is a theorem" or whatever) not a defining characteristic of a mathematical structure? This is exactly what I mean about forgoing mathematical sense in favor of ideological purity. —David Eppstein (talk) 20:03, 6 February 2012 (UTC)

Are you saying we need a category Category:Specific topological spaces? Brad7777 (talk) 21:45, 6 February 2012 (UTC)

I'm saying that we have that category, it is Category:Topological spaces. — Carl (CBM · talk) 21:46, 6 February 2012 (UTC)

Category:Topological spaces doesnt define the articles it contains. It defines alot more. Brad7777 (talk) 21:51, 6 February 2012 (UTC)

The text at Category:Topological spaces says "This is a list of important or interesting topological spaces." which matches what I am saying. For example locally compact space is not a topological space, it is a type of topological space, which is why it should not be in a category whose title is "Topological spaces". — Carl (CBM · talk)

Are you suggesting that we need a category Category:Types of topological spaces? Brad7777 (talk) 22:23, 6 February 2012 (UTC)

I ask because Wikipedia is here to present facts Brad7777 (talk) 15:17, 7 February 2012 (UTC)

I have no idea how "presenting facts" is relevant to anything. I explained above what the two categories mean, and I see no need to rename them. Perhaps you could be more clear and direct in explaining exactly what you mean, because I am unable to tell what you are trying to say. — Carl (CBM · talk) 15:30, 7 February 2012 (UTC)

We already have that category its called Category:Properties of topological spaces.TR 15:32, 7 February 2012 (UTC)

All topological spaces have properties. Topological property explains what a topological property is. You are saying Category:Topological spaces should only include spaces of interest (subjective?) and not for example paracompact space which is a type of topological space. ( ~ like an equilateral triangle is a type of triangle and found in Category:Triangles.) You are saying paracompact space should go in Category:Properties of topological spaces even though it is not a property. It is a type of topological space with a certain property, just like every other topological space including the more specific ones you talk of whose property can be defined as a combination of properties. Yet in the case of the page about a specific property of a topological space, paracompactness, (which redirects to the relevant section in paracompact space,) for some reason you do not it think should be categorized into Category:Properties of topological spaces because it does not fit your personal ideal? That is not objective categorization at all. Brad7777 (talk) 17:53, 7 February 2012 (UTC)

We are saying that properties of topological spaces such as paracompactness should be categorized differently than individual topological spaces such as the Hawaiian earring. Is that so difficult to understand? I'm feeling WP:IDIDNTHEARTHAT is very relevant here. —David Eppstein (talk) 18:14, 7 February 2012 (UTC)

My rejection of the concept is not due to difficulty understanding or ignoring any points of view, I do not disagree that paracompactness and Hawaiian earring should be in different categories? I disagree with the view that both paracompactness and paracompact space should be, when one is more specificied for the category. I also think by WP:DEFINING your concept of a collection of individual spaces is better suited for a list, and disagree with it for the same reason that you wouldn't have Category:Shapes dedicated to articles on unique, interesting, individual (or any other similar words) type shapes. Brad7777 (talk) 21:08, 7 February 2012 (UTC)

We do have such a category: Category:Geometric shapes. In any case, lists do not replace categories, they complement them. This is why we also have List of geometric shapes. — Carl (CBM · talk) 23:18, 7 February 2012 (UTC)

Are you saying Category:Geometric shapes is similar to how you are describing Category:Topological spaces? Actually I think many of those shapes aren't referred to as "the", infact the shapes left are purely due to the "sieve" of subcategories. I guess this all comes down to a question along the lines of: Is a "circular shape" a shape or a type of shape? Brad7777 (talk) 18:56, 8 February 2012 (UTC)

RFC on topological properties

Could those who agree with fixing the categories to match my comment of 18:47, 6 February 2012 please leave some sort of positive comment so I can gauge consensus? — Carl (CBM · talk) 23:18, 7 February 2012 (UTC)

• Support. Ozob (talk) 11:20, 9 February 2012 (UTC)
• Support. Tobias Bergemann (talk) 13:47, 9 February 2012 (UTC)

Paracompact space

The article paracompact space currently begins with the following sentence:

In mathematics, a paracompact space is a topological space with the property of paracompactness.

Not only is this a meaningless sentence, the link paracompactness redirects back to the same article! This seems to be due to a significant edit by Brad7777. I will work on fixing the article, but more eyes on it (and other edits by Brad7777) would be helpful. — Carl (CBM · talk) 20:37, 7 February 2012 (UTC)

If you think there is a problem with my edit, you could let me know on my talkpage, or simply edit it, explaining your reasoning in the summary. (You could edit the grammar so that it says "which has the") WP:SOAP Brad7777 (talk) 21:21, 7 February 2012 (UTC)

At the time paracompactness redirected to a specific section, which is no longer needed. I apologize for the utter ridiculousness of it. Brad7777 (talk) 21:24, 7 February 2012 (UTC)

Categorizing redirects

The links Cofinite topology and Finite complement topology currently redirect to Cofiniteness#Cofinite topology, and I would like to add these redirects to Category:Topological spaces. However, given the discussion above concerning Category:Topological spaces and Category:Properties of topological spaces I thought I should ask before doing anything that might be seen as pouring oil into the fire. The article Cofiniteness itself is already in Category:General topology.

(There is an editing guideline at Wikipedia:Categorizing redirects concerning the categorization of redirects, and I think categorizing a redirect to a subsection of a larger article is covered by the section Subtopic categorization.)

— Tobias Bergemann (talk) 14:10, 9 February 2012 (UTC)

Ignoring the issue of redirects for the moment, I think there are three particular types of articles to look at:

1. Articles on particular topological spaces, for example the long line or the topologist's sine curve.
2. Articles about particular topologies, which could be put on different sets. For example, the discrete topology, the indiscrete topology, the Lawson topology
3. Articles about properties of a topological space. Examples include paracompactness, first countability, etc. The difference between this and #2 is that I cannot say "take a set and put the first countable topology on it" but I can say "take a set and put the discrete topology on it".

I think that these three types of articles generally belong in different categories. I'm not certain which those should be, or if the existing categories should be renamed. — Carl (CBM · talk) 15:17, 9 February 2012 (UTC)

I think cycle index needs expert attention

The article on cycle index confuses or elides the distinction between groups generally and permutation groups. Since cycle indices are properties of permutation groups, not of abstract groups, this renders it confusing, and possibly incorrect. I have put a more detailed complaint on the talk page. I hope someone more skilled in algebraic terminology can clean it up. —Mark Dominus (talk) 16:32, 10 February 2012 (UTC)

Looks like every group under scrutiny is a subgroup of the symmetries. If I were you I'd make a note in the intro to that effect, or tweak the major occurences that you found where "group" was unclearly used. Rschwieb (talk) 18:38, 10 February 2012 (UTC)

I have not check the details, but it seems that "group" is never used alone, always as "group of permutations". Thus there is no ambiguity, as "group of permutations" means "finite group acting on a finite set". Thus, in your example on the talk page, the two groups are isomorphic as groups, but are different as groups of permutations. Maybe it could be useful to recall in the lead that a group of permutations of degree n is a finite group acting on a set of n elements and that two isomorphic groups acting on two sets of different orders are not isomorphic as groups of permutations. D.Lazard (talk) 18:56, 10 February 2012 (UTC)

Is a function a rule or an association?

It depends on whether we want to enlighten or to obfuscate (see Talk:Function (mathematics)). Tkuvho (talk) 13:44, 12 February 2012 (UTC)

Fractal fraction

The mathematics article fractal fraction is up for deletion. Please comment at Wikipedia:Articles for deletion/Fractal fraction. — Arthur Rubin (talk) 17:57, 12 February 2012 (UTC)

Horocycle merged to horosphere

The article horocycle was recently merged to horosphere. I've undone this merger, but was quickly reverted. I'd appreciate outside input at Talk:Horosphere. Sławomir Biały (talk) 13:44, 13 February 2012 (UTC)

Surely one is just the one-dimensional specialisation of the other; or, alternatively, the other is a longstanding multidimensional generalisation of the first. Doesn't it make sense to treat both together? -- if not with horocycle under horosphere, then with horosphere under horocycle? Jheald (talk) 14:31, 13 February 2012 (UTC)

I am not so sure. Thus, the remark that the geometry of the horosphere is euclidean is not really significant for horocycles. The statement that a horocycle has geodesic curvature 1 cannot be made for horospheres, etc. Tkuvho (talk) 14:41, 13 February 2012 (UTC)

We have separate articles on circles and spheres. Surely this is the same distinction? —David Eppstein (talk) 16:12, 13 February 2012 (UTC)

Except that here the article seems to deal with general horo-n-spheres, so the distinction is perhaps different. We have n-sphere and circle, so I'm not saying there shouldn't be a separate article if enough material exists on it to justify this (though there is very little at the moment). — Quondum^☏✎ 17:22, 13 February 2012 (UTC)

There probably should be separate articles but seeing as how both are stubs and on related subjects it's not that surprising that an attempt was made to merge them. Our article on hypercycles is longer but apparently in need of more work, and I couldn't find anything on their higher dimensional analogs.--RDBury (talk) 21:01, 13 February 2012 (UTC)

I just found this discussion here. Circles, horocycles and hypercycles (generalized circles) are the 2D variants of generalized spheres (spheres, horospheres or hyperspheres) in Hyperbolic geometry (balls and disks are just the usual interiors). Actual descriptions vary by model and whether 2 or 3d but arise via the intersection of H^n with an affine plane (or an r-sphere as the intersection with an affine r+1 plane)88.82.206.110 (talk) 14:38, 18 February 2012 (UTC)Selfstudier (talk) 14:39, 18 February 2012 (UTC)

Is Correspondence (mathematics) a useful page?

I've just stumbled across the page Correspondence (mathematics). As well as being completely unsourced, it strikes me as a collection of things that really don't belong together—each definition could better be placed on the page for the appropriate topic. Also, the first definition contradicts the definition given at relation (mathematics). Links such as those from the first sentence of function (mathematics) to correspondence (mathematics) only serve to muddy the waters further. Does anyone see this page as worth keeping? Jowa fan (talk) 23:23, 13 February 2012 (UTC)

Maybe a bit slimmed down as a {{mathdab}}. But other articles should be linking to the articles listed at Correspondence (mathematics) rather than linking to Correspondence (mathematics) itself. —David Eppstein (talk) 23:35, 13 February 2012 (UTC)

BTW there is something like mathdab at ru:Отображение (значения) (Russian: Отображение = map). Other interlanguage links apparently correspond to map (mathematics) or are redirected, so the "article" is apparently a PoV fork. Incnis Mrsi (talk) 09:01, 14 February 2012 (UTC)

I see no contradiction between the first definition and the definition at binary relation that it refers to. It would be better I think to distribute the meanings and make it a proper disambiguation page I think, so yes the page would be slimmed down a bit. I see no evidence of any POV and don't know where that idea came from and the other interlanguage links do not support what is said as far a I can see. I wouldn't depend on how things are translated for very much anyway though I do like sometimes to look at other languages to get some ideas. Dmcq (talk) 09:23, 14 February 2012 (UTC)

The page Correspondence (mathematics) says correspondence is an alternative term for a relation between two sets, whereas binary relation says A correspondence: a binary relation that is both left-total and surjective. Jowa fan (talk) 11:32, 14 February 2012 (UTC)

I think the page should not be trimmed down. The many incarnations of correspondences all have something in common: "a point gets mapped to many points". A good article would make this clear. I have added two references. Jakob.scholbach (talk) 12:37, 14 February 2012 (UTC)

I wonder where the binary relation page got that definition of correspondence from. In page 1331 of Encyclopedic dictionary of Mathematics the definition of a correspondence is just any relation plus the two sets with no restriction about being left and right total. Dmcq (talk) 13:18, 14 February 2012 (UTC)

A recent change to function (mathematics) now defines a function as a correspondence. The discussion above is clear enough indication that the term is ambiguous, confusing, and unhelpful. The far better term "rule" is strongly supported by three editors but has met resistance on what seems like pedantic, if not bourbakist, grounds. Further input would be appreciated. Tkuvho (talk) 08:57, 15 February 2012 (UTC)

Well it would be if we can get a citation for the definition of correspondence in the article about binary relation. There's a citation in the article showing its use in function is perfectly correct and the dictionary entry I pointed to supports that as well. Dmcq (talk) 09:07, 15 February 2012 (UTC)

Tkuvho - the term "rule" will, for most people, imply a finite and deterministic rule or algorithm. As I expect you know, not every function can be defined by a finite rule, otherwise every function would be a computable function. The existance of incomputable functions is so fundamental that glossing over it in the article's lead would be a gross over-simplification. For me, the current opening sentence "In mathematics, a function is a correspondence that associates each input with exactly one output" strikes the right balance between accuracy, brevity and clarity. Gandalf61 (talk) 09:38, 15 February 2012 (UTC)

I responded at Talk:Function_(mathematics)#summary_of_correspondence_vs_rule. Tkuvho (talk) 07:48, 16 February 2012 (UTC)

In my opinion the debate follows that, in mathematics, "correspondence" has frequently its usual, non formal, English meaning, as in article function. But it may also have a technical meaning, subject to a formal definition, as in relation (mathematics). Thus I propose to modify the beginning of correspondence (mathematics) as

In mathematics and mathematical economics, correspondence may be used informally with its usual English meaning. It may also have a technical meaning subject to a formal definition.

• In the theory of relations, a correspondence is a relation between two sets, such that every element of each set is related to at least one element of the other.

(For the item, I have kept the definition of Relation (mathematics), but the item must be changed when the definition in Relation (mathematics) will change. D.Lazard (talk) 11:16, 15 February 2012 (UTC)

Have you a citation for that? I've put a citation needed into binary relation because as described above I found a dictionary giving something quite different - and which in fact works very well in the lead of function. I found no definition like the one in that article. Dmcq (talk) 19:15, 15 February 2012 (UTC)

No, I have no citation, but like you I am not sure that this definition is not OR. It is the reason of my comment in parentheses. My feeling is that this first item could be suppressed, the non formal meaning being sufficient for the definition of a function. D.Lazard (talk) 21:26, 15 February 2012 (UTC)

Proposed changes to mathematical categories

Good Olfactory (talk · contribs) has proposed renaming Category:Triangulation to Category:Triangulation (geometry). Discuss at Wikipedia:Categories for discussion/Log/2012 February 14. The same discussion page also contains a proposal to delete Category:Polyhedra rest category and merge it into its parent category. And there are also quite a few renames of mathematical categories proposed at Wikipedia:Categories for discussion/Speedy, e.g. Category:Logical symbols to Category:Logic symbols, Category:Tiling to Category:Tessellation, etc. —David Eppstein (talk) 22:50, 14 February 2012 (UTC)

Charles Wells (mathematician) at AfD

Charles Wells (mathematician) is up for deletion.  --Lambiam 02:44, 16 February 2012 (UTC)

External links at Tangram

There is a small dispute as to whether certain links should be included in the External links section. Additional opinions at Talk:Tangram#EL links removed will be appreciated.--RDBury (talk) 04:51, 17 February 2012 (UTC)

covering set

I always thought that covering set was another term for cover (topology). I was surprised that the covering set article is purely about a number-theoretic meaning. Now I'm not sure whether to add an xref. Can someone take a look? Thanks. 67.117.145.9 (talk) 04:03, 18 February 2012 (UTC)

It may also be confused with covering space. I have added a disambiguation hatnote in covering set. D.Lazard (talk) 08:16, 18 February 2012 (UTC)

Ayme's theorem

WP:OR? Michael Hardy (talk) 03:18, 19 February 2012 (UTC)

Yes. I'd be very skeptical of anything claimed to be a significant new result in Euclidean plane geometry, new and significant being pretty much mutually exclusive at this point in the history of the subject.--RDBury (talk) 05:13, 19 February 2012 (UTC).

Notability and secondary sources (lack thereof) could disqualify this for WP, regardless of "significance". Is there not some WP-related project for this kind of non-encyclopedic result where it does not have to adhere to quite the same criteria as for Wikipedia? It feels though there should be some middle ground between Youtube and Wikipedia. — Quondum^☏✎ 05:59, 19 February 2012 (UTC)

PlanetMath? Though in this case checking against the known centers in the Encyclopedia of Triangle Centers and, if unknown, adding it there looks appropriate. —David Eppstein (talk) 07:33, 19 February 2012 (UTC)

To RDBury. This result is certainly not significant. It is a special case of a general theorem which is certainly well known, even if I have never seen it explicitly written.

Theorem: Let ABC be a triangle. Let Sa, Sb, Sc (Ayme's notation) be three points constructed from the triangle. If these points are permuted by every permutation of A, B, C which leaves fixed the other choices implied by the construction, then the three lines ASa, BSb, and CSc are concurrent.

Proof: The matrix of the coefficients of the barycentric equations of the lines is antisymmetric, and thus has a null determinant.

It is thus easy to construct billions of similar theorems. D.Lazard (talk) 13:47, 19 February 2012 (UTC)

Ayme can post it up on ProofWiki himself, if he likes, and it will then probably (eventually) be categorised as an example of the aforementioned theorem on the coefficents of barycentric equations. But for once I'm in agreement: this is not significant enough for Wikipedia. --Matt Westwood 14:29, 19 February 2012 (UTC)

Conditional statement – a solution needed, not a smoldering edit war

At WP: Articles for deletion/Conditional statement (logic) I proposed to make a conceptdab article, but there was not any movement in this direction. Later, I asked help at WikiProject Logic, to be ignored. Now, at Conditional statement (logic) (edit | talk | history | links | watch | logs) users Artur Rubin and History2007 try to redirect this to material conditional, which I consider as inappropriate. On the other hand, Hanlon1755 (talk · contribs) pushes his own ideas about what is logical condition. Please, help to put the end to redirects' jumble and make a valid disambiguation of the term "conditional" in logic, programming and linguistics. Preferably, as a WP:CONCEPTDAB article. Incnis Mrsi (talk) 13:21, 14 February 2012 (UTC)

The dab page you refer to exists at Conditional statement. -- 202.124.72.200 (talk) 10:19, 15 February 2012 (UTC)

I could, although reluctantly, remember one (static) IP address, but it is not polite to prompt Wikipedia users to waste time for whois and reverse DNS queries and comparisons of persistently changing IPs. Please, register yourself; this is the last time I reply to an IP posting from this ISP. Incnis Mrsi (talk) 18:18, 15 February 2012 (UTC)

---

The war progressed for another 5 days. Now I self-proclaimed a mediation at Talk:Conditional statement (logic)#Conditions for acceptable solution and ask the WikiProject for support. Please, provide an explicit output. Don't give just a silent agreement, because warriors can disrespect my self-imposed conditions. Please, express some will to end the edit war even if the cause and exact conditions seems not so important. Incnis Mrsi (talk) 09:02, 20 February 2012 (UTC)

manifold destiny

There is a discussion at Talk:Manifold Destiny#Birman of Joan Birman's comments concerning Yau. My personal opinion is that the comment is not only incorrect but borders on slanderous, and should not be included. Tkuvho (talk) 07:59, 20 February 2012 (UTC)

An editor thinks it's censhorship here. Please comment. Tkuvho (talk) 12:38, 22 February 2012 (UTC)

Euler Archive

I was trying to track down a reference for the article on Euler's criterion when I found this: http://www.math.dartmouth.edu/~euler/

Is there a special convention or template for citing it?

Virginia-American (talk) 21:51, 21 February 2012 (UTC)

I don't think there is so just use the cite-web template or use cite-book with the url.--RDBury (talk) 23:22, 22 February 2012 (UTC)

Category move proposals

Wikipedia:Categories_for_discussion/Log/2012_February_15

There are four proposals to move categories in the logic department. I think some people who have actually done some study on the subject should take a look. Please do drop in. Greg Bard (talk) 02:19, 22 February 2012 (UTC)

Actually I agree with Greg Bard on not renaming these but haven't any real stake in the matter. I'd probably rename logical syntax to logic syntax rather than using parenthesis and logic symbol instead of logical symbol makes me think of drag and dropping a symbol in designing a circuit. Dmcq (talk) 13:03, 22 February 2012 (UTC)

Interviews about categories

When I saw this Wikipedia:Village pump (miscellaneous)#University research project on categories seeks interviewees I immediately thought of this project.Can't for the life of me say why ;-) Dmcq (talk) 17:57, 22 February 2012 (UTC)

Some extra eyes on matrix (mathematics)

A known problematic editor has set his sights on matrix (mathematics). I have no intention of further engaging with this particular editor. It would be helpful if some project members could keep an eye.TR 07:34, 21 February 2012 (UTC)

Upon being extended an invitation to edit cooperatively to address the concerns we raised, he gave up. This suggests the user was not interested in anything short of the reinstatement of the deleted text. The same tactic might shorten future skirmishes with the same user. Rschwieb (talk) 14:09, 24 February 2012 (UTC)

Merge help

Please discuss and do the merge at Talk:Arithmetic complexity of the discrete Fourier transform. I don't understand this math at all and can't do it myself. D O N D E groovily Talk to me 04:29, 22 February 2012 (UTC)

Solved by redirecting to Arithmetic_complexity_of_the_discrete_Fourier_transform#Bounds_on_complexity_and_operation_counts where one may find the relevant content of this page. The remainder of the page consisted in awful formulas lacking of any explanation, which have not their place in Wikipedia. D.Lazard (talk) 16:03, 24 February 2012 (UTC)

EoM again

I saw that there was an old thread about the Encyclopedia of Mathematics and its new wiki form at http://www.encyclopediaofmath.org. Of the points raised, I'm much the most concerned about the broken links, at present. Do we have a plan of action for fixing them? And, if we can decide about how that could be sorted out, where are we on MathJax or indeed any long-term solution for formulae? Charles Matthews (talk) 16:33, 22 February 2012 (UTC)

On the first issue, afaik there is no concerted effort but I hope people are fixing the broken links when they find them. There are probably more articles where there should be a link to EoM but there is none, broken or not. It seems like one of those tasks that seem like a good idea in principle but are too tedious to garner volunteers to actually get them done.--RDBury (talk) 23:38, 22 February 2012 (UTC)

From experience, this is rather boring and time-consuming. I have already suggested the following patch: a script that looks for eom links with id of the form ?/*, and replaces the id with the title field (space -> underscore). Of course, this can be only semi-automatic (although theoretically the script can also ping the page to check that it exists). Script experts, is this a feasible task? Sasha (talk) 02:01, 23 February 2012 (UTC)

Someone please do this! Sławomir Biały (talk) 13:11, 23 February 2012 (UTC)

Didn't we have a template for EoM?--Kmhkmh (talk) 14:25, 24 February 2012 (UTC)

the issue is as follows. EoM (later renamed springer, and later, SpringerEOM) is a template for EOM. However, the encyclopaedia changed its format a few months ago. Therefore the old links no longer work. The template itself has been fixed; what we are discussing is a way to fix the links (more precisely, change the "id" field from the format A/123456 to the new format Abc_equation). Sasha (talk) 15:26, 24 February 2012 (UTC)

There are 746 transclusions of the template {{SpringerEOM}} to fix. Bulk edit like this are probably done by a semi-automatic tool like WP:AWB.--Salix (talk): 16:42, 24 February 2012 (UTC)

how complicated is it? Does AWB have a ping option? Sasha (talk) 17:02, 24 February 2012 (UTC)

It fairly simple. You need to run it from windows and you start it by giving a list of files you want to edit, its smart enough to find out all the pages which transclude {{SpringerEOM}}. It then goes through the pages 1 by 1 and it can do some substitutions and allow you to adjust the edit. You need to OK each edit. You can go through many pages quickly about 4 a minute.--Salix (talk): 17:49, 24 February 2012 (UTC)

The news from the External link finder is actually not that bad. Just now there were 368 hits: but I took out those not from actual articles, and the number came down to 178. And some of those are multiple uses of the same link. So this could get done, I suggest. Charles Matthews (talk) 22:02, 24 February 2012 (UTC)

(this probably has to do mainly with my stupidity, but) I had trouble using the AWB regexp (and I did not find anything similar to a ping feature). If someone volunteers to post a working AWB script here, I am ready to share the load of running it. Sasha (talk) 22:14, 24 February 2012 (UTC)

You might not be registered to use it, see the AWB page for detail of registration.--Salix (talk): 14:31, 27 February 2012 (UTC)

I've made a simple converter[[6]] which can take the citation from the bottom of the springer page and produces the complete template with parameter for our reference. --Salix (talk): 14:31, 27 February 2012 (UTC)

thanks! (actually, I am AWB-registered, the problem was indeed with my stupidity). Sasha (talk) 15:58, 27 February 2012 (UTC)

Where did "labelled enumeration theorem" go?

The page symbolic combinatorics contains several redlinks to labelled enumeration theorem. It looks like the latter page existed in 2009, since it has been copied at http://citizendia.org/Labelled_enumeration_theorem, but I can't find a deletion discussion for it. Does anyone know what happened here? Jowa fan (talk) 03:51, 23 February 2012 (UTC)

The deletion log of labelled enumeration theorem says "Expired PROD, concern was: this is unsourced junk". PROD's don't have deletion discussions. Follow the link to see how they work. As an administrator I can see the deleted page history. It was prodded with "this is unsourced junk" in 2010 by User:Zahlentheorie who had created the article in 2006. PrimeHunter (talk) 04:04, 23 February 2012 (UTC)

From a brief look at the citizendia version it appears to be a variation on the Polya enumeration theorem. But is it an known theorem with a made up name, original research, or just junk? In retrospect an AfD might have been useful to determine which.--RDBury (talk) 23:15, 23 February 2012 (UTC)

I restored the article so that everyone can look at the content. I recommend adding additional references if the article is kept, to demonstrate that the topic passes the inclusion/notability criteria. This is just a pro forma undeletion, I have no opinion about whether the article should be deleted again. — Carl (CBM · talk) 16:43, 24 February 2012 (UTC)

Just browsing around and following some links, I just noticed that Proofs involving the totient function was PROD-ded in July 2010 ("concern was: wikipedia is not a directory of proofs, but rather of theorems"), while under its old title Totient function/Proofs it was AfD-ded in 2007 : Wikipedia:Articles for deletion/Totient function/Proofs and the result was Keep. Maybe some events I did not notice took place between 2007 and 2010, but might it not be a similar dubious Prod-ding ? French Tourist (talk) 09:45, 25 February 2012 (UTC)

A few minutes later, I notice the strange Wikipedia_talk:WikiProject_Mathematics/Archive_51#Strangest_edit_war_I.27ve_ever_seen. Might it be related with this PROD-ding ? French Tourist (talk) 10:03, 25 February 2012 (UTC)

There is a no double jeopardy for PRODs, see Wikipedia:Proposed deletion#Nominating under 'Before nomination'. So technically the PROD was improper, not that I'd request that it be restored.--RDBury (talk) 15:35, 25 February 2012 (UTC)

Proofs by Dooooot

I don't think any of these "proofs" should be given, for the following reasons:

1. Almost all of the rules for which he provides a "proof" are considered primitive rules in some system
2. The selection of rules used seems arbitrary, and needs a source
3. The proofs do not fall under WP:CALC, so they need sources.

— Arthur Rubin (talk) 03:42, 25 February 2012 (UTC)

You didn't specify which proofs, but I assume one of them is the one given in Hypothetical syllogism. In that case at least I agree and I'd question whether is it encyclopedic as well, generally if the proof is easy enough to assign as an exercise then we don't need to have it here. Another issue is that proofs should be in prose, not a table of symbols. Also, turquoise? This might be raised at the logic project as well.--RDBury (talk) 08:06, 25 February 2012 (UTC)

There's other wikis that go in for that sort of stuff. Proofs here should be either short and unobtrusive or have some element of notability in the literature. I don't think Wikipedia should become a repository for every proof in Mizar for example, they should refer to a source for this sort of thing. Dmcq (talk) 09:42, 25 February 2012 (UTC)

More to the point, you can't provide a proof of particularly this sort of PropLog theorem without first stating exactly which axioms you are working from. In order for the HS proof to be of any worth at all, at least one ought to allow Modus Ponendo Ponens as an axiom (or previously proved). Instead a great pile of other theorems (Transposition, Constructive Dilemma, etc.) are used instead, making this ridiculously overcomplicated. Besides, it uses LEM which unnecessarily removes it from the domain of constructivist proofs. So this proof is IMO seriously unworthy of WP. If all the rest of this user's proofs are like that, then I concur. --Matt Westwood 07:56, 26 February 2012 (UTC)

Oh, and even more to the point, the proofs are circular. To prove absorbtion, conjunction is used. To prove conjunction, absorption is used. As proofs go, these are complete and utter piffle.

Aha, I just see someone's already made that point below. --Matt Westwood 08:00, 26 February 2012 (UTC)

(ec) I was referring to the ones he seems so proud of at User:Dooooot#Proofs I've Written, although there may be others. WikiBooks and WikiVersity (if it's still open) seem better venues. — Arthur Rubin (talk) 09:56, 25 February 2012 (UTC)

Yes they seem reasonable places for someone who wants to go in for this sort of thing. Dmcq (talk) 10:16, 25 February 2012 (UTC)

More to the point, my guess is that the "proofs" are formally invalid, because they confuse levels of the system, normally kept separate by using distinct symbols, e.g. ⊢ versus →. If the "proofs" were valid, we'd call them "theorems of inference". — Quondum^☏✎ 10:39, 25 February 2012 (UTC)

I notice a certain circularity: Modus ponens is used to "prove" Disjunctive syllogism and vice versa. — Quondum^☏✎ 11:18, 25 February 2012 (UTC)

I don't think we should have "proofs" of these rules. I would not object to a truth table in some cases, though. Sławomir Biały (talk) 14:23, 25 February 2012 (UTC)

It does seem a bit funny to prove the inference rule modus ponens. Dmcq (talk) 14:29, 25 February 2012 (UTC)

Such "proof" as Hypothetical syllogism#Proof unlikely is useful, but is misleading in its use of negation and equivalences valid in classical logic only. If you did not get yet why is it incorrect, I resort to the analogy with algebra. Consider an identity $2x^{2}+2(x+1)^{2}=(2x+1)^{2}+1$ and a proof deriving it from $(a+b)^{2}+(a-b)^{2}=2a^{2}+2b^{2}$:

$2x^{2}+2(x+1)^{2}=2((x+{\frac {1}{2}}-{\frac {1}{2}})^{2}+(x+{\frac {1}{2}}+{\frac {1}{2}})^{2})=4((x+{\frac {1}{2}})^{2}+{\frac {1}{4}})=(2(x+{\frac {1}{2}}))^{2}+1=(2x+1)^{2}+1$

Yes, a proof is valid for real, complex and rational numbers, but it is invalid for any field of characteristic 2 (there is no such number as ½) and it is inapplicable to unital rings (because there is no division at all), although the identity still holds. The "universally correct" proof should be:

$2x^{2}+2(x+1)^{2}=4x^{2}+4x+2=(4x^{2}+4x+1)+1=(2x+1)^{2}+1$

I am convinced that a proof may be useful only if it is valid in the most strict theory where a statement in question is a theorem. Incnis Mrsi (talk) 16:54, 25 February 2012 (UTC)

I think a lot of what you're saying is covered in point 2 in the original post. In general it's one of the pitfalls of doing proofs in an encyclopedia rather than than a text book that you don't get to formally establish which axioms are being used and which theorems are "known" and can be used without raising questions of circularity. In many cases you can make reasonable assumptions as to what should be considered common knowledge for the purposes of a proof, but for symbolic logic there are many equivalent formulations of the axioms and rules of inference and having a proof without knowing which formulation is being used doesn't make much sense. In fact in most of these cases the proposition may just as easily be taken as a axiom so giving a proof is unnecessary. I like the idea above of using truth tables as justification rather than formal proofs, they should be enough to convince casual readers, who probably compose a large segment of our readers anyway. Truth tables would be especially useful in cases where the result may be counterintuitive, $\neg p\to (p\to q)$ for example.--RDBury (talk) 04:53, 26 February 2012 (UTC)

If one still did not get the point, I repeat: the problem with some concrete formula, which Wikipedia attempts to present as a theorem (logical one, algebraic or else), is not only in an arbitrary selection of rules (Arthur Rubin) or even axioms. The problem is that Wikipedia, unlike a textbook, must obey WP:NPOV, which means that a description of P→Q, Q→R ⊧ P→R from classical PoV without mentioning other propositional calculi contradicts to the Wikipedia policy. On the other hand, I do not see a grave heresy in proofs of axioms and unordered graphs of proofs. I know what is circulus vitiosus, but if the article on the "axiom" C′ says A, B, C ⊢ C′ and the one about C says A, B, C′ ⊢ C, this does not mean a logical flaw, but only equivalence of {A, B, C} and {A, B, C′}. Incnis Mrsi (talk) 07:57, 26 February 2012 (UTC)

The proofs should be allowed, with qualifying language. Any given proof isn't "the" proof but rather "a" proof. I do understand Rubin's points though. Even the transformation rules template gives a particular set of rules. However, that isn't intended to represent any particular system, but rather gives common rules used in various systems. At some point I think this kind of information (i.e. Dooot) is expected in a comprehensive encyclopedia article on particular rules of inference. Greg Bard (talk) 19:25, 26 February 2012 (UTC)

I think they need to be cited or deleted. If there really is some sort of subtle problem introduced by a logic aficianado, it would be fuel for confusion. Secondly, has anyone figured out why there are two "proofs" here? To all appearances the second seems like a less efficient duplicate of the first. Rschwieb (talk) 20:53, 27 February 2012 (UTC)

Projective range

I came up on the page Projective range. It lacks of a formal definition that I can understand. Should it be expanded or deleted? D.Lazard (talk) 22:47, 26 February 2012 (UTC)

This is standard classical terminology in projective geometry. Several collections of specially related objects are referred to as pencils (a pencil of lines through a point in a plane, a pencil of hyperplanes through a codimension 2 space, a pencil of conics, etc.). In all these cases the dual concept to a pencil is called a range. The page in question is certainly not well written and lacks clarity, but I would say that it needs to be expanded rather than deleted. I don't see myself doing that for at least a couple of weeks. An alternative might be a merge into Duality (projective geometry), where the originator of Projective range has placed an out of context sentence containing a link to the new page. Bill Cherowitzo (talk) 06:06, 27 February 2012 (UTC)

My understanding is that the generic term is "projective form" which would include projective pencils, projective sheaves, etc. So I'd suggest changing the name covering all of these in the article.--RDBury (talk) 07:15, 27 February 2012 (UTC)

Proposing stubs: Zero algebra, Trivial algebra, Flexible algebra

The following "trivial" or "uninteresting" cases seem to have encyclopedic value at least inasmuch as they provide clarity for someone seeking to understand their status. Unlike a field with one element, they appear to be uncontrovertial:

• Zero algebra is used to mean an algebra over a field (or ring) in which the product is given by the map a × b ↦ 0. These are usually uninteresting, but appear to be mentioned in some sources. I imagine it sees use in the classification of algebras.
• Trivial algebra is an algebra over a set of one element (see nLab, mentioned in Quasivariety). It is a category covering several cases such as singleton set, trivial group and trivial ring.
• Trivial algebra over a field (or ring) is an obvious example of a trivial algebra, on par with trivial group and trivial ring. It would seem appropriate for completeness, but I've not seen reference to this specifically.

I've come across another term in a few places and papers, enough to warrant a stub:

• Flexible algebra, defined as an algebra with the property (ab)a = a(ba) for all a and b. (See Planetmath.)

Any opinions on the creation of these stubs? — Quondum^☏✎ 07:21, 27 February 2012 (UTC)

In general I'd oppose creating a stub unless there is reasonable expectation that the article can be expanded beyond that or it would awkward to put the material in another article. For example for zero algebra I's suggest adding it as section of Algebra over a field, then creating a redirect to that section. It would be reasonable to include the zero algebra there anyway as an example. The fact that articles for similar objects should not carry any weight here, see WP:OTHERSTUFF.--RDBury (talk) 09:42, 27 February 2012 (UTC)

Some comments about "zero algebra": There are two notions of zero algebra. The non unital one that you consider, which is, in fact, another name for "module", and the unital one which is the direct sum of the basis ring and a module, with null product for two elements of the module. This is not an "uninteresting" notion, at it allows frequently to extend straightforwardly to modules and submodules some notions which are primarily defined for rings and ideals. For example, this allows, not only to extend the theory of Gröbner bases to modules and submodules, but also to use for submodules any implementation of a Gröbner basis algorithm for ideals. Thus the question is what is the right place for "zero algebra", in module (mathematics) or in algebra (ring theory) or in both. D.Lazard (talk) 10:38, 27 February 2012 (UTC)

Thanks for the input. I have followed RDBury's guideline and avoided stubs (and not even created redirects), but inserted sections for zero algebra in Algebra over a field#Kinds of algebras and examples and a point on flexible algebras in Algebra over a field#Non-associative algebras. I am having difficulty reconciling an algebra with an identically zero product with a module, so I'm leaving that as beyond my present understanding. The rest I've left alone. — Quondum^☏✎ 15:24, 27 February 2012 (UTC)

I came too late for "zero algebra", but put in my 5коп for "trivial algebra". In Wikipedia, it may be referred as a "trivial algebra", although such link lies on the edge of WP:EGG. Zero-dimensional space just has no dimensions at all. Any possible linear structure is not relevant, because may be either trivial or not existent. Incnis Mrsi (talk) 15:50, 27 February 2012 (UTC)

Got wrong, not yet and probably not such. I expected an article about 0d linear space, but it is about a topological one. Something to be disambiguated and fixed. Incnis Mrsi (talk) 15:57, 27 February 2012 (UTC)

Now all is in order, trivial algebra is linkable. By the way, I discovered and fixed a severe mistake. One user thought that "trivial module" is something like "zero algebra" from this topic, which is (according to MathWorld) not true. All three 0-dimensional algebraic entities are now in one article. Incnis Mrsi (talk) 16:47, 27 February 2012 (UTC)

It's probably not so much a severe mistake as it is a difference in convention. A google search immediately returns several instances of "trivial module" meaning any module for which mr=0 for any choice of elements m in the module, r in the ring. Both the concept you put in and this one are "trivial" in some sense so it is natural different people use them different ways. I think we should modify it a bit to reflect this, as is done with zero/trivial ring. It's a little arbitrary to declare one sense correct, here. It only perpetuates the confusion of usage. Rschwieb (talk) 18:06, 27 February 2012 (UTC)

So, I can propose to rename it to zero space to wipe an ambiguity out ultimately. This name has an advantage to omit mentioning of a ground object (either a ring or a field). Happily, I have a technical possibility to kick the current redirect off. Certainly, if there was no objections here to this move. Incnis Mrsi (talk) 18:35, 27 February 2012 (UTC)

I think renaming should depend on which usage dominates. If the trivial product version mr=0 usage is in the minority, I would suggest keeping the name as is, but mention this as an alternative interpretation of the term within the article. Technically, a zero vector space is still over a base ring/field, and thus does not really get rid of mentioning which. One could just as easily omit this mention in the case of a trivial algebra/module. — Quondum^☏✎ 18:54, 27 February 2012 (UTC)

Yes, I agree, it should be based on which usage is predominant among workers in the field. Not being one of them, I'm not sure which one that would be. But I want to urge very strongly that the decision not be based on MathWorld. MW has some uses, but a reliable source for nomenclature it is not. --Trovatore (talk) 00:17, 28 February 2012 (UTC)

Okay, I see how the unital zero algebra works. I generally don't know what is meant by "direct sum", since its meanings can be so different. This would imply that dual numbers constitute a unital zero algebra over the reals. Thanks for the assistance. — Quondum^☏✎ 17:46, 27 February 2012 (UTC)

Exactly, the dual numbers are the unital zero algebra build up from a real vector space of dimension one. I'll add this example in algebra over a field. D.Lazard (talk) 19:00, 27 February 2012 (UTC)

Jean-Claude Sikorav

Jean-Claude Sikorav is a new article by Tkuvho, which will probably soon be listed on AfD. Comments/improvements are welcome. Sasha (talk) 19:52, 27 February 2012 (UTC)

It has just been the topic of a somehow frantic (and sometimes badly informed) deletion review on :fr (the result was "Keep"). The article had been created there by a group of two juvenile students of École Normale Supérieure de Lyon, where JCS teaches, and I am not yet sure whether they were serious or if they were playing a funny joke with Wikipedia. You can have a look at the (quite unhealthy) debate at fr:Discussion:Jean-Claude Sikorav/Suppression. French Tourist (talk) 21:17, 27 February 2012 (UTC)

I agree that, unless there is some clearer sign that the article passes WP:PROF, it is likely to be a subject of a deletion discussion, particularly because it was already deleted once under CSD and undeleted by me. My undeletion was only to give more time to add content. I think the current content of the article does not make for a clear case that the notability guidelines are satisfied. — Carl (CBM · talk) 22:18, 27 February 2012 (UTC)

I think the citations in Google scholar and the award are enough that he would probably pass an AfD. (I'm not convinced that calling out the citation count explicitly within the article is a good idea, though.) —David Eppstein (talk) 23:33, 27 February 2012 (UTC)

Category:Theorems in number theory

Are there any suggestions of subcategories for this category in order to improve the usefulness of this category? At the moment there is around 80 articles in it which may be daunting to somebody looking through the theorems of number theory or maybe not. At the moment there are a few subcats; a couple which are more specific branches of number theory and another relating to the prime numbers, but perhaps there are more that could be added for ease of the user. Perhaps related - where does number theory and algebraic geometry intersect? Brad7777 (talk) 00:45, 28 February 2012 (UTC)

I would suggest "theorems in additive number theory", "theorems in the geometry of numbers", and "theorems on discrepancy" (or perhaps "theorems on equidistribution", a subcat of "theorems in analytic nt") -- if we can populate them in a reasonable way. Also, many of the theorems now in "theorems in number theory" can be moved to either algebraic or analytic n.t. (e.g. Mordell-Weil -> algebraic n.t., Turan-Kubilius -> analytic n.t., ...) Sasha (talk) 05:29, 28 February 2012 (UTC)

Maths rating template name

There is a suggestion at Template talk:Maths rating to rename the template. — Carl (CBM · talk) 11:56, 28 February 2012 (UTC)

Administrator requested

Wikipedia:Sockpuppet investigations/119.154.67.223 notes disruptive editing by three neighboring IPs.

Blocks for disruptive editing are warranted, regardless of the SPI issue.  Kiefer.Wolfowitz 12:12, 28 February 2012 (UTC)

Make that FOUR neighboring IPs.

Please help relieve poor Melcombe from vandal fighting against this Lahore-based terminator/Energizer Bunny from hell.  Kiefer.Wolfowitz 12:18, 28 February 2012 (UTC)

There seems to be about 8 users from this Lahore prefix, perhaps one of whom is not a disruptive editor.

Please protect the pages mathematician, statistics, etc. from IP editors.  Kiefer.Wolfowitz 12:21, 28 February 2012 (UTC)

It looks like the changes are being reverted OK at the moment, and there is some presumption against protection as long as reverts are effective. But, if the problem grows particularly large or particularly long-lived, contact me and I can protect the pages. — Carl (CBM · talk) 14:25, 28 February 2012 (UTC)

{{Maths rating}}

template:Maths rating is under discussion, please see template talk:Maths rating

70.24.251.71 (talk) 05:35, 29 February 2012 (UTC)

Mar 2012

From d to d

An IP has been straightening out all the italic "d"s in dy/dx at fundamental theorem of calculus. I had the impression the consensus in an earlier discussion was otherwise. Tkuvho (talk) 14:04, 21 February 2012 (UTC)

I have undone those changes, in addition to making many other typographical fixes. Ozob (talk) 21:46, 21 February 2012 (UTC)

I don't think it was actually a consensus but more of an agreement that in general people shouldn't change whatever is being used in an article, nothing was put in MOSMATH about it though.--RDBury (talk) 23:15, 22 February 2012 (UTC)

This seems a sensible thing to at least make a note about in WP:MOSMATH. If there is general agreement about what to say. Perhaps under WP:MOSMATH#Notational conventions a bullet stating that since both notations are used in the literature, consistent use of either d or d within an article should not be modified? Opinions? — Quondum^☏✎ 08:27, 23 February 2012 (UTC)

Sounds like a good idea to me. Leonxlin (talk) 04:59, 28 February 2012 (UTC)

Agree. Paul August ☎ 13:25, 1 March 2012 (UTC)

False (logic), contradiction and principle of explosion

A help needed from experts in logic. I recently wrote a small article about the false (I complained about its absence since 2009, and nobody else made it), but I probably failed to explain a subtle difference between false and contradiction. We all understand the difference between logical truth and a theorem, and there should be the same on the dark side of the logic. So, it would be nice to clarify the terminology in "contradiction" and "principle of explosion". What is contradiction: an occurrence or use of the false in proofs? A proof-theoretical interpretation of the false distinguished for historical reasons from, say, truth-functional one? And what terminology ("false", "contradiction", both as synonyms, or distinction) to use in "principle of explosion"? Incnis Mrsi (talk) 18:37, 26 February 2012 (UTC)

I don't really think people understand the relationship between logical truth and theorems at all. All we can agree on with consensus is that they "are related." You should take a look at the history and talk pages of rule of inference, theorem, and logical truth. I recently made a description at Rules of inference,Theorems, and Arguments to address one of the issues which you bring up. In many cases we have popularly used or named theorems which are also rules of inference, and also argument forms, etcetera. So in some cases we have one and not the other. It's not consistent. Greg Bard (talk) 19:25, 26 February 2012 (UTC)

I think one of the main problems lies with the part about contradiction, especially this sentence: "Contradiction means that a statement is proven to be false". In my opinion, this is not correct. A contradiction is a statement that is false for any possible evaluation. That does not necessarily mean the same as "proven to be false". Take for example the sentence "People watch TV" opposed to "People watch TV and People don't watch TV"; the first one can be proven false, but it is not necessarily always false. However, the second sentence is always false because it is an inherent contradiction. So basically what I'm trying to say is that there is a difference between proven something to be false and having something that is always false (a contradiction). I think this contributes in great part to the confusion, as well as the sentences surrounding the one I mentioned. Other than that, I agree with the commenter above that the relationship between logical truth and theorems is probably not clear to everyone. Mythio (talk) 19:31, 26 February 2012 (UTC)

Some people try to convince me what the contradiction is not. But what the hell it is, indeed? Look at the history of False (logic) (edit | talk | history | links | watch | logs) and to its talk page. Initially it was a redirect to Logic. In mid-2009 I changed it to "contradiction" because I felt that it is the closest target of all articles. After a half year it was reverted; more exactly, a user changed it again to Logic, may be independently of the past history. Then I complained to WikiProject Logic about a bad redirect, to no avail. And now, when there is already a small article, no one can explain why "contradiction" was not a possible target for a redirect! Incnis Mrsi (talk) 20:31, 26 February 2012 (UTC)

Simply put a contradiction is a statement that is false in all possible interpretations. False is not the same as a contradiction, since something can be false in some cases and not in all. With this in mind, I hope its clearer why, imo, a redirect to contradiction is not the correct course of action. A possible solution could be Hans Adlers proposal in here. On another note, Its not clear to me what your aiming for with this article when reading your reply; what are you trying to make this article about? For instance the sentence you start with is "false is the opposite to logical truth". The argument could be made that this is incorrect, because reading the definition of logical truth on its page, the opposite would be a contradiction (and hence the article already exists). Could you clarify a bit further what you understand to be the concept of false perhaps? Mythio (talk) 20:56, 26 February 2012 (UTC)

I do not take Hans Adler's proposal seriously first because he eventually did not even attempt anything, and second, because he argued for a merger of all possible targets to Truth value, which is "not the correct course of action" for reasons mentioned in this discussion and also in the discussion just above (I had not so strong feeling yet in 2009). IMHO the logical truth article is a bit confusing in an ambiguity and lack of distinction between (the abstract) logical truth and a property of a statement to be necessary true. It explains in details, what means "necessary", but does not explain, what means "true". What I understand to be the concept of false? First, a proposition which is a priori opposite to the truth, such as "⊥" nullary connective in those versions of propositional calculus which have it. This is not exactly symmetric to "⊤", if we use only material conditional, conjunction and disjunction. We easily can (re)define "⊤" as p→p but cannot define "⊥" if we have not a negation yet. Second, the false as a truth value, which is different from the truth, and which is always assigned to "⊥". Incnis Mrsi (talk) 22:23, 26 February 2012 (UTC)

Perhaps something should be said about how classical logic can get away with treating all non-truths as equivalent to each other? JRSpriggs (talk) 10:27, 27 February 2012 (UTC)

I think the best answer is simply to delete false (logic), given that it's ambiguous between the truth value "false" and the notion of "logical falsehood" (that is, logically necessary falsehood, which is very close to if not the same as contradiction). If it were actually a useful link, I suppose you could set up a disambig page, but I do not understand what is the rationale for having such a link at all. False (logic) is an unlikely search term and a bad internal link; having it around seems to do nothing but encourage overlinking. There is rarely if ever going to be any good reason to link the word false at all. --Trovatore (talk) 03:39, 29 February 2012 (UTC)

I would strongly support keeping the article, which is linked from the dab page False. It logically covers the truth value and "⊥". There is plenty of material around to improve the article with. -- 202.124.75.236 (talk) 12:26, 1 March 2012 (UTC)

I support keeping the article. There is tautology which is the negation of a contradiction; there is theorem, but no nontheorem (which is not the same as the negation of a theorem, and could easily be an article of its own). I don't see why we can't have logical truth and logical falsehood. However False (logic) should be about the truth value, not about contradiction, and not about logical falsehood which are types of sentence or proposition. Greg Bard (talk) 21:35, 1 March 2012 (UTC)

Serif/sans-serif for math expressions in running text

I could put this on the talk page of trivial module but we all seem to be here and it might come up in the other articles, so here goes: Quondam's latest change involved using the {{math}} template to boldface some zeroes. Personally I do not feel this is an improvement. (I concede that my feeling on this may be influenced by the fact that I loathe that template in general, mostly for its imposition of serif fonts in running sans-serif text rather than for the boldface). I would prefer to remove that part of Quondam's edit, while keeping the copyedits. Thoughts? --Trovatore (talk) 19:07, 27 February 2012 (UTC)

AFAIK the template does not bold anything. The intent is consistency of the font of the symbols (including numerals) throughout the text (as distinct from stand-alone lines) within each article. This is a reasonable forum to discuss the idea of a more uniform serif/sans-serif choice or guideline for symbols/math globally across math articles. Replacing {{math}} with {{nowrap}} is easy if consensus is for a sans-serif font. I find the serif font aids interpretation by visually distinguishing math and text without the formatting problems of the <math> tags, but I'll be happy to go with consensus. — Quondum^☏✎ 14:54, 28 February 2012 (UTC)

I prefer serif to sans-serif for math expressions, so I am in favor of {{math}} but at this point I think that changing over to it is somewhat of a waste of effort. What we should be doing instead is pushing harder to get MathJax support made more standard in Wikipedia, relative to its current experimental status, and then using <math>. —David Eppstein (talk) 17:14, 28 February 2012 (UTC)

In isolation serif is better. It's the mixture of serif with sans-serif that I object to. If {{math}} continues with serif, then it should be used only displayed, the same as <math>. --Trovatore (talk) 19:17, 28 February 2012 (UTC)

It is just imitating what <math> does with TeX. The target is to use Tex eventually but at the moment the results can be ghastly inline. If you're really worried by this then you should stick in some private css that ensures {{math}} uses a non-serif font. In the long term you'll need to ensure that Mathjax has some option to do the same sort of thing because many more things will use TeX when it works inline okay. Dmcq (talk) 00:08, 29 February 2012 (UTC)

In my view one of the things that's "ghastly" about inline TeX in the current implementation is the serif/sans mixing. It's not as bad as the mixed sizes, but it's still pretty bad. MathJax is still useful even if we use it only displayed, because it just renders so much better than PNGs. --Trovatore (talk) 00:55, 29 February 2012 (UTC)

I've just started running with MathJax enabled and I'm very happy with its inline capabilities though I'll be using the math template for a while because of problems with the current PNGs and how long I know it will b before it is generally supported. You really do need to have a way of setting the font selected by MathJax and the math template if you want to avoid serif fonts inline. What you want will never be the general default so you'll need an option. Dmcq (talk) 01:12, 29 February 2012 (UTC)

It's not for me. Mixing serif and sans looks bad. We shouldn't do it, for anyone. --Trovatore (talk) 01:16, 29 February 2012 (UTC)

I happen to like it mixed like that. It makes the math variables more clearly variables rather than one-letter words. —David Eppstein (talk) 02:10, 29 February 2012 (UTC)

You know, that might be OK if the typefaces were somehow designed together, like a serif version and a sans version of the same typeface. But I have never actually heard of such a font, and in my estimation the ones that actually render look awkwardly jammed together. The overall effect is something like one of those stereotypical ransom notes with letters cut out of magazines — not so extreme, of course, but along those lines. To me it comes across as distracting and unprofessional.

While there are advantages of serif fonts in mathematics, I think it's worth noting that the Beamer class uses sans, and this has not impeded its widespread adoption. --Trovatore (talk) 02:36, 29 February 2012 (UTC)

Before the debate goes too far, I think it should be noted that this topic has been covered before (e.g. here), and it seems clear to me that consensus on this question will not emerge here. In particular, there is enough support for inline {{math}} use that no recommendation to the contrary will be accepted. I think the inadequacy of the fonts in the context of math and browsers should be addressed as a broader WP issue, not at the template level. So I think the only principles that will emerge are already in place:

• The original writers of an article are free to set their own style
• One may fix inconsistencies of format style in individual articles
• Don't switch the style of an entire article without consensus.

— Quondum^☏✎ 06:46, 29 February 2012 (UTC)

There are a bunch of people who really don't like it when two fonts that aren't extremely similar are used together. Some cry out in pain if they see a poster just using comic sans. For those people there needs to be facilities for changing the font in the math template, in MathML and when MathJax gets used. They are not going to get he default changed, the Tex font is accepted in professional maths books, and in the future there will be even more of it in the running text, so they have to just accept that and move on to what can be done to fix the situation as far as they're concerned. Dmcq (talk) 09:15, 29 February 2012 (UTC)

No, you're quite wrong here. Of course the TeX font is accepted in professional math books — they're written in that font! So it looks fine. It looks horrible when mixed with sans. Having the mixture as a default is unacceptable. --Trovatore (talk) 17:48, 29 February 2012 (UTC)

Do you or do you not accept that you're talking to the wrong people and the math template is the wrong target for doing anything about fixing what you want fixed? That in fact the math template is the easiest one for you to fix for your own use by setting your private css but if you don't engage with MathJax any effort with the math template will eventually be totally wasted? Dmcq (talk) 18:39, 29 February 2012 (UTC)

How am I talking to the wrong people? WikiProject Math is where standards for mathematical articles get discussed. My private use is entirely irrelevant here — I'm arguing to improve the professionalism of the display of our articles. --Trovatore (talk) 20:11, 29 February 2012 (UTC)

The people here have very little control over technical issues on Wikipedia such as the use of MathJax as a default. WP:VPT may be a better choice for that. —David Eppstein (talk) 20:32, 29 February 2012 (UTC)

But what we can discuss is whether it ought to be used inline. --Trovatore (talk) 20:34, 29 February 2012 (UTC)

You're not seriously suggesting we try banning all inline maths? Dmcq (talk) 22:16, 29 February 2012 (UTC)

Not a hard ban, no. But I am saying that if MathJax uses a distractingly different font from the rest of the article, we should try hard to avoid inline uses of it where reasonably feasible, and HTML may still be better than MathJax for unavoidable inlines. --Trovatore (talk) 22:46, 29 February 2012 (UTC)

I think we should avoid using the {{math}} template (and its cousins like {{var}}, etc.) This makes the code more difficult to edit by hand, and it is looking very likely that MathJax will give a much better solution very soon. I think it's time we start to deprecate html (and these funny templates). Sławomir Biały (talk) 11:48, 29 February 2012 (UTC)

The normal Tex to html or png converter could have been fixed ages ago to do most of the things {{math}} patches over like being able to put ≥ in the inline text without getting some png messing it up. $a\geq 0$ or a ≥ 0 anybody? How soon is soon when we couldn'r fix something like that in years? Dmcq (talk) 14:05, 29 February 2012 (UTC)

What might be worth developing in time for Mathjax is a special tool which would search for {{math}} templates and automate converting them to <math> format. That way we needn't deprecate anything for the moment and do a better job both now and eventually. Dmcq (talk) 14:13, 29 February 2012 (UTC)

Just to clear some illusions about MathJax... It too wil use a serif font, even when used inline. It uses webfonts for rendering, so it has the potential to clash with whatever font a user has set for running text. With regard to matching fonts, I know of only one that matches serif and sans-serif in design and size: DejaVu. I you already use DejaVu Sans as the default font, use this CSS to display formulae in {{math}} in a matching serif:

span.texhtml {
  font-family: 'DejaVu Serif', serif;
  font-size: 100%;
}

— Edokter (talk) — 16:47, 29 February 2012 (UTC)

See e.g. this edit for why sans-serif inline math is bad. If we can't distinguish the capital vowel I from the lowercase consonent l from the digit 1 from the vertical bar |, we have a problem. (In the font I use, the digit is clearly distinguishable from the other three, but obviously even that's not true for everyone.) —David Eppstein (talk) 21:47, 1 March 2012 (UTC)

Honestly I like serif better than sans in general. I wish Wikipedia as a whole were written in a serif font (see e.g. a recent discussion at talk:Iago). But the "ransom note" effect is real, and distracting, and detracts from our image of professionalism. The workaround for the issue you bring up is to strain to avoid using those letters as variables. --Trovatore (talk) 21:54, 1 March 2012 (UTC)

I think there are reasons that sans-serif tends to work better with screens than on paper which are very different media, something to do with interlacing and resolutions. MathJax does have some support for sans-serif fonts, but its limited to only the standard letter and numbers. If you look at many of the other symbols in maths $\sum \int \theta$ the fonts used have more in common with serif fonts: varying line widths and little serifs. Going completely over to sans wound end up with a very mixed typography within equations. Better to mix sans text with serif maths, at least those are used for completely different things.--Salix (talk): 01:31, 2 March 2012 (UTC)

I can buy that it may not be workable to make MathJax do sans. But in that case I think MathJax is not really a solution to the inline problem (so basically we still don't have, and may never have, a solution to the inline problem). And if that is the case, then we should continue to avoid inline mathematics to the extent feasible. --Trovatore (talk) 02:11, 2 March 2012 (UTC)

I'm pretty certain there's some straightforward way of getting the normal running text in Wikipedia to use any font you like so you could use a serif font for that if you like. I'm sure someone on the help desk could do that fairly easily. That would probably be quite an easy option to put in the appearance preferences for general use and might be quite popular. Dmcq (talk) 09:40, 2 March 2012 (UTC)

Please quit talking about what I would like for my personal use. That's entirely beside the point. My objection is to a problem that detracts from the professionalism of the appearance of our articles. --Trovatore (talk) 22:18, 2 March 2012 (UTC)

I think this suggests that some thought should be given to coordinating the default fonts (perhaps only for maths articles?) for the main text, {{math}}, <math> and MathJax, much as is done in professional texts. This would mean some override of the browser's default font choice for serif and sans-serif, and carries with it the pitfall that these may not be installed fonts for a large enough base. If serif is to be avoided due to display problems, and widely installed suitable matched serif and sans-serif fonts cannot be found, this problem is probably going to be around for longer than we'd like. — Quondum^☏✎ 13:12, 2 March 2012 (UTC)

It will only be people who are worried by this sort of thing who would set a preference and we can have a help page link in the preferences page we direct them to show them how to download fonts if they have problems. Fonts on the web have a good fallback facility so the main problem is if a font is used that has bad looking characters in it. Dmcq (talk) 23:27, 2 March 2012 (UTC)

The problem is a problem for everybody, not just for people who set preferences. I am completely opposed to shunting it off into preferences. --Trovatore (talk) 23:35, 2 March 2012 (UTC)

I concur with Travatore – in principle. But until we can identify suitable fonts for setting as the Wikipedia defaults with most browsers and typically available fonts, this does not seem achievable. Is there a suitable set of fonts typically available with all browsers that is suited? (DejaVu is not generally installed, and has other drawbacks IMO.) Alternately, is it necessary/desirable to remain with sans-serif in the body of the article, or could we switch to serif (for maths articles)? I personally like the serif/sans-serif contrast between math and text, but jarring discontinuity as would occur with badly mismatched fonts should preferably not occur in the typical default setup. — Quondum^☏✎ 07:49, 3 March 2012 (UTC)

See WP:Typography. There really is not much choice. When I created {{math}}, I took into account what most users would be seeing on screen, with default fonts installed, at default sizes, and tried to match up as best I can. It is impossible to take every deviation into account, presicely because teh lack of standards in web typography. What prevailed in my mind is the legibility of math, which suffers badly in a sans-serif font. — Edokter (talk) — 10:15, 3 March 2012 (UTC)

And thanks very much for that. I see the math template as having done a very good job of patching over some problems with the current TeX processing. It is irrelevant to the future though now that MathJax is fairly imminent. The question is about the differences between MathJax and the normal running text and I'm pretty certain I like the distinction whatever if someone else calls it unprofessional. As you say serif is preferred for maths and it matters more for maths as a wide range of symbols are used, they are not really letters π is just looks different from π as a maths symbol. We're not going to force the rest of the Wikipedia community to adopt serif fonts either. Typography is a matter of preference and such choices should be in preferences. Also it might be worth asking MathJax to allow preferences for fonts in their work too. If somebody wants Wikipedia in Comic Sans let them I say.Dmcq (talk) 11:09, 3 March 2012 (UTC)

What is a product?

A mathematician may say "I have proved that the following products are both equal to 5:

$\prod _{i\in A}x_{i},$

$\prod _{j=1}^{10^{90}}y_{j}.$

If they're both equal to the same number, and a product is the value that results from multiplying, and these are both equal to 5, then these are not two products, but one. Our article titled product (mathematics) says:

a product is the result of multiplying, or an expression that identifies factors to be multiplied.

The latter usage occurs in such expressions as the title of a book called Table of Integrals, Series, and Products or articles titled "Proof that a Product Considered by Schriemann Diverges to Zero". Yet it seems many sources say only that a product is the value of a multiplication operation. A non-logged-in user has been arguing on my talk page that we should therefore omit the "expression" characterization from the definition given in the article.

Opinions of this proposal? Michael Hardy (talk) 16:24, 1 March 2012 (UTC)

The duality of the meanings of terms such as "product" (and this obviously is not limited to product, but includes limit, etc) is one of the most active areas in math education. Certainly we should keep both meanings on the product page and avoid excessive formalism at all cost. Tkuvho (talk) 16:30, 1 March 2012 (UTC)

This is the usual intensional vs. extensional equality issue that appears everywhere. Is $\lim _{x\to 0}x/x$ the same as $\lim _{x\to 5}1$? Is $2\cdot 15$ the same product as $6\cdot 5$? The same issue arises with derivatives and integrals that have equal values, and with whether two groups are the same if they are isomorphic, and with many other objects. The real point is that when mathematicians say "equal" or "same" they can mean many things depending on context. Regarding products specifically, the current language looks good: sometimes the product is identified with its value, some time it is not. — Carl (CBM · talk) 16:31, 1 March 2012 (UTC)

One of the most active areas in maths education? Sheesh. So someone with maths skills has to both want and like to teach children but also be willing and able to put up with this sort of stuff being thrust at them as being the way to teach maths? Explains a few things. Dmcq (talk) 17:07, 1 March 2012 (UTC)

@Dmcq : I doubt that he was proposing to actually tell children about this stuff. Michael Hardy (talk) 22:52, 2 March 2012 (UTC)

Meriam Webster has both meanings: http://www.merriam-webster.com/dictionary/product . -- Jitse Niesen (talk) 17:14, 1 March 2012 (UTC)

Surely the non-ultra-formalist way of saying this would be "...are two expressions with the same value", or "two different formulations for what can be regarded as the same object"? -- The Anome (talk) 17:18, 1 March 2012 (UTC)

Both usages are important. It is counterproductive to favor one over the other. Rschwieb (talk) 17:45, 1 March 2012 (UTC)

This is a special case of the problem of making the proper distinction between an expression, a function, the value of a function for a given value of its argument and the evaluation of an expression. I would say, for the example given by Michal Hardy, "I have proved that the two following expressions both evaluate to 5". In other words, a product is an expression whose leading operator is a multiplication, and saying that two products are equal is an abuse of language and a shortcut for "when evaluating the functions and operators appearing in the two expressions, we get the same result". Thus I would suggest for the article product (mathematics):

"A product is an expression whose leftmost operator is a multiplication. By abuse of language product denotes also the result of the evaluation of the operations appearing in such an expression"

All of this is not WP:OR. I may not cite any math book for this, but it is the basis for any computerization of the mathematics and appears in some way in the manuals and tutorials of every computer algebra system, like Maple (software).

D.Lazard (talk) 18:42, 1 March 2012 (UTC)

Seconding Tkuvho and Rschwieb. D.Lazard, your proposed alternative, whatever its advantages, will do much to make the article unimpenetrable for many readers. (One possible confusion that it will create: it appears to assert that $x \cdot y + z$ is a product.) The current wording is clear, correct, easy to understand, and should be kept as-is. --Joel B. Lewis (talk) 19:37, 1 March 2012 (UTC)

"Unimpenetrable"? Maybe impenetrable? Rschwieb (talk) 20:13, 1 March 2012 (UTC)

Isn't it about the mathematical counterpart of "Sense and reference"? Boris Tsirelson (talk) 19:44, 1 March 2012 (UTC)

I agree that my formulation is not convenient for the level of the readers and that the current wording is convenient. About "leftmost" : "outmost" or "top" or something like that would be better. But the point is that we have to have this kind of things in mind when looking for the best formulation. Another example of today: The first sentence of discriminant was "the discriminant of a polynomial is an expression ..." which is incorrect. I have replaced this by "the discriminant of a polynomial is an element of the ring generated by its coefficients", which is correct but has been reverted as too technical. After discussing with the author of the reversion, the formulation is now "the resultant of a polynomial is a function of its coefficients", which is sufficiently correct (it is not a function, but the value of a function), easy to understand and contents more information that the previouus formulation. D.Lazard (talk) 20:47, 1 March 2012 (UTC)

I have to agree that that way of using the word "leftmost" will be---um------"unimpenetrable" to almost everyone. I understood it here only because of the context of this present discussion. And I think other aspects of that proposed opening sentence are objectionable on grounds almost as cogent as that. Michael Hardy (talk) 22:55, 2 March 2012 (UTC)

Hello to all,

I am that non-logged-in user (but I learned how to log-in now!) who asked the question from Michael.

First let talk about the difference between multiplication and product in Natural numbers (ℕ). Multiplication in ℕis a binary operation which is a function from ℕ×ℕ to ℕ, so it gets two Natural numbers as input and the result or output of this function is another Natural number. The mathematical symbol for multiplication function is ×, so in function notation we can write: ×(3,4)= 12. In infix notation we can put the operation (here ×) between two operands (here factors) and use the notation 3×4=12. But we know a function is a set of single valued ordered pairs. In this point of view multiplication is a set like ×={((1,1), 1), ((1,2), 2), …} and one of its elements is ((3,4), 12) and the output or value or result 12 associated with the pair (3,4).

By the present definition, product refers just to the result (and result can be a number or an expression like Meriam Webster but still refers just to the result). The difference between product and multiplication is like as the difference between element and set.

There is another close example. When you say the function f(x)=x² actually you omit two important parts, domain and codomain. This function is not one-to-one from ℝ toℝ but it is one-to-one from ℕ to ℕ, so you can omit the details if there is no ambiguity.

I agree both usages of the product are important, so it seems we need to change the definition of the product, but how? By inserting in Wikipedia? I think this is not a good idea because a divergence will appear between Wikipedia and other references. It is better to think for a better way. — Preceding unsigned comment added by Sohrab.Rahbar (talk • contribs) 03:09, 3 March 2012 (UTC)

I would find this more concerning if, in my entire life before now, I had encountered a single person who pressed the distinction. IMO, pressing the distinction is more confusing than not. Rschwieb (talk) 15:17, 3 March 2012 (UTC)

Yes. To repeat the key point (but with fewer strange coinages/typos than last time): there may be some technical subtlety in the rigorous definition of a product, but this subtlety has no business being brought up in the introduction of the article product (mathematics), which should be as widely accessible as possible. --Joel B. Lewis (talk) 01:22, 4 March 2012 (UTC)

Mathematical formulas in the lead section of an article

WP:MOSINTRO used to say "Mathematical equations and formulas should not be used except in mathematics articles." So in that state it wasn't really relevant to this project, since it was only about other articles. But in this edit a month ago, an editor (intending to broaden it to allow formulas in technical but non-mathematical articles such as Joule) changed it to instead say "Mathematical equations and formulas should only be used when absolutely necessary." Today this has led to an editor on golden ratio attempting to take all the math out of the lead section there, because math articles are no longer exempt and he didn't see why it was necessary. So anyway, this is just a heads up: discussion on the issue has started at Talk:Golden ratio for the specific editing concerns there, and Wikipedia talk:Manual of Style/Lead section for what the MOS should actually say about this. —David Eppstein (talk) 05:30, 2 March 2012 (UTC)

"in that state it wasn't really relevant to this project, since it was only about other articles"

Is that true? Are mathematical expressions in non-mathematics articles outside the scope of this project? Michael Hardy (talk) 03:18, 4 March 2012 (UTC)

List(s) of mathematics articles/topics

There was a request to rearrange the redirect Lists of mathematics articles. Right now it points at Lists of mathematics topics but the request was to use Lists of mathematics articles to hold List of mathematics articles instead. I opened a thread here to discuss the best way to handle those confusing names. — Carl (CBM · talk) 17:51, 4 March 2012 (UTC)

Wikipedia:Foundations of mathematics

I wrote an essay how to improve standards for articles about mathematical logic. I hope, some day it will become an official guideline. Thanks for your attention. Incnis Mrsi (talk) 07:23, 5 March 2012 (UTC)

Projective resolutions and free resolutions

Projective resolutions and free resolutions is a new article. Projective resolution and Free resolution redirect elsewhere. Should the redirects be altered or should some articles get merged or what? No other articles linked to the new article until a moment ago when I added a cross-reference. If it is not merged into other articles, then some things should link to it. Michael Hardy (talk) 17:31, 17 February 2012 (UTC)

Both redirects are to Projective module#Projective resolution. Thus the new article is useful. I'll redirect Projective resolution and Free resolution to the new article and move the new article to Projective resolution and free resolution. This will add a lot of links to the new article. D.Lazard (talk) 17:52, 17 February 2012 (UTC)

I like the idea of having pages dedicated to homological resolutions, but this page title leaves us in an awkward situation of where to place the flat and injective resolutions. Is four names too many for a page title? Rschwieb (talk) 18:48, 17 February 2012 (UTC)

For the moment Flat resolution and Injective resolution link to sections in Flat module and Injective module. By the way Flat module has a red link to Resolution of a module. I suggest, first, to add a "see also" section in Projective resolution, linked to Flat resolution and Injective resolution. A second step could be to expand Projective resolution and free resolution in order to move it to Resolution of a module. D.Lazard (talk) 20:14, 17 February 2012 (UTC)

I think a good name would be Resolution (homological algebra). This should cover projective (and thus free) resolutions, injective, flabby, flat, acyclic resolutions. The title "Projective resolution and free resolution" is too long and focussing on just these two resolutions is also awkward from a content-point of view. Jakob.scholbach (talk) 15:01, 21 February 2012 (UTC)

I agree that "Projective resolution and free resolution" is too long. But I am not sure that Resolution (homological algebra) is better than Resolution of a module. In fact, in ring and module theory, resolutions are frequently used independently of the consideration of any homology. This occurs especially in the computational theory of polynomial ideals, where the degrees which occurs in a minimal free resolution (Castelnuovo-Mumford regularity) are strongly related to the complexity of computing a Gröbner basis and to the Hilbert series. Most people interested in these questions do not know nothing of homological algebra and the name Resolution (homological algebra) could lead them to miss the page which is relevant to them. In any case, whichever name is chosen, the other should be a redirect. D.Lazard (talk) 16:00, 21 February 2012 (UTC)

I believe that Resolution of a module would be the right scope for this situation. The full blown categorical concept would probably best be tackled in its own article. Rschwieb (talk) 21:30, 21 February 2012 (UTC)

What about resolution (algebra)? I am concerned that resolution of a module is too restrictive a title, as it does not include resolutions in general abelian categories (such as categories of sheaves or categories of complexes of modules). Surely we need an article about those. Ozob (talk) 21:38, 21 February 2012 (UTC)

Well, that's a surprise. Resolution (algebra) already exists and is about just this topic. Ozob (talk) 21:40, 21 February 2012 (UTC)

Good catch, I suppose that'll be a better starting point for this material! Rschwieb (talk) 00:49, 22 February 2012 (UTC)

(unindent) I have tried my hand at resolution (algebra)--improve it if you can! Jakob.scholbach (talk) 14:10, 22 February 2012 (UTC)

Resolution (algebra) is looking pretty good. Earlier I sorted some redirects for consistency and weeded out a few circular redirects caused by the recent activity. (The resolution pages all point toward resolution, the dimension pages point toward the correct sections in injective, projective, and flat articles.) Rschwieb (talk) 02:54, 23 February 2012 (UTC)

One more thing: the article mentions projective resolutions are unique up to chain homotopy. I would guess the same can be said for injective and flat resolutions, but I'm not familiar enough with the subject matter to verify. Is this the case? Thanks. Rschwieb (talk) 14:24, 23 February 2012 (UTC)

I am not sure, but, as far I remember, this uniqueness is a consequence of the fact that one may pass from a projective module to another one by a chain of operations consisting in adding (direct sum) a projective module or removing a direct factor. This is certainly not true for flat modules and probably not for injective modules (I am not familiar with them). D.Lazard (talk) 18:29, 23 February 2012 (UTC)

OK then the answer is at least not obvious. I'll leave it as it is until someone certain comes along. Rschwieb (talk) 21:25, 23 February 2012 (UTC)

I have just noted that resolution (algebra) contains another important class of resolutions, which generalizes all the other ones. I have tried to clarify the corresponding section which was not understandable, even with some background in homological algebra. I hope that the result is better and mathematically correct. D.Lazard (talk) 11:50, 5 March 2012 (UTC)

Factor theorem at AfD

Factor theorem is up for deletion.  --Lambiam 02:44, 4 March 2012 (UTC)

Well, guess who has moved from categorizing articles to proposing them for deletion? Sławomir Biały (talk) 02:58, 4 March 2012 (UTC)

Your point being? Brad7777 (talk) 08:12, 4 March 2012 (UTC)

WP:POINT. Please do not use AfD in this fashion. Use the Talk pages of articles in egregious cases. Deletion nominations of articles that are clearly encyclopedic is misuse of the system. It is putting a gun to the head of the community, saying "work on this because I'm telling you to". It takes effort away from other efforts to improve the site. We all have our priorities, and we should respect the rights of others not to jump to attention to deal with them. Charles Matthews (talk) 12:50, 4 March 2012 (UTC)

Not to mention, you might want to follow the earlier advice of this same project: focus on content for awhile before you use semi-automatic tools like Twinkle and HotCat to categorize pages (and now to take them to AfD, apparently). The community opinion seems to have had zero effect on your disruptive behavior. Sławomir Biały (talk) 13:42, 4 March 2012 (UTC)

No I will not change my focus. You should notice my projects are beyond the scope of WP:MATH and not controlled by this community. If you disagree with something that I have done from the perspective of your project, then I am happy to discuss it and adapt to it as long as it is not nihilistic. Comments like "Well, guess who has moved from categorizing articles to proposing them for deletion?" are only for one purpose. My behaviour has only been disruptive once you have resorted to WP:SOAPBOX. Please if I make any further mistakes, could you point out the specific problem like Charles Matthews has done? Thanks Brad7777 (talk) 16:59, 4 March 2012 (UTC)

The specific problem is that you are using automated tools to do thousands of edits, some of which are problematic. I can give many examples of specific edits that are a problem. But this is missing the point. Stop using the tools. You've shown repeatedly that you can't be trusted with them. Sławomir Biały (talk) 11:39, 5 March 2012 (UTC)

According to my edit counter; out of the 5946 edits I have done, only 134 have been deleted. However, I will stop using the tools on political grounds. Brad7777 (talk) 13:52, 5 March 2012 (UTC)

We have a large backlog of articles tagged as unsourced, as does WP in general. In this case, as with many of them, the content falls under WP:CK, at least for mathematicians, and the article was created back when standards for new articles were rarely enforced. For articles created now I'd say strict enforcement of notability requirements is needed, we certainly don't want to add more to the backlog, but for established articles it isn't reasonable to expect that people will be cleaning up unreferenced tag in a timely manner. In any case WP:BEFORE has guidelines on how to cut down on spurious nominations, though in my experience no matter how hard to try to follow it you stand a good chance of being criticized for not following it whenever you do an AfD.--RDBury (talk) 12:01, 4 March 2012 (UTC)

Brad, if you continue in this fashion you stand a large chance of being blocked. CRGreathouse (t | c) 03:39, 5 March 2012 (UTC)

George Boole

This is one of our more interesting articles relating to the history of mathematics. I have been working it over to sort material, and remove some of the more obvious misunderstandings from old text. There are a couple of minor queries left on the Talk page. It could easily be 50% bigger, and as usual more inline referencing is needed (quite important here because Boole has been praised for the wrong things in the past).

Boole was famous in his own time for differential equations. His stuff looks like D-modules to me; that line of attack traces back to Thomas Gaskin and a notorious Tripos question (not as celebrated as the one which set the Stokes theorem, but that might be historical injustice in a way). Without OR rearing its ugly head, it appears that a better job of explaining what Boole actually did would be possible on the basis of some recent research papers that are still behind paywalls. Drop me a note if you come up with anything. Charles Matthews (talk) 13:04, 4 March 2012 (UTC)

Hi Charles,

do you know Boole's inequality for (what is now called) the Hilbert Stieltjes transform? If you wish, I can send you a reference to one of the modern surveys in the (EST) evening.

Sasha (talk) 18:24, 4 March 2012 (UTC)

e.g. the introduction and Ch. 7 of this book of Cima, Matheson, and Ross, or the survey of the same authors. Sasha (talk) 03:30, 5 March 2012 (UTC)

Similar remarks in more detail: a) Boole's work in analysis, in particular, the 1857 paper JSTOR 108643, deserves to be mentioned. It contains several interesting things, perhaps it's worthwhile reading it (or is there a good secondary source)? b) One of the results in this paper of Boole is an identity (see page 26 in the review linked above) for the measure of the set where

$\sum a_{i}/(x-b_{i})>\lambda$

c) This identity and its generalisations play an important role in the modern theory of Stieltjes transform (see again p.26): it is an identity for singular measures (pure point measures are essentially covered by Boole's argument), and an inequality for arbitrary measures.

Best, Sasha (talk) 15:06, 5 March 2012 (UTC)

Two pages to glance at, and a question

1. Algebraic structure is now less of an abomination (I hope.) I cut way back on universal algebra detail, and several examples that didn't really seem important. If there is some representative structure that isn't mentioned, I hope someone brings it up on the talk page.
2. I came across Quantum differential calculus and tagged it as needing attention. I have the vague feeling that there was probably an article covering this material already under a different name, (but can't find such an article). Please let me know if you find this is the case.
3. I would also like to edit the algebraic structure template to have less things. For one thing, I think it's kind of silly to put commutative ring and ring with unity on it. The template is certainly never going to contain every single algebraic structure in wikipedia, so I was hoping to put just the most representative things on it. Please let me know if I'm crossing some line with any edits. Rschwieb (talk) 20:48, 5 March 2012 (UTC)

Algebraic structure template

In reply to question 3 above regarding {{algebraic structures}}:

If abelian group is on there, then commutative ring should be too. The study of commutative rings is a huge discipline, and I don't see anything silly about having a link to it in the template. Personally I'd rather see the template expanded to include Unique factorization domain and Principal ideal domain and Euclidean domain, then the chain of inclusions on those pages could be replaced by the template.

Ideally the template would have collapsible sections along the same lines as {{calculus}}. We could have one big division for types of rings, one for groups, one for modules (including vector spaces and Lie algebras), and one for magma, semigroup, monoid (not sure of a good collective name for those three). I don't have the necessary template super-powers to make this happen myself. Is anyone else game? Jowa fan (talk) 23:47, 5 March 2012 (UTC)

I like the idea for collapsable sections with important types underneath. The reason I think having "ring" and "commutative ring" and "ring with unity" (I guess I should have objected to abelian group too) is because it looks to me like "car", "red car", "green car" on the same list. However the collapse tab to put commutative ring etc underneath ring would certainly make me happy by getting them off equal footing. Everyone interested should drop by Template_talk:Algebraic_structures to discuss. Rschwieb (talk) 02:05, 6 March 2012 (UTC)

Losing "ring with unity" wouldn't bother me at all. On the other hand, (noncommutative) ring theorists and people studying commutative rings seem to be doing two quite different sorts of things, so I believe it's worth keeping "commutative ring". (Imagine a world in which red cars really did go faster. Then it would make sense to have both "car" and "red car".) Jowa fan (talk) 06:58, 6 March 2012 (UTC)

The placement of articles on fields of mathematics into Category:Fields of mathematics

There are many articles on fields of mathematics, examples include algebra, geometry etc. There also exists a category Fields of mathematics. This category at the moment contains a few selected eponymous categories aswell a few articles related to the term "fields of mathematics". The category Fields of mathematics is a set category, i.e a category named after a class so I think it would be logical to include all articles that fit this class, i.e all fields of mathematics like algebra, geometry etc. I have brought this idea up before but as I was a new editor I was not able to explain it. I hope those who saw my previous effort now understand what I mean. I think not only this logical, it is also very practical for a user-browser of Wikipedia, particularly those with interests across the scope of mathematics, who do not necessarily want to have to dig deep through the subcats. Of course, this should't be done without consesus, so views? Brad7777 (talk) 20:29, 28 February 2012 (UTC)

So you would like to move more field categories here? There are about 20 subcats now, but it seems like that might go way up depending on what you are aiming to include. Do you have a concrete list of additions to that category or at least an estimate on how many things would go in? Rschwieb (talk) 14:09, 1 March 2012 (UTC)

I mean adding the articles to this category. These would not be taken from their current categories, they would have just an additional category Category:Fields of mathematics. There is an estimate on Glossary of areas of mathematics. Brad7777 (talk) 17:53, 1 March 2012 (UTC)

Sorry, I knew you just meant adding but since I never mess with categories I might have misspoke. The glossary appears to have hundreds of items, but I don't know if they should all go in. It would certainly seem logical to have areas of mathematics categorized under Fields of mathematics. Will anyone else contribute their 2 cents? Rschwieb (talk) 20:19, 1 March 2012 (UTC)

There may be a couple that do not belong there (or the glossary). I think it is also worth noting that many of the terms do infact link to the same article. Brad7777 (talk) 18:06, 4 March 2012 (UTC)

Important— does anybody disagree with this idea? Brad7777 (talk) 18:06, 4 March 2012 (UTC)

Current state seem to be about fine. It does mean Category:Mathematics is quite clean, the isn't a real need for article like Geometry to be in this category as they can easily be found in the category of the same name. Only minor point is I don't think Category:Trigonometry needs to be this high up the tree. --Salix (talk): 19:32, 4 March 2012 (UTC)

I'm not sure how it would make any difference to Category:Mathematics either way? I meant articles such as geometry and trigonometry be placed into Category:Fields of mathematics mainly for the reasons I stated above, but also for the point you have just demonstrated — which is to disagree with the subcats of this category. If all articles were placed in c:fields of mathematics it would not be such a problem for people finding specific fields of mathematics. The fact that people have different views of the heterarchy of mathematical disciplines and the direct subcats of c:fields of mathematics are unavoidably arbitrary means this category will be quite dynamic in terms of its structure, making it difficult to determine where a article on a field of mathematics will be. (Not all fields have eponymous categories to further complicate things for the user). Brad7777 (talk) 20:01, 4 March 2012 (UTC)

It certainly sounds plausible to put major fields of mathematics under Fields of math, but the list at glossary of mathematics is far too large. A minimalist subset could be transferred, but hundreds of subfields would be doomed to be outside of this structure. Trying to include them would face us with the intractable problem of sorting intermixed disciplines. Can one even call trigonometry a field?! Rschwieb (talk) 16:19, 5 March 2012 (UTC)

I can see how sorting the intermixed disciplines would be a problem, would m theory, statistical mechanics, econometrics or mathematical sociology for example be included? I would be inclined not to include these, my distinction would be they could not be classed as pure mathematics, but the problem I see with this distinction then is do we include the article applied mathematics or fuzzy mathematics? I could be using the term field incorrectly however, as i am unsure of its actual definition? Brad7777 (talk) 13:16, 6 March 2012 (UTC)

We still need a short list of proposals of what fields you think should move. As I glance at it, quite a few of the broad fields are already there, and I can't immediately see what's missing. A good place to start would be to pick a subset of first level areas on Mathematics_Subject_Classification. I will suggest a few additions for comment: commutative algebra, algebraic geometry, field theory, category theory, universal algebra, differential equations, functional analysis, differential geometry, algebraic topology, probability theory, statistics, numerical analysis, information theory, mathematical physics, game theory. Rschwieb (talk) 14:22, 6 March 2012 (UTC)

Conic sections template

A new template, Template:Conic sections was recently added to the articles on conic sections. I'm not convinced this is an improvement and if not whether it can be made into one by tweaking the template. My main objection is that previously the lead images in Ellipse were an ellipse and a rather nice photo of Saturn, but now the lead image has all the conic sections, which makes it a bit unclear what the article is about, and Saturn has been pushed down "below the fold". Is it just me and if not what should be done?--RDBury (talk) 03:33, 5 March 2012 (UTC)

No, it's not just you. The graphic in the template is quite nice (although a little misleading in the hyperbola case), but the template as a whole doesn't add much, and I'd rather see the specific images for "ellipse" coming before the generic picture of conic sections. Jowa fan (talk) 04:14, 5 March 2012 (UTC)

I don't like images in navigation templates at all. Often they distract from the purpose of the template, which is navigation, instead they become more a "look at me" device dominating the pages they are on. Particular egregious examples are {{Groups}} with a large Rubiks cube. Why not just have it as plain navigation template like {{Calculus}}.--Salix (talk): 13:21, 5 March 2012 (UTC)

I like this new image better than that of Saturn, but I find the "no images in templates" viewpoint most persuasive. Rschwieb (talk) 15:58, 5 March 2012 (UTC)

Images work in some infoboxes, Template:Taxobox is a good example. But in that one the image is a parameter so what you're looking at is what the article is about. I'm thinking that for now a navbox approach would actually work better for conics.--RDBury (talk) 21:52, 5 March 2012 (UTC)

I created the template to try to help tie the conics together more and to get a more consistent feel between the articles on the conic sections. I thought adding a simple image made in the same style to the template for each section would help achieve this. Do you think that removing the sub-pictures would make it better? Also even if it doesn't work for the individual sections would it not still be good for the general conic section article?

Once I get some more time I would like to help rewrite the articles to make them more complementary. I think that a template of some sort would help in achieving this goal. Any thoughts?

Phancy Physicist (talk) 04:45, 7 March 2012 (UTC)

I think navigation templates work a lot better in a wide format at the bottom of the article rather than in a narrow format at the top of the article. The top of the article is supposed to be where you're learning what the article's subject is, and instead you get distracted by this big flashy box telling you all of the other things that it isn't. —David Eppstein (talk) 05:24, 7 March 2012 (UTC)

MathJax update

I'm making good progress on integrating MathJax into the Math extension and hope to make it available as an experimental option shortly (it'll definitely be on an experimental wiki very soon!). Currently there are some problems with Chrome and with our JavaScript debug mode which I hope to resolve. list of all bug dependencies

After that it should be mostly testing to make sure things work, and then we'll see if we need to make fixes to upstream MathJax or additional customizations (eg custom latex commands that might not be translated yet). --brion (talk) 20:44, 5 March 2012 (UTC)

Thanks very much for your hard work on this feature, which as you know is something many of us have wanted for a long time. —Mark Dominus (talk) 19:18, 7 March 2012 (UTC)

You are welcome. :> Nageh (talk) 19:45, 7 March 2012 (UTC)

mathJax progress

On this page on bugzilla.wikimedia.org, we find this comment from Brion Vibber:

Getting closer! MathJax, once enabled in the extension, now is available as a third rendering mode (beyond PNG and 'leave as tex'), so won't interfere with other things when turned on.

It can then be opted-in by anybody who wants to help try it out while we continue poking at things...

Michael Hardy (talk) 00:30, 6 March 2012 (UTC)

OK, I just tried to set my preferences, and I find:

• Always render PNG
• Leave it as TeX (for text browsers)

But I see no third option. Michael Hardy (talk) 00:41, 6 March 2012 (UTC)

for 'now' I would guess it means what ever version of MW gets that patch. It does say 'Target Milestone 1.20mwf deployment' so that will be the next version if all goes to plan, due heaven knows when given that we're only days into 1.19.--JohnBlackburne^words_deeds 00:49, 6 March 2012 (UTC)

Well, it says "now is available". Michael Hardy (talk) 00:55, 6 March 2012 (UTC)

Available in the source code, not deployed. Nageh (talk) 01:00, 6 March 2012 (UTC)

And I just checked the test wiki and it's not there yet (if you have universal login it works there too so no need to register). That is probably the place to go to try it out first.--JohnBlackburne^words_deeds 01:14, 6 March 2012 (UTC)

My impression is that the English Wikipedia is usually the last or among the last to get the benefit of any changes to the mediawiki code, because we're so big and they want to find the bugs in smaller wikis first. —David Eppstein (talk) 02:05, 6 March 2012 (UTC)

The code needs a quick review before deployment to the 1.19 wikis; I think you guys are probably our best testers for math stuff so English Wikipedia will certainly be among those that get it soon. :) --brion (talk) 21:06, 7 March 2012 (UTC)

Quick review:

1. In wiki2jax.js, "\displaystyle" does not need curly braces as it does not take a parameter.
2. In ext.math.mathjax.enabler.js, the function call to TEX.Parse.Augment() can be removed in its entirety as MathJax 2.0 includes support for specifying the line spacing in newlines.
3. I assume you have uploaded also the output HTML-CSS jax's STIX font directory. In that case you should include "STIX" as one of the "availableFonts".
4. In texvc.js, quick-and-dirty support for color is not needed anymore as MathJax 2.0 includes an extension for the color command. See this diff.
5. In TeX-AMS-texvc_HTML.js, if you remove the hackish color support from above, you must include "color.js" as one of the preloaded "TeX" extensions since otherwise the \color macro will be interpreted wrongly (MathJax 1.0-style instead of TeX-style). Also, you must include "cancel.js", which will not be loaded automatically.

Cheers, Nageh (talk) 22:28, 7 March 2012 (UTC)

Category:Rules of inference and Category:Theorems in propositional logic

In principle, the former should contain only rules such as A ⊢ B, and the latter should not contain rules at all, only facts such as (axioms) ⊢ B. But after a mass addition of articles by Gregbard there is much confusion in the theorems' category. Modus ponens is not a propositional theorem by no means. Incnis Mrsi (talk) 12:49, 4 March 2012 (UTC)

Really? "by no means?" There are several sources naming "((P --> Q) & P) --> Q" as modus ponens. Every rule of inference (of prop logic) can be stated as a theorem of prop logic and vice versa. Although the rules produced would quickly become quite complex. that's why commonly you see about 19, with some extras that are often interchanged for others. Greg Bard (talk) 09:38, 5 March 2012 (UTC)

Nope. First, which "rule of inference (of prop logic)" corresponds to p → p, a trivial one, you can say? … well, to classical logic's (p → q) ∨ (q → p) and (p → q) ∨ p? No rule corresponds to these theorems. Second, you apparently cannot get rid of the confusion between a "rule of inference (of classical propositional calculus)" and a rule of inference as an abstract concept. BTW my new essay has a section about this. Incnis Mrsi (talk) 10:00, 5 March 2012 (UTC)

So you don't see that one can always construct a rule of inference out of a theorem of propositional logic. There are an infinite number of theorems, and so too with r.o.i.s but only a few have names. Modus ponens is the most famous. In the case of your examples, a formal system could have a rule (a metalogical statement) that "If "P" is written on a line of a proof, then you can write "P" on a subsequent line of the proof." corresponding to p → p This is a trivial rule which is probably not contained in hardly any logic ever published. Not every theorem is used as a rule of inference or as an axiom. For any that are named, some account should be given. Greg Bard (talk) 10:19, 5 March 2012 (UTC)

p → p would correspond to the rule I call "reiteration". See deduction theorem#Virtual rules of inference. JRSpriggs (talk) 10:42, 5 March 2012 (UTC)

I agree that the Bard is adding confusion, but A ⊢ B and ⊢ A → B are difficult to distinguish; only in cases where the latter makes no sense (i.e., modus ponens) should it not be considered a theorem. — Arthur Rubin (talk) 09:15, 5 March 2012 (UTC)

What is it that you are confused about? Greg Bard (talk) 09:38, 5 March 2012 (UTC) In response to your two formulas, the question is the difference between logic and metalogic. All of the ones on this list are theorems. Greg Bard (talk) 10:32, 5 March 2012 (UTC)

First, if they are theorems of propositional logic, then they are tautologies, which is the correct term, so that should be the category. In fact, the deduction theorem states that exactly all theorems of propositional logic are the tautologies. That being said, every rule of inference of the form

• $P_{1},P_{2},\cdots P_{n}\vdash Q$

is equivalent to the tautology/theorem

• $\vdash P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$

(forward derivation: conditional proof; backward derivation: what most rational people call the rule of tautology, but some — editor — has managed to get another article at that name)

So the category is misnamed, at best. Modus ponens, in particular is worthless if written as $P\land (P\rightarrow Q)\rightarrow Q$, as you have to use modus ponens (rule) to obtain modus ponens (rule) from modus ponens (tautology).

— Arthur Rubin (talk) 16:28, 5 March 2012 (UTC)

Arthur, we are engaging in some civil discourse here, and again I have seen the same pattern. You throw words around in a way that is so careless, as to affect your credibility. All theorems are tautologies so calling tautologies theorems is "misnamed?" Obviously that is not true at all. The same objects are called both in different contexts. However, "tautologies" as a category will surely place these articles in more philosophy category trees than mathematics categories. Your suggestion is inconsistent with the form of subcats in category "mathematical theorems." So you basically have a lot of explaining to do on that suggestion. Secondly, you are completely incorrect in saying that the given theorem called "modus ponens" can't be derived without a modus ponens inference rule. It certainly can be derived in a formal system that does not also contain the modus ponens inference rule. I am a little surprised at that mistake Art. You should know better. Greg Bard (talk) 20:11, 5 March 2012 (UTC)

Comment While the last paragraph achieves its purpose of disagreement, it could have been better with less tongue-clucking and more concrete evidence. Overlooking this and pressing onward, can someone suggest the proper talk page for this discussion to continue, and maybe a short list of qualified editors to request comment from? Rschwieb (talk) 14:08, 6 March 2012 (UTC)

Say listen, Arthur said there was some "confusion" and being the decent, good faith editor that I am, I wanted to get to the bottom of it. It turns out there isn't any confusion. Just more rhetoric from Arthur. So, you should more appropriately direct your concern to Arthur vis-a-vis "clucking." I asked the question in innocent good faith, and it turns out, it's just Arthur's bad attitude AGAIN. Shame on you. Being as fair-minded as I am, I feel I have to say that I do think that the formulation that Arthur has provided concerning the deduction theorem is excellent, and should be included in both the theorem, and tautology article. Greg Bard (talk) 09:29, 7 March 2012 (UTC)

Let's suppose for now that we all appreciate what is going on, and move on with the evidence supporting each side. Rschwieb (talk) 13:50, 7 March 2012 (UTC)

There is a many-to-many correspondence between rules of inference ($P_{1},P_{2},\cdots ,P_{n}\vdash Q$) and theorems of the predicate calculus ($\vdash P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$), and a one-to-one correspondance of the latter with tautologies ($\vDash P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$).

For example, modus ponens is

• $P,P\rightarrow Q\vdash Q$

As a theorem, is it:

1. $P\land (P\rightarrow Q)\rightarrow Q$
2. $(P\rightarrow Q)\land P\rightarrow Q$
3. $P\rightarrow ((P\rightarrow Q)\rightarrow Q)$
4. $(P\rightarrow Q)\rightarrow (P\rightarrow Q)$

(Note theorem #4 is an instance of the the theorem $P\rightarrow P$, which, in turn, corresponds to the "rule" $P\vdash P$.)

For the reverse corresponance, if you use the first formulation, then

$P\land Q\rightarrow Q\land P$

corresponds to the rules

1. $P,Q\vdash Q\land P$
2. $P\land Q\vdash Q\land P$
3. $\vdash P\land Q\rightarrow Q\land P$

If you use the second formulation:

$P\rightarrow (Q\rightarrow P\land Q)$

corresponds to the rules

1. $P,Q\vdash P\land Q$
2. $P\vdash Q\rightarrow P\land Q$
3. $\vdash P\rightarrow (Q\rightarrow P\land Q)$

In any case, all rules of inference (of "standard" (non-intuitionistic) propositional logic) correspond to one or more theorems in propositional logic, and the reverse. Either there should be only one category, or only those "rules" which correspond to theorems which are used as theorems should be included in the "Theorems" category, and only those theorems which are actually used as rules should be included in the "Rules" category. — Arthur Rubin (talk) 15:43, 7 March 2012 (UTC)

Or we could go with Incnis Mrsi's approach; only those rules which are stated as rules should be in the "Rules" category, and only those theorems which are stated as theorems should be in the "Theorems" category.

In any case, the present duplication of categories is unacceptable. — Arthur Rubin (talk) 16:04, 7 March 2012 (UTC)

I was also hoping citations would surface to dispel philosophical qualms. Rschwieb (talk) 16:05, 7 March 2012 (UTC)

I admit to not being a philosopher. — Arthur Rubin (talk) 19:00, 7 March 2012 (UTC)

Arthur, I think you are forgetting how WP works. Certainly you, I, or any of the talented people here at WP:MATH can construct a r.o.i out of any theorems and vice-versa. However there really are only about 19 or so that are actually published as r.o.i. That is the standard. Whether or not the "rules of inference" category should also be a subccategory of "theorems of propositional logic" is something I am open-minded to, either way. However, just because Arthur doesn't like it, is no reason to move or delete either of those categories. Just because you aren't looking for r.o.i doesn't mean someone else isn't. Show some respect. If articles are removed from "theorems" then the "r.o.i." cat needs to be placed as a subcat of the "theorems" cat. I wouldn't prefer that. Greg Bard (talk) 21:02, 7 March 2012 (UTC)

"R.o.i." being part of "theorems" would be absurd. "Theorems" being part of "r.o.i." would not be absurd, as $\vdash P$ is a perfectly good rule of inference. Perhaps {{catseealso}} in both categories would be more appropriate. But perhaps I don't understand how Greg Bard's argument is consistent with Wikipedia policies and guidelines.

Still, I don't see why either my approach (in the related category if called, in the literature, a "r.o.i" or a "theorem", or both), or Incnis Mrsi's approach (in the related category if we call it an "r.o.i" or a "theorem", or both) wouldn't be consistent with WP:CAT, if the {{catseealso}}s are in place. See, for example, the following excerpt from WP:CAT:

• Articles should be categorized by the defining characteristics of the article topic.

— Arthur Rubin (talk) 23:24, 7 March 2012 (UTC)

Arthur, theorems as a subcat of r.o.i. is absurd. A rule of inference itself is a metalogical statement about a logical system. A theorem is a statement from within a logical system. So, you are precisely incorrect. The question is how are we to organize under category:logical expressions. All of these things that we are talking about are theorems of some system, and are used as rules of inference in some systems based on the fact that they are derived as theorems. So the way they should be organized under logical expressions is that some are in both r.o.i and theorems based on whether or not systems have been published expressing them as such. Like I said, I can see r.o.i under the theorems category or side by side with it under logical expressions, like it is now. I cannot see theorems under the r.o.i. category at all. Greg Bard (talk) 18:33, 9 March 2012 (UTC)

Actually your statement really is absurd. Rereading the first sentence of the last section — how can a metalogical statement be a "theorem". Any theorem (of the propositional calculus, anyway) $P$ constitutes a rule of inference $\vdash P$, while rules of substitution constitute theorems only by use of the rule of tautological equivalance from Rubin, probably called other things in other systems. However, I think side-by-side is better, with both trimmed significantly to those rules of inference actually used as rules of inference in reliable sources, and those theorems actually stated as theorems in reliable sources. — Arthur Rubin (talk) 06:10, 10 March 2012 (UTC)

Edits at Divisor function and Riemann hypothesis

A succession of anonymous/new editors have been editing divisor function and Riemann hypothesis, inserting what looks like a claim to have proved the result unconditionally, supported only by a preprint at vixra.org. More eyes on both articles would be welcome. —David Eppstein (talk) 16:06, 6 March 2012 (UTC)

For context, vixra.org is a version of arxiv.org that is specifically for cranks. From their website: "ViXra.org is an e-print archive set up as an alternative to the popular arXiv.org service owned by Cornell University. It has been founded by scientists who find they are unable to submit their articles to arXiv.org because of Cornell University's policy of endorsements and moderation designed to filter out e-prints that they consider inappropriate. ViXra is an open repository for new scientific articles. It does not endorse e-prints accepted on its website, neither does it review them against criteria such as correctness or author's credentials." Sławomir Biały (talk) 16:40, 6 March 2012 (UTC)

Its still ongoing. Someone should protect Riemann hypothesis at least. Sławomir Biały (talk) 00:52, 7 March 2012 (UTC)

Anyone want to work through the pages with references from Vixra (http://en.wikipedia.org/w/index.php?title=Special:LinkSearch&limit=500&offset=0&target=http%3A%2F%2Fvixra.org) to see whether they make sense in their respective articles? I'm leaning toward no in most of the ones that I looked at.Naraht (talk) 15:07, 7 March 2012 (UTC)

It's not up to us on Wikipedia to referee papers, if somebody wants to do that and thinks there actually is something there worth bothering about then of course you could say here even though officially this isn't a forum, but it still couldn't go into the article until it was peer reviewed outside of Wikipedia. Dmcq (talk) 15:28, 7 March 2012 (UTC)

I glanced them over, and they don't really make sense. Even if they did make sense, they don't appear to contain any new deep mathematical ideas (in contradistinction to many of the supposed proofs of these big theorems that at least have the superficial appearance of great depth). There is zero chance that this approach will show anything like what the author claims, even if cleaned up and made readable. Of course, I make my standard offer to the author: I will read and provide detailed feedback for $1000 (US), payable in advance. Sławomir Biały (talk) 15:44, 7 March 2012 (UTC)

If vixra authors were unable to place their texts on the arxiv, they are unlikely to get published in reputable venues, which would seem to argue against their inclusion at wiki. Tkuvho (talk) 13:13, 9 March 2012 (UTC)

Strong and weak (logic)

I am not familiar with English terminology, but something like it certainly should exist. A proposition is strong if it entails many other propositions. The proposition P is stronger than Q if P├ Q (provability/deducibility partial order relation) or P ⊧ Q (semantic partial order relation). Also, it may be generalized to theories. A theory is stronger if it has more theorems that another, which uses the same formal language. For example, classical propositional calculus is stronger than intuitionistic one, and an inconsistent theory is the strongest possible.

I could use titles strong and weak (logic) or strong and weak propositions, which is better? Also, which sources should I search for definitions? Incnis Mrsi (talk) 06:50, 9 March 2012 (UTC)

Is there really enough to say about that to justify creating an article? — Carl (CBM · talk) 11:26, 9 March 2012 (UTC)

Imagine a text:

“ Wizzle's theorem has a stronger antecedent and hence is weaker than Woozle's theorem. But Wizzle's theorem admits a generalization to bobjects in Poozle's spaces which cannot be obtained as a consequence of Woozle's theorem. Pizzle's conjecture for Poozle's spaces was stronger than both Wizzle's and Woozle's theorems, but Squizzle recently built a counterexample to it (and also to generalized Woozle's theorem) in a foo-dimensional Poozle's space. At Winnie-the-Pooh symposium it was discussed that in foo-dimensional case some weakened version of Woozle's theorem may be true, which is not equivalent to Wizzle's theorem. But for all known bobjects the corresponding statement is a really a consequence of either the foo-dimensional Wizzle's theorem or this theorem in some degenerate space. ”

Happily we have logical equivalence, but how do you propose to link "weaker", "stronger" and "weakened"? Or should I explain this inline? Incnis Mrsi (talk) 13:14, 9 March 2012 (UTC)

Wikipedia articles should not be written merely to document jargon. I'm pretty sure all the content of what you propose to write is covered elsewhere. So basically I don't think you should do this at all. --Trovatore (talk) 01:38, 10 March 2012 (UTC)

I think your definition (P is stronger than Q if P├ Q) suggests that entailment is the underlying concept (although that article is a mess). -- 202.124.74.200 (talk) 01:34, 10 March 2012 (UTC)

Merging localization of a ring to localization of a module (or other way)

Do we really need two separate articles for a basically one single topic: localization in commutative algebra (or algebraic geometry)? For one thing, the constructions are the same. For another, it's simpler to have one article to discuss basic facts like local property. For example, "noetherian" is not local property. But if localization of a module has a section on local property, it probably should have a mention of this. -- Taku (talk) 15:14, 10 March 2012 (UTC)

My experience tells me that such mergers often result in disastrous articles. It would be better to start a new article like localization (algebra), and gradually merge/rewrite these articles into that one on an equitable basis. But at the moment, having two decent articles on similar topics is probably better than having one article with an uneven, confusing, and inconsistent merger. Sławomir Biały (talk) 16:04, 10 March 2012 (UTC)

Right (especially, "experience" part). I for one cannot promise to deliver coherency. -- Taku (talk) 17:17, 10 March 2012 (UTC)

Ah, I actually just completed the merger: localization (algebra). It differs very little from the existing ones. I forgot to say in the above, but I think an important example of the localization of a module is that of localization of an ideal and I think it seems easier to add discussion on it to this new article. -- Taku (talk) 18:05, 10 March 2012 (UTC)

Mathematical fallacy

If anyone is looking for a fun diversion, bringing mathematical fallacy into decent shape looks like a project with collaboration potential. See my comment at Talk:Mathematical fallacy. Sławomir Biały (talk) 00:36, 11 March 2012 (UTC)

Conventions for ordinals

I'm currently in a discussion (see my talk page) with another editor on the meaning of the phrase "the first 5 Fibonacci numbers". My interpretation is 1, 1, 2, 3, 5, but the other editor, based on conventions used in computer languages such as C and Python, thinks it would be 0, 1, 1, 2, 3. The other interpretation has some merit in that most authors start the sequence with 0, so it comes down to whether you consider 0 the 0th number or the 1st number in the sequence. My preferred solution is to avoid the issue altogether my rewording the phrase, but we've been back and forth several times now so I thought it was time to raise the issue in a larger forum.--RDBury (talk) 14:45, 7 March 2012 (UTC)

I don't think there's any ambiguity in the phrase "the first 5". If the sequence starts with element #0, then "the first 5" elements are elements 0, 1, 2, 3, and 4. If the sequence starts with element #1, then "the first 5" elements are elements 1, 2, 3, 4, and 5. But even if you consider element #0 "the 0th element", the phrase "the first 5" means elements 0–4, not elements 1–5. —Mark Dominus (talk) 15:49, 7 March 2012 (UTC)

Agree completely: "first five" does not mean "six" regardless of indexing conventions. Also, even if the indexing starts with 0, it could be that F(0) = 0 or F(0) = 1, the choice of index does not determine the choice of initial conditions for the recurrence. Any prticular formulas will depend on both an indexing convention and a choice of initial conditions. — Carl (CBM · talk) 15:56, 7 March 2012 (UTC)

I think that it is more clear in general to just say "From F(1) to F(n)" or "From F(0) to F(n-1)", because then the reader knows exactly what is intended. Under zero-based numbering F(0) is both the zeroth and first element of the sequence. — Carl (CBM · talk) 16:24, 7 March 2012 (UTC)

The phrase is ambiguous, otherwise the issue would not have come up. The way the article was worded it said "The sum of the first n Fibonacci numbers is the (n + 2)nd Fibonacci number minus 1." This triggered a "correction" by the other editor which I then reverted and the resulting discussion is mostly on how the phrase should be interpreted. The two interpretations give different results for "the sum of the first 5 numbers", 12 in one case and 7 in the other, and only one interpretation makes the statement correct.--RDBury (talk) 16:40, 7 March 2012 (UTC)

Whether "first five" works there does not depend on whether the first one is called F(0) or F(1), it depends on whether the first one is equal to 0 or equal to 1, in other words it depends on the initial condition of the recurrence, because it is a property of the actual sequence, not a property of the numbering of the sequence. Based on the formula in the article, and assuming F(0) = 0 as the article does, it would work to phrase that sentence in the article as "the sum of the Fibonnacci numbers F(1) through F(n)" thus avoiding the entire issue. — Carl (CBM · talk) 16:48, 7 March 2012 (UTC)

I think the notation used in the article is pretty much universal, otherwise we seem to be in agreement. I rephrased it in the article as "[The] sum of the first Fibonacci numbers up to the nth is equal to the n+2nd Fibonacci number minus 1."--RDBury (talk) 17:28, 7 March 2012 (UTC)

I agree that the quoted statement is true, but if the indexing begins at 0 then it does not match up with the formula $\sum _{i=1}^{n}F_{i}=F_{n+2}-1$ that is just below it in the article. With zero-based numbering, $F_0$ is the first (and zeroth) number, and when read literally the formula states that the sum of the second through $n+1$st numbers is equal to one less than the $n+3$rd number. — Carl (CBM · talk) 18:50, 7 March 2012 (UTC)

I am the "other editor", and there is one thing I do not understand. The mathematical formula says "sum from i = 0 to i = n". The text should just say the same, is all I meant. If somehow it is more clear that the text says "the sum from i = 1 to i = n", then it should be the mathematical formula that should be changed to say the same. The problem is not one of counting from zero or from one. The text and the formula should simply be consistent with each other. Is there an editorial agreement about that? Olivier Danvy (talk) 18:58, 7 March 2012 (UTC)

Let's link to the section being discussed: Fibonacci_number#Combinatorial_identities. I agree that there's a lot of potential for confusion. To my mind, if we have a sequence beginning F₀, F₁, F₂,..., then F₀ is the first element, F₁ the second element and so on. But it's liable to be interpreted differently by different people. What is the reason for writing out all the formulae in words as well as in symbols? Perhaps the nineteenth-century charm of the prose style is enjoyable, but in this case it causes more trouble that it's worth. Why not just delete all the verbal descriptions, and then there's no argument about the meaning of nth? Jowa fan (talk) 23:57, 7 March 2012 (UTC)

Going back to the original question, the sequence "1, 1, 2, 3, 5" is more aesthetically pleasing than "0, 1, 1, 2, 3". The former captures more of the essence of how the F. numbers actually look. You say to people: "What sequence goes 1, 1, 2, 3, 5 ..." and they're far more likely to say "Of yes, Fibonacci numbers", but "0, 1, 1, 2, 3" just isn't so obviously recognisable as a signature.

In my mind the mathematical pedantry is obscuring the message. If you *must* be accurate, say "Fib nos. F1 to F5 are 1, 1, 2, 3, 5" which bypasses the whole fussy question. --Matt Westwood 06:04, 8 March 2012 (UTC)

I agree with this, I think this is where the fundamental difficulty in resolving this issue comes from. The top of the article defines F₀ to be 0 and F₁ to be 1. But then the identities in the combinatorial identities section start summing from F₁, which isn't the first Fibonacci number according to the definition at the top at all! Therefore the sentence "the sum of the first Fibonacci numbers up to the nth" (which would be F₀ + F₁ + F₂ + ... + F_n-1) clashes with what the formula says, because the formula starts at i=1. This problem exists for several of the combinatorial identities. A radical way to solve the problem would be to chose a different definition at the beginning of the article. That's quite radical though. The other option would be to be explicit and write "summing the numbers F₀, F₁, F_n gives F_n+1-1". Leaving it as it is feels extremely unsatisfying to me, because it is muddled, inconsistent and wrong. Cfbolz (talk) 15:23, 13 March 2012 (UTC)

Work might start on Outline of algebraic structures

After I felt like Algebraic structures was in recovery, I reexamined restoring the outline version to usefulness. It has many problems, some of which might have been caused by the whole outline/list fiasco. I've proposed some changes on the talk page, and I hope a few other WP:Math members are willing to check it out from time to time. Among the recommendations: organize it more like Algebraic structure, include a section on the usual order of learning things in intro, decrease total number of mentioned structures, remove example list. I'm awaiting response from WP:Outlines concerning if they want to help. Rschwieb (talk) 14:23, 12 March 2012 (UTC)

'New' math rendering options

Check your preferences: with MW 1.9 the math rendering options are down to two: always PNG and display TeX. See the RfC here: [7]. Renders some of the Math MOS redundant, such as MOS:MATH#Forcing output to be an image and MOS:MATH#Very simple formulae. Probably the whole section needs rewriting.JohnBlackburne^words_deeds 02:19, 1 March 2012 (UTC)

You mean MW 1.19 which has just been rolled out. PrimeHunter (talk) 03:00, 1 March 2012 (UTC)

That's really really stupid if it means what I think it means. Anything like that should have been delayed until MathJax or another way of displaying stuff properly inline had been implemented properly. Dmcq (talk) 13:02, 1 March 2012 (UTC)

Yep it is what I thought. I was testing MathJax so I didn't see it before. Luckily or unluckily people seem to have tried avoiding <math> inline in lots of places so the effect isn't as bad as it might be. I really do think it would be a good idea to have a conversion tool to help change {{math}} uses to <math> when MathJax comes along, this latest business is going to force even more instances of <math> to be turned into {{math}} to avoid the ugliness of the inline PNGs. Dmcq (talk) 13:17, 1 March 2012 (UTC)

At some point soon (i.e. maybe during 2012), mathJax should become the default for everyone. Developers are working on it. Does this latest roll-out have anything to do with progress in that direction? Michael Hardy (talk) 16:17, 1 March 2012 (UTC)

The big problem now is the baseline problem with $x^{a}$ being positioned too low. Brion said he was going to investigate this in the RfC, but it looks like it hasn't happened.--Salix (talk): 16:59, 1 March 2012 (UTC)

The relevant bugs are the following:

• Bug 31406 - Set $wgMathUseMathJax = true on Wikimedia wikis
  • This depends on/blocks other bugs
• Bug 32694 - Use baseline shift when positioning inline math PNGs

Helder 17:18, 1 March 2012 (UTC)

I've now responded to the former bug, it looks like MathJax might be just round the corner.--Salix (talk): 18:38, 1 March 2012 (UTC)

---

Apparently I missed something with MathJax. Does anybody use it to browse articles in English Wikipedia and is it really functioning? Incnis Mrsi (talk) 17:44, 17 March 2012 (UTC)

User:Nageh/mathJax is a ready-to-use solution. Turn off the rump of WP:texvc and use this script. Incnis Mrsi (talk) 19:06, 18 March 2012 (UTC)

Iteration of mathematical curves

The new article titled Iteration of mathematical curves is at best currently a mess, and possibly a violation of WP:OR. Further opinions? Michael Hardy (talk) 15:31, 11 March 2012 (UTC)

There's also Jasinski Flower, by the same editor (who is probably Andrzej Jasinski). Sławomir Biały (talk) 15:45, 11 March 2012 (UTC)

Having looked at them I've put a prod on them as non notable and probably self promotion. Dmcq (talk) 20:33, 11 March 2012 (UTC)

A number of times laterly I've seen "non" used like this as if it were a separate word rather than a prefix. Have schools stopped teaching that there is such a thing as a prefix? Michael Hardy (talk) 15:52, 13 March 2012 (UTC)

The other day a young news reporter caught my attention with the awkward phrase "...want to be able to not be concerned..." Rschwieb (talk) 01:05, 14 March 2012 (UTC)

It is a phrase I only use on Wikipedia but it seems to be a fairly standard phrase here which is why I used it, there's even a redirect WP:Non-notable Dmcq (talk) 01:22, 14 March 2012 (UTC)

Michael was objecting not to non-notable but rather to non notable. --Trovatore (talk) 01:47, 14 March 2012 (UTC)

Well that's just un acceptable. Are you il literate or some thing? (This post is just to annoy Michael Hardy.)  :-D Sławomir Biały (talk) 11:24, 14 March 2012 (UTC)

Your non sense is un necessary and in appropriate, Slawomir! :) User:Rschwieb|Rschwieb]] (talk) 13:58, 14 March 2012 (UTC)[[

This does highlight the messy state of out articles on curves. We have

• Curve
• Plane curve - a stub
• Algebraic curve
• Differential geometry of curves
• List of curves
• Gallery of curves

all of which overlap somewhat, none of which are particularly complete. What sees to be missing is an article on parametric curve the closest there being Parametric equation.--Salix (talk): 08:04, 14 March 2012 (UTC)

Would some one like to talk to the author of that Iteration of mathematical curves and Jasinski Flower? I am pretty certain they are OR but I don't really feel I'm the right person to try sand get them to move it to somewhere better or workon what Wikipedia does. They've put an effort into it and there's some talent and I'm more of a putter downer. Dmcq (talk) 22:44, 16 March 2012 (UTC)

Segal–Shale–Weil distribution and Metaplectomorphism

Boodlepounce believes these articles are nonsense. Can anyone at the project refute Boodlepounce's assessment by verification from reliable sources? Boodlepounce (talk) 21:33, 15 March 2012 (UTC)

Although Boodlepounce definitely raises a valid point, Boodlepounce might be taken more seriously at first blush if it referred to itself in the first person. Bad Boodle! Sławomir Biały (talk) 23:14, 15 March 2012 (UTC)

Currently they may deserve {{context}}. Segal–Shale–Weil distribution certainly does not deserve deletion. Charles Matthews (talk) 10:56, 19 March 2012 (UTC)

Wikipedia:Categories for discussion/Log/2012 March 19#Category:Matrices

A discussion on disambiguation. Please have a look. Charles Matthews (talk) 10:53, 19 March 2012 (UTC)

One proposal suggests renaming all categories that have a dab page, which would just waste time and memory. We would have groups (mathematics), fields (mathematics), idiocy (Wikipedia category discussions), etc.

The combination of fatuous bluster and sloth in these discussions is unmatched in Wikipedia: One should not expect that the category experts have taken any time to read the articles or their ledes.  Kiefer.Wolfowitz 12:10, 19 March 2012 (UTC)

Articles needing expert attention

In their infinite wisdom a number of editors have decided it would be a good idea to delete {{expert-subject}}. This means Category:Mathematics articles needing expert attention will soon be empty. Is anyone interested in preserving this list of articles somewhere (or taking the template to WP:DRV)? —Ruud 13:10, 9 March 2012 (UTC)

I would appeal the deletion. I don't see consensus for deletion in the discussion contrary to what the closing admin claims. Frankly, this is one of the templates I think are useful. This is not just about notifying editors but also about warning readers about problematic content and inviting potential expert readers to contribute. Nageh (talk) 13:17, 9 March 2012 (UTC)

It seems useful to me too. Let me know where to write if an appeal forms. Rschwieb (talk) 16:00, 9 March 2012 (UTC)

I've opened a deletion review at Wikipedia:Deletion review#Template:Expert-subject. —Ruud 16:43, 9 March 2012 (UTC)

The closing statement did say "after adding 'attention=yes' or equivalent parameter in the corresponding WikiProject banner". This may well be a good thing to do to {{maths rating}}. Maybe an {{expert-mathematics}} template might be a workable solution. The big problem is that few other projects monitor these, so there is a case for a project specific template. Curiously there is a big discrepancy between Category:Mathematics articles needing expert attention with 158 articles and Wikipedia:Pages needing attention/Mathematics/Lists#Articles needing expert attention with only 34 articles.--Salix (talk): 18:35, 9 March 2012 (UTC)

The issue noted in the last sentence is now fixed. -- Jitse Niesen (talk) 15:50, 10 March 2012 (UTC)

I've created a mathematics specific version {{expert-maths}} as an experiment. It has an additional reason parameter to indicate what the problem is.--Salix (talk): 22:06, 10 March 2012 (UTC)

Do you suggest to start moving articles there from {{expert-subject}}? Sasha (talk) 22:25, 10 March 2012 (UTC)

Its too early for that as the Deletion review is still pending. So I'm just gauging opinion at the moment. The main question is whether we want something to appear in the main article space as this template does or talk namespace as adding a parameter to the project banner would do.--Salix (talk): 22:56, 10 March 2012 (UTC)

I note that the deletion review closed with a "relist" decision, but the template was never relisted. Is it necessary to start another deletion review? -- 202.124.75.161 (talk) 06:42, 18 March 2012 (UTC)

{{expert-subject}} has been relisted for TfD discussion. Nageh (talk) 10:08, 20 March 2012 (UTC)

Lebesgue integration

There is a problem with the picture of „intuitive explanation“. Which one is better/„not too false“? a,b or c? In my opinion a) is the worst one, but it is back in the article.

a)

b)

c)

--Svebert (talk) 22:10, 18 March 2012 (UTC)

Well, (b) is clearly wrong by any measure. Where is the simple function s (from the definition of the Lebesgue integral) that is $\leq f$ in this picture? This image appears to represent an upper Darboux sum for the Riemann integral of f. The image (c) is probably marginally better than (a), although both convey the same basic idea. Sławomir Biały (talk) 22:33, 18 March 2012 (UTC)

Pls. see p. 146 of [8]. I don't get your comment with „where are the simple functions in figure b)“...Figure a) is totally misleading.--Svebert (talk) 23:04, 18 March 2012 (UTC)

Sorry, I can't see the page you just linked. I was referring to the definition in our article Lebesgue integral, which is quite standard. There is nothing about (b) that seems to be correct from this point of view. Sławomir Biały (talk) 23:26, 18 March 2012 (UTC)

Lebesgue partitioned the y-axis, not the x-axis. Michael Hardy (talk) 23:18, 18 March 2012 (UTC)

Here is the reference again: Bernd Siegfried Walter Schröder (12 November 2007). Mathematical analysis: a concise introduction. John Wiley & Sons. p. 146. ISBN 978-0-470-10796-6. Retrieved 19 March 2012.. You are right, Lebesgue partitioned the y-axis and Riemann the x-axis. But what figure a) shows definitively doesn't happen in Lebesgue integration. The Lebesgue integral is defined as follows:

$\phi =\sum _{i}\alpha _{i}\chi _{A_{i}}$

$\int _{\Omega }\phi {\mbox{d}}\mu =\sum _{i}\alpha _{i}\mu (A_{i})$

here $\phi$ is the simple function, which is essentially a sum of characeristic functions on some sets $A_{i},\,i=1\dots n$. These sets are parts of the x-axis in the shown pictures. The integral now, „looks up“ the bigness of every $A_{i}$ and scales it with the appropriate factor $\alpha _{i}$ of the simple function.

Please explain to me, where are horizontal slices shown in figure a) in the definition? Figure a) is totally misleading because it shows that some parts of the x-axis (some $A_{i}$) are added several times to obtain the integral. But in the definition every $A_{i}$ is considered exactly 1 time in the sum.

The idea of lebesgue integration is reflected much more precise with figure b) and c): One partitions the y-Axis in say N equal parts with length $\Delta y$. So one can assign for every such y-interval $y_{i}+\Delta y$ an interval on the x-axis (in general disjoint /scatterd). Each such interval on the x-axis is now one set $A_{i}$. The lebesgue integration now measures the bigness of every $A_{i}$ only one time and scales this bigness with the appropriate factor $\alpha _{i}=y_{i}$. In both figures b) and c) exactly this is shown. The measure of the sets $A_{i}$ are the x-axis parts of rectangles with same color.

This is what Henry Lebesgue said: Lebesgue integration is that what a careful businessman does. If he has to count his money than Riemann would just count the coins as they come: 1,1,4,4,5,4,3,1. The careful businessman would order the coins after there value: 3*1+3+3*4+5. (Here $\mu (A_{1})=3,\mu (A_{2}=0),\mu (A_{3})=3,\dots$).--Svebert (talk) 09:29, 19 March 2012 (UTC)

Here is another good reference: [9]--Svebert (talk) 10:36, 19 March 2012 (UTC)

The horizontal slices are the same horizontal slices that appear on page 146 of the reference you gave. Sławomir Biały (talk) 10:50, 19 March 2012 (UTC)

? except that there are also vertical slices and the sets $A_{k}$ are „scattered“...

I understand your point, that the lebesgue-figures of b)/c) can also be considered as figures for Riemann-integration with non-equidistant partition of the x-axis. But I think a figure for the intuitive explanation should be in 1D otherwise the figure is too complicated and I personally dont know a better explanation than b)/c) for 1D.

Back to lebesgue integration (I am talking only for 1D integrations in the following): The point of lebesgue integration is not that one partitions the y-axis instead of the x-axis, also it is a good starting point for the explanation. The point is, that the partitions can be scattered. They don't have to be intervals. Therefore an optimal picture should have huge oscillations (like the one of the wolfram-reference) to make clear that the partitions dont have to be connected.

Therefore figure a) misses this „scatterd partitions“ point. Also it is totally misleading and even wrong! For me the picture shows sets $A_{i}$ which are not pairwise disjoint (the sets $A_{i}$ are the projections of the slabs onto the x-axis). If you refer to definition 9.21 of the book-reference above, you read „Let $A_{1},\dots A_{n}$ be pairwise disjoint sets“. Also I dont understand what part of figure b) is wrong, could you please be more precise?--Svebert (talk) 11:20, 19 March 2012 (UTC)

The main with (b) is that it is based on an approximation of f from above rather than below, and so it has no connection with the definition of the Lebesgue integral, which uses approximations from below. As for the emphasis on the sets $A_{i}$, I agree that it could be made clearer in the image (although none of the images really does this well). Even so, the Lebesgue integral of a nonnegative function can be defined by

$\int f=\lim _{n\to \infty }2^{-n}\sum _{k=1}^{\infty }\mu \{x|f(x)\geq k2^{-n}\}$

which is what (a) illustrates directly. Sławomir Biały (talk) 11:53, 19 March 2012 (UTC)

I have to agree with User:Svebert that the horizontal bars in a) are misleading. I've never seen this horizontal slice picture used to describe Lebesgue integration (or if I did, I promptly discarded it). It does not seem to embody the simple function approximation. I think c) is patently superior to a). It incorporates the partition of the y-axis using dotted lines instead of solid. Diagram a) looks like the beginnings of a "washer" approximation of volume of a revolutionary solid to me. Rschwieb (talk) 13:47, 19 March 2012 (UTC)

The horizontal slicing is actually a very common way of explaining the Lebesgue integral. It even appears in the reference Svebert gave. In addition, it is described in the Folland text referenced in the article. More references to this perspective are available upon request. Sławomir Biały (talk) 14:03, 19 March 2012 (UTC)

I noticed your comment that it appeared in that reference, but I do want to throw its commonality into question. I guess the question for weighing if it should be included is "how high is the percentage of texts using the horizontal bar picture?". The estimated range right now is too broad: "quite common" to "never seen it used". Rschwieb (talk) 15:02, 19 March 2012 (UTC)

Well, I think the relevant sample is "how many textbooks attempt to illustrate the Lebesgue integral with a picture"? Of this sample, we can start to ask which of them do it by dividing the range, and which do it by some other means. Sławomir Biały (talk) 15:07, 19 March 2012 (UTC)

Presumably the correct measure of commonality is its proportion (not frequency) among texts using an illustration, but other than that I have no idea how what you wrote is different from what I wrote. And I really do mean it to be constrained to "how many use the picture", since we all agree on the definition of the Lebesgue integral but we disagree on the effectiveness of picture a). So there's no mistake, I want to say that we should be comparing the relative proportions of both type a) and type c) illustrations to measure their commonality. Rschwieb (talk) 20:01, 19 March 2012 (UTC)

I agree that figure b) has the problem that it doesnt obey $\phi \leq f$. I will fix that. But I totally disagree that the reference I gave use the „slab-picture“. Both references which I posted above explain lebesgue integration with figures like b)/c). Of course without the flaw that in b) $f>\phi$.--Svebert (talk) 20:29, 19 March 2012 (UTC)

@Slawomir: Pls show me a reference except Folland which uses the „slab-figure“ (I cant access the Folland-reference). Thanks.--Svebert (talk) 20:29, 19 March 2012 (UTC)

The figure (b) has now been substantially improved, especially with the addition of the horizontal rulings. While I don't think it adequately conveys the fundamental difference between the Riemann and Lebesgue integrals, I think it should be given by itself as an independent illustration of the "simple function" definition of the Lebesgue integral. Could this be separated from the Riemann integral?

One doesn't actually need to know anything about simple functions to have an intuitive grasp of the meaning of the Lebesgue integral, and this probably points to an overall fault in our article. Probably the simplest definition I know for a nonnegative measurable function f, the Lebesgue integral is simply

$\int f:=\int _{0}^{\infty }f^{*}(t)\,dt$

where

$f^{*}(t)=\mu \{x|f(x)>t\}$

and the integral on the right is an ordinary (improper) Riemann integral. The idea implicit here is that, intuitively speaking, we can rearrange the function values by sliding all of the horizontal slabs to the left in the picture (a). You'll note that this integral agrees with the limit in my earlier comment

$\int f=\lim _{n\to \infty }2^{-n}\sum _{k=1}^{\infty }\mu \{x|f(x)\geq k2^{-n}\}$

--Sławomir Biały (talk) 23:18, 19 March 2012 (UTC)

Looks like b) is much improved now! I like it better now than the other two. It also has the added benefit of having more variety (it's more than just a hill.) Rschwieb (talk) 13:10, 20 March 2012 (UTC)

Sorry Slawomir, but I dont understand your comments. It took me 10 minutes to understand the "nearly circular" definition of $f^{*}(t)=\mu \{x|f(x)>t\}$.

I still dont understand what this weird f* function has to do with the defintion of the lebesgue-integral (except that both include the measure $\mu$ of a set). I only see that the function rotates x und y axis for a box-like function. And that for a tent-like function f, f* is linearly going down. And that in those two examples the integral of f and of f* from 0 to infinity are the same. I dont understand what this has to do with the slabs and the lebesgue integration.

Perhaps I am just not smart enough, however, i am not a mathematician.

We are talking about the "intuitive explanation" of lebesgue integration, not that kind of explanation what only experts understand. This slab-picture is not intuitive because i still cant put the definition of the lebesgue integral together with this horizontal-slab-picture (and i really thought about it a long time). Additionally I gave 2 references which do not show your "totally obscure" horizonztal explanation. As I said the Folland reference is not accessible for me. Pls show me a book on google-books which explains this horizontal-slab-picture to me. --Svebert (talk) 19:42, 20 March 2012 (UTC)

I think this approach is described in Lieb and Loos. I don't know about availability on Google books. Sławomir Biały (talk) 19:57, 20 March 2012 (UTC)

As for the connection with the slab figure, $f^{*}(t)dt$ is the area contained in an infinitesimal slab at level t. Sławomir Biały (talk) 21:40, 20 March 2012 (UTC)

Thanks for the reference! I found your explanation (except for the figure, but the formulae etc.) here: Elliott H. Lieb; Michael Loss (2001). Analysis. American Mathematical Soc. ISBN 978-0-8218-2783-3. Retrieved 21 March 2012. on page 12.

ok, now I see, that they define the lebesgue integral without simple functions and with your weird f* function.

$(*)\int _{\Omega }f(x)\mu (\mathrm {d} x):=\int _{0}^{\infty }f^{*}(t)\mathrm {d} t$.

where the right-hand side is a normal riemannian integral.

Now I realized, that the lebesgue integration article really lags clear definitions. If one knows the definitions for i) simple functions, ii) non-negative functions and iii) "all" functions, then one knows where to look at in the article. But otherwise it is totally unclear where one finds the definitions of the lebesgue integral in the article.

Every time I talked about showing a picture for the intuitive explanation for the lebesgue integral I had only the definition for the case i) in mind. Slawomir, you had all the time the case ii) in mind.

Slowly I can understand what you are talking about, Slawomir. And after sketching f and f* again, I finally see that f*(t)dt corresponds to a red slab in figure a).

I summarize: After hours of overthinking the figures and definitions and with your comments I got the connection between figure a) and lebesgue integration.

But there is the huge problem, that nobody (except people who already dissolved the riddle of fgure a) with support of other books and good comments of slawomir) can understand the connection between the figure a) and the lebesgue integration. 1. the article doesnt make clear to which defintion the figure refers (I thought all the time on i) and than there is no chance to work it out). 2. The steps you gave to me to understand the pciture are missing in the article.

Proposal: Rewriting the Integration and Intuitive interpretation part. The Integration-part has to be rewritten so that we have three paragraphs with clear definitions for the cases i), ii), iii). The intuitive part must clearly refer to either case i) or case ii) with the appropriate figure and enough text and formulae to understand the figures.

I still prefer figure b). But I must agree that figure a) is not wrong, but is totally useless without a deliberated explanation. Although I think figure b) is more common and much more easy to understand than figure a)

Off topic: Why are here so less people discussing with us???? I thougt the en:wp has much much more authors than de:wp and on the mathematics-portal there we have discussions with much more authors. Is here anywhere a better place (more authors) to discuss these math problems???--Svebert (talk) 11:14, 21 March 2012 (UTC)

to me the picture a) and the definition of Sławomir seem the most natural. However, as Svebert points out, this definition is not well-explained in the article. So the problem is with the article and not with the picture.

It would be nice to explain in the article why the formula (*) above (Svebert -- sorry for redacting your comment) is true for the Riemann integral (by Fubini theorem), and then that the RHS is defined in a much more general setting. Sasha (talk) 17:02, 21 March 2012 (UTC)

Yes, that seems like a very good suggestion. Sławomir Biały (talk) 20:53, 21 March 2012 (UTC)

Disambiguation needed - Conjugation

I have been working through all the pages that have links to the disambiguation page Conjugation, but I have been unable to resolve those listed here. I am hoping that an expert from this project will be able to fix these. Thanks. Trace identity, SL2(R), David Spiegelhalter, Complete group. Derek Andrews (talk) 16:42, 19 March 2012 (UTC)

Only David Spiegelhalter is left. --Joel B. Lewis (talk) 18:19, 19 March 2012 (UTC)

the last one barbarously resolved (by myself) using the Gordian Knot method. Sasha (talk) 16:48, 21 March 2012 (UTC)

Helmholtz decomposition is wrong

Dear members of world mathematical community!

The Fundamental theorem of vector calculus, (Helmholtz decomposition) states that any sufficiently smooth, rapidly decaying vector field in three dimensions ${\mathbf {F} }$ can be constructed with the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field (scalar potential $\varphi$ and a vector potential ${\mathbf {A} }$)

${\mathbf {F} }=-\operatorname {grad} \psi +\operatorname {rot} {\mathbf {A} }\Rightarrow {\mathbf {F} }=\operatorname {grad} \varphi +\operatorname {rot} {\mathbf {A} }$ (1*)

However, the gradient of scalar function does not form the vector field. As well known from textbook [1, p. 15] « … under co-ordinate change the gradient of function transforms differently from a vector »: hence the theory requiring (1) must be false. The next unpleasant things we can see for such well-known classical rules. In mathematics and physics the rot (or curl) is an operation which takes the vector field ${\mathbf {A} }$ and produces another vector field $\operatorname {rot} {\mathbf {A} }$ . However it is well-known that $\operatorname {rot} {\mathbf {A} }$ is an Antisymmetric Tensor . Therefore under co-ordinate change the tensor $\operatorname {rot} {\mathbf {A} }$ transforms differently from a true vector. For elimination of these contradictions the Fundamental theorem of vector calculus can be written as follows:

${\vec {F}}=\operatorname {grad} \varphi +\operatorname {rot} \operatorname {rot} {\vec {A}}$. (2*)

This formula completely corresponds to transformed Navier–Stokes equations(NSE) for incompressible fluids ($\operatorname {div} {\dot {\vec {u}}}=0$)

$\rho {\vec {F}}-\operatorname {grad} p+\mu \nabla ^{2}{\dot {\vec {u}}}=\rho {\ddot {\vec {u}}}\Rightarrow \rho ({\vec {F}}-{\ddot {\vec {u}}})=\operatorname {grad} p+\operatorname {rotrot} \mu {\dot {\vec {u}}}.$ (3*)

Here,

${\vec {F}}={\vec {F}}_{1}+{\vec {F}}_{2}+\cdots$ vectors sum of a given, externally applied forces (e.g. gravity ${\vec {F}}_{1}$ , magnetic ${\vec {F}}_{2}$ and other), $p$- pressure (scalar function), ${\dot {\vec {u}}}$- velocity vector, ${\ddot {\vec {u}}}=d{\dot {\vec {u}}}/dt$ - acceleration vector, $\rho$ - density (const), $\mu$ - viscosity (const), $\nabla ^{2}$ - Laplace operator.

Equations (3) and (2) are consistent. Hence there is no reason to say that the theory requiring (2) must be false. As we can see from NSE the sum - $\operatorname {grad} p+\mu \nabla ^{2}{\dot {\vec {u}}}=-(\operatorname {grad} p+\operatorname {rotrot} \mu {\dot {\vec {u}}})$ forms the vector field.

Note that we will receive the formula (2) also after similar transformation of the Navier–Stokes for a compressible fluid and after transformation of the Lame equations for an elastic media.

From this brief note follows that Helmholtz decomposition is wrong and demands major revision. This follows from comparison of two articles in Wikipedia (http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations and http://en.wikipedia.org/wiki/Helmholtz_decomposition ).

Therefore let's try to formulate the text for editing of this article: http://en.wikipedia.org/wiki/Helmholtz_decomposition .

1.B. A.; Fomenko, A. T.; Novikov, Sergeĭ Petrovich (1992). Modern Geometry--methods and Applications: The geometry of surfaces, transformation groups, and fields] (2nd ed.) . Springer. (p. 15).ISBN 0387976639.

--Alexandr (talk) 18:35, 7 February 2012 (UTC)

Do you have counterexamples to Wiles' proof of Fermat's last theorem, too? Tkuvho (talk) 18:49, 7 February 2012 (UTC)

To Continuum-paradoxes: Your argument against the Helmholtz decomposition assumes that the decomposition must be invariant under coordinate transformations. However, the decomposition theorem does not claim that the decomposition is so invariant. So your argument fails.

In any case, you must provide a reliable secondary source for any such "fact" which you wish to include in Wikipedia. Your original research is not acceptable. See WP:NOR. JRSpriggs (talk) 07:39, 8 February 2012 (UTC)

On one hand, Alexandr is right (and should not be asked for "counterexamples to Wiles' proof of Fermat's last theorem, too"). The gradient of a function is a covector rather than vector, of course. On the other hand, working in a Euclidean (rather than just linear) space it is possible, and quite usual, to treat its dual space as (another copy of) the same space (see Linear functional#Dual vectors and bilinear forms). Or, in terms of transformations (if you prefer this old language): only orthogonal transformations are relevant. Boris Tsirelson (talk) 08:52, 8 February 2012 (UTC)

Fomenko et al is certainly a standard reference. This is all the more reason that I find their discussion of gradients bizarre in the extreme. The exterior derivative df is the usual notation and terminology for the associated covector. The gradient of a function is almost always taken to be the vector, exploiting the usual identifications as mentioned by Boris. I don't think we need to relate to Fomenko's odd choice of terminology. Tkuvho (talk) 09:14, 8 February 2012 (UTC)

The vector potential in the invariant version of the Helmholtz decomposition is a pseudovector. However most sources do not make this distinction, so I don't think our article should either. If someone is bothered by it, then we can add a remark about it somewhere. Sławomir Biały (talk) 12:33, 8 February 2012 (UTC)

However Fomenko does make a distinction and if people are going to go on to deal with manifolds it seems a good idea so I think a note at the very least is called for. Personally I don't like pseudovectors as it strikes me as a kludge or not quite figured out half way to there kind of idea. Dmcq (talk) 13:13, 8 February 2012 (UTC)

On a manifold, it's the Hodge decomposition (which is invariant by design). The boundary conditions are different. Those for the Helmholtz decomposition only really make sense in Euclidean space. Sławomir Biały (talk) 13:31, 8 February 2012 (UTC)

In quantum mechanics when they have CP violated do they talk about that in terms of pseudovectors or what do they call it when things don't look the same in a mirror thanks? Dmcq (talk) 18:23, 8 February 2012 (UTC)

Chirality? Sławomir Biały (talk) 22:07, 11 February 2012 (UTC)

To Continuum-paradoxes: In my previous comment above, I should have said that the Helmholtz decomposition is invariant under the group of translations and rotations ($\mathbf {R} ^{3}\rtimes SO(3)\,$), but not under more general curvilinear coordinate transformations. In the smaller group, there is no difference between the behavior of contravariant vectors (what some call vectors) such as the rate of flow of a fluid and the behavior of covariant vectors (what some call covectors) such as the gradient of temperature, nor between ordinary vectors and axial vectors. JRSpriggs (talk) 11:26, 10 February 2012 (UTC)

It's the other way around: vectors are covariant (go in the same direction), covectors are contravariant (go in the opposite direction). Thus, you push forward a tangent vector, but pull back a differential form. Tkuvho (talk) 20:11, 11 February 2012 (UTC)

I see that the page you referenced says otherwise. There is a problem of terminology here. Tkuvho (talk) 20:14, 11 February 2012 (UTC)

It's an unfortunate abuse of language that I have at various times tried to minimize on Wikipedia: referring to vectors as "contravariant" and covectors as "covariant". What is in fact the case is that the components of a vector in a coordinate system are contravariant and those of a covector are covariant. So it is infinitely preferable to talk about whether the components of some quantity are covariant or contravariant than whether the something itself is. Sławomir Biały (talk) 22:07, 11 February 2012 (UTC)

How would that work in abstact index notation? One is no longer allowed to say whether a tensor is covariant or contravariant? Or do we only talk about covariance and contravariance of "placeholders"? Tkuvho (talk) 12:49, 12 February 2012 (UTC)

Well, it's not really meaningful to talk about covariance and contravariance of abstract tensors. The co/contravariance refers to the behavior under what physicists call passive diffeomorphisms, whereas tensors themselves are actually invariant. In an abstract index setting, I think it's common to refer to the indices themselves as covariant or contravariant. But this is also an abuse of language that should probably be minimized. Sławomir Biały (talk) 13:05, 12 February 2012 (UTC)

This is not how the term is used in category theory. See contravariant functor. Here I am using the term "category theory" in a very loose sense. This usage of "contravariant" and "covariant" has certainly "permeated the fabric of modern mathematics", to quote Carl. Tkuvho (talk) 13:28, 12 February 2012 (UTC)

Actually, it is precisely the same notion as that in category theory, provided that a vector or a covector is defined to be a functor that associates a list of numbers to a frame, where both frames and lists of numbers carry the structure of a GL(n)-torsor. But it is not the same in the category of manifolds and mappings between them. However, I much rather prefer to think of the vector as existing independently of how it is described in coordinates (that is invariant under passive diffeomorphism), so calling a vector "contravariant" because of how its components transform seems to put the cart before the horse. Sławomir Biały (talk) 13:36, 12 February 2012 (UTC)

I agree, it is best not to think of it in terms of coordinates. Thus, if you think of a differential 1-form intrinsically as an assignment of an element of T* at every point, then a diffeomorphism will result in a pullback of the differential form. Therefore differential forms are contravariant according to the definition found at contravariant functor. Tkuvho (talk) 13:41, 12 February 2012 (UTC)

Yes, I agree with this. My point is that it depends on what category you are working in. Some define a tensor as an equivariant function from the frame bundle to a representation of GL(n). The GL(n) action gives morphisms on the frame bundle, and linear maps define morphisms of the representation. From this point of view, a vector is definitely a contravariant functor. If, on the other hand, you consider a vector as a functor on a category of manifolds whose morphisms are local diffeomorphisms, then it is covariant. This is why I find it to be an abuse to call the vector itself contravariant: what we are really talking about is its representation in terms of GL(n) torsors. Sławomir Biały (talk) 13:55, 12 February 2012 (UTC)

Well, I think that you two are dealing in pointless abstractions. I am all for using coordinates and indices which represent numbers designating specific directions in spacetime (the local tangent space). In physics, they begin with equations for each component separately and only later realize that these components can be combined into something like a matrix (i.e. tensors). Thus, to my mind, a tensor is its components as a function of: the event, the choice of coordinate system, and the values of the indices. JRSpriggs (talk) 20:26, 12 February 2012 (UTC)

So, for you a vector is contravariant, period. Things are not necessarily so absolute for the rest of the world, though. It cannot hurt to insist on referring that components transform contravariantly or covariantly, accordingly. Most reliable sources do this already. Sławomir Biały (talk) 22:05, 12 February 2012 (UTC)

Dear Participants of discussion!

Many thanks for your professional comments. Please, pay attention to addition in my message (Notation 1). However I ask (if it is possible) not talk this problem outside of rectangular Cartesian co-ordinates. It can be made later (after consensus for rectangular Cartesian co-ordinates). I ask to apply only short phrase without difficultly translated words. Remember that your comments are reading all over the world by means of computer translators.

Notation 1.

The vector fields cannot be constructed out of scalar fields using the gradient operator. Therefore so-called Laplacian field is not a true vector field. Thus, the requirements $\operatorname {rot} {\dot {\vec {u}}}=0,\operatorname {div} {\dot {\vec {u}}}=0$ are inconsistent for true vector fields.

This result confirms the proof about impossibility of irrotational velocity field in this old university textbook [10]p. 100-101. 2. Other unpleasant things we can see for many well-known classical equations in Wikipedia. For example the Euler equations (fluid dynamics) can be written as follows

$-\operatorname {grad} p=\rho (\operatorname {div} {\ddot {\vec {u}}}-{\vec {F}})$

Note that such equations have no sense as exact vector equations because $\operatorname {grad} p$ is not the true vector.

Here Helmholtz_decomposition we can read: “This theorem is of great importance in electrostatics, since Maxwell's equations for the electric and magnetic fields in the static case are of exactly this type.[2]” Thus Maxwell's equations have no sense as exact vector equations. We can to continue a list of similar incorrect mathematical physics equations in Wikipedia.

--Alexandr (talk) 12:05, 14 February 2012 (UTC)

You seem to be very confused. The gradient is defined as a vector (see, for instance, Borisenko and Taparov "Vector and tensor analysis with applications"). There is no problem with the equations you have listed. Sławomir Biały (talk) 12:58, 14 February 2012 (UTC)

I see that Covariance and contravariance of vectors states that the gradient is covariant. Is this consistent with the approach you developed above? Tkuvho (talk) 13:46, 14 February 2012 (UTC)

No. That should probably be clarified somehow. It's true that the partials transform covariantly, but these are the components of the differential. The gradient involves the inverse metric tensor. Sławomir Biały (talk) 14:02, 14 February 2012 (UTC)

It may be a good idea to make a note of it at Talk:Covariance and contravariance of vectors. Tkuvho (talk) 12:33, 15 February 2012 (UTC)

It probably doesn't help matters that in applied mathematics, people talk about "covariant components" and "contravariant components" of a given vector. This could be a big source of the OPs original confusion. Sławomir Biały (talk) 12:59, 15 February 2012 (UTC)

To Sławomir Biały. I have formulated my conclusion on the basis of this university textbook; 1.B. A.; Fomenko, A. T.; Novikov, Sergeĭ Petrovich (1992). Modern Geometry--methods and Applications: The geometry of surfaces, transformation groups, and fields] (2nd ed.) . Springer. (p. 15).ISBN 0387976639. Authors of this textbook – authoritative mathematicians: http://www.mathnet.ru/php/person.phtml?&personid=8368&option_lang=eng http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=4537 http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=21899 As well known from this textbook « … under co-ordinate change the gradient of function transforms differently from a vector ». Therefore the gradient of scalar function does not form the vector field. Thus, your objections «You seem to be very confused…. » concern first of all these authors.

I can present other and newer arguments that gradient of scalar function does not form the vector field.

--Alexandr (talk) 11:38, 17 February 2012 (UTC)

You should consult other books. What Fomenko et al define is usually called the differential. The gradient is usually defined to be the vector obtained from the differential by applying the inverse metric. See for instance Definition 2.3.9 of Abraham, Marsden, Raitu "Manifolds, Tensor Analysis, and Applications". Basically any book on tensor analysis agrees with me. Look at James Simmonds "A Brief on Tensor Analysis" (Springer UTM); Arfken and Weber "Mathematical methods for physicists", Chapter 2. Even in any calculus textbook you will see the definition that the gradient of a function is the vector whose magnitude is the greatest rate of change of the function and whose direction is the direction in which that rate of change occurs. (Under this definition, the gradient will transform as a vector.) Sławomir Biały (talk) 12:11, 17 February 2012 (UTC)

The gradient is the list of the coefficients of the differential of the function. The differential is a linear form, and thus, by definition of the dual vector space, is an element of the dual of the working space. A basis of this working space being chosen, the gradient is thus the vector of the coefficients of the differential on the dual basis (the members of the dual basis are the linear forms which send a basis vector to 1 and the others to 0). This being stated, to know if the gradient is a vector field depends on which definition of a vector field you choose (the definition in vector field is ambiguous): If a vector field is a function of the working space into its associated vector space, then the gradient is not a vector field for this definition. If a vector field is a function of the working space into an arbitrary vector space, then the gradient is a vector field for this definition. Whichever definition is chosen, the metric of the working space (dotproduct) induces an isomorphism between the working vector space and its dual. But this isomorphism may not be considered as an identification. This is the reason of the distinction between vectors and covectors, which are both vectors but in different spaces. — D.Lazard (talk) 14:49, 17 February 2012 (UTC)

No, the gradient is a vector, not a covector. The differential is the covector you describe. The gradient is the vector whose inner product with another vector is the differential of the function applied to the vector. This is the definition of the gradient. It is not in the dual space. The gradient has no meaning without a metric. (See also symplectic gradient for the symplectic version of this idea.) Sławomir Biały (talk) 16:06, 17 February 2012 (UTC)

I do not agree with you. You may be right if you consider only the usage of the gradient in physics. In the study of the functions of several variables, and in particular in optimization, the gradient is defined and used independently of any metrics, like in a sentence like the gradient is null at the local extrema of a differentiable function. The covector property of the gradient is clear in the conjugate gradient method, because the direction of the minimum of a quadratic function is not the gradient but its conjugate direction. D.Lazard (talk) 16:52, 17 February 2012 (UTC)

Gradient descent is a good example of what I mean. If it makes sense to "move in the direction of the gradient" then the gradient is a vector. One cannot move in the direction of a covector. Sławomir Biały (talk) 17:14, 17 February 2012 (UTC)

Dear Participants of discussion!

The assumption “vector fields can be constructed out of scalar fields using the gradient operator and so-called Laplacian field is a true vector field” is 100 years old. This assumption have many “Strict proofs”, covered in hundreds of textbooks, and taught each year to many thousands of students. It is difficult to believe that all “Strict proofs” are wrong. Therefore has changed nothing after edition in 1979 of the textbook Modern Geometry in which it is written '« … under co-ordinate change the gradient of function transforms differently from a vector » The convincing counterexample is necessary. Such counterexample I bring to your attention. This counterexample kills mentioned “Strict proofs”. I will specify a source of this counterexample later.

Counterexample. As we well know the divergence of any vector field on Euclidean space is a scalar field. Therefore as an example let's calculate the divergence of an acceleration vector $\operatorname {div} {\ddot {\vec {u}}}$ . The acceleration vector components can be written as

${\ddot {u}}_{i}={\frac {d{\dot {u}}_{i}}{dt}}={\frac {\partial {\dot {u}}_{i}}{\partial t}}+{\dot {u}}_{x}{\frac {\partial {\dot {u}}_{i}}{\partial x}}+{\dot {u}}_{y}{\frac {\partial {\dot {u}}_{i}}{\partial y}}+{\dot {u}}_{z}{\frac {\partial {\dot {u}}_{i}}{\partial z}},(i=x,y,z)$

After taking an operator div we have

$\operatorname {div} {\ddot {\vec {u}}}={\frac {\partial {\ddot {u}}_{x}}{\partial x}}+{\frac {\partial {\ddot {u}}_{y}}{\partial y}}+{\frac {\partial {\ddot {u}}_{z}}{\partial z}}={\frac {\partial }{\partial t}}\operatorname {div} {\dot {\vec {u}}}+{\dot {u}}_{x}{\frac {\partial }{\partial x}}\operatorname {div} {\dot {\vec {u}}}+{\dot {u}}_{y}{\frac {\partial }{\partial y}}\operatorname {div} {\dot {\vec {u}}}+{\dot {u}}_{z}{\frac {\partial }{\partial z}}\operatorname {div} {\dot {\vec {u}}}+{}$

${}+\left[{\left({\frac {\partial {\dot {u}}_{x}}{\partial x}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{y}}{\partial y}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{z}}{\partial z}}\right)^{2}+2\left({{\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}+{\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}+{\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}}}\right)}\right]$ (1)

As we can see this formula can be written as

$\operatorname {div} {\ddot {\vec {u}}}={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+(\operatorname {div} {\dot {\vec {u}}})^{2}$ (2)

if and only if such equality is true

$\left({\frac {\partial {\dot {u}}_{x}}{\partial x}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{y}}{\partial y}}\right)^{2}+\left({\frac {\partial {\dot {u}}_{z}}{\partial z}}\right)^{2}+2\left({{\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}+{\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}+{\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}}}\right)=(\operatorname {div} {\dot {\vec {u}}})^{2}$ (3)

The realization of (3) require such equality:

${\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}}+{\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}+{\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}}={\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{y}}{\partial y}}+{\frac {\partial {\dot {u}}_{y}}{\partial y}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}+{\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}$ (4)

Note that equality (3) can make sense only for $\operatorname {rot} {\dot {\vec {u}}}\neq 0$ In the case $\operatorname {rot} {\dot {\vec {u}}}=0$ all terms in brackets of (3) are positive and $\operatorname {div} {\dot {\vec {u}}}=0$ is impossible. Thus the requirements $\operatorname {rot} {\dot {\vec {u}}}=0,\operatorname {div} {\dot {\vec {u}}}=0$ for vector field are inconsistent. As we well know ${\dot {\vec {u}}}=\operatorname {grad} \varphi ,_{}\nabla ^{2}\varphi =0$ , if $\operatorname {rot} {\dot {\vec {u}}}=0,\operatorname {div} {\dot {\vec {u}}}=0$. Therefore the vector fields cannot be constructed out of scalar fields using the gradient operator and so-called Laplacian field is not a true vector field.

--Alexandr (talk) 12:20, 27 February 2012 (UTC)

If this counterexample were true, it would be a counterexample to the chain rule, having nothing to do with the covariance and contravariance of vectors. Since this is clearly ridiculous, you must have made a mistake. Your error seems to be in going from (1) to (2). Sławomir Biały (talk) 13:25, 27 February 2012 (UTC)

Dear Sławomir Biały !

I hope, that your doubts will disappear after consideration of these well-known analogies which You can see in textbooks:

$\operatorname {div} {\mathbf {\vec {u}} }=\varepsilon _{\operatorname {o} }={\frac {1}{\delta V}}d(\delta V)$

$\operatorname {div} {\dot {\vec {u}}}={\dot {\varepsilon }}_{\operatorname {o} }={\frac {1}{\delta V}}{\frac {d(\delta V)}{dt}}$ (5)

Here, $\delta V$ - infinitesimal volume, $\varepsilon _{\operatorname {o} }$ - volume deformation, ${\mathbf {\vec {u}} }$ - infinitesimal displacement vector ( ${\vec {u}}$ - any displacement vector), ${\dot {\varepsilon }}_{o}$ -velocity of volume deformation. By analogy, the acceleration divergence $\operatorname {div} {\ddot {\vec {u}}}$ probably can be written as ( ${\ddot {\varepsilon }}_{\operatorname {o} }$ - acceleration of volume deformation)

$\operatorname {div} {\ddot {\vec {u}}}={\ddot {\varepsilon }}_{\operatorname {o} }={\frac {1}{\delta V}}{\frac {d^{2}(\delta V)}{dt^{2}}}$ (6)

It is only a hypothesis on the basis of obvious analogy. The acceleration of volume deformation can be transform so

${\ddot {\varepsilon }}_{o}={\frac {1}{\delta V}}{\frac {d^{2}(\delta V)}{dt^{2}}}={\frac {1}{\delta V}}{\frac {d}{dt}}\left({{\frac {\delta V}{\delta V}}{\frac {d(\delta V)}{dt}}}\right)={\frac {1}{\delta V}}{\frac {d}{dt}}\left({\delta V\operatorname {div} {\dot {\vec {u}}}}\right)=$ $={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+\operatorname {div} {\dot {\vec {u}}}{\frac {d(\delta V)}{\delta Vdt}}={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+(\operatorname {div} {\dot {\vec {u}}})^{2}$. (7)

As you can see this equality is exact. Therefore our hypothesis is correct if (4) are satisfied and, for example, such additional conditions are satisfied

${\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{y}}{\partial y}}={\frac {\partial {\dot {u}}_{x}}{\partial y}}{\frac {\partial {\dot {u}}_{y}}{\partial x}},{\frac {\partial {\dot {u}}_{x}}{\partial x}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}={\frac {\partial {\dot {u}}_{x}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial x}},{\frac {\partial {\dot {u}}_{y}}{\partial y}}{\frac {\partial {\dot {u}}_{z}}{\partial z}}={\frac {\partial {\dot {u}}_{y}}{\partial z}}{\frac {\partial {\dot {u}}_{z}}{\partial y}}$ (8)

These equalities satisfy (4). Therefore in this case formula (1) can be written as (2) also. I will specify a source of this counterexample later.

--Alexandr (talk) 17:31, 11 March 2012 (UTC)

Well, I'm seeing a few fundamental errors in this. The first one is in equation (5). But the bottom line is that even if you did have a counterexample that would turn mathematics on its head, it's offtopic for the encyclopedia. We can only report what reliable sources say (and do so in proportion to their relative weight). So, if you can get your counterexample published in a top mathematics journal, and it is discussed by mainstream vector calculus textbooks, then (and only then) can we report on it here. For better or worse, those are the rules. Sławomir Biały (talk) 20:10, 11 March 2012 (UTC)

Dear Sławomir Biały ! You have written:

1. «Well, I'm seeing a few fundamental errors in this. The first one is in equation (5)».

However equation (5) follows from comparison of the continuity equation

${\frac {1}{\rho }}{\frac {d\rho }{dt}}+\operatorname {div} {\dot {\vec {u}}}=0$ (9)

and conservation of mass law

${\frac {d(\delta m)}{dt}}={\frac {d(\rho \delta V)}{dt}}=\delta V{\frac {d\rho }{dt}}+\rho {\frac {d(\delta V)}{dt}}=0\Rightarrow {\frac {d\rho }{\rho dt}}=-{\frac {d(\delta V)}{\delta Vdt}}$ (10)

Therefore

${\frac {d(\delta V)}{\delta Vdt}}=\operatorname {div} {\dot {\vec {u}}}$

Where you see first fundamental error?

2.«But the bottom line is that even if you did have a counterexample that would turn mathematics on its head, it's offtopic for the encyclopedia…».

This problem we will discuss later.

--Alexandr (talk) 11:44, 23 March 2012 (UTC)

You haven't correctly taken a time derivative in going from the first equation in (5) to the second, or in going from the second equation of (5) to equation (6), etc. But as I said, this discussion is pointless. It's also not our job to point out errors in your calculations. But be assured, you are making errors. The way to understand these things would be to enroll in a class on vector calculus and discuss your findings with the professor. While I've already said more than is usual for me, my standard offer in evaluating such claims is $1000 (US), payable in advance, if you would like me to seriously engage your purported counterexample and identify the mistakes. Sławomir Biały (talk) 12:36, 23 March 2012 (UTC)

Much ado about differing differential vs gradient conventions. What the hell is going on? — Kallikanzarid^talk 14:32, 25 March 2012 (UTC)

Well, Alexandr above claims to have found a counterexample to the chain rule, having nothing whatsoever to do with different conventions (although he doesn't seem to realize this). Sławomir Biały (talk) 18:26, 25 March 2012 (UTC)

Dear Sławomir Biały !

Thanks for your comments!

1.“You haven't correctly taken a time derivative in going from the first equation in (5) to the second” The going from first equation in (5) to the second carried out differently. I wrote above ${\mathbf {\vec {u}} }$ - infinitesimal displacement vector ( ${\vec {u}}$ - any displacement vector). As you can see we have different vectors. Therefore the time derivative is pointless.

2.“or in going from the second equation of (5) to equation (6)”

The second equation of (5) and equation (6) obtained independently.

However this discussion is from other field (continuum mechanics).

Very important comment:

“Alexandr above claims to have found a counterexample to the chain rule”

The velocity vector of Cartesian 3-space ${\dot {\vec {u}}}={\dot {\vec {u}}}(x,y,z,t)$ for a fix time $t={\bar {t}}$ can be represented as ${\dot {\vec {u}}}={\dot {\vec {u}}}(\varsigma )$ , $\varsigma =\varsigma (x,y,z)$ . This representation is well known as a vector function of scalar argument (or vector-valued function). Then according to chain rule [Vygodsky M.J. (1977) Manual on Higher Mathematics (12th edition). http://eqworld.ipmnet.ru/ru/library/books/Vygodskij1977ru.djvu (Russian). ASIN: B001U5VF9O (English)]

${\frac {\partial {\dot {\vec {u}}}}{\partial x_{i}}}={\frac {\partial {\dot {\vec {u}}}}{\partial \varsigma }}{\frac {\partial \varsigma }{\partial x_{i}}},(x_{i}=x,y,z)$ . (11)

Formulas (11) can be written explicitly concerning ${\frac {\partial {\dot {\vec {u}}}}{\partial \varsigma }}$. Therefore this common factor can be eliminated. As a result we have

${\frac {\partial {\dot {\vec {u}}}}{\partial x_{i}}}={\frac {\partial {\dot {\vec {u}}}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}}$ (12)

In component form formulas (12) look like

${\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}={\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}},{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}={\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}},{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}={\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}{\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}}$ (13)

Relations (13) can be written explicitly concerning ${\frac {\frac {\partial \varsigma }{\partial x_{i}}}{\frac {\partial \varsigma }{\partial x_{j}}}}$. Therefore this common factor can be eliminated. Thus

${\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}={\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}},_{}{\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}={\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}},_{}{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}={\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}$ .

We have the same result (8) !!!!!!!!! As we can see our conjecture about (8) is true. This conjecture has appeared after such transformation of counterexample (1)

$\operatorname {div} {\ddot {\vec {u}}}={\frac {d}{dt}}\operatorname {div} {\dot {\vec {u}}}+(\operatorname {div} {\dot {\vec {u}}})^{2}-$ $-2\left[{\left({{\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}-{\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}}\right)+\left({{\frac {\partial {\dot {u}}_{x}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}-{\frac {\partial {\dot {u}}_{x}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}}\right)+\left({{\frac {\partial {\dot {u}}_{y}}{\partial x_{i}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{j}}}-{\frac {\partial {\dot {u}}_{y}}{\partial x_{j}}}{\frac {\partial {\dot {u}}_{z}}{\partial x_{i}}}}\right)}\right]$ (14)

--Alexandr (talk) 19:31, 10 April 2012 (UTC)

Tau (2π)

What do folks here think about the article Tau (2π)? Recall the AfD last year. In that AfD, the sources presented were news items in the mainstream press. Consensus seemed to be that an article could be spun out from those sources. But now I'm concerned that many of the works cited in that article are not reliable, but rather various wacky "manifestos" pushing the τ concept. Furthermore, parts of the article are not cited at all. What should be done? Sławomir Biały (talk) 11:46, 13 March 2012 (UTC)

If it is an article about the number, then it should be moved to 2π (mathematical constant) because this name is the most recognizable and at least not more ambiguous than "Tau". Also, because this τ-notation is much less known than the π-notation, all formulas should be presented in two ways: with "τ" and with "2π". Incnis Mrsi (talk) 12:08, 13 March 2012 (UTC)

If the use of the "new number" cannot be sourced in reliable publications, the page should go to AfD. Tkuvho (talk) 13:45, 13 March 2012 (UTC)

I propose to rename the page Tau (2π) against pi (π) debate and to insert at the beginning of the lead something like "The constant π = 3,14159... is widely used in many scientific and engineering areas, including mathematics, physics, astronomy, electrical engineering, signal processing, ... It has been proposed to replace π by τ = 2π and a debate has followed, in which none of the international scientific organizations has been involved and which has not been echoed in any major scientific publication. This page presents the rationales which have been developed in this debate". Per wp:BRD, I'll do these changes immediately. This is not incompatible with AfD. D.Lazard (talk) 14:00, 13 March 2012 (UTC)

P.S.: I have modified the lead, but I am unable to move to a title containing Greek letters. Thus it is moved to Tau against pi debate. D.Lazard (talk) 14:34, 13 March 2012 (UTC)

Instead of wasting time with an AfD, I suggest we simply redirect this to pi and include a brief note there that at least one person supports replacing pi by tau=2π. Tkuvho (talk) 15:59, 13 March 2012 (UTC)

What "new number"? What "replacing π by"? There is a lot of sources about the "2π" constant and its importance (for example, as a conversion factor from turn (geometry) to radian). These are less sources which propose a special symbol for this constant. But if one tried to compose an article focused on these proposals, he would have to write about the number, eh? So, it will be either an article about the number or not an article. I repeat: the article has to be moved just to 2π (mathematical constant), without mentioning of any controversies in the title (because "2π" is recognizable, but "Tau against pi debate" is not). Mentioning this τ-notation in the article itself, as well as links from "τ" and "turn (geometry)" will be enough. Incnis Mrsi (talk) 08:30, 14 March 2012 (UTC)

Some pretty good arguments have been put forward for tau and the subject did gain international press. Hence an AfD is ridiculous, the proposed "debate" title doesn't cover the article and the attempt to shove it down various users throats has been thwarted (no consensus). The subject was allready deemed notable and WP:NPOV demands we give it a fair treatment instead of trying to bury it in another article. Hence I strongly oppose the suggestions made here. Kleuske (talk) 10:09, 14 March 2012 (UTC)

The symbol τ isn't used in favor of 2π in any scientific sources. What do the news items actually say about it? That's what the article should be based on. Sławomir Biały (talk) 10:37, 14 March 2012 (UTC)

Yeah, here's some wacky college called MIT – and who's ever heard of them – that apparently considered tau notable enough to center their new student admissions announcements around it. Yes, tau is very new. Extremely new. So consider how remarkable it is that a year and a half after it first appeared, that MIT did this. How about a little patience here, instead of destroying people's work? If you're wrong, you'll just have to recreate the page, and soon. If you're right that tau isn't going to go anywhere, you'll get your chance to kill off the page soon enough. Joseph Lindenberg (talk) 11:04, 14 March 2012 (UTC)

I'm not sure if your being serious about that MIT link, but there is no way that can be used as a scholarly reliable source in an encyclopedia article. Sławomir Biały (talk) 11:14, 14 March 2012 (UTC)

No, I'm not suggesting citing it in the article. But it should make you ask yourself if you aren't being hasty, given that this article already exists. Ask yourself what conversations must be going on at MIT for them to use something like that. Given that creating the article was OK'd less than a year ago, I don't see why today on Pi Day, you're suddenly determined to kill it. Joseph Lindenberg (talk) 11:53, 14 March 2012 (UTC)

I've cleared out at least the most blatant original research at that article. There is more, but it is going to require looking at sources. However, there seems to be a complete lack of reliable sources on this subject. I'm looking at the AfD debate, and there were a few news items mentioning tau, but pretty thin on details. Here are the "reliable" sources mentioned at the AfD: [11], [12], [13], broadcast, article,

• • Eoin O'Carroll (March 14, 2011). "Pi Day: Why we celebrate 3.14..." The Christian Science Monitor.
  • Elizabeth Landau (March 14, 2011). "La constante matemática pi tiene un rival: tau" (in Spanish). CNN México.
  • Michiel Hendryckx (June 30, 2011). "Weg met 3,14159265... ?". De Standaard (in Dutch).
  • Jacob Aron (January 8, 2011). "Michael Hartl: It's time to kill off pi". The New Scientist. 209 (2794): 23. doi:10.1016/S0262-4079(11)60036-5.

I've looked through most of these, and it really doesn't seem like enough to base an article on. The only other reliably published source is Palais's op-ed in the Math Intelligencer http://www.math.utah.edu/%7Epalais/pi.pdf (and I think op-eds can only be used as primary sources for the opinions of their authors). If there really is nothing else, then this will be a very short article indeed. Sławomir Biały (talk) 11:11, 14 March 2012 (UTC)

AFAIK there's no requirement that sources be "scholarly", just reliable. If there is such a requirement, we can delete quite a lot of articles, thus making maintaining the encyclopedia a lot easier. So please, where do i find that guideline? Kleuske (talk) 11:29, 14 March 2012 (UTC)

Did I make that argument anywhere? Or are you just creating a straw-man? Please, just find any reliable sources for the subject. What the article will look like should be dictated by those. Sławomir Biały (talk) 11:40, 14 March 2012 (UTC)

P.S. I could have made that argument, and been on solid footing per WP:SCHOLARSHIP and WP:NEWSORG. While there is no absolute requirement that sources be scholarly, on scientific subjects they should be. If the article is about the constant, then scholarly sources are needed. If it's just about the cultural phenomenon, then news items might pass muster. But the article simply can't use news items to justify its existence (as a piece about the cultural phenomenon) only then to document the purported "scientific" notion (sourced to various blogs, etc.). That's original research. Sławomir Biały (talk) 11:48, 14 March 2012 (UTC)

The idea of basing such an article on a "cultural phenomenon" is interesting, but since we are discussing this at WPM, the discussion needs to focus on its scientific merits. Regardless of an outcome of a future AfD, we should be able to reach a consensus whether such an article can stand as a scientific piece. If we agree that it can't, this does not necessarily predetermine the outcome of an AfD, but it does clarify this particular issue. Tkuvho (talk) 11:54, 14 March 2012 (UTC)

It's clear that there is no merit for a scientific article on the subject, given the lack of scientific sources. The only reliable sources are various fluff news items about "tau day" and suchlike, documenting a cultural phenomenon rather than a legitimate scientific debate. The article needs to be rewritten based on those sources. Sławomir Biały (talk) 11:59, 14 March 2012 (UTC)

This is clear to the two of us, but other editors seem to have expressed themselves otherwise. Do we all agree that there is no meric for a mathematical/scientific piece? Tkuvho (talk) 12:04, 14 March 2012 (UTC)

After looking at the available reliable sources, they seem for the most part to be about "tau day", rather than documenting the constant itself or any supposed debate about it in a serious way. Any thoughts about rewriting the article to be about tau day instead from these sources, and then moving it to tau day? Sławomir Biały (talk) 12:07, 14 March 2012 (UTC)

You're going to have an article about Tau Day but no article about tau? Joseph Lindenberg (talk) 12:14, 14 March 2012 (UTC)

If there is a consensus that we are talking about a cultural rather than scientific phenomenon, then tau day may be more appropriate. Tkuvho (talk) 12:17, 14 March 2012 (UTC)

A day in honor of the number that shall not be named. Uh huh. Joseph Lindenberg (talk) 12:24, 14 March 2012 (UTC)

I appreciate your sense of humor. Note however what while we don't have an article on dry, we do have one on dry humor. Tkuvho (talk) 12:42, 14 March 2012 (UTC)

Yeah, encyclopedias don't usually have many articles about adjectives. Nouns, on the other hand... Joseph Lindenberg (talk) 13:02, 14 March 2012 (UTC)

There seem to be reliable sources about the day, but not the constant. So, yeah. Sławomir Biały (talk) 12:28, 14 March 2012 (UTC)

In [[Talk: Tau (2π)], I have started a discussion to move to tau versus pi debate. It seems a better title for the cultural phenomenon. D.Lazard (talk) 12:34, 14 March 2012 (UTC)

Can't wait to see what MIT and its applicants think of Wikipedia when at 6:28 pm today, they discover tau no longer exists. If tau doesn't exist, "tau time" doesn't exist, so I guess all those applicants to MIT will just never find out if they got in. Yeah, I'm making jokes, and I know the opinions of the smartest high school seniors in the country aren't relevant here, but if you read through the comments, there's an awful lot of support for tau. It's one thing to delay allowing an article to be created. Removing one on a subject that's gotten this popular this fast and is accelerating, well... Tell ya what. Try something. Go to google and type "pi is". Just "pi is". See what the first autocomplete choice is. Joseph Lindenberg (talk) 12:53, 14 March 2012 (UTC)

Do you really think that an humoristic blog is the official position of MIT? D.Lazard (talk) 13:00, 14 March 2012 (UTC)

Do you think MIT takes its reputation so lightly that they'd email that out to every single applying freshman and their parents, and actually alter the time when they post the notices online, if there were just one or two crackpots in the basement of the math building who supported tau? Would the Dean of Admissions approve being portrayed as appeasing a few crackpots? Or do they realize this could be taking off quickly, and it would be best for MIT's reputation to get on early, even if only half-way. I realize it isn't an official statement of MIT's position. But they're moving in the opposite direction of what you're proposing. Joseph Lindenberg (talk) 13:28, 14 March 2012 (UTC)

Then your second to last sentence is an admission of the uselessness of that page. Let's pretend for a moment that the opinions of one well-reputed school should influence WP. Under that assumption, we have to remember that even the "smartest" people are allowed to have some silly opinion that you should pay no heed to (one example, Jeremy Silman: excellent chess author, and also a proponent of astrology.) These sort of opinions are especially endemic to young people, who can get overexcited about things they perceive as new. MIT, is of course interested in getting young people excited so naturally this sort of thing makes a good impression on students. Rschwieb (talk) 13:39, 14 March 2012 (UTC)

I dont see what relevance the MIT comic has to the continued discussion. It has already been agreed that it is not a reliable source. Sławomir Biały (talk) 13:44, 14 March 2012 (UTC)

My point is it's a clear indication of the growing legitimacy of tau. Again, I'm not saying to cite it in an article, but maybe you should postpone this action. Joseph Lindenberg (talk) 14:12, 14 March 2012 (UTC)

Do you really think the Dean of Admissions at MIT would allow himself to be portrayed as supporting astrology? Has MIT ever said they changed their notification date because it was a bad day astrologically? Showing him wearing cut-off suit pants and skateboarding is how they appealed to the young people. Their parents won't see any harm in that. But if you're paying $40,000 tuition to send your kid there for a first-class sci/tech/math education, you're not going to want to see anything that even looks like them endorsing crackpot science/math. And MIT knows it. And MIT employs public relations experts to make sure that never happens. That cartoon wasn't just some random doodling by a secretary who then sent it out for giggles. That kind of thing gets scrutinized very carefully before being sent out. There's a lot of money at stake in their reputation. Joseph Lindenberg (talk) 14:07, 14 March 2012 (UTC)

I am not sure about "random doodling for giggles" but I think is is possible that questionable material would be used in such a situation to "liven up" a presentation so as to attract, as you put it, the $40,000 etc. Tkuvho (talk) 14:21, 14 March 2012 (UTC)

These seem to be blogs by various alumni. They in no way represent anything approaching an official position of the university (or the dean of admissions for that matter). Sławomir Biały (talk) 14:25, 14 March 2012 (UTC)

Uh, no. That was the official email sent out to all applicants notifying them when the decision would be posted. An individual alumnus couldn't change the time MIT posts those decisions to 6:28pm. Joseph Lindenberg (talk) 14:33, 14 March 2012 (UTC)

Oh, if you're saying that because at mitadmissions.org it says for more information, see this guest blog entry, that's a joke. The supposed guest is Sir Nigel Blogberry. He's based on Sir Nigel Archibald Thornberry, who was apparently a kids' TV character when these applicants were kids. You can be sure MIT had to pay for the rights to use it. Like I said, this wasn't some casually put together thing. Joseph Lindenberg (talk) 14:45, 14 March 2012 (UTC)

Because the thing that marketers know attracts teenage kids most isn't sex, alcohol, sports, or gee-whiz technology. It's multiplying a math constant by 2. Joseph Lindenberg (talk) 14:28, 14 March 2012 (UTC)

I just checked the "contributions" of User:Joseph Lindenberg. They started last summer, number in the hundreds, and focus exclusively on the Tau article. Under the circumstances, it is unlikely we will be able to change User:Joseph Lindenberg's mind about the usefulness of the page. I do want to encourage User:Joseph Lindenberg to diversify his contributions to wiki. Tkuvho (talk) 14:46, 14 March 2012 (UTC)

Thanks for the info: that explains a lot. Rschwieb (talk) 16:02, 14 March 2012 (UTC)

yeah... It's also ad hominem _and_ you still have to convince the creator of the article. To wit, yours truly. Wanna have a look at *my* track record? (hint, check three language projects) Kleuske (talk) 17:26, 18 March 2012 (UTC)

Kleuske, I'm not keeping track of who is taking what position here (and really I'm not even sure what's in dispute), but no, no one has to "convince the creator of the article", not in principle anyway. I don't want to come across too aggressive on that, because we strive for collegiality, but having started an article does not give you any special privileges with regard to it. See WP:OWN. There are arguably some limited exceptions regarding things like variety of English used (see WP:RETAIN), and maybe some similar issues like citation style, basically things that don't affect the article much but that people get exercised about anyway. --Trovatore (talk) 20:05, 18 March 2012 (UTC)

Varieties of English and such things are not what i'm concerned about and i know about WP:OWN. Nevertheless, the project is based on concensus, which is absent. Given the date on which the assault on the article was launched (pi-day), i cannot help suspecting a lot of WP:POINT in the debate. Kleuske (talk) 20:29, 18 March 2012 (UTC)

If you want a consensus, you should avoid words like assault, cease to "suspect a lot" other editors and to qualify their edits of "madness". The point is that the previous version of the article was mainly WP:OR and that it did not respected the rules WP:undue and WP:GEVAL. In particular, I read in WP:undue: "If a viewpoint is held by an extremely small (or vastly limited) minority, it does not belong in Wikipedia regardless of whether it is true or not and regardless of whether you can prove it or not, except perhaps in some ancillary article. Keep in mind that, in determining proper weight, we consider a viewpoint's prevalence in reliable sources, not its prevalence among Wikipedia editors or the general public." As there is no reliable source supporting tau against pi, this not only justifies the new version of the article but would be a valid reason to delete it. D.Lazard (talk) 21:28, 18 March 2012 (UTC)

I honestly don't understand the argument about reliable sources that's been raised time and again in this debate. While many of the documents referred in the article are indeed in the form of manifestoes, videos, web pages, and such, I believe that we can agree that they do come from fairly established mathematicians and educators. I don't think it's fair to call them unreliable. You might argue about them being primary sources, but for that there is also plenty of third-party coverage of the Tau concept. I think that the severe amputation that has been done to the article was a disservice to Wikipedia, and the insistence on deletion even more so. --Waldir ^talk 19:30, 19 March 2012 (UTC)

@Waldir: No "established mathematicians" have used tau in their work (beyond the manifestos and youtubes), contrary to your claim. Your comments are therefore WP:POV. Tkuvho (talk) 08:57, 23 March 2012 (UTC)

Merge proposal

I am planning to merge tau (2π) into turn (geometry) since the tau article is a WP:POVFORK of the turn article. Any thoughts on this? Sławomir Biały (talk) 10:51, 22 March 2012 (UTC)

This could be done. But, at talk:tau (2π), there is a move request for renaming the page "The tau movement". The two proposals seem to be not compatible. IMO the discussion of Sławomir's merge proposal should be delayed after the closing of the move request. D.Lazard (talk) 11:07, 22 March 2012 (UTC)

That move proposal seems to be dead on arrival. In any event, as I said, we need to get clarity on what the article is actually about. If it's about the mathematical constant, then it should be merged to turn (geometry), because in that case these articles are about the same thing. If it's about the "movement" (a dubious term for a couple of random dudes who think a turn should be given the symbol τ), then the question is whether that movement is notable enough for its own article. I would say "no". There seems to be a lack of serious sources that address the so-called "movement". Press coverage about "tau day" could be used in an article about tau day (perhaps), but these human-interest stories are clearly insufficient to document any kind of "movement". Sławomir Biały (talk) 11:15, 22 March 2012 (UTC)

The move proposal has the great advantage to separate clearly the math questions from the non math one. If the move is done, keeping or deleting the article will be only a question of the real existence of such a movement and of the notability of tau supporters, and the debate will not be polluted by opinions on the math constants. If the move is rejected, I support the merge. However, merging now will induce to mix math and non math questions in the discussion and, probably, prevent a clear conclusion of the discussion. D.Lazard (talk) 12:16, 22 March 2012 (UTC)

Just a caution: though I agree that the "tau movement" is not notable, and possibly even that "tau" is also not notable enough to justify an article of its own, there is a gulf of semantic (and probably formal) difference between the constant tau and the geometric concept "turn" (or cycle, revolution or whatever), notwithstanding their connection/relationship in the geometric context when choosing the (very natural, but not inevitable) units of radians. The suggested merge therefore seems inappropriate; I would have thought a merge of tau (2π) as a section in the article pi would have been more appropriate (possibly not stressing the symbol τ, but rather that 2π is natural and is more prevalent constant than π is). Imagine the reaction of mathematicians to renaming the article pi to halfcycle. — Quondum^☏✎ 12:38, 22 March 2012 (UTC)

Whatever your belief about the meaning of "turn" in geometry, the article turn (geometry) is about the constant 2π. We should not have two articles about the same constant. We can debate what the final target should be, e.g., 2π. But it's clear that these articles should get merged. Sławomir Biały (talk) 12:43, 22 March 2012 (UTC)

I which case a merge may be appropriate, but definitely not under the disambiguator "(geometry)", and not under a geometric term such as "turn". A merge of both to something like tau (mathematical constant) would then make sense if you do not think they should both be merged into pi. — Quondum^☏✎ 12:49, 22 March 2012 (UTC)

I agree that the names are bad. But I think tau (mathematical constant) emphasizes a fairly uncommon usage of the symbol τ in mathematics (see Talk: tau (2π) for discussion on this very point). I think twice pi would be the most common and NPOV article title. Sławomir Biały (talk) 12:51, 22 March 2012 (UTC)

On the contrary, I believe that is a reason to make sure the article turn (geometry) is about the geometric concept, and tau (2π) is about the number. If the contents of "turn (geometry)" currently focus on the constant 2π, that needs to be fixed (and relevant content moved to "tau (2π)"). --Waldir ^talk 14:50, 22 March 2012 (UTC)

This tau-madness continues for some reason incogitable to me. Turn (geometry) is a unit of angle, and 2π is a number. Who does not understand the difference? If one suppose that 2π is the same as turn, then 1 is the same as radian and π/2 is the same as right angle, isn't it a crap? There is only one natural topic for an article, the number 2π, but Sławomir Biały invents some unnatural things for more than a week. Incnis Mrsi (talk) 12:55, 22 March 2012 (UTC)

This is evidently an old debate and I'm new to it, so I don't want to stick my neck out, although it is clear Sławomir is not confusing terms in the post above. I will simply add my support for a name centred on the constant 2π (i.e. not tau or turn, but maybe twice pi or similar). — Quondum^☏✎ 14:15, 22 March 2012 (UTC)

I agree with Incnis Mrsi, and franky, I can't think of a better name than "tau (2π)" for the article. It's concise, precise, unambiguous and intuitive. All the proposals for merge or renaming I've seen would IMO only harm the title in one of these dimensions, and make it harder to find for those interested in the topic. I can't see any benefit in doing so. --Waldir ^talk 14:50, 22 March 2012 (UTC)

the distinction between number and geometry seems artificial. Besides, the manifesto of Palais already appears at turn (geometry). "Tau" is best redirected there. It is senseless to have two pages on the same subject. Tkuvho (talk) 15:02, 22 March 2012 (UTC)

(@Incnis Mrsi) I hadn't appreciated this distinction until you just now pointed it out. So, you suggest moving it to 2π, as has already been attempted? That seems reasonable, and would then possibly have adequate scope for an article. Sławomir Biały (talk) 15:38, 22 March 2012 (UTC)

Just like mathematicians have adopted Pi as a shorthand notation for 3.14... (which happened many years after it began being used), the proponents of 6.28... have agreed on Tau for the same reason. Since there is no opposition among proponents of 6.28... as a circle constant to the use of Tau (quite the contrary), it seems natural to use that in the title of the article just like pi does. --Waldir ^talk 15:56, 22 March 2012 (UTC)

Agreed. Everyone who doesn't call it 2π calls it tau now, including Bob Palais. Furthermore, notice something interesting in the two MIT blog posts (here and here), including the many discussion comments, and the Boston Globe article quoting MIT's Dean of Admissions. NOBODY EVER MENTIONED Michael Hartl or Bob Palais. Seriously, go and look. Tau is no longer the name proposed by Michael Hartl, etc. It's the name many people are using to refer to the number. They're not arguing over whether 6.28... should be called tau. They're arguing over whether tau should be used instead of pi in education. Even people who hate that idea are using the name tau like it's already the accepted name. Joseph Lindenberg (talk) 16:21, 22 March 2012 (UTC)

And just because something doesn't (yet) appear in math journals and textbooks doesn't mean it's not a legitimate term. Wikipedia has a page titled "fortnight". It's supposedly a unit of time, but you never see it in any physics journal or textbook. Does that mean we should AfD it, or move it to a subsection under "day"? Joseph Lindenberg (talk) 16:31, 22 March 2012 (UTC)

Joseph, you seem to be laboring under the mistaken notion that the "tau" thing is opposed by people who "hate the idea" that "tau should be used instead of pi in education". This is a conspiracy theory of yours. Please try to internalize the fact that the reason people at WPM are sceptical about the "tau revolution" is because it is not notable. Tkuvho (talk) 16:52, 22 March 2012 (UTC)

Hear, hear! Rschwieb (talk) 17:23, 22 March 2012 (UTC)

Maybe I am indeed mistaken about the motivations of some of the people involved here at Wikipedia. There are definitely people who explicitly say they "hate" the idea of switching to tau. But I increasingly realize some of the people here at Wikipedia may just be sticklers about their footnotes. I search for discussions of this topic online, and I'm constantly seeing people in favor of tau. Most just recently heard about it. I read through the comments by those MIT applicants. I read some of the 5,800 comments on Vi Hart's video, which has surpassed 800,000 views. There's a lot of evidence out there of a lot of people coming to favor tau. Unfortunately, there is a time lag before the appearance of the footnotable sources. Maybe the difference is you guys aren't watching this issue as closely as I am. That's not a criticism. I'm just trying to explain how we have such different views. But this is why I keep urging a little patience. I see something growing rapidly. Can't we table this for a few months? I have no intention of spending years defending this page if I'm wrong. Joseph Lindenberg (talk) 18:03, 22 March 2012 (UTC)

Invest some of your energy into studying WP:CRYSTAL. Tkuvho (talk) 18:23, 22 March 2012 (UTC)

You will notice that I've never written any of my predictions into the article text itself. Joseph Lindenberg (talk) 18:29, 22 March 2012 (UTC)

Thought: No! Turn is an angle. One turn or full rotation is 360 degrees, 400 gradians, 2π radians, or τ radians. Tau is not a turn. Tau is a number, the number of radians in one turn. 1/4 turn is τ/4 radians, is π/2 radians. π is a number, NOT a derived unit that means "half a turn". If Tau should redirect to turn, it follows that 360, 400, and 2π should also redirect to turn, which would be absurd. (Currently, 2π redirects to Tau (2π), as it should.) The proposed merge would be a sloppy a conflation. A876 (talk) 18:25, 22 March 2012 (UTC)

Note: Tau is interesting, and has its merits, but this section (Merge proposal) IS NOT THE PLACE TO DISCUSS that question. Please discuss it elsewhere; in fact (uncommon request), Editors: please Cut your own off-topic comments mistakenly posted here, and Paste them someplace else. A876 (talk) 18:25, 22 March 2012 (UTC)

Tkuvho and Rschwieb, if A876 is serious, you've got my permission to move the whole subtree of our discussion to tau's talk page. Joseph Lindenberg (talk) 20:26, 22 March 2012 (UTC)

I actually consider a turn to be a unit of angular measurement, just like degrees and radians are. But whether it's an angle or an angular unit, that's clearly very different from being a number. Joseph Lindenberg (talk) 18:37, 22 March 2012 (UTC)

• Oppose – the fact that there are tau radians in a turn is not a good reason to merge tau and turn, and more than you would merge 360 (number) and Turn. Dicklyon (talk) 05:52, 23 March 2012 (UTC)

RfC

I have started started an RfC. Please comment. Sławomir Biały (talk) 18:55, 25 March 2012 (UTC)

history of algebra or history of calculus?

An IP insists on adding material on the history of algebra in the history of calculus page of calculus, claiming in the latest revert that there is "no need to discuss" the addition. see here. Tkuvho (talk) 13:40, 15 March 2012 (UTC)

There's been a couple of people who stick in those the Arabs discovered everything or puffing things up to unreasonable proportions and they keep having to be pruned back, they do it to whole swathes of Wikipedia not just maths. Dmcq (talk) 13:57, 15 March 2012 (UTC)

The material being re-added may be appropriate at the history of algebra page. That's a subject of a separate discussion. But here it seems to hinge on the play on words on the term "calculus". Tkuvho (talk) 14:03, 15 March 2012 (UTC)

It may be a mistake, or confusion between "calculus" and "calculation". The IP seems to be French-speaking: he or she added a French source. Many French-speaking people make this mistake when trying to speak English, probably because en:calculus reads like latin "calculus" (="calculation" or "computation" = fr:calcul). en:calculus = fr:analyse (mathématiques) --El Caro (talk) 16:53, 15 March 2012 (UTC)

The French words for "calculation" and for "calculus" are both "calcul". RobHar (talk) 02:34, 26 March 2012 (UTC)

The two IPs involved trace back to Pakistan, using the geolocate tool. Rschwieb (talk) 22:45, 15 March 2012 (UTC)

Simple Wikipedia needs help with mathematics...

Hello all,

Simple English Wikipedia is one of the smaller Wikipedia projects; it tries to explain topics using simpler language. The big challenge there is to not sacrifice accuracy while explaining the topic at hand. Today, I extended the System of linear equations article there; I added the information that such systems are commonly represented and solved using matrices. I also added a section describing the general process of solving such systems, and links to common methods. The problem I found was that most of these (even the common ones, like Gaussian elimination or Cramer's rule) do not have articles there. We are a small community, and none of us has a background in mathematics. I am aware that there may be some concurrency between English and Simple English, and that in the minds of some people Simple English Wikipedia has a bad reputation. We would therefore look forward to any topic-specific help you could provide. --Eptalon (talk) 12:05, 24 March 2012 (UTC)

Nice article, but combining accuracy with clarity is something we struggle with in the mathematics community. Hopefully we can put our clear-speaking caps on and lend a hand, although some articles probably can never be put in simple terms. -- 202.124.73.23 (talk) 14:03, 24 March 2012 (UTC)

Merge help needed - Inertia tensor of triangle

Should Inertia tensor of triangle merge to List of moment of inertia tensors? Please comment at Talk:Inertia tensor of triangle#Merge proposal. I'd also appreciate if someone in this project could actually complete the merger (assuming the wiki community supports it, of course) since I don't know the math here. Thanks, D O N D E groovily Talk to me 12:32, 25 March 2012 (UTC)

restricted randomization

Restricted randomization has been nominated for deletion. Here's the discussion: Wikipedia:Articles_for_deletion/Restricted_randomization.

Apparently everyone has ALREADY forgotten that in 2002 probably 10% of Wikipedia articles were just copied from either the US Geographic Names Data Base or a federal agency web site on telecommunications. An article would say,

In telecommunications, the Atlantic Ocean is an ocean bounded on the east by Europe and Africa and on the west by the Americas, across which the transatlantic cable was laid.

It was crazy, but the policy was that we were to work on and improve them. Now this article is nominated for deletion only because its initial version is copied from a (non-copyrighted) federal government web site. The article needs work, but it's nowhere near as bad as lots of others that survive. Michael Hardy (talk) 17:50, 25 March 2012 (UTC)

This article is actually our only article on split-plot designs! Clearly it needs improvement. Michael Hardy (talk) 18:26, 26 March 2012 (UTC)

The question needs to be asked: why exactly is this article not considered a copyright violation? The original site [14] doesn't have a clearly visible copyright notice, but I also can't see any explicit waiver of copyright or any statement giving permission for the content to be reproduced elsewhere. (I agree that we should have an article on this topic; I just want to understand this issues fully before I comment at the deletion discussion.) Jowa fan (talk) 06:57, 27 March 2012 (UTC)

Works created by U.S. Federal Government employees (as part of their employment) cannot be copyrighted, under U.S. copyright law. No copyright, no copyvio. —David Eppstein (talk) 07:07, 27 March 2012 (UTC)

There used to be a specific template for NIST:

 This article incorporates public domain material from the National Institute of Standards and Technology

(I had the same question, a couple years ago, regarding Optimal design, for which the NIST material too closely followed Montgomery's textbook, which too closely followed Box & Draper's textbook, which too closely followed Box's article on alphabetic optimality, which too closely followed Box....)  Kiefer.Wolfowitz 07:08, 27 March 2012 (UTC)

Haha, with the internet today you can easily find many examples of what people might call plagiarism today.--Milowent • ^hasspoken 12:15, 27 March 2012 (UTC)

When you see an apparent case of plagiarism, please investigate it before deleting our text. Sometimes it is the other site plagiarizing us. For example, see Talk:Axiom of choice#Plagiarism?. JRSpriggs (talk) 13:04, 27 March 2012 (UTC)

Category:Featured articles on Mathematics Portal

As a result of this CfD discussion, 37 articles have Category:Featured articles on Mathematics Portal on their talk page. That's fine, but it is awkward how the category is stuck at the bottom of the page, where it will inevitably cause confusion to those adding comments in the last section. For example, click "edit" for the last section at Talk:Golden ratio and see that if you were adding a new comment, you should insert it above the "Category" line. Perhaps the category should be included as an option in {{Maths rating}}? Johnuniq (talk) 11:32, 27 March 2012 (UTC)

{{maths rating}} does not support portal pages; it's just for articles. But we could make a different template for these talk pages, like {{FA on Math Portal}}, that could be put at the top and which would categorize the articles. I'd be happy to do that if people want it, I think that the bare category at the bottom is indeed a problem. — Carl (CBM · talk) 15:26, 27 March 2012 (UTC)

But all the pages in Category:Featured articles on Mathematics Portal are standard articles which already have the template, an extra field would be easy enough to implement. Alternatively it is only a convention that categories need to be at the bottom of the page. It might be easier just to move these to the header.--Salix (talk): 16:35, 27 March 2012 (UTC)

I misunderstood, and thought these were portal pages. Since they're articles, I'm neutral between using the math rating template or a new one, or moving the category up (although I fear that some misguided bot will get confused in the third case and move it back to the bottom). — Carl (CBM · talk) 16:40, 27 March 2012 (UTC)

Yes bots might be a problem. I've now added a "portal" field to {{maths rating}}. Just add {{maths rating| ... | portal=true}} to place it in the category. I'm not entirely sure of the purpose of the category.--Salix (talk): 08:20, 28 March 2012 (UTC)

class="texhtml" (used by template: math)

Should we make fonts in class="texhtml" look similar to ones used by user:Nageh/mathJax? Currently an article intermixing <math> and {{math}} formatting, e.g. Quaternions and spatial rotation, looks patchy. The letter x shows an especially ugly contrast between the (default browser) "italic" and cursive fonts used in both texvc PNGs and mathJax. Incnis Mrsi (talk) 07:55, 27 March 2012 (UTC)

No. In fact, the STIX fonts, used by the MathML renderer (and supported also by the HTML/CSS renderer once MathJax is available as an official Wikipedia/MediaWiki option), match quite well with the {{math}} template font. Since even the STIX and TeX fonts have different font faces hard-coding any font values is not a good idea. However, you can always specify a custom font family using CSS code in your common.css file. Btw, I noticed a discussion on the MathJax user mailing list, suggesting that a future release may support the selection between serif and sans-serif fonts, which may address objections previously raised regarding the clash between maths fonts and surrounding text fonts. Nageh (talk) 13:55, 27 March 2012 (UTC)

I think that we should wait to see what happens with a site-wide mathjax rollout before we worry about these things. The {{math}} template is not widely used, and is mentioned but not encouraged WP:MOSMATH. Once mathjax is enabled, I expect we will be able to merge {{math}} and <math>, eliminating the issue. — Carl (CBM · talk) 15:24, 27 March 2012 (UTC)

It would be very nice to have the option to specify the fonts to MathJax, I like a strong distinction between maths and text but others find the distinction very jarring and want to be able to join both into sentences. I don't think we need worry too much about the {{math}} template, I believe that soon and at long last we will have good rendering of inline <math> and be able to phase the math template out. Dmcq (talk) 16:45, 27 March 2012 (UTC)

These reasonings of Nageh and Dmcq sound good, but have actually nothing to do with the problem: which formatting guidelines ought en.WP to follow today. For example, see the recent clash in Robinson arithmetic. CBM, probably with some followers, tries to eradicate {{math}}, arguing that pre-existing raw wiki markup is better. When MathJax finally came, there will be no consensus again on how to implement it in such cases, and conflicts will erupt yet another time. CBM and Dmcq speak about merger of {{math}} and <math> like such a decision were already taken. But when en.WP will have a good <math>, numerous compatibility problems with HTML formatting will preclude the conversion to <math> in many cases, and such a move will be not so easy as one could imagine. Incnis Mrsi (talk) 10:32, 30 March 2012 (UTC)

Unlike with {{math}} and <math>, when we have MathJax available as the default for readers, I will support using MathJax alone for both inline and displayed formulas. I find the appearance of MathJax on other sites, such as mathoverflow.net, to be perfectly acceptable, and I'm willing to live with the change to the current HTML math to get its benefits. On the other hand I don't see any strong benefits to the {{math}} template as it is currently formatted, although some disagree. In my LaTeX documents the math is not typically in a larger, different font, so that seems quite strange to me on Wikipedia. But I am not trying to eradicate {{math}}; for example if someone starts a new article they are welcome to use any style they want. — Carl (CBM · talk) 10:50, 30 March 2012 (UTC)

What means "any strong benefits"? We may dispute the comparison of {{math}} to various <math> implementation (such as unclickable PNG/texvc and client-side resource consuming MathJax), but {{math}} has at least one advantage over a raw wiki code: it explicitly labels an expression as mathematical and hence protects it from various automated and semi-automated stupid changes. Incnis Mrsi (talk) 11:05, 30 March 2012 (UTC)

I'd be happy to search for {{math}} and replace it with <math> and redo the formulae in the articles I watch when MathJax comes along so I see the math template as being a good marker that way. Dmcq (talk) 12:01, 30 March 2012 (UTC)

Original work

Dear mathematicians,

A contributor has put a theorem of his own in an article (Expander graph). He exhibits formulas that are not referenced in any academic source. Despite what he's saying, it requires much more than "routine calculations" to reach his result.

There was an interpretation mistake of one of the sources that led to a mistake in his formulas. This mistake stayed in the article during one year and a half. I did not succeed in convincing him that was the very illustration of the dangers of doing original work.

He "fixed" the formulas, but I'm still not perfectly convinced that the new version is correct. And no one can tell, since the result is not in the sources.

I also had him to remove a definition that was not in the sources (this time with success).

I would your need help to let him understand that, if something is not in the sources, it has nothing to do on wikipedia.

Discussion is here: Talk:Expander graph#"Original research" template.

Thanks in advance, --MathsPoetry (talk) 07:45, 28 March 2012 (UTC)

If the result is not published it should be swiftly removed regardless of correctness. Tkuvho (talk) 08:52, 28 March 2012 (UTC)

Ditto, and you can depend on support here if you remove questionable unsourced material and OR. Rschwieb (talk) 13:28, 28 March 2012 (UTC)

The question is whether it is indeed original research, as claimed above, or whether it is just a change of notation and routine calculations, which are allowed. I'm not sure myself, even after reading the source. -- Jitse Niesen (talk) 14:05, 28 March 2012 (UTC)

Tkuvho & Rschwieb, please have a look at the disputed paragraph; I am not sure you will retain your opinion after that. Sasha (talk) 14:28, 28 March 2012 (UTC)

I imagine what I wrote above was slightly misread, as I didn't make any comment on whether the material was OR or not. My opinion that OR should be deleted won't change. I am completely unaware if the content in dispute is OR or not, that is for someone familiar with the material to decide. Rschwieb (talk) 15:53, 28 March 2012 (UTC)

thanks for the clarification. Obviously, I agree with your opinion. Sasha (talk) 16:07, 28 March 2012 (UTC)

This seems to be a borderline case. On the face of it, it is a routine calculation, as long as you understand the different notations involved. However, the original editor did make an error that lost a factor of ${\sqrt {2}}$ (since corrected) so maybe its not quite as routine as it appears. Gandalf61 (talk) 14:38, 28 March 2012 (UTC)

There should be no question that this is not OR. MathsPoetry is obviously having a positive effect on the article, but I don't understand the particular focus on removing (rather than correcting) what is an immediate corollary of the cited work. The fact that a factor of 2 got lost in changing notations is not important at all, and putting the word "wrong" in boldface doesn't make it more so. --Joel B. Lewis (talk) 14:55, 28 March 2012 (UTC)

There are two points to it. First, I don't think it's an "immediate corrolary". I am not even sure his result is correct. Second, I don't think it's up to us to derive new corollaries from existing work.

Some background information: I'm no English speaker (sorry if my written English is suboptimal), and I am the guy who wrote the French article on expander graphs.

As a sidenote, I don't agree that losing a factor of 2 is not important: wrong math formulas have been online during one year and a half, due to that mistake.

Thanks to all for your kind advice on this. --MathsPoetry (talk) 16:25, 28 March 2012 (UTC)

I realize the subject is quite technical, so I have provided an outline of the proof of my contradictor on Talk:Expander graph#Ylloh's proof. This should enable you to judge whether it is an immediate corollary or not. I tried to make the presentation as neutral as possible, and I only did my remarks about possible problems after the demonstration. Best, --MathsPoetry (talk) 18:06, 28 March 2012 (UTC)

Apr 2012

Persistent vandalism/self-promotion of Angle trisection

Some user is repeatedly vandalizing angle trisection in an attempt to insert links to his own webpage. (He has successfully managed to get such links included on a variety of other, non-math, pages; this appears to be the only purpose of the account.) If someone with appropriate powers could do something to prevent this, it would be wonderful. --Joel B. Lewis (talk) 18:04, 29 March 2012 (UTC)

Now accompanied with legal threats: http://en.wikipedia.org/w/index.php?title=Angle_trisection&curid=91111&diff=484576133&oldid=484575649 (btw, the claim of copyright violation is obviously absurd.) --Joel B. Lewis (talk) 18:38, 29 March 2012 (UTC)

Now discussed at Wikipedia:Administrators' noticeboard/Incidents#Angle trisection, both editors blocked for a day. Could be a page to watch for further trouble,--Salix (talk): 23:02, 29 March 2012 (UTC)

Yes, please keep an eye on it -- I've agreed to leave it alone for a bit, but it seems extremely likely to me that the other user will continue to self-promote (as e.g. he continues to assert that he has a 1995 copyright on the idea of using repeated bisection to trisect an angle -- https://en.wikipedia.org/w/index.php?title=User_talk:WIKI-1-PIDEA&diff=484617642&oldid=484606285 ). --Joel B. Lewis (talk) 01:51, 30 March 2012 (UTC)

There's always someone wrong on the internet ;-) I wouldn't worry, there's enough people watch that article. Dmcq (talk) 11:51, 30 March 2012 (UTC)

The concerned editor has been indefinitely blocked, see User talk:WIKI-1-PIDEA#March 2012. — D.Lazard (talk) 10:03, 1 April 2012 (UTC)

Robin Williams (in character): "I want to bisect her angle"

The project members may be interested in the article about Robin Williams and Steve Martin at the USA's Mathematical Sciences Research Institute (MSRI), which features e.g. William's ad-libbing about a math geek wishing "I want to bisect her angle". [15] Or not.

 Kiefer.Wolfowitz 10:25, 1 April 2012 (UTC)

John Rainwater April Fools DYK: Peter Orno delayed

The pseudonymous mathematicians John Rainwater and Peter Orno were approved for the 2012 April Fools DYK in April 2011. John Rainwater's DYK should appear in a few hours. Peter Orno's DYK has been delayed.  Kiefer.Wolfowitz 10:30, 1 April 2012 (UTC)

Merge help needed - Ordered ring

I need help with math merging. There is consensus at Talk:Partially ordered ring to merge in the page Ordered ring, but I don't know the math and have no idea how to do it. I was hoping that one of your math whizzes here could do that for Wiki. Thanks, D O N D E groovily Talk to me 02:26, 4 April 2012 (UTC)

Featured picture candidate

The ceiling of the 400 year old Sheikh-Lotf-Allah mosque in Isfahan, Iran

This picture has been nominated as a featured picture here it has been pointed out that the picture has little or no encyclopaedic value in describing symmetry to the reader. I am wondering is that correct ? Some editors in the discussion don't think so. Penyulap ☏ 04:52, 4 April 2012 (UTC)

Terminology of inflexion points

In the page inflexion point it is said (in other words) that it is a point where a curve has a contact of odd order with its tangent. The name of a contact of even order higher than two is not given. In French, it is "méplat", but the article Meplat does not give this meaning. What is the correct English word?.

By the way, "flex" is frequently used instead of "inflexion point" and this is not mentioned in the article.

D.Lazard (talk) 16:22, 7 April 2012 (UTC)

Matrix multiplication

Given the importance of this article, and it hasn't really improved since last posted my own suggestions for improvement on the talk page (to which no one has responded to, or even at all since then, recently archived by myself), I intend to just re-write most of the first half of the article.

There is plenty of repetition and it just dribbles on and on. All that's really needed it the general definition and a couple of concrete examples, followed by the properties. By no means will remove anything referenced or the image already included, though the first half only has one reference, I (and surley many others) have access to loads (and if ordinary multiplication is such a trivial concept, why aren’t there more anyway??).

The "too technical" banner has been there a long time also... about time this was sorted out. F = q(E+v×B) ⇄ ∑_ic_i 23:17, 7 April 2012 (UTC)

Coons surface

Coons surface is a really messy new article. Work on it. Michael Hardy (talk) 19:55, 7 April 2012 (UTC)

I'm not knowledgable on that specific topic to re-write, but still cleaned it up and removed the clean up banner. F = q(E+v×B) ⇄ ∑_ic_i 09:23, 8 April 2012 (UTC)

Combinatorial game theory

I don't want to edit the article as it is completely outside my area of expertise, but the recently added section on Fraser Stewart's PhD thesis reads to me like a shameless (self?-)promotion of a topic of marginal importance for this introductory article. Can someone knowledgeable have a look at it?—Emil J. 17:45, 8 April 2012 (UTC)

Judging from the way it is written, it is fully dependent on ideas from the dissertation. It might well be self-promotion, as there is a Fraser Stewart on google with email ending in computing.dundee.ac.uk, and geolocate puts the IP in the UK. I'll remove the section for now on the grounds that this dissertation is not notable. Rschwieb (talk) 19:55, 8 April 2012 (UTC)

Help needed with pi article

I'm planning on nominating the pi article soon for Featured Article status. I'm looking for math-knowledgable editors to review the article for accuracy & prose quality .... just post any comments or ideas for improvement on the article's Talk page. The criteria for FA are at Wikipedia:Featured_article_criteria. Thanks in advance for any help. --Noleander (talk) 14:04, 9 April 2012 (UTC)

Group theory templates

Hi, I noticed at least two group theory templates. There is the one at Abelian group and the one at group theory. They both have their strong points. The one without the picture is easier to navigate, and I like the last two items. On the other hand, the one with the picture is pretty neat, and pretty much subsumes the one without the picture. Should we think about merging or do we just use them haphazardly? Rschwieb (talk) 18:58, 9 April 2012 (UTC)

Probably should be merged. --Noleander (talk) 19:46, 9 April 2012 (UTC)

I merged them into the template with the picture: {{Groups}}. I put the misc groups at the bottom, into a new region called "Other" ... so an editor who is an expert in groups should probably review those articles and see if they are better off in another region in the template. --Noleander (talk) 20:11, 9 April 2012 (UTC)

saccheri quadrilateral: obtuse angle

Looking for help here about Saccheri quadrilateral. :)--Nickanc (talk) 22:12, 9 April 2012 (UTC)

New WPM guideline

Recent discussions at Talk:twice pi suggest that it may be helpful to have an explicit guideline to the effect that youtube videos and yellow media reports are not considered to be reliable sources for math-related articles. Tkuvho (talk) 14:52, 2 April 2012 (UTC)

Bogus mathematical theories that nevertheless receive significant popular attention should be considered notable. Yellow media should not be considered reliable in terms of their mathematical content but should certainly be considered sufficient to establish notability, and at least somewhat reliable when it comes to statements about cultural impact. 69.195.54.191 (talk) 18:58, 8 April 2012 (UTC)

This seems misguided since the article topic in question is more notable for its cultural impact than anything else. It's like Time Cube. Fringe/minority viewpoint, popular in spurts among the media, but not insane like Time³, instead just frivolous. --Cybercobra (talk) 16:11, 2 April 2012 (UTC)

Cybercobra, you must be coherent with yourself: Half a month ago you have requested (and obtained) to revert the move of this article to "Tau against pi debate" with the reason "Significantly altering an article's topic". And now you say that the notable part of this article is the report by the news of this supposed debate. If the article topic is not about a mathematical constant but about its notability in popular culture, the article title and the two first sentences should be changed, for not mislead the reader: Presently, both asserts that the topic is a mathematical constant. D.Lazard (talk) 17:07, 2 April 2012 (UTC)

Obvious target candidate: 2π in popular culture. Sławomir Biały (talk) 21:34, 2 April 2012 (UTC)

Come on, guys, how many times are we going to keep spinning around the same issues? We need to stop conflating 2π and Tau for the sake of argument. The former is a well-sourced (mathematically speaking) concept regarding the usage of a different circle constant, and the latter is a recent proposal that received considerable adoption especially (but not exclusively) in non-mathematical circles. They are indeed inseparable as far as article content is concerned (both should be present in an article about this whole issue) but we can't discuss about the article by arguing for or against only one part of it. "2π in popular culture" would make sense if we decided to keep only the tau part (and then again wouldn't, for inexplicably keeping Tau out of the title), but again, omitting the background to the current surge of interest in 2π is just misleading and a disservice to readers. This would only make sense if the content grew so large that it would make reading the article cumbersome (case in point: Pi Day).

Regarding this proposal, I am entirely against more rule creep that attempts to define rigid boundaries and automatize the editorial process. We have enough policies and guidelines, we just need to use our common sense and be willing to consider compromise solutions. This is how Wikipedia works. Besides, Wikipedia is a general reference work, not a mathematical compendium. Nothing prevents a math-related article to include relevant non-mathematical content (see Pi#Outside the sciences for instance), which should naturally follow the appropriate proportion as agreed by editors. --Waldir ^talk 05:10, 3 April 2012 (UTC)

I agree that guidelines should not be created for the sake of having more guidelines. However, in this case we have encountered persistent misconceptions on the part of editors who think, for example, that youtube videos have weight in notability discussions. If not a guideline, perhaps we could have an extra question in the FAQ at the top of this page. Tkuvho (talk) 11:56, 3 April 2012 (UTC)

We already have the needed guidelines: WP:YOUTUBE and WP:ELNO. Nageh (talk) 12:29, 3 April 2012 (UTC)

Thanks, I did't see this. The clause about "case-by-case basis" could be clarified in the context of math pages. I think there is room for stronger opposition in the context of scientific pages. Again, having such a guideline may help us to orient well-meaning but misguided editors and save everybody time. Tkuvho (talk) 12:37, 3 April 2012 (UTC)

The other link you provided does not seem to say anything about media, tabloid or otherwise. Tkuvho (talk) 12:39, 3 April 2012 (UTC)

WP:ELPOV is also worth to be considered. D.Lazard (talk) 12:44, 3 April 2012 (UTC)

It would be nice if there were some concrete way to address the issue of "yellow media". This is not the first time this issue has arisen in science-related articles of the media running some story of dubious scientific merit, simply because some scientist somewhere had said something. My favorite example is Wikipedia:Articles for deletion/Jacob Barnett, which was picked up as a viral news story because upon posting his idiotic ramblings to YouTube, Jacob Barnett's mother contacted an MIT physicist who encouraged Barnett to continue studying math and physics. The media spun this as "Boy genius challenges all of modern physics" or other such ridiculousness. The point is, as a rule news media should not be allowed as a reliable source for this sort of thing. The news is a reliable source for news (e.g., what Russia is doing at the moment), less so for all the other stuff presented as a sideshow to the news. Sławomir Biały (talk) 12:47, 3 April 2012 (UTC)

I agree with the thrust of your comment but would like to limit it somewhat. Every now and then there are legimitate pieces on science that appear in the popular media. I would formulate an objection in terms of "tabloids" to avoid making them too sweeping. Sensationalism may be in the eye of the beholder, but when a number of WPM members behold an item of science "news that's fit to sell" and eye it with suspicion, this should be enough to block it systematically. Tkuvho (talk) 13:02, 3 April 2012 (UTC)

Note that twice pi currently has 13 (!) references to make the point that B. Palais proposed a new symbol for 2 pi, one of them a "Life of pi over" piece from the friendly Times of India. I have no previous experience with this best-selling journal but if anyone has additional evidence of it engaging in tabloid tactics to reach its best-selling status, they are invited to step forward with the information. Tkuvho (talk) 13:15, 3 April 2012 (UTC)

I propose the following addition to the FAQ at the top of this page: Question. Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues? Answer. Mathematical content of YouTube videos is often unreliable, whereas media reports are typically sensationalistic. This is why they are generally avoided. Tkuvho (talk) 14:11, 4 April 2012 (UTC)

The change proposed above was performed without any consensus in this discussion. I reverted it for now. --Waldir ^talk 09:15, 10 April 2012 (UTC)

Stacks project dump

I don't have any particular plan, but what does anyone think of dumping materials from Stacks project [16]? (Apparently, there is no Wikipedia article on the project.) On the one hand, this is the quickest way to increase our coverage of scheme theory, and even more reliable (more reliable than some random graduate student.) On the other hand, ah..., there might be an issue like quality for instance. (The project is licensed under GFDL, which is compatible with Wikipedia. I know some people like/enjoy actual writing. But I'm more interested in the ends than the means. -- Taku (talk) 12:48, 10 April 2012 (UTC)

Oh, the materials I have in mind are statements of theorems and examples. -- Taku (talk) 12:51, 10 April 2012 (UTC)

Index notation

There are several articles which explain the meaning and use of this notation:

1. Index notation
2. Tensor
3. Antisymmetric tensor
4. Einstein notation
5. Raising and lowering indices
6. Abstract index notation
7. Covariance and contravariance of vectors

yet the specialized notations of commas, semicolons, sqaure/round brackets (e.x. $A^{\alpha }{}_{,\beta },A_{\alpha ;\beta },\,A_{[\alpha \beta ]},\,A^{(\alpha \beta )}$) seem to be dispersed, so readers will have to search them out (even if linked) which is not much help. It would be convenient to add a list of all the attributes just as a summary in one place (in an obviously titled article - like abstract index notation so people will look there and its easier for editors to remember that link), then linking to all of the main articles from there.

proposed summary:

Covariant tensor Indices are lowered (subscript): $A_{\alpha \beta \gamma \cdots }$ Contravariant tensor Indices are raised (superscript): $A^{\alpha \beta \gamma \cdots }$ Mixed tensor Indices are raised and lowered: $A_{\alpha }{}^{\beta }{}_{\gamma }{}^{\delta \cdots }$ Indices can be raised and lowered using the metric tensor. Partial derivative Comma before the index of spatial variable: $A_{\alpha \beta \cdots ,\gamma }=\partial _{\gamma }A_{\alpha \beta \cdots }={\dfrac {\partial A_{\alpha \beta \cdots }}{\partial x^{\gamma }}}$ Covariant derivative Semicolon before the index of the tangent vector: $A_{\alpha \beta \delta \cdots ;\gamma }$ Symmetric part of tensor Round ( ) brackets around the number of symmetrized indices, then permutations, divided by the factorial of the number of indices in round brackets: two symmetrized indices $A_{(\alpha \beta )\gamma \cdots }={\dfrac {1}{2!}}\left(A_{\alpha \beta \gamma \cdots }+A_{\beta \alpha \gamma \cdots }\right)$ example: $A_{(\alpha }B_{\beta )\gamma }={\dfrac {1}{2!}}\left(A_{\alpha }B_{\beta \gamma }+A_{\beta }B_{\alpha \gamma }\right)$ three symmetrized indices $A_{(\alpha \beta \gamma )\delta \cdots }={\dfrac {1}{3!}}\left(A_{\alpha \beta \gamma \delta \cdots }+A_{\gamma \alpha \beta \delta \cdots }+A_{\beta \gamma \alpha \delta \cdots }+A_{\alpha \gamma \beta \delta \cdots }+A_{\gamma \beta \alpha \delta \cdots }+A_{\beta \alpha \gamma \delta \cdots }\right)$ p symmetrized indices, sum over all permutations: $A_{(\alpha _{1}\alpha _{2}\cdots \alpha _{p})\alpha _{p+1}\cdots \alpha _{q}}={\dfrac {1}{p!}}\sum _{\alpha _{1}\alpha _{2}\cdots \alpha _{p}}A_{\alpha _{1}\alpha _{2}\alpha _{3}\cdots \alpha _{p}\cdots \alpha _{q}}$ Antisymmetric part of tensor Square [ ] brackets around the number of antisymmetrized indices, simalarly two antisymmetrized indices $A_{[\alpha \beta ]\gamma \cdots }={\dfrac {1}{2!}}\left(A_{\alpha \beta \gamma \cdots }-A_{\beta \alpha \gamma \cdots }\right)$ three antisymmetrized indices $A_{[\alpha \beta \gamma ]\delta \cdots }={\dfrac {1}{3!}}\left(A_{\alpha \beta \gamma \delta \cdots }+A_{\gamma \alpha \beta \delta \cdots }+A_{\beta \gamma \alpha \delta \cdots }-A_{\alpha \gamma \beta \delta \cdots }-A_{\gamma \beta \alpha \delta \cdots }-A_{\beta \alpha \gamma \delta \cdots }\right)$ example: $F_{[\alpha \beta ,\gamma ]}={\dfrac {1}{3!}}\left(\partial _{\gamma }F_{\alpha \beta }+\partial _{\beta }F_{\gamma \alpha }+\partial _{\alpha }F_{\beta \gamma }-\partial _{\gamma }F_{\beta \alpha }-\partial _{\beta }F_{\alpha \gamma }-\partial _{\alpha }F_{\gamma \beta }\right)$ p antisymmetrized indices, sum over cyclic permutations: $A_{[\alpha _{1}\alpha _{2}\cdots \alpha _{p}]\alpha _{p+1}\cdots \alpha _{q}}={\dfrac {1}{p!}}\epsilon _{\alpha _{1}\alpha _{2}\cdots \alpha _{p}}A_{\alpha _{1}\alpha _{2}\cdots \alpha _{p}\cdots \alpha _{q}}$

Reference which includes all of these: Gravitation, MTW, 1972, p.85-86, §3.5 . If no-one objects I'll add it to the end of abstract index notation (an alternative place would be tensor but there is a section which links to abstract index notation anyway...). F = q(E+v×B) ⇄ ∑_ic_i 09:28, 10 April 2012 (UTC)

The point that such a collected summary would be useful is well-made. I would however argue against such a central summary being placed under abstract index notation, since that is a side-branch and does not cover all uses of the notation). I would suggest that such a summary should rather be placed under tensor as the more central article. — Quondum^☏ 11:32, 10 April 2012 (UTC)

I had that in another mind, so you think in tensor under the subsection Abstract index notation? F = q(E+v×B) ⇄ ∑_ic_i 11:45, 10 April 2012 (UTC)

The title of the article abstract index notation may be misleading. It is not about the index notation which uses numbers as indices. It is about a system which merely indicates which aspects of a tensor are equivalent or may be contracted with which other aspects. As such, I would avoid that article like the plague that it is. JRSpriggs (talk) 12:27, 10 April 2012 (UTC)

Well, in its own subsection titled as "summary of notation" under notation in the tensor article, or whatever. Thanks both of you for clarifying this in the right direction, I thought they were the same somehow... F = q(E+v×B) ⇄ ∑_ic_i 12:40, 10 April 2012 (UTC)

(@JRSpriggs) I don't follow you. How exactly is abstract index notation a plague? This is standard terminology in physics and differential geometry, not a misleadingly titled article. Sławomir Biały (talk) 12:41, 10 April 2012 (UTC)

I think the point has been made and agreed that abstract index notation (or even such a section heading) is unsuitable for the purpose suggested by F = q(E+v×B) ⇄ ∑ici. Speaking of this, an alternative to tensor for such a summary may be the article Einstein notation. So my suggested candidates are these two articles, and I would welcome comments. — Quondum^☏ 14:18, 10 April 2012 (UTC)

The article Einstein notation is about the summation convention (as Einstein himself introduced) and pretty much every application of it in linear algebra. The link summation convention itself redirects to there. When people read tensor equations which happen to include commas/semicolons/brackets etc, the first place they will think of is tensor and hope to find the notation there. So I'd be inclined for the previous suggestion: in the article tensor, under the section notation, and start a new subsection called "summary of index notation for tensors" (or words to that effect) and simply paste the contents of that box under the heading. =) F = q(E+v×B) ⇄ ∑_ic_i 15:43, 10 April 2012 (UTC)

Btw., the historical name is Ricci calculus , see Schouten (1924) Der Ricci-Kalkül.--LutzL (talk) 16:49, 10 April 2012 (UTC)

(ec) The article does create the impression that the phrase Einstein notation is synonymous with Einstein summation convention, but it also seems possible that it is a broader term to describe the use of superscripts, subscripts etc. to index coefficients, plus potentially all the twiddles in your proposed summary; if this is the case, the Einstein summation convention would be merely one facet thereof. I would not be surprised if this article focuses primarily on the summation convention as a result of a misconception amongst WP editors. I am having difficulty googling references that authoritatively support either view. I would appreciate input from people with experience on this point. — Quondum^☏ 16:54, 10 April 2012 (UTC)

I would like to ask a math historian about the origins of the summation convention and index convention. Tensor calculus was around before Einstein, and it wouldn't be surprising if these conventions were already in use before Einstein. Rschwieb (talk) 17:37, 10 April 2012 (UTC)

Fourier, I believe. --Matt Westwood 17:42, 10 April 2012 (UTC)

Its perfectly fine add a historical note about the notations when the time comes, but shall we add the box or not? If so where? Einstein notation would be unsuitable since that article does, and should, concentrate on the summation convention which is just one part of the index notation (and Einstien's contribution to the notation). It’s also trivial to get used to, and is without fail explicitly stated and linked "we are using the summation convention in this equation/what follows". What isn't trivial is knowing what the "punctuation" in the indices read. (Even a couple of tensor analysis books I have do not even include the index "punctuation": the theoretical physics book sourced above does, but do typical readers have access to degree-level books?).

By the way, there is another convention not included for spinors (since presumably not used for tensors): dotted indices for right-chiral spinors (no implication to include though)... F = q(E+v×B) ⇄ ∑_ic_i 18:10, 10 April 2012 (UTC)

Let us assume that the article Einstein notation is about the summation convention, and that if there is conflict with actual usage, then it is a matter of renaming that article. Then IMO the answer is simple: the summary should be in Tensor, I propose under a subsection of its own in the section Notation. The ues of each notation can later be elaborated under the following section, Operations. — Quondum^☏ 18:46, 10 April 2012 (UTC)

I said identically above... F = q(E+v×B) ⇄ ∑_ic_i 19:54, 10 April 2012 (UTC)

(Again you're repeating youself). Anyway the summary is really good, and by the look of it no one opposes the main article on tensors, so why don't you just add it? Maschen (talk) 20:05, 10 April 2012 (UTC)

The point of coming to this Wikiproject page is to discuss things for improving maths articles. Just as well I did, since everyone above has provided careful guidance (else would have just pasted it to abstract index notation by my own sore misunderstanding of that name, but waiting a little was worth it). You're right though - it'll be done now... and take discussion to the talk page there... F = q(E+v×B) ⇄ ∑_ic_i 20:15, 10 April 2012 (UTC)

Done, see here. Thanks, F = q(E+v×B) ⇄ ∑_ic_i 20:26, 10 April 2012 (UTC)

Nice work! Maschen (talk) 20:44, 10 April 2012 (UTC)

Actually, that is quite terrible (And I'm not just talking about the MOS rape going on there). It doesn't make much sense to talk about notation conventions for (covariant) derivatives in an article that is just about normal tensors, not tensor fields. (Not to mention that it suggests that this notation is universalm while it is my experience that the comma/semicolon notation is slowly going extinct, and rightly so I might add.) I will revert for now.TR 07:00, 11 April 2012 (UTC)

Thank you fantastically!! - do what the hell you like!!... For one thing: it wasn't just for covariant tensors either, and in the cited source it happens that those comma/semicolon derivatives are in those index positions, which is why it was written that way. Anyway its on you now... I tried... F = q(E+v×B) ⇄ ∑_ic_i 07:45, 11 April 2012 (UTC)

To Sławomir Biały: So called 'abstract index notation' is for people who want to use index notation (because it is by far the most convenient way to express the ideas) while still pretending that they are not using index notation to manipulate arrays of numbers but instead some abstract notion of tensors which requires the use of "$\otimes$" and such. So it allows people to do algebraic manipulations with indices, but if you dare to try to figure out what it means by substituting actual numbers, then you are violating the arbitrary rules of 'abstract index notation'. What a load of s--t. JRSpriggs (talk) 03:21, 11 April 2012 (UTC)

I'm actually not a huge fan of indices, abstract or otherwise, but your rather imperious viewpoint seems to betray a lack of basic familiarity with the notation. I'm sorry that you have this issue, but please don't try to impose it on the rest of us. Sławomir Biały (talk) 12:05, 11 April 2012 (UTC)

Potential alternative: Create an entire article dedicated to "index notation for tensors/tensor fields", and merge all notation content from

1. Index notation (leave the computer science stuff and re-direct the maths section - for an introduction)
2. Einstein notation (explain summation convention + applications)
3. Raising and lowering indices (explain + applications)
4. Symmetric tensor (explain the symmetrization notation)
5. Antisymmetric tensor (explain the antisymmetrization notation)
6. the summary above [can be expanded and integrated into new article (assuming no reverts of course)]

into it (if articles become empty, they will clearly be redirects to the new main article). For articles 4 and 5, rather than "merge" I mean "copy and paste", but give a couple of examples in more detailed explanation.

That way, when it comes to explaining a tensor equation (in physics, maths or anything else) - we just link to that one article every time and everything will be in one place for convenient reference (the article which uses whatever metric and signature is a separate link with explanation):

"For details on the summation convention and how to raise and lower indices etc.. see the article tensor notation."

and of course it will not have to be re-explained in any other article because it can be linked?... The reason for kicking up such a fuss on this particular concept is becuase it's hoped to make life easier for the typical reader is all...

On the other hand... what are the chances of people agreeing with this thought? None. (Really - no offense taken, if you have a genuinely good reason to disagree please tell). F = q(E+v×B) ⇄ ∑_ic_i 08:51, 11 April 2012 (UTC)

There is Tensor notation that could be used as a central summary (currently a redirect to Glossary of tensor theory). The name is probably too broad for the purpose, though. There is also Tensor index notation, which might be quite suitable (currently a redirect to Einstein notation, which I feel should be renamed to Einstein convention). How about using Tensor index notation for your proposal? On a side note, until an article is found for this, I feel it should remain in Tensor. — Quondum^☏ 09:15, 11 April 2012 (UTC)

I think having a separate article on tensor index notation is probably a good idea. Having a place to link to for explaining notation is good, and having all the notation gathered in one place is good as well. I would not actually merge any of the notational content from the articles mentioned above though. Having the notation explained along side the concept it is supposed to express is very useful as well. There is no reason why we shouldn't have both.TR 09:22, 11 April 2012 (UTC)

As said this is only a potential alternative which may not happen, but thanks for pointing out the better link and title. For now (in principle) the summary above in the tensor article is plenty, but user:TimothyRias has reverted twice [17] already... F = q(E+v×B) ⇄ ∑_ic_i 09:20, 11 April 2012 (UTC)

The section is very much misplaced in the tensor article, because it discusses notation that is specific to tensor fields, which are not discussed in that article. This is why I reverted the addition there. The idea of adding this section to the tensor article is a red herring.TR 09:27, 11 April 2012 (UTC)

I do not see any major problem with such articles, as the topic itself is quite confusing and (some time ago) even controversial. But I see a minor problem, that the tensor article does not explain the hierarchy of notations, i.e. which notation is related to which and how exactly. I think, WP ought to explain the following points:

• "Abstract index notation" and "Penrose graphical notation" are two inherently invariant notations suitable for tensors of arbitrary ranks;
• "Einstein notation" is essentially the same as "abstract index notation" with the metric tensor, although there may be some minor differences and application semantics in Einstein notation;
• The simple "index notation" may be considered as a low-level translation of the abstract index notation for finite-dimensional spaces, but it is not inherently invariant;
• Covariance and contravariance of vectors is a matter of semantics, not of notation;
• dx_k (also written as dx^k for compatibility with EN/AIN) and ∂ ∕ ∂x_k is yet another notation suitable for tensor fields, its semantics relies on differential geometry, but it is syntactically compatible with EN/AIN and index notation;
• Differential forms are antisymmetric (0, k)-tensors;
• The common algebraic notation of vectors and operators (as well as quite similar bra-ket notation) is virtually another tensor notation, but restricted to (1, 0), (1, 1) and possibly (0, 1)-tensors. It is inherently invariant, like AIN and PGN.

Incnis Mrsi (talk) 09:29, 11 April 2012 (UTC)

Well, I didn't imply symmetric and antisymmetric tensor should be merged and pulled into new articles fully, but if we didn't merge Index notation, Einstein notation, Raising and lowering indices they would then be redundant. Also - the Einstein notation article really should be trimmed down, its too long for what it actually is ("set two indices equal - then sum over these components?" too much repetition of vector representations). The main statement and a few examples (like vector calculus operations given in less prose) would be plenty.

Given that Quondum suggested to rename as Einstein convention, why not:

• just shorten the content there (at least slightly), then with out merging anything for now:
• copy and paste Raising and lowering indices and the summary into it
• amalgamate everything into one article,
• rename as tensor index notation (removing double redirects).

Then we can decide on whether to leave alone or blank + redirect the pasted articles. F = q(E+v×B) ⇄ ∑_ic_i 09:44, 11 April 2012 (UTC)

Note that there are many links bound to "raising and lowering indices" and probably it should exist even more such links, because this is a concrete operation: contraction with the metric tensor. I do not think that the article should be merged to another article. But I see a problem with index notation: IMHO a dab page should exist there, not an article. What now constitutes "index notation" may be moved to tensor index notation (I could eliminate that redirect) and rewritten, to preserve the edit history. Incnis Mrsi (talk) 10:15, 11 April 2012 (UTC)

Forgot to mention, by all means we can include Incnis Mrsi's suggestion. For now I'll begin reducing bits of Einstein notation. F = q(E+v×B) ⇄ ∑_ic_i 10:14, 11 April 2012 (UTC)

Also, it has been suggested that content from articles like antisymmetric tensor and symmetric tensor be merged out somewhere else. I think this is a bad idea as well. I think things should basically be kept where they are (modulo Incnis Mrsi's suggestion). If someone wants to add something to an article like index notation, that sounds fine, but not at the expense of other articles. Sławomir Biały (talk) 10:28, 11 April 2012 (UTC)

(ec)I am not sure about renaming Einstein notation to tensor index notation. The Einstein summation convention is just that the convention to leave out the summation symbol for repeated indices. By itself this convention is quite notable, and warrants its own article. (I agree however that the current article may be a bit long.)

I am also not entirely convinced that merging Raising and lowering indices into a general article about notation is the best idea. "Raising (or lowering) an index" is more than just notation, it is an operation that changes the type of a tensor. Again I agree that the current Raising and lowering indices article is not very good, and I see why you would want to do something with it. But I think that merging it into the notation article may lead to the misleading suggestion that Raising an index is just a notational thing, rather than a mathematically meaning full operation (this is a form of duality). TR 10:31, 11 April 2012 (UTC)

I think the suggestion is (optionally) renaming to Einstein notation to Einstein convention which seems not to be contradicted by what you (T) are saying, and to replace the link at Tensor index notation with a short article including the notation summary under contention. I agree that Raising and lowering indices should remain its own article (as you say, it is not a notation), though mention thereof is appropriate in the notation article for understanding the notation with differing index positions for the same symbol. — Quondum^☏ 10:52, 11 April 2012 (UTC)

I may have misunderstood. But which article is F=q(E+v^B) talking about then when he suggests "rename as tensor index notation (removing double redirects)"? Since tensor index notation currently redirects to Einstein notation, I assumed he was suggesting to rework the Einstein notation article and rename it tensor index notation. TR 11:31, 11 April 2012 (UTC)

About double redirects, I don't know. Just in case any appear is what I must have been thinking.

Approx 6000 bytes of repetition has been cut from Einstein notation. Still tweaking now, but is everyone OK with the new state of the article? Will anyone revert back? Anything you think was good that I removed and should be added back? etc... (as said above, I'll not move/merge at this stage, or ever actually...)

If no-one would like to merge, then is there going to be a new article just on tensor index notation or not? I can't tell from above. Can understand that you would rename Einstein notation, and not merge anything leaving the articles where they are, but there seems to be nothing against (or a descision for) copying and amalgamating into a new article... F = q(E+v×B) ⇄ ∑_ic_i 11:32, 11 April 2012 (UTC)

I really don't understand what is being proposed at all. Here is what I suggest:

1. Leave Einstein notation alone. This is about the Einstein summation convention, which is a separate topic for an article, distinct from "tensor index notation". If that is unclear from the article title, then move it to Einstein summation convention over the redirect.
2. Leave all of the articles Index notation, Tensor, Antisymmetric tensor, Raising and lowering indices, Abstract index notation, Covariance and contravariance of vectors alone (as well as possibly any others I might have missed)
3. Create a new article Ricci calculus (or tensor index notation, although the former is preferable) which covers the basic rules for the tensor indices (symmetrization, skew symmetrization, covariance and contravariance, and covariant differentiation). This article can be linked from the various related articles as needed.

Best, Sławomir Biały (talk) 12:05, 11 April 2012 (UTC)

I didn't know what exactly was being proposed either. Thank you for suggesting a new article where we can write about this. If you were to revert my edits on Einstein notation, I'll not be offended, but there really was too much dribble for nothing so removed as much as possible... F = q(E+v×B) ⇄ ∑_ic_i 12:20, 11 April 2012 (UTC)

Those edits were probably ok. I haven't looked at them in detail, but I doubt it's necessary. Sławomir Biały (talk) 12:33, 11 April 2012 (UTC)

Thats fine. Thanks again Sławomir Biały for the clear-cut suggestion - Ricci calculus has been created. =) F = q(E+v×B) ⇄ ∑_ic_i 12:38, 11 April 2012 (UTC)

Yes, I agree this is a nice name Sławomir, and I would suggest redirecting tensor index notation from its current target to Ricci calculus. As per F=q(E+v^B)'s comments, the bulk of the current article on Einstein notation really belongs in Ricci calculus, as it is irrelevant to the Einstein summation convention; that it is there attests to the confusion surrounding the name Einstein notation. — Quondum^☏ 13:47, 11 April 2012 (UTC)

I thought I would just do it, instead of debating over things. Tensor index notation now redirects to Ricci calculus. Now is the time to add historical sources for fluency with Ricci's work and the contents of the article. =) F = q(E+v×B) ⇄ ∑_ic_i 13:54, 11 April 2012 (UTC)

This seems a most satisfactory solution. May suggest that any further discussion continues on talk:Ricci calculus?TR 14:37, 11 April 2012 (UTC)

Yes. One last thing: shall we move this section Coefficients on tensors and related from Einstein notation to a new section in Ricci calculus? By no means merge/rename or move anything else, since Einstein notation is pretty much fine now, but that section doesn't help understand the summation convention at all. They're just formulae, but where to put them? (Quondum - sorry, this is what you meant all this time, havn't you?)F = q(E+v×B) ⇄ ∑_ic_i 15:21, 11 April 2012 (UTC)

I agree that section is out of place where it is now. By all means move it, rewrite it to make sense, etc. Sławomir Biały (talk) 18:50, 11 April 2012 (UTC)

It will be cut and pasted to Ricci calculus. F = q(E+v×B) ⇄ ∑_ic_i 18:53, 11 April 2012 (UTC)

To Sławomir Biały: With what aspect of "the notation" do you think my allegedly imperious viewpoint betrays a lack of basic familiarity? And I am not trying to impose my view on anyone; just stating the facts as I see them. JRSpriggs (talk) 10:06, 12 April 2012 (UTC)

First of all, it is entirely in your mind that numerical indices need to be introduced to understand anything, no more so than they need to be introduced to understand expressions written without any indices at all. (But you probably wouldn't understand these expressions either, given that your antipathy to abstract indices seems to extend to expressions involving the symbol "$\otimes$" as well.) People I know who use the notation do not mentally substitute numbers in for the indices. Indeed, they do not do this any more than algebraists writing down a polynomial in an indeterminate cannot understand what it represents without substituting values in for the indeterminate. Secondly, it's wrong to say that the notation does not permit the use of numerical indices. To do this, you just need to introduce a basis and contract the free abstract indices against the elements of the basis. (There are even different conventions to distinguish numerical indices from abstract indices, as well as indices in different vector bundles such as spinors.) Sometimes it is useful to do this, since in practice there are often anisotropies that can be exploited in a frame (not necessarily a coordinate frame, e.g., PNDs for the Weyl tensor may not be integrable). Finally, the advantages of such a notation are clear to anyone who has used it: expressions are invariant when written in this notation, unlike in classical numerical index notation. With classical index notation, one often sees horrors like $\partial v^{i}/\partial x^{j}$, for instance, but a more subtle point is things like $dv^{i}$. In classical index notation, there is ambiguity in this expression: it could be the exterior derivative applied to the components $v^{i}$ or it could be the covariant exterior derivative applied to the vector. One of these is invariant and the other isn't. In abstract indices, you have no choice but to interpret $dv^{i}$ as a covariant exterior derivative. The idea that the "rules" are somehow "arbitrary" (your words) is ludicrous. Sławomir Biały (talk) 12:45, 12 April 2012 (UTC)

Reasonable numbers of published works

Can someone inform me on policies delineating how many publications it is reasonable to list in an article on a living person? David Hestenes currently has 47. That seems kind of gratuitous to me, but again, I have no idea what the policies suggest. Rschwieb (talk) 18:31, 11 April 2012 (UTC)

My rule of thumb would be: each one needs to have something to distinguish it. Books (but maybe not edited volumes) and papers that have won awards can always be listed. Papers about which there is a separate review article (not just a MathSciNet entry). Papers that are in the top five for citations by that author. Beyond that, as in the case you mention, it starts to look too indiscriminate to me. —David Eppstein (talk) 18:50, 11 April 2012 (UTC)

You might see Wikipedia:Notability (people)#Basic criteria and Wikipedia:Biographies of living persons. F = q(E+v×B) ⇄ ∑_ic_i 18:58, 11 April 2012 (UTC)

There were (may still be) numerous WP:POV problems with the article, which I recently took a whack at. At the end of March, User:Xtr rossi began massive edits, and appears to be editing only that article. It appears this is the editor responsible for the bevy citations and less-than-neutral descriptions. You can see the claims of success and popularity were uncited, but nary a Hestenes publication was forgotten :(

I haven't altered the citations yet, I'm not sure what to do. If I find time, I will try to apply the "most cited" criterion you mentioned, David Eppstein. Thank you both for the advice. Rschwieb (talk) 19:38, 11 April 2012 (UTC)

I tried to add inline citations [18], but it breaks down since there is no [1] or [19] inline with the article text, yet they are there in the list... I’ll tell him off at user page for this... Why should others have to clean these things (an easily preventable mess...). =/

Good job for raising this problem Rschwieb, its pretty bad... F = q(E+v×B) ⇄ ∑_ic_i 20:24, 11 April 2012 (UTC)

Those two citations might have been lost when I was cleaning up the POV. There might be a COI here too... a diagram uploaded by the user as "own work" (now visible at geometric calculus is very similiar to this one at Hestenes website. Rschwieb (talk) 21:52, 11 April 2012 (UTC)

No worries, not suprised you lost the citations (if so) the way he did it. Yes that image does appear to be copied and claimed for his own. Yet why did you add it ? Do anyone know if that's his website? F = q(E+v×B) ⇄ ∑_ic_i

I like the graphic, but it was just out of place in a biography... is there a reason it shouldn't be used at all? Rschwieb (talk) 23:00, 11 April 2012 (UTC)

I had no implication against using it - you suggested there might be a COI but then added the image to Geometric calculus, which seemed contradictory. Nevermind I guess... =) F = q(E+v×B) ⇄ ∑_ic_i 23:20, 11 April 2012 (UTC)

My opinion is that all of the geometric algebra stuff is a bit on the fringes (WP:FRINGE), and the GA viewpoint is often pushed in articles where it is not really helpful, nor does it typically conform to WP:WEIGHT. Hestenes is certainly one who has made quite a cult industry out of appropriating the works of others and rebranding them under the rubric of "geometric algebra", and for that he is certainly notable. But his notability as a legitimate physics researcher is dubious at best. I think the lack of secondary sources definitely bears this out. Indeed, as do the (exclusively primary) sources referenced in the article: for instance, the "long series of papers" referenced in the article includes many papers of dubious scientific merit (for instance those published in the American Journal of Physics, which is apparently not a research journal). I would suggest removing everything in that article that cannot be attributed to reliable secondary sources, including the long publication list of debatable worth. The most relevant policies here are WP:PSTS and WP:BLP, although if push comes to shove other policies are also relevant. Sławomir Biały (talk) 00:05, 12 April 2012 (UTC)

I think I could handle math papers but I never learned the proper tools to check numbers of citations for papers in other fields. What's the best tool? Thanks Rschwieb (talk) 00:17, 13 April 2012 (UTC)

It varies a lot by field. For many of them, ISI/Web of Science is good, but for computer science it's not, and I generally use Google Scholar instead. For math I'm not sure; MathSciNet is very good at finding all published math papers but much less good at counting citations. —David Eppstein (talk) 02:00, 13 April 2012 (UTC)

I think generally, a bio should contain no list of published papers. In almost all cases it is better to provide an external link to either: 1)a Bibliography by the author himself. 2)A search of any appropriate indexing service providing a list of all published works. The only reason to really deviate from this, is if the published work is in itself notable (but possibly not notable enough for its own article) or if the published work is important for establishing the notability of the subject.TR 11:07, 13 April 2012 (UTC)

Hm, now I've got conflicting advice: "use top cited works" and "none, use external links if possible". Is either of these in print somewhere so that I can decide? Rschwieb (talk) 13:46, 13 April 2012 (UTC)

π peer reviewer needed

The pi article is in need of a peer reviewer at Wikipedia:Peer review/Pi/archive2. The reviewer should be someone familiar with FA criteria. Thanks. --Noleander (talk) 17:01, 13 April 2012 (UTC)

new article about mesh-free method of computational fluid dynamics needing initial review

Viscous vortex domains method is a very new, quite short, article that needs might benefit from expansion after a quick look-over by someone vaguely familiar with mathematics & mechanics (or your local variant of such concepts...) and then the "new unreviewed article" template removing. I'm informed that it's half physics and half mathematics (don't they overlap still?) so I'll post at the Physics project as well if I get time. Many thanks! --Demiurge1000 (talk) 21:09, 13 April 2012 (UTC)

777sms's crusade for Planet Math

User 777sms (talk · contribs) has been going through all our articles systematically changing the "planetmath" template to the "PlanetMath attribution" template. This introduces an implication that we have actually borrowed material in those articles from Planet Math where no such implication was previously present. While that may be appropriate in some cases, I suspect that there are many other cases where we have not borrowed from them, but merely wanted to make another source available to the user. What, if anything, should we do about this? JRSpriggs (talk) 06:42, 14 April 2012 (UTC)

Has anyone tried talking to this user? He or she may be doing it out of ignorance, not realizing the difference in meaning between these two templates. —David Eppstein (talk) 06:46, 14 April 2012 (UTC)

I only just became aware of this problem. Since you mentioned it, I have left a message for him/her to see this thread and respond here. JRSpriggs (talk) 06:56, 14 April 2012 (UTC)

Note [19]. This probably explains most of the edits, and is a good idea. (But this editor really has to use edit summaries to avoid this kind of misunderstanding. But he positively refuses to do so.) Sławomir Biały (talk) 10:43, 14 April 2012 (UTC)

The editor's "explanation" for this refusal is https://en.wikipedia.org/w/index.php?title=User_talk:777sms&diff=next&oldid=413744431 --Joel B. Lewis (talk) 13:03, 14 April 2012 (UTC)

There was an ANI in January 2012 on 777sms' refusal to provide edit summaries. The ANI is here. The consensus in that ANI was that edit summaries are optional. and refusing to supply them is not grounds for sanctions; unless the editor is doing something else wrong. In that ANI, there was no additional problem with their edits (beyond the absence of edit summaries), so no action was taken. --Noleander (talk) 13:16, 14 April 2012 (UTC)

Two users being of that opinion isn't consensus, if I may say so. ;) Nageh (talk) 13:36, 14 April 2012 (UTC)

Citing from WP:Editing policy: "...the more radical or controversial the change, the greater the need to explain it. Be sure to leave a comment about why you made the change." It seems that this is being a controversial change that needs to be explained. Nageh (talk) 13:42, 14 April 2012 (UTC)

I agree that edit summaries should be provided; and I concur that the ANI was rather brief and not very conclusive. I'm just pointing out the ANI so other editors can gather the background. --Noleander (talk) 17:14, 14 April 2012 (UTC)

Just to make sure I've understood correctly: the old "Planetmath" template has been renamed to {{PlanetMath attribution}}, and the other edits consist of pointing things to the renamed template? Jowa fan (talk) 13:27, 14 April 2012 (UTC)

We now have three different templates {{PlanetMath}} a simple link, {{PlanetMath reference}} a full citation, {{PlanetMath attribution}} for pages which incorporates material from PlanetMath. There is also {{PlanetMath editor}} which is only used, on one talk page and should probably be deleted. I think in most cases {{PlanetMath attribution}} is incorrect and should be changed to one of the other two.--Salix (talk): 17:49, 14 April 2012 (UTC)

Bulk nomination of some polygons with a large number of sides

Please comment on Wikipedia:Articles for deletion/Chiliagon and give your opinions. Double sharp (talk) 03:16, 15 April 2012 (UTC)

I, for one, disagree that these 10 polygons are non-notable, and the purpose of the AfD is to decide whether they are. WP:Canvassing notes that notifications of this kind should be "neutrally worded with a neutral title." -- 202.124.73.129 (talk) 15:45, 15 April 2012 (UTC)

Deciding whether an article is notable isn't the only purpose of AfD, but I've changed the wording of the heading anyway. Double sharp (talk) 13:09, 16 April 2012 (UTC)

Physicist uses math to beat traffic ticket

This incident might be notable enough for a Wikipedia article.

• Buzz Blog: Physicist Uses Math to Beat Traffic Ticket

—Wavelength (talk) 20:24, 15 April 2012 (UTC)

Please do not make an article on it. I think it's a rather old joke. In college, I heard a physicist use it in a word problem on the speed of a snail being observed by some graduate students. Rschwieb (talk) 13:39, 16 April 2012 (UTC)

In a word - no. In more words - you added this to wikiproject physics, with no success of agreement. F = q(E+v×B) ⇄ ∑_ic_i 14:54, 16 April 2012 (UTC)

Complete Elliptic integrals

Could someone check out what I've said at Talk:Elliptic integral#possible error in formula for complete elliptic integral of the first kind at en.wikipedia.org/wiki/Elliptic_integral that I'm not making a complete something else thanks. It has long been a bit confused and it would be nice to fix it all up properly. Dmcq (talk) 09:53, 17 April 2012 (UTC)

HighBeam

Wikipedia:HighBeam details an opportunity for experienced Wikipedia editors to have free access to HighBeam Research, an invaluable resource for locating reliable sources for articles and content related to politics as well as other subjects.

The notice above is being circulated to various WikiProjects, but AFAIK hasn't appeared here yet. What do people think of this? Michael Hardy (talk) 01:18, 22 April 2012 (UTC)

I got one of the first-round accounts. So far I've found it quite useful for finding fairly recent US newspaper stories (say within the last 30 years); this might be helpful in sourcing some of our mathematical biographies and has definitely been helpful to me in some non-mathematical articles. I haven't tried to use it to find mathematics journal articles, though, because I get access to many of those through my employer. —David Eppstein (talk) 02:29, 22 April 2012 (UTC)

I went to the HighBeam web site, where I have no account, and I was able to do some searches, but the difference between having and not having an account was that I could read only the beginnings of the articles I found. I entered "Karlis Kaufmanis" and found a few things, but not much beyond what I'd already found elsewhere. (I created the article about him recently and have found a dearth of information to expand the article.) Michael Hardy (talk) 02:59, 22 April 2012 (UTC)

I got an account as well. It's overall use for math is somewhat limited but still it can be useful in particular for those who do not have access to journal archives like JSTOR or others. Afaik there are still account available since not all 1000 accounts were used up in the original application period.--Kmhkmh (talk) 05:42, 22 April 2012 (UTC)

Edit war at vector space

There is an edit war with some IPs at vector space regarding the example of complex numbers. I have started a discussion at the talk page. Please comment there. Sławomir Biały (talk) 13:58, 22 April 2012 (UTC)

Input needed at pi regarding alternate tau = 2*pi

Input would be helpful in the pi Talk page regarding how much mention, if any, should be made in the pi article about the proposed alternate constant tau = 2*pi. The discussion is at Talk:Pi#tau_material.3F. --Noleander (talk) 16:06, 22 April 2012 (UTC)

D.Lazard's edits in Sturm's theorem and Root-finding algorithm

Hello,

I started editing these articles because of "orphaned article" message on the article "Budan's theorem" that my students and I have worked on for the past month. My function was to fine-tune the article at the end.

I am astonished that the author of the Sturm article claims that Sturm's method is available "in every computer algebra system". That is simply not true; he admits as much by claiming, in his other article on root finding algorithms, that maple uses the Vincent-Collins-Akritas method as the default method! Add to this Mathematica, which always had the VAS algorithm, (S works for Mathematica), Sage also, etc etc ... and you get the degree of accuracy of his statement.

Besides, Sturm's method is to be compared with other methods, like VCA and VAS; why does he not want this comparison? I believe that Lazard (whom I have never met or interacted with in the past) is the one who tries to impose HIS limited point of view on the readers. Besides, (assuming good intentions) his knowledge of English did not allow him to differentiate (in the article on root finding algorithms) between "Uspensky's method" and "modified Uspensky's method" and he used the first thinking the two expressions are interchangeable.

Also, on Sturm's theorem he talks about bounds and the only one that came to his mind was what he calls Cauchy's bound; Cauchy gave a bound ONLY on the positive roots and NOT on the absolute value of the roots. The mathematicians of the 19th century knew better. See Bourdon's algebra.

In summary, I have only ADDED material to the above mentioned articles and DID NOT ERASE anything Lazard wrote. I expect the same courtesy from him as well. He got his point of view and I have mine and I think both need to be taken into consideration. But we both have to write accuracies. So, I expect Sturm's method to be reverted to the previous version where I was saying that Sturm's method was used by "everybody until about 1980 --- when it was replaced by methods derived from Vincent's theorem", along with the supporting references.

And I close with the following: If Lazard does not like anything on the Budan article he should say so and explain the reason he does not like it. Saying that the article is "... entirely devoted to the personal views of Akritas on the history of mathematics" proves nothing; he should tell us his own views -- if he has any. My views have already been judged by peers.

Alkis Akritas2 (talk) 12:17, 19 April 2012 (UTC)

With regards to this article, editors will need to remain alert and judge the appropriateness of possible self-citation in the references. Rschwieb (talk) 13:31, 19 April 2012 (UTC)

For most Akritas assertions, my answer is simply "Look on the history of these articles and on the reasons given in the edit summaries". However, for wikipedians who are not familiar with this subject, I have to give some technical information.

• For counting and locating the real roots of a polynomial, there are two main algorithmic methods, Sturm's theorem, and a method based on Descartes' rule of signs and Vincent theorem. The first true algorithm based on the latter method was called "Uspensky algorithm" by its authors (Collins and Akritas himself). As this algorithm implies a change of variable at each step of a recursion, it has been improved by several authors mainly by a better way of changing of variable or, I believe, by replacing this change of variable by a continuous fraction expansion. This leads to several variants of "Uspensky algorithm", that most authors (except Akritas) continue to call "Uspensky algorithm".
• As explicitly stated in Collins-Akritas paper, Uspensky algorithm is not due to Uspensky.
• When Uspensky algorithm was widely known under this name by the computer algebra community, Akritas decided to rename it. As far as I know, he has not been followed. He decided also to try to attribute it to an earlier author, which seems an historical mistake, as "Uspensky algorithm" was new as an algorithm, even it is based on a series of previous theorems (Descartes rule of signs, Budan's and Vincent's theorem): As usual, a new result uses previous knowledge.
• For the comparison of the various algorithms, the existing knowledge is that they have all the same worst case time complexity. However the variants of Uspensky algorithm are, in practice, faster than Sturm's algorithm, mainly because the worst case complexity is always reached with Sturm's algorithm while it is rarely reached with the other algorithms. As far as I know, there is no reliable comparison between the variants of Uspensky algorithm. This the reason while Akritas edit in root-finding algorithm may not been kept. However, if the default root-finding algorithm of Mathematica uses a variant of Uspensky algorithm, this has to be said.
• Sturm's theorem is not a well written article. In particular, a section on complexity is lacking.

D.Lazard (talk) 14:08, 19 April 2012 (UTC)

The root finding article also still has content which should be examined by more editors for WP:COI and WP:POV problems. Rschwieb (talk) 19:50, 19 April 2012 (UTC)

Just a comment on the history: Vincent wrote his "theorem", in fact an algorithm to derive the continued fraction expansion of each (positive) root of a polynomial, in 1834, the available publication in Compte Rendu (vol. 1) is from 1836. There he cited the extension of Decartes rule by Budan and Fourier. Uspensky wrote an article (or book section) on his interpretation of Vincents algorithm, eliminating the continued fraction part for an easier complexity result. Akritas added the Cauchy bound and step sizes greater than one to the original Vincent algorithm and provided a complexity result for the modified algorithm.--LutzL (talk) 09:19, 20 April 2012 (UTC)

And a comment on contents: I would really like to see the Budan article split into two or three with a separate Vincent method article. The Akritas extentions and results could be a second part of that article or even another separate article. And no, at the moment I will not insert myself between the "clash of giants".--LutzL (talk) 09:19, 20 April 2012 (UTC)

First, there is no clash whatsoever. I believe Lazard has made constructive criticism on various points and will eventually accept the fact that there cannot be a Uspensky's method, because otherwise everybody would be taking somebody else's method, double its computing time and present it as his/her own. This is precisely what Uspensky did to Vincent's (exponential) method, as is shown in the diagrams of Budan's thorem, and therefore one can talk only about Vincent's (exponential) method. I am sure Lazard will be persuaded when I show him the printed evidence. And instead of looking at the "... the history of these articles and on the reasons given in the edit summaries", as Lazard suggests, I suggest that we look at the articles THEMSELVES; they can be found on my webpage at the University of Thessaly.

Second, Lazard should read the Collins-Akritas paper to the end; he seems to stop in the middle where we describe what we erroneously called "Uspensky's algorithm" (the process seen in Budan's theorem) and it seems that he never reached the end of the paper where we talk about "modified Uspensky's method". It is the latter that has been renamed the Vincent-Collins-Akritas (VCA) method. More on the topic in a forthcoming article in Wikipedia.

Third, after I published the "There is no "Uspensky's method" the computer algebra community realized the fallacy and started calling it "Collins-Akritas" (partly right) or "Descartes' method" (totally wrong). It was a Frenchman who called it the "Vincent-Collins-Akritas" (VCA) method.

Fourth, even a great supporter (German) of calling the VCA method "Descartes' method" recently changed tack and calls it the Vincent-Collins-Akritas method.

Finally, with my students, we do plan to write a separate article about Vincent's theorem and the methods derived from it. We just came back from Easter recess, and are ready to go. Then Lazard will be persuaded by the historical evidence. Till then,

Akritas2 (talk) 11:16, 23 April 2012 (UTC)

Response to LutzL: Uspensky did not eliminate the "... continued fraction part for an easier complexity result". Both Vincent's method AND Uspensky's implementation of Vincent's theorem use continued fractions and are BOTH exponential in nature; in fact, Uspensky's is twice more exponential because he doubles the work done by Vincent. See Budan's thorem and Vincent's figure right above it to get a clear picture. What I did was to make Vincent's exponential method polynomial in time. To prove it, back in 1978, I had made some plausible assumption, but in 2008 Sharma proved it without any assumptions whatsoever. Akritas2 (talk) 11:55, 23 April 2012 (UTC)

Category:Theorems in Galois theory

Category:Theorems in Galois theory, which is within the scope of this WikiProject, has been nominated for deletion. If you would like to participate in the discussion, you are invited to add your comments at the category's entry on the Categories for discussion page. Thank you.. --BrownHairedGirl (talk) • (contribs) 15:17, 23 April 2012 (UTC)

User:Akritas2's edits in Sturm's theorem and Root-finding algorithm

User:Akritas2 has recently edited Sturm's theorem and Root-finding algorithm in order to add references to his publications and introduce his personal point of view on the subject. I have reverted his edits per wp:COI, wp: NPOV wp:OR and lacking of secondary sources. He has reverted my reverts. I may not revert again, because, knowing personally the guy, I am sure this will lead immediately to an edit war. For the same reason, I cannot discuss constructively with him. Could someone look at this problem?

He has also created Budan's theorem, a page which deserve some attention.

D.Lazard (talk) 15:11, 14 April 2012 (UTC)

Hello,

I started editing these articles because of "orphaned article" message on the article "Budan's theorem" that my students and I have worked on for the past month. My function was to fine-tune the article at the end.

I am astonished that the author of the Sturm article claims that Sturm's method is available "in every computer algebra system". That is simply not true; he admits as much by claiming, in his other article on root finding algorithms, that maple uses the Vincent-Collins-Akritas method as the default method! Add to this Mathematica, which always had the VAS algorithm, (S works for Mathematica), Sage also, etc etc ... and you get the degree of accuracy of his statement.

Besides, Sturm's method is to be compared with other methods, like VCA and VAS; why does he not want this comparison? I believe that Lazard (whom I have never met or interacted with in the past) is the one who tries to impose HIS limited point of view on the readers. Besides, (assuming good intentions) his knowledge of English did not allow him to differentiate (in the article on root finding algorithms) between "Uspensky's method" and "modified Uspensky's method" and he used the first thinking the two expressions are interchangeable.

Also, on Sturm's theorem he talks about bounds and the only one that came to his mind was what he calls Cauchy's bound; Cauchy gave a bound ONLY on the positive roots and NOT on the absolute value of the roots. The mathematicians of the 19th century knew better. See Bourdon's algebra.

In summary, I have only ADDED material to the above mentioned articles and DID NOT ERASE anything Lazard wrote. I expect the same courtesy from him as well. He got his point of view and I have mine and I think both need to be taken into consideration. But we both have to write accuracies. So, I expect Sturm's method to be reverted to the previous version where I was saying that Sturm's method was used by "everybody until about 1980 --- when it was replaced by methods derived from Vincent's theorem", along with the supporting references.

And I close with the following: If Lazard does not like anything on the Budan article he should say so and explain the reason he does not like it. Saying that the article is "... entirely devoted to the personal views of Akritas on the history of mathematics" proves nothing; he should tell us his own views -- if he has any. My views have already been judged by peers.

Alkis (talk) 12:29, 19 April 2012 (UTC)

Observations of an outsider: To help reduce the backlog, I patrol a few new pages each time I log into WP. I approved the Budan's theorem article but marked it as needing improvement. Improvement by several interested editors is notable. From my browsing related articles, it appears that both of you are well known and highly respected in your field. Wikipedia is richer with contributions from both of you.

Alkis, within Wikipedia, Lazard's observations are correct. Nine of the 17 citations in the Budan's theorem article refer to your papers. Even though your work was peer reviewed and correct, it is still your work expressing your point of view which is a potential conflict of interest. I judge that the solution is simple. You wrote that "my students and I have worked on" the article. Now it the time to back away and challenge your students to take over, to edit the Budan article and related articles. Your students' styles may express the material in a way that seems more relevant to their peers (who are more likely to read the article than your or my peers). When your students write or edit an article, your papers become valid second or third party rather than primary sources. Don't just use student accounts to avoid these objections; challenge your students to think and write for themselves. Everyone will benefit. Take care, DocTree (talk) 23:12, 19 April 2012 (UTC)

Indeed Doctree, I felt uneasy myself about this fact and have solicited the help of two professors of the history of mathematics. One told me this is ok, as nobody else has dealt with this subject. I am waiting for the other one as well (to come back from a conference where she went) and I will ask them to write a report. Moreover, as you can see from the the talk page of Sturm's theorem (17:16, 22 April 2012 (UTC)) I have even invited Lazard to evaluate our page.

Akritas2 (talk) 11:41, 23 April 2012 (UTC)

For the quick access of readers, the following contributed sections are relevant: Budan's_theorem#Historical_background, Sturm's_theorem#History_section_and_other_related_methods, and Root-finding_algorithm#Finding_roots_of_polynomials. The issue is that it appears there are little to no independent citations which argue the same thing. While the material may be true, I'm worried that the current level of citation does not meet WP's level of verifiability. Rschwieb (talk) 13:39, 24 April 2012 (UTC)

To the above list of sections I would add Sturm's_theorem#Number_of_real_roots

Akritas2 (talk) 14:46, 25 April 2012 (UTC)

PlanetMath as source?

Any opinions on this? Please comment here. Sławomir Biały (talk) 11:57, 15 April 2012 (UTC)

This set the problem of sources for the result of a mathematical computation. The present rule for such a sourcing is to provide a text containing the result. IMO, this is archaic, as most of the time, such a result is the result of built-in a function of most computer algebra systems. Thus, in this case, a source could be "result of Laplace function of Maple (software) applied to the first column of the table". This is, not only, more reliable than a text source, as typos are avoided, but also more useful for the reader, as giving him a way to obtain the result for similar inputs, not appearing in the table. Is there some guideline for this kind of sources? D.Lazard (talk) 12:30, 15 April 2012 (UTC)

Perhaps some like Wolfram Mathworld are good for external links in the last resort, but not so much PlanetMath (it’s not that brilliant anyway). In any case, it’s better to just use books obviously. I have many so if people use websites like this as sources, I (or anyone) will try to replace them as and when. (Perhaps that was obvious anyway...) F = q(E+v×B) ⇄ ∑_ic_i 14:12, 15 April 2012 (UTC)

Aside from any quality concerns, it also does not look very durable. The front page at Planetmath says they recently lost all changes since last October in a crash after "many months of instability". Rschwieb (talk) 14:24, 15 April 2012 (UTC)

Well planet math is community wiki without any read editorial by noted experts but just by the community at large (like WP), hence it is normally not suited as a source. However it is still sometimes or even often well suited to listed under external links.--Kmhkmh (talk) 08:41, 25 April 2012 (UTC)

Double exponential function

We have a persistent single-purpose account active on Double exponential function who has been adding material which is somewhat relevant but in (what I feel is) an unencyclopedic style that unbalances the article, and has shown no attempt to engage other editors on the subject. More eyes on it would be helpful. —David Eppstein (talk) 20:58, 25 April 2012 (UTC)

MediaWiki 1.20wmf1 deployed and broken

Tracked in Phabricator
Task T38059

This is just to inform you that MediaWiki version 1.20wmf1 has just been deployed, but its TeX output is broken, unfortunately. In particular, this means that you will see a lot of "Misplaced &" errors or spurious "&"s in MathJax. Nageh (talk) 20:23, 23 April 2012 (UTC)

Ok, I have implemented a work-around. Bypass or clear your cache to reload the script. Nageh (talk) 23:57, 23 April 2012 (UTC)

Not sure if this is related but the < math > font is no longer working at golden ratio and probably many other pages. Tkuvho (talk) 20:02, 26 April 2012 (UTC)

Hmm, it just came back. Tkuvho (talk) 20:03, 26 April 2012 (UTC)

Probably it took too long loading one of the scripts. Nageh (talk) 20:15, 26 April 2012 (UTC)

Definitions of operator symbols

When trying to get a quick overview of a topic in mathematics, a reader sometimes encounters a barrier with the inability to quickly determine what an operator symbol means. As a (maybe too easy) example, consider the following extracts from the article Chain rule:

1. "...the chain rule expresses the derivative of the composite function f ∘ g in terms of the derivatives of f and g..."
2. "The rule is sometimes abbreviated as $(f\circ g)'=(f'\circ g)\cdot g'.\,$"

Please note, I am not alleging that anything is wrong with the chain rule article. However, for someone who is not familiar with the use of $\circ$ to denote function composition, there might be three reasons for initial confusion:

1. The reader may not immediately be able to figure out what the symbol means.
2. The symbol for function composition is present in two very different sizes, which might not be seen as the same symbol.
3. The small instance of the symbol could be mistaken for the raised-dot symbol used for multiplication.

If $\circ$ had been a word instead of a symbol, its initial use would have carried a link to an article about the symbol. But we do not (as far as I know) have a way to turn a symbol into a link, as in [[$\circ$]], which does not work.

What is the best practice for an article-writer (or editor) to use when an operator definition is needed? Is there a nice way to add a footnote-style link to an operator?

Incidentally, the problem usually arises for symbols less familiar than $\circ$. For example, what is the definition of $\vDash \!\,$ . . . and how would I best make that definition available to a reader? Dratman (talk) 22:37, 26 April 2012 (UTC)

In the instance you mention, one could simply insert the words "where $\circ$ denotes composition of functions" in an appropriate place. I would think something like this is possible in almost every instance. (By the way, I agree that the size difference in this case is really atrocious. Is there a better HTML (or whatever) symbol, or is that really it?) --Joel B. Lewis (talk) 23:35, 26 April 2012 (UTC)

There seems to be a difference between the "correct" unicode symbol U+2218 RING OPERATOR (∘) and Latex's \circ ($\circ$). The unicode U+25CB WHITE CIRCLE (○) might actually be a better fit. Perhaps \circ and U+25CB are typographically the same but both semantically wrong.--Salix (talk): 08:35, 27 April 2012 (UTC)

White circle is used on the Function composition page and I've now changed Chain rule to use it as well.--Salix (talk): 08:41, 27 April 2012 (UTC)

To me (in Firefox with the Verdana font size 16), the unicode U+25CB does not appear to be a circle. Rather it is flattened with the vertical diameter smaller than the horizontal diameter. The other two are true circles. JRSpriggs (talk) 08:49, 27 April 2012 (UTC)

AFC input needed

Please could a knowledgeable member of this project take a look at Wikipedia talk:Articles for creation/Carlitz exponential and let us know weather it is notable and accurate? I'm a mathematical dunce and would appreciate some expert input into this submission's suitability. Pol430 talk to me 13:21, 27 April 2012 (UTC)

It seems perfectly acceptable to me, so I created the article at Carlitz exponential. -- Jitse Niesen (talk) 15:48, 27 April 2012 (UTC)

I tagged it an orphan. Then I created one link from another article, but probably there should be more. (I also did some edits to bring it closer to the norms of WP:MOSMATH and WP:MOS. Michael Hardy (talk) 21:56, 27 April 2012 (UTC)

Thanks to both of you for the assistance :) Pol430 talk to me 23:06, 29 April 2012 (UTC)

Antarctica Journal of Mathematics at AfD

See Wikipedia:Articles for deletion/Antarctica Journal of Mathematics. -- 202.124.74.240 (talk) 11:24, 30 April 2012 (UTC)

May 2012

Kernel (mathematics)

Kernel (mathematics) has been tagged as a disambiguation page, but it runs afoul of WP:INCOMPDAB and in accordance with that policy is likely to be merged/redirected into Kernel (disambiguation)#Mathematics; furthermore, in accordance with WP:MOSDAB, most of the information will be stripped, except for one blue link per line and the minimum amount of information needed to direct a searcher to the most appropriate article for a given meaning. Since the page has 60 incoming links, it is likely that dozens of disambiguators will be drawn to this page, and will edit it to implement those guidelines, either by drastically culling its content, or by redirecting it to the existing section at Kernel (disambiguation). However, it would be a shame to lose all the work that has been put into this page, so perhaps some other formulation can be arrived at where it is not tagged as a disambiguation page. Cheers! bd2412 T 15:25, 2 May 2012 (UTC)

IMO, there is the matter here for two concept pages. Firstly, kernel of a mapping for a subset that measures how far the mapping is from being injective or being an homomorphism. Secondly, kernel of a functional transformation, for a (functional) parameter of some class of functional transformations or mappings. I have edited in this way the general definitions in Kernel (mathematics). As the first usage seems much more frequent than the second one, I propose to split this article into two articles which could be named Kernel (mathematics) and Kernel (functional mapping), with a hatnote in the first one. D.Lazard (talk) 17:24, 2 May 2012 (UTC)

I don't understand why User:BD2412 makes such dire predictions. WP:INCOMPDAB is a guideline, not policy, and the top of that page states that occasional exceptions may apply. Kernel (mathematics) is one of those exceptions. It's been reasonably stable for some years now. There's nothing on the talk page that suggests people are dissatisfied with it, and I don't see a merge proposal listed anywhere. What reason is there to believe it should change in the near future? Jowa fan (talk) 23:28, 2 May 2012 (UTC)

It is likely to change because this page is now near the top of the monthly report for Wikipedia:Disambiguation pages with links. Those are the pages that draw the most attention from disambiguators. Of course, the page will go off of that list if the incoming links are fixed so that they point somewhere else. bd2412 T 14:43, 3 May 2012 (UTC)

Two-way ANOVA

Two-way analysis of variance is an article that needs a lot of work. Probably more than one person can do in one day. Michael Hardy (talk) 16:49, 3 May 2012 (UTC)

MathJax

Is anyone else having problems viewing maths text? All <math>...</math> strings are being displayed as $...$ with the LaTeX code being shown explicitly. — Fly by Night (talk) 20:11, 2 April 2012 (UTC)

Sorry, my bad. See User_talk:Nageh/mathJax#Troubleshooting. Nageh (talk) 20:44, 2 April 2012 (UTC)

On a related note, when is Wikipedia finally going to switch to MathJax? It has been working for me flawlessly for quite some time now (except all the text art in italic and bold with html super/subscripts instead of math looks bad in comparison - as it should), but when I arrive to a Wikipedia link without being logged in, I still see the legacy math rendering as images. Jmath666 (talk) 01:21, 7 April 2012 (UTC)

The last update I saw on this was on Wikipedia_talk:WikiProject_Mathematics/Archive/2012/Mar#MathJax_update. See also the list of dependencies of bug 31406. Helder 20:17, 9 April 2012 (UTC)

Some progress on this its now live on mediawiki.org.--Salix (talk): 06:35, 18 April 2012 (UTC)

It's a pity that my changes are repeatedly being ignored without feedback. That implementation is pretty broken. Nageh (talk) 10:28, 18 April 2012 (UTC)

Are you going through the bug tracking system. I find dev tend to look at that rather than the wiki pages. Quite a few MathJax bugs don't seem to me linked to the master MathJax bug bug 31406. So they might be missed. I've added a couple to the block list.--Salix (talk): 10:48, 18 April 2012 (UTC)

Well, ok, I have created an account, and commented on a couple of these bugs. Nageh (talk) 12:17, 18 April 2012 (UTC)

Per bugzilla:31406#c24, the experimental MathJax option is now available on your preferences. In case anyone find some other bug which was not reported yet (see this list), please report it directly on bugzilla. Helder 16:45, 3 May 2012 (UTC)

Tracked in Phabricator
Task T38059

Helder, maybe you can answer me since the developers have apparently decided to ignore me. Why is the MathJax option being rolled out but bugs introduced in MediaWiki pointed out by me weeks ago are not being fixed? There is little point in testing a broken implementation of MathJax. Nageh (talk) 16:53, 3 May 2012 (UTC)

Do you have a test case of a broken page?--Salix (talk): 16:58, 3 May 2012 (UTC)

I have detailed the problem here. Nageh (talk) 16:59, 3 May 2012 (UTC)

Ah Help:Displaying a formula#Differential equation <math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math> is broken giving $u''+p(x)u'+q(x)u=f(x),\quad x>a$. I've added that as a testcase in 36059 and set that as blocking 31406.--Salix (talk): 17:18, 3 May 2012 (UTC)

All maths that contains <, >, or & is broken. Nageh (talk) 20:40, 3 May 2012 (UTC)

I'm don't know. Maybe it was because the prority/severity fields were set to "Normal". I changed the fields today and added links to this section, to de:Portal Diskussion:Mathematik#Mathjax wird getestet! and to the village pump. Other possibility is that the bug was added as a dependency to T33406 too late (only after Erik Möller said it was "ready to be enabled site-wide as an opt-in preference", and less than two hours before the setting was actually changed by Reedy). Helder 09:35, 4 May 2012 (UTC)

FAQ

I added the following to the FAQ at the top of this page following what seemed to be a favorable discussion last month: "Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues? A.: Mathematical content of YouTube videos is often unreliable. Media reports are typically sensationalistic. This is why they are generally avoided." This was promptly deleted by a tauist. It would be useful to put on the record a WPM opposition to such dubious sources. Tkuvho (talk) 11:51, 3 May 2012 (UTC)

Well though I personally have no objection against the explanation as stated, it may be considered somewhat misleading. First of all youtube as such is just distribution channel, which carries anything from total garbage to rather high quality. There indeed many university lectures available on youtube as well as educational films from reliable authors and it might be fair to say that they are currently underutilized in math articles. In doubt video material (on youtube or elsewhere) should just be treated like other material we recommend for further reading or alternative presentations (books, articles, websites, applets & demonstrations). Add them if they reasonably can be considered useful to readers of a particular wp article and don't add them otherwise.--Kmhkmh (talk) 12:11, 3 May 2012 (UTC)

Removing the FAQ seemed a bit peremptory, as a FAQ is not a guideline, the latter having received some discussion; also the proposal for the FAQ stood without being challenged until it was deleted. I feel that WP:YOUTUBE is not stated strongly enough for the subject area of mathematics, and could be enhanced. WP:ELNO is a bit diffuse and open to interpretation. Some YouTube links may be suitable for pedagogical purposes (a see also?) rather than for reference, and that distinction perhaps needs to be made somewhere in WP:EL. We do experience occasionally insistent additions of YouTube links, but the question to ask is: since it comes down to experienced editors removing unsuitable links in the end, what would be the best guideline/FAQ to have in place to refer persistent editors to in the case of maths articles? — Quondum^☏ 12:52, 3 May 2012 (UTC)

Changing WP:YOUTUBE guidelines may not be easy. At the very least we should be clear on this at our own FAQ. Tkuvho (talk) 13:27, 3 May 2012 (UTC)

Ok you lost em completely. Did I miss something here? Who is suggesting to delete the FAQ? As i understood it the question was about Tkuvho's text addition.--Kmhkmh (talk) 12:58, 3 May 2012 (UTC)

That reversion was by Waldir (talk · contribs) back on 10 April 2012‎. In his edit summary, he said "There was no consensus for this change.". This is not an adequate reason to revert, so I would like to hear Waldir's explanation. Perhaps we can agree on a modified version of the change.

To Tkuvho: By the way, what do you mean by "tauist"? JRSpriggs (talk) 12:57, 3 May 2012 (UTC)

The most "serious" piece to date on the subject of tau is by one Abbott, entitled: "how I converted to tauism" or something like that. Tkuvho (talk) 13:25, 3 May 2012 (UTC)

The background for this dispute concerns the recent controversy over the article Talk:Tau (2π). In my opinion, Waldir and others were attempting to use mainstream media to establish the notability of the concept, and then attempting to use those same sources to write an article that purported to be about a serious mathematical phenomenon. It seems clear to me that if this kind of bait-and-switch can be construed as permitted under our policies, then someone needs to take a hard look at those policies and see where they need to be clarified. Sławomir Biały (talk) 13:18, 3 May 2012 (UTC)

I think i misread your meaning of "relying". So to be clear, in my posting above I was talking about video material being underutilized in external links and not about its use as sources.--Kmhkmh (talk) 14:09, 3 May 2012 (UTC)

That's a valid point. Would you care to suggest an alternative wording that would make this clear? Tkuvho (talk) 14:44, 3 May 2012 (UTC)

Quoting myself above: "... suitable for pedagogical purposes (a see also?) rather than for reference, and that distinction perhaps needs to be made somewhere" – perhaps similar wording clarifying the pedagogical–reference distinction for what purpose a link is serving should be used. — Quondum^☏ 15:16, 3 May 2012 (UTC)

How about this: "Q. Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues? A.: Mathematical content of YouTube videos is often unreliable, though some may be useful for pedagogical purposes rather than references. Media reports are typically sensationalistic. This is why they are generally avoided." Tkuvho (talk) 16:50, 3 May 2012 (UTC)

Fine by me. If it's impractical to modify the guidelines to reflect the particular caution relating to the more stringent requirements for mathematics references, then a FAQ can fill the role. If people have objections to the wording, it can be fine-tuned. — Quondum^☏ 09:55, 4 May 2012 (UTC)

It seems that comments in this discussion still ignore the point that some YouTube videos are indeed reliable. As Kmhkmh said, YouTube is primarily a distribution channel, and we should probably do better than say "all content on YouTube is unreliable". For example, there was a minor claim at Raptor code, which I knew was true but was tagged with {{dubious}}, and the only (but reliable) source I could find on this was a talk given by the primary inventor at a university, which recorded his talk and put it on YouTube. But maybe this is just an exception to the rule, not worthy of further mention? Nageh (talk) 11:35, 4 May 2012 (UTC)

Though I agree that there are videos tat can be considered (somewhat) reliable (tutorials from reliable authors/publishers, academic lectures, conferences or talks by reputable scholars,...) they are still a poor choice for sourcing content, as all math statement being mentioned in those can usually be found in proper written publications as well, which would be the preferred choice. You probably can argue better sourcing some claim with a video lecture (where it is mentioned) than with no source at all, but the problem starts with claims who are not known to (obviously) true or even disputed in such cases having a statement in lecture as the only source is not good enough. Also in such harmless undisputed cases lecture notes/sripts might probably better as a "emergency source" than a video of a talk or lecture.--Kmhkmh (talk) 12:04, 4 May 2012 (UTC)

So while it might be permissible in your case or some other rare cases it is not a sourcing practice we should encourage. Note the discussion was about "using videos/youtube more often" rather than "explicitly forbidding any use" and your scenario is more dealing with the latter rather than the former. However outside of sourcing issues, we nevertheless could use videos more often for pedagogic/further information reasons under external links.--Kmhkmh (talk) 12:04, 4 May 2012 (UTC)

Yeah, I agree. And definitely, such sources should not be encouraged. Nageh (talk) 12:09, 4 May 2012 (UTC)

A dubious new category

Today, Wackywill1001 (talk · contribs) created Category:E (mathematical constant) as a subcategory of Category:Mathematical constants. Yet it contains articles which are not about mathematical constants and only incidentally about e. JRSpriggs (talk) 15:02, 4 May 2012 (UTC)

xdvi

I've created a new article titled xdvi. It's still quite stubby. Have fun improving and extending it. Michael Hardy (talk) 16:54, 4 May 2012 (UTC)

Evaluating sums -- hopeless?

I was looking at the article Evaluating sums to see if I could improve it, but I think I've decided that it's hopeless: the title subject is so over-broad that there's no possible way to give a comprehensive encyclopedic treatment, while the article as written might be better titled methods of computing certain numerical series known to bright high school students. And, of course, all of the content is included in articles like arithmetic progression and Taylor series, where it has appropriate context. I don't care enough about this to learn how to go about proposing articles for deletion, but perhaps someone who agrees might go about it. --Joel B. Lewis (talk) 23:17, 7 May 2012 (UTC)

I went over the article in an attempt to save it, but the patient flatlined. CRGreathouse (t | c) 15:20, 8 May 2012 (UTC)

Article as code repository?

The section Computer program of the article Look-and-say sequence consists of code in Python and Javascript to generate the sequence that is the subject of the article. Is it usual practice to have such code in Wikipedia articles? (By the way, if anyone had any reliable sources for the section on "pea pattern", that would be wonderful.) --Joel B. Lewis (talk) 00:08, 8 May 2012 (UTC)

This comes up periodically; I think some past discussions can probably be found in the archives of Wikipedia talk:WikiProject Computer Science. My own feeling is that (1) code or pseudocode is an appropriate way of describing algorithms, when that algorithm is relevant for the content of the article; (2) pseudocode is generally preferable to code, but code may be clearer in some cases when using language-specific features that are difficult to describe in pseudocode such as the yield keyword and regular expressions of the example you link to; (3) because the purpose of including code is to explain algorithms to people rather than to provide a code repository for programmers to copy from, we should never have multiple redundant implementations of the same algorithm in different languages; if multiple implementations are included (as they are in this case) it should only be to describe algorithms that are significantly different from each other (as they are in this case); (4) we shouldn't require the exact same source code to be present in a reliable source (that would likely be a copyvio) but it is reasonable to require the algorithm itself to be sourced. Despite having contributed to the Python version for this article I don't have a strong opinion on whether the algorithms described in this case are relevant enough to the main topic or free enough of original research to be included. —David Eppstein (talk) 00:31, 8 May 2012 (UTC)

Since this is something that keeps coming up from time to time, would it make sense to have better integration with something like Wikisource, where detailed implementations can be included? Or is this just inviting other problems? Sławomir Biały (talk) 13:23, 8 May 2012 (UTC)

There is also http://rosettacode.org. Helder 13:26, 8 May 2012 (UTC)

List of things named after Charles Hermite

We have a new List of things named after Charles Hermite. Work on it! Michael Hardy (talk) 04:08, 9 May 2012 (UTC)

You might want a link to it from the article on Charles Hermite. JRSpriggs (talk) 06:03, 9 May 2012 (UTC)

Polyhedra

Hi all,

Double sharp and I were discussing earlier about the coverage of uniform and pseudo-uniform polyhedra on Wikipedia. In fact, we've just started work on a few articles. (The main discussion is on my talk page, though I am not really that active in it.) Please help out!

Thanks,

Your old friend, "The Doctahedron" 68.173.113.106 (talk) 21:27, 8 May 2012 (UTC)

I've created pseudo-uniform polyhedron. It's still incomplete, with only one section filled in. Double sharp (talk) 10:04, 9 May 2012 (UTC)

Paper written by a particular person?

Is the Bachmann who wrote this paper Paul Gustav Heinrich Bachmann? My guess is yes, but I am not sure how to confirm it. The paper does not give his full name. I need to know this, because I want to wikilink him in an article. -- Toshio Yamaguchi (tlk−ctb) 06:34, 10 May 2012 (UTC)

Searching for the author Bachmann at Zentralblatt seems to confirm it. The topic of P. Bachmann at the time period is number theory and Fermat's theorems, and in some entries the name is expanded to "Bachmann, Paul [-1920]". For instance, here. So I'd say, in this period there is only one P. Bachmann publishing in mathematical journals, P. is Paul, and the data and topics coincide with the biography above.--LutzL (talk) 08:28, 10 May 2012 (UTC)

I wikilinked the name to Paul Gustav Heinrich Bachmann. Thanks. -- Toshio Yamaguchi (tlk−ctb) 11:43, 10 May 2012 (UTC)

The ultimate problem of this kind is probably that of Charles Paul Narcisse Moreau. It is suspected, and reasonably probable, that three people named Moreau are really all the same person, and some people have made considerable efforts to confirm or refute that hypothesis without success. Michael Hardy (talk) 16:25, 11 May 2012 (UTC)

Eilenberg-Ganea theorem

I'm good at math but not this good. The article Wikipedia talk:Articles for creation/Eilenberg-Ganea theorem was not moved to article space because of concerns with inline citations. While I agree that the concerns exist, the article appears to be ready for the article space as long as {{More footnotes}} is added. Can someone who might actually know what they are talking about take a look at it to see if it is able to be moved? Ryan Vesey Review me! 20:12, 11 May 2012 (UTC)

Some aspects of the article pretty thoroughly violated WP:MOSMATH, and to a lesser extent WP:MOS, but I've fixed those. (Apparently someone thought everything in non-TeX math notation should be indiscriminately italicized, including even parentheses and digits, etc., and wrote \text{sup} instead of \sup, and various other things like that. In fact, some things on the same line where "\text{sup}" appeared didn't use \text where \text was appropriate and artificially added spacing between words.) There was also a mathematical thing that didn't make sense: "$\sup _{k}\{[{\text{condition involving }}k]({\text{ true or false depending on }}k)\}$" appeared. Where $\sup _{k}$ appears, I expect "$\sup _{k}({\text{something whose value depends on }}k)$". Finally I thought what was probably meant was "$\sup\{k:[{\text{condition involving }}k]({\text{ true or false depending on }}k)\}$" was probably meant, and I changed it to that. Michael Hardy (talk) 23:02, 11 May 2012 (UTC)

The author is a relatively new user. It might be good to leave him/her a note describing WP:MOSMATH. Do you believe the page could be moved to article space? Ryan Vesey Review me! 23:06, 11 May 2012 (UTC)

File:Formal languages.png

Is it appropriate in Portal:Logic/Selected article/3? It certainly is not appropriate in any of the articles to which Greg has added it over time. — Arthur Rubin (talk) 15:21, 13 May 2012 (UTC)

This is a formal written request for members of WP:MATH to cease and desist from further removal of the File:Formal languages.png from articles in which it appears until such time as productive criticism which may lead to its amendment arises. Please be advised that "i don't like it" and any other formulations thereof DO NOT qualify as productive. Heretofore, the only criticism I have seen which shed any light at all is that it is "simple." So what more complex concepts are needed. I say none. It is meant to be a simple diagram custom made for the articles in which it appears. I took the time and effort to make it. Show some respect for their efforts of others. Greg Bard (talk) 21:36, 13 May 2012 (UTC)

Formal request has no meaning in this context. If you want to argue over images the most relevant consideration is WP:PERTINENCE. Please sign your talk page 'missives' with ~~~~. See WP:TPO about moving the comments around. Dmcq (talk) 21:19, 13 May 2012 (UTC)

Take it for what it is worth. If I continue to have problems, I will take it to ANI, if this isn't the place for formalities. Greg Bard (talk) 21:36, 13 May 2012 (UTC)

Please do so as you seem unable to treat people here with consideration and respect as per WP:CIVILITY. Dmcq (talk) 21:48, 13 May 2012 (UTC)

Absolutely outrageous. Someone takes it upon themselves to consistently go through deleting all instances of an image created by a user for a specific and useful purpose (on what grounds we haven't been told) and when he protests about it, all you can do is complain about the fact that he rearranges stuff around on a talk page? Shame on you.

For what it's worth I can't see any reason for deleting that File:Formal languages.png link. While there may be "civility" issues over the talk page, which appears to be objected to on pharisaical grounds, the consistent deletion of this file is a more important issue and needs to be addressed. In my view, it's a good icon as it encapsulates the whole field of formal languages in one easy little picture. --Matt Westwood 22:15, 13 May 2012 (UTC)

Thank you for your attention to this issue, and thank you for observing that while all I want to do is move forward, certain people here would rather do nothing but make problems. I still haven't seen a single contribution that would consist in something that a productive editor could use to improve the image to their satisfaction. That should tell you everything you need to know about this issue, and the maturity of certain editors. Please do monitor this issue. You could serve as a reasonable mediator, as I prefer not to deal with this community (WP:MATH), in general.Greg Bard (talk) 23:49, 13 May 2012 (UTC)

Nice idea, but I lack the patience and commitment - the main bulk of my energies lie elsewhere as the deletionists have sourced me on WP. --Matt Westwood 05:06, 14 May 2012 (UTC)

This image has been discussed on this page twice before: [20] and [21]. It has probably also been discussed on various of the respective talk pages of the affected articles; it's difficult to gauge. Sławomir Biały (talk) 23:23, 13 May 2012 (UTC)

The image is not totally correct in that not all theorems are well formed formulae, at best formal theorems are. I'm happy however for it or something like it to be in articles in circumstances where the 'formal' is explicit or implied like the formal theorem section of theorem. The problem I had with it before was that it kept on being made larger and larger and the text below it longer and longer. Illustrations are supposed to illustrate the text. We should not be putting in mini essays under illustrations. As to the behaviour above being absolutely outrageous, civility is a policy and listed in WP:5P, but WP:PERTINENCE is part of the guideline WP:IMAGES. Policy is more important than guidelines and civility is more important than illustrations. Dmcq (talk) 23:43, 13 May 2012 (UTC)

Okay, so the illo needs improvement. I still believe that before deleting it out of hand, an attempt is made to amend it (or at least to flag that need up) rather than just delete something because it's not liked, for whatever reason. --Matt Westwood 05:06, 14 May 2012 (UTC)

Please also see the bit in WP:5P about 'Since all your contributions are freely licensed to the public, no editor owns any article; all of your contributions can and will be mercilessly edited and redistributed.' and compare to the bit about formal warning above about removing the contributors image. Dmcq (talk) 23:52, 13 May 2012 (UTC)

Ultimately yes, but have a heart. Deletionists have ruined WP for me and many others. --Matt Westwood 05:06, 14 May 2012 (UTC)

I have never seen a reason for inclusion of the image. It's marginally acceptable, although misleading, in theorem and WFF, but has no place in symbol (formal). It's certainly not central enough in Portal:Logic to belong there. — Arthur Rubin (talk) 07:16, 14 May 2012 (UTC)

Well just having had a quick look at the other entries in Portal:Logic/Selected_article I can't say I think any of them are exactly wonderful. However it really is up to people interested in that area to stick better stuff into the portal and I'd only start removing things which were actually badly wrong at the moment. One thing I will say is that the size of the image is about right there I think rather than having the super heavyweight text size used in the articles. I had a look too at the article symbol (formal) and I'm rather confused by it. There is a bit there saying that for instance logical constants are not formal symbols. However the diagram just refers to symbols and strings. I think perhaps there is the same problem there as was in the article theorem where at one stage theorems and the idea of formal theorems as strings following some rules were mixed up together and not properly distinguished. Dmcq (talk) 08:29, 14 May 2012 (UTC)

No. At no point does the article state or imply that a logical constant is not a formal symbol. It says that it is not a symbol of anything. That is to say that a logical constant is an abstract idea. It does not appear to the mind as a particular image. Therefore it is not a symbol of anything in particular.Greg Bard (talk) 08:42, 14 May 2012 (UTC) HEY! You'll have to forgive me. There was a just such a false statement that was added by someone that I was unaware of. I have removed it. It was a valid observation of your part. Greg Bard (talk) 08:51, 14 May 2012 (UTC) Also, Dmcq, I see in an earlier paragraph that you express some concerns with the image which may be addressed in a well crafted caption. Greg Bard (talk) 09:20, 14 May 2012 (UTC)

Magdy's Exchanger at Afd

Please see Wikipedia:Articles for deletion/Magdy's Exchanger. Magdy's Exchanger appears to be original research by Ahmed Magdy Hosny (talk · contribs). JRSpriggs (talk) 23:43, 13 May 2012 (UTC)

Electrodynamic tether

I noticed the reason for the Wikify tag on the article Electrodynamic tether. I have no idea how to do that, and I don't know if other editors at Wikipedia:WikiProject Wikify do either. Can someone here try to make those improvements? Ryan Vesey Review me! 02:52, 16 May 2012 (UTC)

Gosh, that article is something of a monster. The images-as-figures issue is now resolved; I don't do wikitables, but resolving them shouldn't be hard for someone who knows the syntax. Joel B. Lewis (talk) 17:00, 16 May 2012 (UTC)

I think you might do better to ask at Wikipedia talk:WikiProject Physics or Wikipedia talk:WikiProject Engineering. JRSpriggs (talk) 17:16, 16 May 2012 (UTC)

Formatting question

Easy question to answer I'm sure, I just can't seem to find the answer. We prefer to write "[[homomorphic image]]s" to "[[homomorphic image|homomorphic images]]", right? I mean that we prefer to put the s outside the linking rather than require using the pipe. Rschwieb (talk) 12:13, 16 May 2012 (UTC)

The WP Manual of style WP:LINK says that either is okay, but most editors put the "s" outside the brackets:

Plurals and other derived names. When forming plurals, you can do so thus: [[apple]]s which includes the final "s" in the link like this: apples. This is easier to type and clearer to read in the source text than [[apple|apples]]. This works not just for "s", but for any words that consist of an article name and some additional letters. For details, see Help:Link. (This does not work for affixes beginning with hyphens, apostrophes, or capital letters.)

In theory, both approaches will look identical to the reader (the "s" will be blue in both situations). --Noleander (talk) 12:58, 16 May 2012 (UTC)

From WP:LINK#Piped_links

Piping and redirects. Per § Link specificity above, do not use a piped link where it is possible to use a redirected term that fits well within the scope of the text. For example, let's assume the page A Dirge for Sabis is a redirect to the page The Sword of Knowledge, and while you're editing some other article, you want to add a link to A Dirge for Sabis. You may be tempted to avoid the redirect by directly linking to it with a pipe like this: [[The Sword of Knowledge|A Dirge for Sabis]]. Instead, write simply [[A Dirge for Sabis]] and let the system handle the rest. This has the added advantage that if an article is written later about the more specific subject (in this case, A Dirge for Sabis), fewer links will need to be changed to accommodate for the new article.

I think this suggests a general principle of transparency being preferred (avoiding piped links when an unpiped link will do). — Quondum^☏ 13:16, 16 May 2012 (UTC)

Since we have some bots which will remove the pipe in this case, I would say yes to avoid an extra edit. But do not edit the source merely to change that one thing. Only change it incidentally when the opportunity arises while editing something else in that section. JRSpriggs (talk) 16:49, 16 May 2012 (UTC)

Thanks for the advice, all. Rschwieb (talk) 21:14, 17 May 2012 (UTC)

Weisstein and Wolfram as source ?

My recent edit in absolute value has been reverted and the summary of the reversion links to Wolfram research and Weisstein as source. I agree that sourcing to Weisstein is frequently easy. But it is a commercial ressource, which is not peer reviewed. Is it correct to use it as authoritative source? D.Lazard (talk) 11:35, 9 May 2012 (UTC)

First of all we need to distinguish between MathWorld (Weisstein) and WolframAlpha. And secondly we need to distinguish between actual sourcing and using some external site as a discussion/plausibility argument. Personally I'd consider the comment in the version history as the latter rather than the former.

Whether a source is commcercial or not doesn't really matter imho. Strictly speaking are many/most scholarly publication commcercial since they are published through commercial publishing companies. Peer reviewed publications are certainly preferred, but in many cases we resort to other reliable (scholarly) publications which have nor undergone a peer review in the sense of a peer review process (for instance many textbooks).

MathWorld is certainly a "mediocre" source in some regard, however formally it qualifies as a reliable source and in many situations it is perfectly to be used as a source (however it might always be replaced by a better source of course as peer reviewed journal publication or some well received textbook).

WolframAlpha might be more controversial, in theory it could be treated like some tertiary source (say an encyclopedia or some scientific database). However since its content is partially program generated that might be a questionable call still.--Kmhkmh (talk) 13:24, 9 May 2012 (UTC)

It's perhaps worth noting that in this case, the changes being made were totally inane: things like replacing x/|x| with |x|/x and a*sign(a) with a/sign(a). (Actually the latter was not just inane but also wrong.) On general principle: the idea that the order of the symbols on Wikipedia should be required to match the order produced by any Wolfram product is absurd; the "reference" to WolframAlpha is particularly absurd, because who knows if it will remain stable in the order that it writes its output? (I'm also skeptical that it counts as a reliable source.) --Joel B. Lewis (talk) 13:55, 9 May 2012 (UTC)

Well you can certainly argue that there was some oversourcing as in sourcing well known domain knowledge and/or sourcing any any sentence or sign. The actual content dispute in this case didn't make much sense either and we certainly don't need WolframAlhpa to tell us how to write formulas.--Kmhkmh (talk) 15:08, 9 May 2012 (UTC)

The last section was referenced entirely to Wolfram Alpha. I have removed this section. The penultimate section had no references at all, and was unreferenced for a very long time. That section prominently bore a citation needed tag until it was inappropriately removed by some editor, who then proceded to fill it up with more original research. I have removed that section as well. The same editor added things like:

$\int |f(x)|\,dx=\operatorname {sgn} f(x)\int f(x)\,dx$

to the article (also now removed). This article needs to be watched by more people who actually know something, since there is clearly a WP:RANDY at work. Also, I'm sure a glance at the discussion page is enough to convince a mathematician that the Dunning-Kruger effect is in full swing there. Sławomir Biały (talk) 14:16, 9 May 2012 (UTC)

I certainly don't think that W|A is a WP:RS. At best it qualifies as a tertiary source, but I've seen enough unambiguously wrong material from it that I wouldn't trust it even as that. (I used to send in error reports, but I've stopped.) I'm fine with MathWorld (though additional sourcing is best, as usual). CRGreathouse (t | c) 17:02, 11 May 2012 (UTC)

Additional eyes at absolute value are needed. There is an editor keen on adding several sections of original research, including the one sourced entirely to Wolfram Alpha. Sławomir Biały (talk) 21:09, 18 May 2012 (UTC)

---

KlappCK (talk · contribs) insists that some of his edits were valid. I am convinced that the sense of an article has higher priority than formatting, and (basic correctness of) formatting has a priority over tweaks such as replacement of \frac with \tfrac. If one apparently degrade the sense of an article, other users should not hesitate to summarily remove all tweaks to restore the correct sense. I do not object against KlappCK's formatting tweaks, although a user who easily disrupts a complicated content and starts edit wars over an OR section cannot enjoy my personal trust. Incnis Mrsi (talk) 07:40, 19 May 2012 (UTC)

Affine Grassmannian

Could someone please check the validity of this edit? — Fly by Night (talk) 23:22, 19 May 2012 (UTC)

I have corrected this mistake, but the article has multiple issues: the Grassmannian is a smooth algebraic variety defined over any field. Therefore it is a manifold if the basis field is the real or the complex one. It is defined independently of any Euclidean structure and any inner product; nevertheless they are introduced without any explanation in the definition. And so on. D.Lazard (talk) 03:03, 20 May 2012 (UTC)

Unless I've made an arithmetic mistake or the articles on the Euclidean group and the orthogonal group lie about their dimensions (but they look fine to me), the original edit is correct. Just take the dimension of E(n) minus those of E(k) and O(n − k). I.e. I think D.Lazard's correction is wrong (the n² terms will cancel). RobHar (talk) 03:07, 20 May 2012 (UTC)

I agree and I have corrected my edit. It remains that it is crazy to use Euclidean metrics and orthogonal group, that have nothing to do in this purely affine question. D.Lazard (talk) 07:11, 20 May 2012 (UTC)

While it's true that we should have a definition of the affine Grassmannian as a scheme, the definition as it currently appears is more accessible, rather than describing it as a certain scheme representing some moduli problem. Also, to be fair, the article is actually called "Affine Grassmannian (manifold)". Since this is a vector bundle over the Grassmannian, is it simple to write down a sheaf of O_Gr-algebras whose relative Spec is the affine Grassmannian? RobHar (talk) 13:52, 20 May 2012 (UTC)

IMO the best definition for this article is that which is implicit in the second section: quotient of the set of the sequences of n−k independent affine forms by the action of the the linear group of rank n−k. This may be written in an elementary way. Then the proof that it is a manifold (in case of a real or complex basis field), a smooth abstract algebraic variety, a scheme, a sheaf, ... is almost immediate as soon as one knows these notions. D.Lazard (talk) 17:56, 20 May 2012 (UTC)

I am not sure what's wrong with defining it to be the collection of affine planes. The second one introduces coordinates, one also easily shows that the resulting collection is a manifold. Expressing this in terms of k-forms may be a nice theorem, but it is hardly a definition. Tkuvho (talk) 12:33, 21 May 2012 (UTC)

Is the Kronecker delta a function, or "notational shorthand"

The Kronecker delta article seems unsure of its subject's identity. Please discuss at Talk:Kronecker delta#Clarification: is the Kronecker delta a function, or "notational shorthand"?. --TSchwenn (talk) 17:04, 21 May 2012 (UTC)

Original research classification of magic cubes

The Pantriagdiag magic cube (AfD discussion) article is currently listed for deletion. Other articles in the same vein are diagonal magic cube, pantriagonal magic cube, pandiagonal magic cube, and perfect magic cube. I observe that we seem to have a bit of a problem with magic cube classification. I refer you to the second sentence of magic cube classes, whose boldface is in the article itself:

This new system is more precise in defining magic cubes.

The new system, it turns out, is the invention of Harvey Heinz (talk · contribs), who put up his new system on two sets of WWW pages and in a self-published book (Harvey D. Heinz Publishing), and who came to Wikipedia and wrote all of these "-agonal" articles, the magic cube classes article, and also the perfect magic cube#An alternative definition section of the perfect magic cube article. Wikipedia seems to be presenting an acknowledged idiosyncratic and novel classification of this subject.

Uncle G (talk) 15:09, 22 May 2012 (UTC)

List of scientific constants named after people

The list of scientific constants named after people includes a section on mathematical constants. The mathematical and physical parts should each be a hundred times as long as it is. Work on it. Michael Hardy (talk) 22:17, 22 May 2012 (UTC)

Template:WikiProject Mathematics

I would like to resurrect Template:WikiProject Mathematics. It is no longer used. Template:Maths rating is used instead. I think it is nice to be consistent with other wikiprojects. Makes the housekeeping easier. Is there WP-wide guidelines on this sort of thing? -- Alan Liefting (talk - contribs)

There is no wiki-wide guideline. There was a recent discussion in March [22] that resulted in the current name being kept.

There aren't actually any housekeeping problems with the current name. On the other hand, unlike other projects, we do not need to tag articles just to say they are related to math; the name "maths rating" emphasizes that the purpose of the template is rating information. — Carl (CBM · talk) 01:59, 23 May 2012 (UTC)

Hmmm. This makes it a little harder for editors who work across all WikiProjects. From the discussion it looks like I am not the only one who has run into this little glitch. -- Alan Liefting (talk - contribs) 02:14, 23 May 2012 (UTC)

In general, if you don't deal much with mathematics articles and aren't comfortable assessing them, there's no reason why you need to worry about the {{maths rating}} template at all, you can just ignore it. — Carl (CBM · talk) 02:18, 23 May 2012 (UTC)

Category template deletion

Wikipedia:Templates_for_discussion/Log/2012_May_23#Template:Category-Logic.2Fheader

I wonder what you guys think about this template deletion at Category:Logic. Greg Bard (talk) 01:18, 24 May 2012 (UTC)

I see it has provoked Wikipedia:Village pump (policy)#Competition for the worst Wikipedia page - be in to win!. Personally I was just ignoring the deletion talk as I have a bit of a laissez faire attitude unless things really cause trouble and also I think that business is rather unfair about the template. Dmcq (talk) 18:17, 25 May 2012 (UTC)

Power spectrum estimation

Our coverage of power spectrum estimation (spectral density estimation) seems very weak, with very little bringing together or contrasting the different methods, or giving historical perspective. Indeed, most articles looking for a signal processing treatment of the subject appear to have been being redirected to spectrum analyzer, about a hardware box with very little discussion of algorithms usually used in pure-software methods.

In particular, there is very little discussion of all-poles versus all-zeros methods. There appears to be nothing at all about John Parker Burg or the Burg algorithm. We have quite a detailed article on the Levinson recursion, but nothing to say that this is perhaps its most important application. Linear predictive coding appears to exist in a silo of its own, without even a link to ARMA modelling; while in turn the article on ARMA models doesn't appear to mention power spectrum estimation at all. Autoregressive model is a bit better, but doesn't give any sense how a pure AR fit is likely to compare to other fits.

It probably doesn't help that spectral analysis goes to a dab page, and the top link spectrum analysis that probably ought to be merged into spectroscopy.

This is very poor. Given the importance of this topic in signal processing and applications, we ought to be able to match at minimum the level of discussion in Numerical Recipes at least. But at the moment we're way short. Anybody out there willing to step up to the plate? Jheald (talk) 09:23, 26 May 2012 (UTC)

Cross-posted to WT:WPSTATS, WT:PHYSICS Jheald (talk) 09:29, 26 May 2012 (UTC)

Discussion moved to Talk:Spectral density estimation#Coverage. --TSchwenn (talk) 17:12, 26 May 2012 (UTC)

maclaurin

The following footnote at Colin Maclaurin is sourced at a personal page at the university of rochester:

"Neither Newton nor Leibniz – The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala". MAT 314. Canisius College. Retrieved 2006-07-09."

I wonder if it is the optimal source for the information. Tkuvho (talk) 08:20, 29 May 2012 (UTC)

It is a powerpoint and a book or article would be better. But to be frank I was pleasantly surprised by its quality. It might be I've come across too many people pushing the evidence way past where it should go when bigging up their countries contributions.. Dmcq (talk) 09:00, 29 May 2012 (UTC)

In any case, it is not clear which assertion is sourced from this course. In fact I can not understand the paragraph referring to this source, especially the sentence "At the time, Maclaurin was unaware and published his work in Methodus incrementorum directa et inversa, Maclaurin series which are Taylor series expanded around 0, and are not attributed to Maclaurin due to the past discoveries, ...". Can someone understand this? D.Lazard (talk) 09:17, 29 May 2012 (UTC)

My guess would be that the footnote is only used for the assertion that some form of Maclaurin series was known to the Kerala school. There is another reference for this assertion in Taylor series which points to an article by Dani; that might be a better one but I cannot access it. Regarding the sentence D.Lazard quotes, Methodus incrementorum directa et inversa was written by Taylor, so something has gone wrong there. I rewrote the paragraph using the article by Gradiner referred to, so hopefully it makes more sense now. -- Jitse Niesen (talk) 11:25, 29 May 2012 (UTC)

The Canisius College link is broken 2013-05-01

Content fork in Finitely generated projective module

The page Finitely generated projective module has been created recently. IMO, this is a redundant content fork and this page has to be merged into Projective module. I have started a discussion in Talk:Finitely generated projective module and the author of the article disagrees. Please comment there. D.Lazard (talk) 13:04, 27 May 2012 (UTC) — (Links corrected after reading next post. D.Lazard (talk) 14:13, 27 May 2012 (UTC) )

I think you mean Finitely generated projective module. --Zundark (talk) 13:52, 27 May 2012 (UTC)

OOPS. You are right. Such a long title is, may be, another reason to merge. D.Lazard (talk) 14:13, 27 May 2012 (UTC)

Actually the precise term would be "finitely generated projective module over a commutative ring possibly without unity" (sorry, couldn't resist) The exclusion of unity is useful in allowing a commutative Banach algebra, as I understand. I think the subject suffers from a lack of catchy name. -- Taku (talk) 15:54, 30 May 2012 (UTC)

Jun 2012

Bell's theorem

The article on Bell's theorem has been hijacked by crackpot Joy Christian and his cronies. Any attempt to remove references to Christian's discredited work (not published in any peer-reviewed journa, and shown o be fundamentally flawed by a long list of authorities in the fieldl) is immediately "undone" by Christian himself or his supporter Fred Diether. Conflict of Interest!

But if nobody cares about this article better to leave it to the crackpots. Richard Gill (talk) 18:31, 29 May 2012 (UTC)

Here's a silly question. If authorities have taken the trouble to point out the flaws in Christian's work--i.e. if Christian's work has received significant coverage in reliable sources--does that make it notable? I guess you're hoping that the answer is no, but the question does need to be asked. Jowa fan (talk) 03:18, 30 May 2012 (UTC)

It certainly can do okay or give it enough weight in an another article for inclusion I don't believe that is true in this case though. Dmcq (talk) 07:40, 30 May 2012 (UTC)

Generally, in an article about the crackpots, notability is the most relevant criterion. However, in an article about a mainstream scientific topic, we should not treat fringe views, as this often gives them equal WP:WEIGHT. The goal of an encyclopedia article on something like Bell's theorem is to give the reader a treatment of the subject as it is understood by the vast majority of standard, peer reviewed sources. Sławomir Biały (talk) 14:46, 30 May 2012 (UTC)

Thanks, Sławomir, I think that applies in this case. Jowa fan (talk) 00:10, 31 May 2012 (UTC)

Richard Gill called me “crackpot Joy Christian.” I wonder what his criterion of crackpot is. I let the readers judge for themselves. Here are my credentials: Dr. Joy Christian obtained his Ph.D. from Boston University in Foundations of Quantum Theory in 1991 under the supervision of the renowned philosopher and physicist Professor Abner Shimony (the “S” in Bell-CHSH-inequality). He then received a Research Fellowship from the Wolfson College of the University of Oxford, where he has remained affiliated both with the college and a number of departments of the university. He is an invited member of the prestigious Foundational Questions Institute (FQXi), and has been a Long Term Visitor of the Perimeter Institute for Theoretical Physics, Canada. He is well known for his contributions to the foundations of quantum and gravitational physics, including quantization of Newton-Cartan theory of gravity, generalization of Special Theory of Relativity to incorporate the objective passage of time, and elimination of non-locality from the foundations of quantum physics. A partial list of his publications can be found here: http://arxiv.org/find/all/1/au:+Christian_Joy/0/1/0/all/0/1 — Preceding unsigned comment added by 86.148.6.36 (talk) 22:03, 31 May 2012 (UTC)

As for the paper in question, "Disproof of Bell's Theorem", http://arxiv.org/pdf/1103.1879v1.pdf , is published in my peer-reviewed book, http://www.brownwalker.com/book.php?method=ISBN&book=1599425645, and is widely discussed on the Internet. My work has also been cited in several *published* articles, at least two of them in the Physical Review (not to mention its citations in some lesser known journals). I have given invited talks about my work on several occasions during the past five years. The book itself is only just published, and citations to it will undoubtedly follow in due course. On the other hand ALL of Richard Gill’s misguided, erroneous, and unpublished arguments against my work have been comprehensively debunked, many times over, not only by me but also by several other knowledgeable people on the FQXi blogs. I myself have given a systematic refutation of his misguided arguments in the following two papers: http://arxiv.org/abs/1203.2529 and http://arxiv.org/abs/1110.5876 -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 22:13, 31 May 2012 (UTC)

Whether or not you are a crackpot, your book is not peer-reviewed, and your result is not generally accepted. If discussed in peer-reviewed articles, it may be mentioned as a claimed disproof of Bell's Theorem. — Arthur Rubin (talk) 07:18, 1 June 2012 (UTC)

@Arthur Rubin: My book IS peer-reviewed. My work IS cited and discussed in Physical Review and other journals, and NOT as negatively as you are trying to suggest. You have no proof of what you are claiming. You are clearly biased.

On a different note, I urge the Wikipedia community to remove Richard Gill’s slanderous name claiming from his post above. As you can judge from my qualifications I listed above, his name calling has no justification whatsoever. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk • contribs)

Your book IS NOT peer-reviewed. That would mean the publisher submitted it to your peers for review before publication. If it were reviewed in Phys.Rev., that would not constitute peer review; it might indicate notability, but not reliability.

As for Gil, he shouldn't have called you a crackpot. However, there are people much more established than you are who call you a crackpot, so I'm tempted to modify the places where you were called a crackpot to "so-called" crackpot. — Arthur Rubin (talk) 08:18, 1 June 2012 (UTC)

@Arthur Rubin: My book *IS* peer-reviewed. There are also people who call me a genius; so perhaps you should refer me as a “so-called genius.” -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 08:38, 1 June 2012 (UTC)

Nonsense. If your book was peer-reviewed, your publisher would have said so. And you need a cite that people call you a genius. — Arthur Rubin (talk) 08:40, 1 June 2012 (UTC)

Nonsense. My book *was* peer-reviewed, and my publisher does say so. I do not have to cite people who call me a genius. One can see that from my one-page paper itself: http://arxiv.org/abs/1103.1879 — Preceding unsigned comment added by 86.148.6.36 (talk) 09:18, 1 June 2012 (UTC)

From your one-page paper itself I see that indeed, your idea of what is stated by Bell theorem is far from that of Bell. Thus, treating you as the next genius after Bell, I'd rename your paper as follows: "Disproof of Christian strengthening of Bell theorem". Boris Tsirelson (talk) 11:33, 1 June 2012 (UTC) :-)

Boris, I respectfully disagree (if I understand you correctly). Bell claimed that no functions of the form A(a, L) = +/-1 and B(b, L) = +/-1 can reproduce correlations of the form E(a, b) = -a.b. “This is the theorem” (his exact words). What Bell did not realize is that this claim is true if and only if the co-domain of the functions A(a, L) and B(b, L) is NOT a unit parallelized 3-sphere, S^3. My one-page paper shows an explicit construction of the fact that when the co-domain of A(a, L) and B(b, L) is taken to be S^3, the correlations are inevitably E(a, b) = -a.b. I urge you to have a look at this longer paper to see my compete argument: http://arxiv.org/abs/1201.0775 . Thanks. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 12:10, 1 June 2012 (UTC)

Ah, now I see, thank you for the clarification; I was not able to understand your text "as is", but now I know what did you really mean. Well, then we agree: “This is the theorem” was said by Bell about (+/-)-valued functions. For vector-valued functions, this is exactly what I called "Christian strengthening of Bell theorem"; and it is wrong, of course, so you are able to disprove it, of course. But in fact, for vector-valued functions it was "disproved" by Bell himself, in the same (historic) article; by doing this he showed that quantum spin measurements can indeed violate Bell inequality. Boris Tsirelson (talk) 13:24, 1 June 2012 (UTC)

I am afraid you still haven’t understood what I have shown. The functions A(a, L) and B(b, L) both Bell and I are postulating for measurement results are (+/-)-valued functions only, but the co-domain I am using is S^3 instead of the real line. In other words, A(a, L) and B(b, L) for me are maps of the form +/- 1 = A(a, L) = R^3 x H maps to S^3, where H is the hidden variable space. So A(a, L) and B(b, L) in my model are pure binary numbers, +1 or -1. They are not vector-valued, although they have been constructed out of a product of two bivectors. The difference is in the co-domain of these functions only, not in the actual values of A and B, which are still scalars, +1 or -1. Note that scalars, +1 and -1, are as much a part of the 3-sphere as the bivectors are. – Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 14:20, 1 June 2012 (UTC)

Yes, I haven’t understood. Yes, the two-point space {-1,+1} can be treated as embedded into the sphere (as a pair of opposite points), but this embedding does not change their correlation.

Anyway, the discussion becomes too specific for this page. If you like, we can continue it on my (or your) talk page. Boris Tsirelson (talk) 15:05, 1 June 2012 (UTC)

I have added some explanation of my model on your talk page. -- Joy Christian

Whatever the outcome of this discussion, it is clear that we should not cite Joy Christian's self-published work (WP:SELFPUB). There has been a long tradition of criticism of Bell's theorem from the fringes of physics. If mention of this is to be included in the article, it should be sourced to a reliable secondary source documenting such criticism and the replies of the scientific mainstream (WP:NPOV,WP:PSTS). Otherwise, including criticisms sourced to the primary literature is considered to be original research, and is forbidden by Wikipedia policy. Sławomir Biały (talk) 13:51, 1 June 2012 (UTC)

Bell's Theorem (bis)

Comments on Talk:Bell's_theorem#Seeking_consensus_to_exclude_the_disproof_of_Bell.27s_theorem will be appreciated. Thanks. History2007 (talk) 00:42, 1 June 2012 (UTC)

• As a brief aside, I just wanted to say that the whole episode is a bit amazing and embarassing, and I'm sad to see geometric algebra caught in the middle :( Rschwieb (talk) 01:18, 1 June 2012 (UTC)

I urge the Wikipedia community to remove Richard Gill’s slanderous name claiming from his post above. As you can judge from my qualifications I listed above, his name calling has no justification whatsoever. -- Joy Christian — Preceding unsigned comment added by 86.148.6.36 (talk) 06:13, 1 June 2012 (UTC)

Both of you, would you mind going and bothering Wikipedia talk:WikiProject Physics instead? I don't know what we have to do with the matter. --Trovatore (talk) 08:42, 1 June 2012 (UTC)

It is a physics result, but it is mainly based on simple maths and logic rather than needing any great understanding of physics. I see the notification here as being reasonable. The 'discussion' should definitely be at the articles talk page though. Dmcq (talk) 08:48, 2 June 2012 (UTC)

betterexplained?

I don't recall http://betterexplained.com/archives/ being discussed in this space so I would like to raise the issue of whether this is a reliable source. Also, would it be appropriate to cite it in a footnote in the lede of an article. Tkuvho (talk) 07:29, 1 June 2012 (UTC)

A similar question with regard to http://plato.stanford.edu/ In this latter case, there are some serious factual errors. The chronic problem with these websites is that they are by no means peer reviewed. The peer review process certainly does not eliminate all errors, but its absence does not help, either. Tkuvho (talk) 07:33, 1 June 2012 (UTC)

We use many non peer reviewed sources such as textbooks and Stanford's Encyclopedia of Philosophy is comparable to that and hence a reliable source.

As far as betterexplained.com is concerned I wouldn't regard that as a reliable source and it's beyond me why you even would want to compare that to Stanford's Encyclopedia of Philosophy. They have hardly anything in common other than being available online.--Kmhkmh (talk) 09:12, 2 June 2012 (UTC)

MathJax issue

Tracked in Phabricator
Task T38059

I'm not sure if this is a known issue, but there seem to be some inconsistencies in the way the Wikimedia parser processes TeX and MathJax. Consider <math>a<b</math>:

$a<b$

versus <math>a\lt b</math>

Failed to parse (unknown function "\lt"): {\displaystyle a\lt b}

If MathJax is enabled, the first equation does not display correctly but the second one does. If "Render as PNG" is enabled the first equation displays correctly, and the second generates a parse error "Failed to parse (unknown function\lt)". This seems to be quite bad, since half of users will see one or the other of the two errors! Sławomir Biały (talk) 14:19, 31 May 2012 (UTC)

Now after writing this, the first equation seems to dispay correctly. Strange. Sławomir Biały (talk) 14:20, 31 May 2012 (UTC)

Perhaps related to this bug [23], though I don't see exactly how that would cause it.--JohnBlackburne^words_deeds 14:35, 31 May 2012 (UTC)

Yep. The first problem is bug 36059. Helder 15:12, 31 May 2012 (UTC)

In light of the fact that MathJax is "still experimental", I don't think the preferences page should also say that it is "recommended for most browsers". These two directives seem to be incongruous. Sławomir Biały (talk) 16:39, 31 May 2012 (UTC)

Obviously, this is the wrong place to complain about it (and that fixing this bug, pointed out even before the release, has been described as not being of a high priority). Just in case you missed it, the perceived editor-developer divide is being debated for a while now. Nageh (talk) 17:02, 31 May 2012 (UTC)

I don't want to join a fight particularly. It seems like this recommendation would be a trivial thing to change in the next update. Sławomir Biały (talk) 17:39, 31 May 2012 (UTC)

Worth bearing in mind that the "math" tags are not handled well by MathJax - they're deprecated. If you want to use MathJax then go the whole way. Then you can use dollar signs as delims or backslash-openround, backslash-closeround instead. But dollar delims IMO make more sense because they're not as fiddly to type as backslash-openround, backslash-closeround. --Matt Westwood 07:34, 3 June 2012 (UTC)

Shouryya Ray on AfD

See Wikipedia:Articles for deletion/Shouryya Ray.

Is this person notable?

Are the news media's claims about him true or merely sensationalist exaggerations that help sell newspapers?

Opine at the page linked to above. Michael Hardy (talk) 16:45, 3 June 2012 (UTC)

Lester Dubins

I was surprised that we had no article on Lester Dubins. I've just created one. It needs further work, both within the article itself and in other articles that ought to link to it. Michael Hardy (talk) 17:31, 3 June 2012 (UTC)

pi: 9th Top-priority FA article for project

The pi article has been nominated for Featured Article status. If successful, this will be the ninth Top-priority FA article for the Mathematics project. Editors familiar with the FA criteria are welcome to provide input at Wikipedia:Featured article candidates/Pi/archive1. --Noleander (talk) 12:33, 15 May 2012 (UTC)

The pi article mentions the series:

$\pi ={3}+{\frac {4}{2\times 3\times 4}}-{\frac {4}{4\times 5\times 6}}+{\frac {4}{6\times 7\times 8}}-{\frac {4}{8\times 9\times 10}}+\cdot \cdots$

A reviewer at FAC asked what the origin of this series is (who, when). Does anyone have a reliable source that identifies the origin of this series? Sources are available that define the series, so that is not a problem: it is the origin that is needed. Thanks in advance. --Noleander (talk) 20:01, 15 May 2012 (UTC)

I notice a lot of references to Eric Weistein's website, including the reference for this series. I wouldn't consider him a reliable source on anything. It's probably worth trying to find a better source. Sławomir Biały (talk) 20:12, 15 May 2012 (UTC)

Weisstein is used as a source only for "motherhood" factoids: formulae that are represented in hundreds of math texts (e.g. definition of polar coordinates). I don't mind changing those cites to hardbound math books, but I'm pretty certain that there was consensus within the Math project that Weisstein is a valid RS for simple or basic math-related facts. Is that not true? Of course, Weisstein should not be used as a source for contentious or complex material. --Noleander (talk) 20:22, 15 May 2012 (UTC)

If MathWorld is not an acceptable RS for basic math facts, I have at hand A guide-book to mathematics by Bronshteĭn and Semendiaev (H. Deutsch, 1971). Any objection to using that for area of a circle, etc? --Noleander (talk) 20:40, 15 May 2012 (UTC)

... also, just to clarify, the issue here is not the validity of the series (it is documented in many RSs) but rather: does any editor here know of additional detail about the origin of that series, so that additional detail could be incorporated into the article? At the moment, the article does not contain any statement about the origin of that series. --Noleander (talk) 20:24, 15 May 2012 (UTC)

All right, I think we are in good shape now: user:RJHall found a source for the above mentioned series. And, following the sage advice of user Sławomir Biały, I'm eliminating the use of MathWorld as a source in the article (just a couple more to go). So, no more help needed on this issue. --Noleander (talk) 22:56, 15 May 2012 (UTC)

Hello everyone! I would appreciate if a few people could lend their expertise over at the nomination page, even if it is just to confirm that one little section is not a piece of nonsense. I am just concerned about the little things, the off emphasis here, the obscure odd fact inserted there, that have a way of getting into even (or especially?) meticulously-researched articles, and that bespeak inexpertness. For example, detailed discussions of π's relationship to the Mandelbrot set fractal and the sinuosity of a meandering river (which are above my head) appear in the middle of other content, like a discussion of Euler's identity (the importance of which even I can understand) or the Fourier transform (which I have at least heard of). It just strikes me as a little fishy, though for all I know the article is perfectly well balanced. Which is why I'm asking for some help. Thanks! Leonxlin (talk) 19:33, 31 May 2012 (UTC)

Pi has passed its nomination! Leonxlin (talk) 01:27, 6 June 2012 (UTC)

Some/several MathJax-Formulae are not displayed (correctly)

Tracked in Phabricator
Task T38059

Hello

Did I do something wrong/incomplete? I use Firefox 12.0 (enabled Java & Javascript) on Linux as my browser but sometimes/often mathematical formulae are not or are wrongly displayed. E. g. in the page [24] in the table-style of all these matrices there appears a literal "amp;" for the column separator, or in section "Classification", subsection "Elliptic transforms" the formula "0 \le \mbox{tr}^2\mathfrak{H} < 4.\," is not interpreted at all - it is displayed rawly! (This is the first formula in this article , several follow, but the formulae before seem to be displayed correctly). Thanks in advance for any useful help. Achim1999 (talk) 14:22, 5 June 2012 (UTC)

This is a known bug in the software. Any equation with <, > or & in will not work with the current MathJax. It has been patched in the source so it should not be too long until it that is rolled out. For now you can use User:Nageh/mathJax which is a working implementation of MathJax.--Salix (talk): 15:33, 5 June 2012 (UTC)

Thank you very much. Now I "only" have problems to create my "custom skin file", but I will try. :-)

Achim1999 (talk) 16:16, 5 June 2012 (UTC)

Well it seems to work, the fiel must be named "vector.js" not "skin.js".

At least the rendering is now better and my described errors has gone. The new mistake I observed is: the fraction lines are unusually thick and what is very bad, are too short. So, certain formulae like in the subsection "Determining the fixed points" of the Moebius transformation article become unreadable. A further bug in MathJax, I guess. :-/ Achim1999 (talk) 16:28, 5 June 2012 (UTC)

Thats odd, Moebius transformation#Determining the fixed points looks fine for me. It could be a browser related bug, which browser are you using? You might want to bring this up at User talk:Nageh/mathJax.--Salix (talk): 16:52, 5 June 2012 (UTC)

Yepp, I'm afraid you are right. As I wrote at the beginning of this section, I used Firefox 12.0 under Ubuntu (at work). Now I'm logged into another system (my private) running Gentoo & Firefox 3.6.17. The same section now looks okay. Here fraction(line)s are displayed fine. :-/ Achim1999 (talk) 17:53, 5 June 2012 (UTC)

If its a browser bug it might be worth discussing it with the MathJax people [25]. That would help them sort it out for anyone else who gets the same problem.--Salix (talk): 21:59, 5 June 2012 (UTC)

Poincare's definition of manifold

I added Poincare's original definition of a differentiable manifold at Manifold#Poincar.C3.A9.27s_original_definition. Poincare defined a manifold as a subset of euclidean space which is locally a graph (see details there). This definition is arguably more accessible to a general reader than the more abstract definition involving atlases, charts, and transition functions. The lede could profit from focusing on the subset-of-R^n definition instead of the abstract definition. However, another editor feels that the reader does not need the crutch of Euclidean space to understand the concept of a manifold, and my changes to the lede were repeatedly reverted. Which definition should the lede be based on? Tkuvho (talk) 11:37, 4 June 2012 (UTC)

Having the historical definition in a section on history makes sense, but for example that definition makes it quite hard to see that the graph of the absolute value function, as a subset of $\mathbb {R} ^{2}$ is a manifold (not differentiable at 0), or the unit circle as a subset of $\mathbb {R} ^{2}$ (not locally a graph).

A similar thing happens with the concept of function; the historical definitions were simultaneously more limited in some ways and more broad in other ways than the modern definition, so we can't start the article with them. — Carl (CBM · talk) 12:09, 4 June 2012 (UTC)

I for one have serious difficulty understanding what is meant by the wording. Use of the term "graph" in place of "function" confuses. Also the implication that every manifold is globally embeddable in a Euclidean space should not be implicit in the (modern) definition, even if this is (nontrivially) provable. So, no, not Poincaré's definition in the lead. — Quondum^☏ 12:35, 4 June 2012 (UTC)

The lede as it currently stands (i.e. using a map on the surface of the earth as an example) is utterly perfect. My vote is: leave it like it currently is - non-mathematicians will be able to access it admirably from there. --Matt Westwood 13:38, 4 June 2012 (UTC)

@Carl: the graph of the absolute value function is not really relevant as it is not a smooth manifold (actually as an abstract Riemannian manifold it is perfectly differentiable at 0 also). The circle is indeed locally a graph, either over the x-axis or over the y-axis. As Whitney proved, the two definitions are exactly equivalent. This means that the atlas definition is only different from Poicare's definition in that it is harder to follow. It is neither more limited nor more broad.

@Quondum: y=f(x) is a function; the set of points (x,y) satisfying y=f(x) is its graph in the plane. I think most calculus students are more comfortable with the notion of a graph of a function than with transition functions between charts.

@WestwoodMatt: The current lede does not really tell you what a manifold is. Note that the abstract definition ends up using differentiable functions in the end, as well: the transition functions have to be differentiable functions. The only difference is the abolition of intuition in the abstract definition, according to Arnold. Tkuvho (talk) 13:45, 4 June 2012 (UTC)

A circle is not locally a graph, there's no neighborhood of the 3 o'clock point around which the curve passes the vertical line test. It could be that you mean that the circle is the image of the real line under a suitable embedding, but that is not what "is the graph" means, because the circle is not the graph of that embedding (the graph is at best a noncircular subset of $\mathbb {R} ^{3}$). Whitney's theorem is about embeddings of manifolds, but the embeddings are not generally graphs of functions. — Carl (CBM · talk) 19:08, 4 June 2012 (UTC)

In this setting, a graph means that there exists locally an affine coordinate system in which the manifold is a graph. Nevertheless, under the naive meaning of "graph" as it is used elsewhere in mathematics, it is clearly problematic to say this. Sławomir Biały (talk) 19:36, 4 June 2012 (UTC)

@Carl: you are correct that Whitney's theorem is about embeddings of manifolds. Indeed embeddings are locally graphs of functions by the implicit function theorem (that's the content of the implicit function theorem). Tkuvho (talk) 14:27, 5 June 2012 (UTC)

Sławomir Biały already mentioned what you seem to be ignoring, which is that you are not talking about things that are locally graphs of functions in the usual sense of the term. The "original definition" of a manifold is not going to be more enlightening if it requires readers to apply unusual or field-specific definitions to the terms it uses. As it is usually considered, the implicit function theorem doesn't apply to the side points of the unit circle, because a certain matrix isn't invertible at those points. In fact they use this as an example in implicit function theorem. — Carl (CBM · talk) 02:21, 6 June 2012 (UTC)

Carl, what you seem to be ignoring that our page implicit function theorem is only a special case of a more general implicit function theorem applicable to any smooth submanifold or regular parametrisation thereof. Thus, whenever the gradient of the defining expression is nonzero, the implicit function theorem applies. I explained this in terms of your example, namely the circle, at Manifold#Poincar.C3.A9.27s_original_definition. I usually defer to your judgments when it comes to issues of mathematical logic. Have some common sense to acknowledge that this is not a field you are an expert in, and that your original opposition was based on a misconception. No "unusual or field-specific definitions" here. Tkuvho (talk) 11:27, 7 June 2012 (UTC)

I am quite happy to believe that the way you're using the terminology is common in the area. I'm simply saying that it is not as clear to people outside the area as one might think. — Carl (CBM · talk) 11:44, 7 June 2012 (UTC)

I do not like the definition through graphs of functions, because it is less intuitive (at least for me) and it uses implicitly the implicit function theorem, which is far of being trivial (it is needed to show that a circle, defined as usual by its implicit equation, is a manifold). On the other hand, I do not like either the use of "scale" in the first sentence of the graph, because it appears in neither formal definition. Thus, I propose for the first sentence: "In mathematics (specifically in geometry and topology), a manifold is a mathematical object that, near each point of it, looks like Euclidean space". This has the advantage to be very close to the definition by charts (except that nothing is said on the transition maps, which are needed only for technical reasons). In fact the definition by charts and atlas is simply a formalization of this informal definition. D.Lazard (talk) 16:12, 4 June 2012 (UTC)

@D.Lazard: Thanks for your input. I respect your sentiment in "not liking" the implicit function theorem. However, this theorem is standard for an advanced calculus course. The lede shouldn't be an occasion for pleasing the personal tastes of this or that editor, but rather dictated by the goal of greatest possible accessibility. Certainly the chart definition is an indispensible technical tool, but again the goal of the lede is not necessarily to provide technical tools. Rather, it is to give the reader an idea of the subject matter of the page. Tkuvho (talk) 16:22, 4 June 2012 (UTC)

@Tkuvho: I agree with you that the lead should "dictated by the goal of greatest possible accessibility". But it should, in a non technical formulation, be as close as possible as the technical definition. I "like" the implicit function theorem, what I do not like is to use it implicitly where it is not really relevant. IMO, the "greatest possible accessibility" implies to use only mathematical notions which are unavoidable for given an idea of the subject. Here "near every point" is unavoidable because neighborhoods appear in every definition. On the other hand, "scale" is not needed. The definition through graphs involves a (at least partial) choice of coordinates, which is also not needed. D.Lazard (talk) 16:57, 4 June 2012 (UTC)

I didn't put the "scale" in. Feel free to delete it. As far as choice of coordinates is concerned, it is unnecessary. One can use a coordinate plane in the ambient R^n without the need to choose new coordinates. Tkuvho (talk) 14:30, 5 June 2012 (UTC)

I don't really think the lead is perfect at present. In fact, it seems to be worse than the version from three years ago. I'd like to discuss possibly bringing back this earlier revision of the lead. In any event, I don't think it is a good idea to emphasize Poincare's original definition of manifold. Not many sources do this, and at least the motivational examples section of the article would need to be rewritten from this point of view. Sławomir Biały (talk) 16:37, 4 June 2012 (UTC)

The current version of the lede expects the reader to know what a homeomorphism is, what a topological space is, and what a neighborhood is. Is this more accessible than the graph of a function? Tkuvho (talk) 11:30, 6 June 2012 (UTC)

I think you are arguing that "graph of a function" would be easier to understand for people outside the area. I do know what a manifold is, but I don't find the "graph" explanation clearer even for one-dimensional manifolds, and it's much harder for me to visualize a 3-dimensional manifold as a graph of a function than as something locally homeomorphic to $\mathbb {R} ^{3}$. (And either way we have to know what a neighborhood is, because it's "locally a graph of a function".) — Carl (CBM · talk) 11:44, 7 June 2012 (UTC)

May I point out that this whole discussion should be taking place at talk:manifold, not here.TR 12:28, 7 June 2012 (UTC)

List of scientific constants named after people

The List of scientific constants named after people may not be notable, according to a recent tag put at the top of the article. Apparently what is needed is a literature citation showing that the topic of scientific concepts named after people has received attention from the authors of refereed publications. Michael Hardy (talk) 02:49, 9 June 2012 (UTC)

You should add a further category "political naming enforcement" for this page or have you not meet scientific constants fighting for naming of different people names? :-/ Achim1999 (talk) 15:15, 9 June 2012 (UTC)

I've cited a scholarly source and deleted the "notability" tag. Michael Hardy (talk) 17:08, 10 June 2012 (UTC)

Probabilistic-Complexity Theory

After barely glancing at the new article titled Probabilistic-Complexity Theory, I'm already getting suspicious of it. Wikipedia-newbieisms are not a reason for suspicion of anything but Wikipedia-newbieism, but what is the state of mind of someone who writes a paragraph that starts like this?:

As of now, research is still being done on this theory, but[.....]

Michael Hardy (talk) 17:22, 10 June 2012 (UTC)

Sounds like OR, if not a flat-out hoax. JRSpriggs (talk) 17:27, 10 June 2012 (UTC)

Probabilistic complexity is a valid subject of study in computational complexity theory. What this article describes, though, appears to be pure crankery and original research of a type that fails WP:FRINGE. I've attempted a redirect to the same target as Probabilistic complexity but we'll see whether that lasts. —David Eppstein (talk) 17:29, 10 June 2012 (UTC)

This article also had a prime example of another good indicator that the "abort" button must be hit: "The human brain also interacts with this invisible field,..." Rschwieb (talk) 21:47, 10 June 2012 (UTC)

In the context in which I read the sentence, "As of now, research is still being done on this theory" seemed to mean that when research is no longer being done, it's perfect. As if the writer were unaware of the fact that fields in which research is being done are considered to be of greater interest than those in which it's not. Michael Hardy (talk) 02:03, 11 June 2012 (UTC)

Polynomiography

Can anyone confirm Polynomiography is a valid, notable topic? The question arises after discussions at Talk:Fractal art#Dr. Bahman Kalantari about claims that Kalantari is the inventor of fractals not Benoît Mandelbrot. Input by mathematically minded individuals on the topic would be appreciated. - Shiftchange (talk) 03:12, 11 June 2012 (UTC)

New article created on dual tensors

See here. I have enough understanding to start this article, and did so for reasons in the link, but still no expert (yet) so if anyone who can add extend its scope - please do. You have my many thanks. =) F = q(E+v×B) ⇄ ∑_ic_i 15:35, 10 June 2012 (UTC)

The excitement did not last long... it seems to be the same as the Hodge dual... so it may be deleted/merged already! =( The main article on the Hodge dual seems so much less followable (NOT saying that its badly written, techincal details are definitley neccersary), that I still wanted to create the new one... F = q(E+v×B) ⇄ ∑_ic_i 15:51, 10 June 2012 (UTC)

For the record this is now a redirect to Hodge dual. F = q(E+v×B) ⇄ ∑_ic_i 12:29, 13 June 2012 (UTC)

Modified langle and rangle templates for inline angular brackets

These templates are currently in the database as unused: for ⟨ see p.6 no 5579 and for ⟩ see p.9 no 8935. Recently after reworking them (and wasting a silly amount of time messing around with aligning things, which shouldn't have happened), I added them to ⟨|⟩.

Aesthetically they look ok (sort of), but the concern is they may cause spacing irritations, due to the glyphs in the template (but these are the closest ones matching angular brackets).

What do others think? Any objections to usage? WikiProject Physics has been notified. F = q(E+v×B) ⇄ ∑_ic_i 12:27, 13 June 2012 (UTC)

According to the unicode standard, these aren't the right symbols for angle brackets. These are &#x3008; and &#x3009; which are Chinese punctuation symbols. Again, according to the standard, you should use &#x27E8; and &#x27E9;. However, be warned that these don't display in many browsers. As a result, it's probably better to avoid using inline angle brackets entirely or, if you do use them, then just to use <math> mode. Sławomir Biały (talk) 13:20, 13 June 2012 (UTC)

One of the benefits of templates is that workarounds can be implemented and documented, and fixed once browsers become more capable. In that sense I think that the use of the incorrect unicode symbols would be admissible in a template, even though they should never be permitted directly inserted into an article. I think total avoidance of the an inline representation due to lack of support is worse than a template-based workaround. — Quondum^☏ 14:28, 13 June 2012 (UTC)

Thanks - all points are fair eneogh, I did anticipate the suggested resort to <math>. The principle motivation was for inline bra-ket notation which would look so much neater in html than LaTeX. For now the templates will not be used (much), at least modified to the proper angular brackets. On the contrary - they are in use for the Bracket article... F = q(E+v×B) ⇄ ∑_ic_i 15:15, 13 June 2012 (UTC)

But - the chinese characters are also not supported by all browsers, so some other people will only see a box with ${}^{30 \atop 08}...{}^{30 \atop 09}$ in it.--LutzL (talk) 15:23, 13 June 2012 (UTC)

The chinese characters are now irrelevent as they have been replaced. F = q(E+v×B) ⇄ ∑_ic_i 15:25, 13 June 2012 (UTC)

"Parity of zero" should be the gold standard for math articles

Parity of zero explains why zero is even in an easy-to-read format that I just don't see in other articles, namely Riemann hypothesis. 68.173.113.106 (talk) 21:08, 28 May 2012 (UTC)

So you think our articles should go on for pages and pages about trivialities rather than even attempting to explain anything complicated. That's useful to hear (really!) but I suspect not everyone would agree. —David Eppstein (talk) 22:34, 28 May 2012 (UTC)

And the Degrees of evenness section should be launched directly into the sun.Naraht (talk) 02:15, 29 May 2012 (UTC)

Why? (Fair warning, I wrote it, so I may be a little defensive here.) Melchoir (talk) 03:37, 16 June 2012 (UTC)

I don't think that the article is a useful model for this project. Its contents are not really about mathematics but rather math education; the math is trivial and the pedagogy complex. CRGreathouse (t | c) 04:03, 29 May 2012 (UTC)

There's inherent difficulties in the Riemann hypothesis that are absent in Parity of zero. One would really need to compare articles of about comparable difficulty I think. That was like comparing quantum mechanics to Newton's laws of motion. Dmcq (talk) 08:45, 29 May 2012 (UTC)

Completely agree. The main contributors to parity of zero have done an excellent job, but it is not too hard to write simply about simple subjects. It is much harder to write simply about complex subjects. Gandalf61 (talk) 08:58, 29 May 2012 (UTC)

I see. Maybe we could start a campaign to improve the readability of certain math articles, starting with moderate-readability articles, then working our way up to the really confusing ones. The main reason why I never read them is because they're that confuzzling. 68.173.113.106 (talk) 00:31, 9 June 2012 (UTC)

Well, you know, the subject itself is confusing. Good writing can certainly help (or maybe better stated, bad writing can hurt), but there is no way to make advanced mathematics understandable without some serious effort on the reader's part. Still, absolutely, writing them better is a good thing. --Trovatore (talk) 01:39, 9 June 2012 (UTC)

Golden Section

The featured article has become subject to an (almost) edit war and imho some at partially questionable edits. Hence some 3rd opinions and watchful eyes are needed and appreciated.--Kmhkmh (talk) 22:05, 13 June 2012 (UTC)

Do you mean Golden ratio? Also, I can't make sense of your first sentence -- perhaps you left out some words? --Joel B. Lewis (talk) 22:53, 13 June 2012 (UTC)

Sorry I end to skip words when typing quickly. I hope it is clear now and yes golden ratio and golden section are 2 words for the same thing more or less.--Kmhkmh (talk) 23:04, 13 June 2012 (UTC)

The truth behind is: he is also massivly involved in the german "Goldener Schnitt" article rewriting/fighting which currently happens and in german it is called "golden section". And I withdraw because of the chaos (and opinion pressing about new article design) there. Ask him, why he suddenly must spring in action here, triggering this wasteful issue. ;) Regards Achim1999 (talk) 23:12, 13 June 2012 (UTC)

I'd like to add, "chaos" that you helped to create by questionable and unsourced edits and I'd like to avoid a a repetition of that in en.wp.--Kmhkmh (talk) 09:08, 14 June 2012 (UTC)

I like to add the wording "chaos" was coined not by me, but by a 3rd! And it was not for my contributions, but for the overall situation which currently exists! There are even a guy who must press others to NOT vote! :-( Achim1999 (talk) 10:47, 14 June 2012 (UTC)

Perhaps you two could both stick to discussions of content instead of bringing a flame war here? Thanks. --Joel B. Lewis (talk) 12:21, 14 June 2012 (UTC)

THere's hardly a flamerwar (yet). I answered exactly once to your question and once to Achim's comment.--Kmhkmh (talk) 12:28, 14 June 2012 (UTC)

Diophantine approximation

While we are at it, Diophantine approximation may also need a watchful eye. Achim has added a lot of interesting content, but it could do with some copy editing.—Emil J. 12:59, 14 June 2012 (UTC)

I have started to fix the grammatical errors and opaque wording in Achim's rewrite of Diophantine approximation, and improve its style. I am not checking its mathematical content, just clearing away some of the undergrowth. Maybe someone can follow on behind me and verify the contents ? The sparseness of references in the early parts of the article is somewhat concerning. Gandalf61 (talk) 12:39, 15 June 2012 (UTC)

I have commented Achim1999's edits in the talk page. In summary I prefer the old version, although it was a stub. D.Lazard (talk) 14:29, 15 June 2012 (UTC)

Brubeck, a database of topological information

What do we think of http://www.jdabbs.com/brubeck/? The author is currently asking for feedback here: http://www.reddit.com/r/math/comments/v3y40/introducing_brubeck_an_open_searchable_database/

As a dedicated database, it supports capabilities that a general-purpose wiki like Wikipedia doesn't, including a kind of automated theorem proving. I'm thinking that our articles should link to matching Brubeck entries in the External links section. For example, Knaster–Kuratowski fan should link to http://www.jdabbs.com/brubeck/spaces/cantors-teepee/. But before I create a template in Category:Mathematics source templates and start adding it to articles, I wanted to ask: does anyone object? Melchoir (talk) 03:25, 16 June 2012 (UTC)

Template:Infobox conic section

I have come across {{Infobox conic section}}, and thought perhaps you folks might like it. The infobox is currently not used on any articles. If you don't want it, it can probably be deleted. — This, that, and the other (talk) 10:53, 16 June 2012 (UTC)

References in mathematics articles

I noticed there are very few references to literature in mathematics articles. Is this because mathematics can be easily checked for correctness without consulting literature? When should I consider adding references when adding new content? Lennartack (talk) 15:23, 16 June 2012 (UTC)

Anything dealing with the history, discovery, people, and current research of the specific concept should be cited, and perhaps also applications. Mindmatrix 20:46, 16 June 2012 (UTC)

Let's be honest — it's because we're lazy. The paucity of references should be viewed as something to fix, not something to copy. (On the other hand, I don't think we need to get manic about inline cites — a single general-reference citation for an exposition lasting a paragraph or two is probably sufficient IMHO, provided that everything in it does in fact appear in the cited work.) --Trovatore (talk) 20:56, 16 June 2012 (UTC)

I think if we can aim to get one citation per section that would be good. The problem I've come across a bit too often is people sticking in something they have worked out themselves. I'm a bit easy on that sort of thing if there seems a good reason, but having a citation with a range of page numbers would help keep peoples minds on the idea of summarizing what's there instead of doing their own thing. Dmcq (talk) 21:27, 16 June 2012 (UTC)

In my experience, it helps in keeping track of what appears in which general reference to repeat the general reference (using named refs) every paragraph that it is used (usually at the end). This is especially useful if several general references are used in a section. This is especially useful for future editors trying to improve the exposition, since they do not have to repeat the earlier work of figuring our what is treated where.TR 21:55, 16 June 2012 (UTC)

Suggested FA drive topic: Otto E. Neugebauer

• Don't know if you folks do FA drives, but I ran across a bio of Otto E. Neugebauer on the Internet, and have claimed him as a hero.– Ling.Nut (talk) 09:11, 17 June 2012 (UTC)

Good luck with that — biographies tend to be easier than technical articles for getting though FA, and having a goal like this makes it easier to find improvements to make. But that one needs some effort to get into shape — for one thing, it doesn't even have a section describing his scholarly contributions and their impact. —David Eppstein (talk) 16:53, 17 June 2012 (UTC)

...and it kinda has a faint copyvio-ish odor as well, though I haven't scrutinized it carefully. i don't actually have time to work on it, right now.. posted this hoping others might see it as a worthy task. But... a few months from now, I will probably have time. We'll see. Tks! – Ling.Nut (talk) 02:33, 18 June 2012 (UTC)

... but not too "precise"

I looked at the article Fermat's little theorem and saw an example of a pet peeve of mine: In the "generalizations" section is the formula

$\forall a\in \mathbb {Z} :\quad a^{m}\equiv a^{n}{\pmod {p}}$.

A lot of people who know what is intended by "divisible" have never been exposed to logical $\forall \;$ or set theory $\in \;$ notation, much less have any idea what $\mathbb {Z} \;$ is supposed to mean. It is, IMO, much better to say "for any integer a ...." or even "for any integer a (positive, negative, or zero) ..."

Virginia-American (talk) 12:33, 18 June 2012 (UTC)

Yes, though this example would be bad form in basically any mathematics context. I've changed it. (Actually, it looks like someone more obsessive than I could make a whole bunch of the non-logic articles more readable simply by going through and replacing every instance of \forall with English words.) --Joel B. Lewis (talk) 12:59, 18 June 2012 (UTC)

The WP:MOSMATH explicitly discourages using quantifier notation in mathematics articles. Sławomir Biały (talk) 14:49, 18 June 2012 (UTC)

Well I think that notation is fine if the entry level for the topic is university mathematics. That's definitely not true though for things like Fermats' little theorem! Dmcq (talk) 14:58, 18 June 2012 (UTC)

I don't think there is ever a situation where the writing is improved by using this notation. You never see it in research level mathematics, and almost never in university level mathematics writing, either graduate or undergraduate. Sławomir Biały (talk) 15:52, 18 June 2012 (UTC)

I think replacing the formula by text is a good idea here. BUT "any" should not be used as a quantifier in this context; it is too ambiguous. Use "every" instead. —David Eppstein (talk) 16:06, 18 June 2012 (UTC)

Yes, absolutely, neither "\forall" nor "any" should be used if they can be avoided. (And indeed the FlT article now reads "... for every ....") --Joel B. Lewis (talk) 16:37, 18 June 2012 (UTC)

Have you access to 'Prime curios' book?

If you have access to the book Prime Curios!: The Dictionary of Prime Number Trivia based on the prime curios website could you check it actually includes the coincidences mentioned in Talk:Mathematical coincidence#Prime curios please in the diff putting in 999779999159200499899 and some business about changing from bases 2 and 3 to base 10. Thanks. Dmcq (talk) 16:15, 18 June 2012 (UTC)

Zinbiel algebra

Some doubt has been cast over the validity of the redirect Zinbiel algebra. Views from experts would be welcome. South Jutland County (talk) 21:30, 18 June 2012 (UTC)

What does the first sentence actually mean, and where can one find a discussion of the doubt that is being cast? (Incidentally, to save other users who, like me, don't see it immediately: "Zinbiel" = "co-Leibniz" = Leibniz written backwards. --Joel B. Lewis (talk) 21:56, 18 June 2012 (UTC)

Probably here : Talk:Operad theory#Dubious reference. Anne Bauval (talk) 22:15, 18 June 2012 (UTC)

Thanks. This is not my area of mathematics, but MathSciNet has 19 publications in which the title or review include the word "Zinbiel", by a variety of authors in several languages, dating to 2002. It looks completely legitimate to me. --Joel B. Lewis (talk) 23:17, 18 June 2012 (UTC)

Note that both South Jutland County (talk · contribs · deleted contribs · logs · filter log · block user · block log) and G.W.Zinbiel (talk · contribs · deleted contribs · logs · filter log · block user · block log) (who created the article) are almost certainly sockpuppet accounts of the community-banned user Echigo mole/A.K.Nole. Please see Wikipedia:Sockpuppet investigations/Echigo mole. Mathsci (talk) 06:49, 19 June 2012 (UTC)

Mathematical language must be precise

I suspect that I will need help in a project I am about to undertake. Several articles use the term "evenly divisible" to mean "divisible" which is okay in a non-technical article but not okay in mathematics (it would be like calling 1 a prime number for instance). What bothers me isn't that editors would use this word but that they react with hostility when I attempt to change it - some people feel like they "own the article".

The first resistance I met was in the Y2K article: [26]. One of them suggested that I use "exactly divisible" which is not preferred but I am prepared to compromise this way. I also got reverted on Fermat's Little Theorem [27]. This article relates to number theory so I will not compromise here. Since I am talking to other mathematicians (I hope), maybe some of you could weigh in on the edit wars I post here. Connor Behan (talk) 03:47, 18 June 2012 (UTC)

The phrase "edit wars" should ring warning bells. You've posted two links to pages where you have started an edit war. It's not something to be proud of.

In most contexts, "evenly divisible" means the same as "divisible". The choice of one or the other is just a matter of taste. Personally I prefer "divisible" for mathematics articles such as Fermat's little theorem, but see no reason to delete "evenly" from non-technical pages such as Year 2000 problem. That's only my personal opinion; I doubt that there will be a strong consensus either way. I hope that any further discussion of the topic will remain civil. In particular, public declarations that you refuse to compromise won't go down well on this site. Jowa fan (talk) 05:05, 18 June 2012 (UTC)

We agree on what terminology should be used in mathematics articles :). It seems like we don't agree on what it means to start an edit war - I cited two sources for why my edit made the page better... the people who reverted the change (which even to a non-mathematician should be inconsequential) did not.

Compromise was too strong a word; here's what I meant. A part that worries me is that people seemed to genuinely believe that the standard definition of divisibility allowed 3 to be divisible by 2. I am willing to be civil and take the time to calmly explain why I think they are wrong. But I would not admit that they are right anymore than I would admit that a person saying 1 + 1 = 3 is right. Connor Behan (talk) 06:20, 18 June 2012 (UTC)

There should be something in articles for people who aren't familiar with the stuff but could cope with part of it straightforwardly. The articles are not just compendiums of knowledge, there is a relationship to the people who want to find the stuff. If knowledge is not accessible except to those who already know it then there is zero information in them. As to exactly divisible in an article aimed at a pretty low level that is good. They have spent time at school being drilled into figuring out what seven divided by three is. There is no point paring the language down to the bare essentials and leaving a beautiful struucture that only a mathematician will appreciate. Dmcq (talk) 08:09, 18 June 2012 (UTC)

Exactly divisible is probably better than evenly divisible, because the latter could conceivably be read as implying that the quotient is an even number. --Trovatore (talk) 08:14, 18 June 2012 (UTC)

Good point, more words means more ways to get the wrong meaning ;-) Divisible with no qualification can often be better. I reacted badly to the title 'Mathematical language must be precise' which implied unreadable articles to me. Dmcq (talk) 08:43, 18 June 2012 (UTC)

IMHO, a good way to avoid any ambiguity could be to replace "be divisible by" by "be a multiple of". Personally, I find that "year multiple of 100" sounds better than "year divisible by 100", together with avoiding any ambiguity. D.Lazard (talk) 09:30, 18 June 2012 (UTC)

"Multiple of" has the same problem as "divisible"; a non-mathematician might think it could be a non-integer multiple. This could be a particular problem in calendar-related articles, because there are a lot of cranks running around in that subject area who are pushing some version of calendar reform, or pushing some calendar on religious grounds. Such cranks like to seize on ambiguities, both by making arguments within Wikipedia, and basing arguments in other fora on Wikipedia articles. Jc3s5h (talk) 12:08, 18 June 2012 (UTC)

I think D. Lazard's suggestion to use (integer) multiple is good. Another possiblity is a footnote that says *here, and generally in number theory, "divisible" means "divisible without a remainder".

I don't have a source in front of me, but IIRC Richard Feynmann said (paraphrasing) "of course, 5 is divisible by 2." If someone is unfamilar with number theory and its conventions, restricting numbers to be integers may take a bit of getting used to.

In the original post, Connor Behan said

... Several articles use the term "evenly divisible" to mean "divisible" which is okay in a non-technical article but not okay in mathematics (it would be like calling 1 a prime number for instance).

I disagree. Calling 1 prime is unambiguously wrong (even though Gauss did so sometimes). Saying "exactly" or "evenly divisible", or "divisible without a remainder", or "an (integer) multiple" of is at worst a bit wordy, and may be clearer to Wikipedia's intended audience. Saying "exactly divisible" the first time or two in an article, and then quietly dropping the abverb, seems clearest to me.

Virginia-American (talk) 12:12, 18 June 2012 (UTC)

I disagree that "saying 'exactly divisible' the first time or two in an article, and then quietly dropping the abverb, seems clearest". This approach works well in general writing: "Finnias Tiberius Flubberbuster III of Green Meadow, Wyoming...Mr Flubberbuster...." But in formulas or when writing rules or other legalistic text, any variation in wording often implies a difference in meaning. A reader who has just finished reading several articles, in Wikipedia and elsewhere, about the differences between the Gregorian, Revised Julian, and Julian calendar is apt to be thinking in a mode characteristic of legal scholars or computer programmers, and immediately assume that if the words "divisible" and "evenly divisible" occur in the same document, they must have different meanings. Jc3s5h (talk) 16:36, 18 June 2012 (UTC)

I don't think "exactly divisible" is an improvement over "evenly divisible". A person who hasn't been trained to think that "divisible" applies the quotient of two integers is an integer may think "exactly divisible" means the result is a rational number as opposed to an irrational number.

Is there any evidence whatsoever that any speaker of English has been confused by either of the terms "evenly divisible" or "exactly divisible"? These are long-standing parts of standard English usage; "evenly divisible" has had a wiktionary page for 7 years. Language is inherently somewhat vague, but this is the least-convincing example of this problem I've ever seen brought up on Wikipedia. As long as no one demands that we being using "is an aliquot part of", though, I'll be okay. --Joel B. Lewis (talk) 16:54, 18 June 2012 (UTC)

I've never seen the phrase "exactly divisible" before. In the contexts where it's being suggested for use, I already know what it's supposed to mean. I don't know what I would make of it in an unfamiliar context. Jc3s5h (talk) 17:08, 18 June 2012 (UTC)

Maybe I'll repeat myself, but, IMO, "divisible" should be avoided when it may be easily replaced by "multiple". A mathematical reason is that multiplication is defined prior to division, and it is always better, when reasonable, to use the most basic definitions. But the main reason is that "divisible" may be ambiguous inside mathematics (divisibility inside the integers vs inside the rationals) as well as outside mathematics. Here is an example, which is not far from Y2K article:

Every year is (exactly, evenly) divisible by four into four quarters, but year 2001 is not divisible by four.

D.Lazard (talk) 17:18, 18 June 2012 (UTC)

I suggest that you-all just use the word "divisible" and attach a footnote the first time it is used in an article, saying "In number theory, divisible means with an integer quotient and no remainder.". JRSpriggs (talk) 17:54, 18 June 2012 (UTC)

Footnotes are generally a very bad idea for this sort of thing. As a general comment, this entire issue seems to be trying to find a solution for a non-problem. It is generally clear from the context what "divisible" means. If not, then the editor should try to make it clearer using his or her best judgement. There's simply no need as I see it to mandate any particular one size fits all solution. Sławomir Biały (talk) 18:13, 18 June 2012 (UTC)

Could you elaborate on why footnotes are a bad idea? I thought the footnote idea sounded pretty good until I read your comment. After all parity (mathematics) and number do a similar thing but in parentheses. Connor Behan (talk) 20:48, 18 June 2012 (UTC)

Footnotes in Wikipedia are generally reserved for providing references. Mandating a solution that conflicts with this basic use is a bad idea. Add to that the fact that footnotes encourage unclear writing, and more difficult reading. Sławomir Biały (talk) 21:50, 18 June 2012 (UTC)

Evidence that "evenly divisible" can be misinterpreted is [28], [29], [30], [31], [32], [33] and [34] which took me a few minutes to find on Google. Connor Behan (talk) 20:19, 18 June 2012 (UTC)

Meanwhile, the same five minutes spent would have led you to believe that it's also completely unreasonable to use "is divisible by", since this seems to cause endless confusion: [1] [2] [3] [4] [5]etc. I particularly like [6], in which it is explained that "Divisible in math terms means capable of being evenly divided, without remainder." Meanwhile, the same test proves that "multiple" is also unusable: [7] [8] [9]. (Actually this exercise leads me to believe that "integer multiple" is the best way to go -- multiple does seem to cause fewer problems than any version with "divisible".) Language has a little bit of ambiguity in it, always; replacing "evenly divisible" with "divisible" removes none of the ambiguity at all. --Joel B. Lewis (talk) 21:03, 18 June 2012 (UTC)

Your evidence for "divisible" and "evenly divisible" being equally ambiguous is not very convincing. In the links you posted, people are simply asking what "divisible" means, possibly because it's a word they've never seen before - like "ecclesiastical". In the links I posted, people demonstrate proficiency in English and mathematics and still seek clarification on the word "evenly divisible" because they think it is ambiguous on mathematical grounds. However, I agree that "integer multiple" is better than either of them. Connor Behan (talk) 21:29, 18 June 2012 (UTC)

In any event, none of these links either way seem to be to Wikipedia discussions, so I don't think they have much weight in this matter. Sławomir Biały (talk) 13:59, 19 June 2012 (UTC)

Input from editors who describe themselves as able to contribute to Wikipedia with an intermediate level of proficiency in English, like D.Lazard, is quite helpful. I hope there will be comments from editors who are native speakers of a few different varieties of English, and who attended elementary schools during different decades. Most of us learned such basic words in elementary schools, but those schools have a nasty habit of introducing new terminology to new generations. (I never heard of cursive writing while I was in school, even though I learned to do it. Now the converse is becoming true; they're taught the word "cursive" but not how to do it.)

As for the example "Every year is (exactly, evenly) divisible by four into four quarters, but year 2001 is not divisible by four", neither Julian nor Gregorian calendar years, whether common or leap, can be divided into four quarters each of which contains the same number of whole days. So I don't understand the purpose of the example. Jc3s5h (talk) 18:46, 18 June 2012 (UTC)

"Evenly divisible" is standard English for divisible with no remainder, supported by a wide variety of sources: dictionaries, textbooks, encyclopedias, and general usage. There is nothing imprecise about it. The adverb "evenly" does not refer to multiples of two in this usage--indeed it's the other way around: "even," as in an even number, means the number can be evenly divided in half. It is common in mathematical writing to just say "divisible" but this is an elliptical expression for "divisible with zero remainder" or just "evenly divisible." In ordinary english "divisible means "able to be divided." Implying "with no remainder" makes sense to mathematicians because any two non-zero numbers are "able to be divided" in fields. That's not so obvious to laypeople, so using the qualifier "even' is appropriate in articles likely to be read by them. Our guideline Wikipedia:Make technical articles understandable says to "write one level down" and "avoid overly technical language." That seems appropriate guidance here.--agr (talk) 19:06, 18 June 2012 (UTC)

I think I'm taking from all this that saying abc is a multiple of 4 is better than saying abc is /evenly/exactly// divisible by 4. Dmcq (talk) 20:51, 18 June 2012 (UTC)

Surely you need to say "is an integer multiple of 4" in order to actually remove the ambiguity? --Joel B. Lewis (talk) 21:03, 18 June 2012 (UTC)

But is it appropriate guidance for an article about mathematics? You seem to be saying that a word cannot be imprecise for a specialized field if it is common English. There are many examples against this; "brontosaurus", "generally", "decelerate", "accuracy / precision" and "countable" to name a few. Another argument is that sticking to one phrase or the other would make Wikipedia more consistent. Even before I started changing articles, a search for "divisible" turned up 1100 articles while a search for "evenly divisible" turned up 90 articles. Connor Behan (talk) 20:48, 18 June 2012 (UTC)

I'm not quite sure what Connor Behan is getting at, but a word may be used in a specialized way if any reader with a hope of reading the article would understand that the specialized meaning applied. For example, an advanced physics article could use the word "force" without explicitly stating it is the vector that results from multiplying the scalar mass by the vector acceleration. There would be no need to mention that the meaning "a group of soldiers" does not apply. But some of the articles that have been edited, such as calendar articles, are not primarily math articles.

I agree with others who endorse "integer multiple", but wikilink integer because I've taught some high school and middle school, and guarantee that some of these students are unfamiliar with the word "integer". Jc3s5h (talk) 21:15, 18 June 2012 (UTC) corrected 22:30 UTC.

There are words and phrases in ordinary English that are ambiguous in a technical context. "Evenly divisible" isn't one of them. It has only one meaning, divisible with no remainder, and is widley understood by lay people and specialists alike. "Integer multiple," on the other hand, is technical jargon, never used in ordinary speech. The mere fact that you suggest wikilinking "integer" makes my point. Every published explanation of "leap year" I have found uses the term "evenly divisible." Sources are king here. We should not be replacing a commonly understood, unambiguous term with jargon just to solve a problem that does not exist in the first place.--agr (talk) 13:08, 19 June 2012 (UTC)

Here is one counter example of a person, that had never heard the phrase "evenly divisible" before it turned up here. "Integer multiple" is a perfectly fine common English phrase.TR 15:20, 19 June 2012 (UTC)

The fact that you haven't heard the phrase "evenly divisible" is not a disproof of the (true) statement that it is widely understood. Any of the terms under discussion is understandable with 2 minutes on google; I agree with agr that "integer multiple" will be a less familiar phrase to most people than "evenly divisible". --Joel B. Lewis (talk) 15:53, 19 June 2012 (UTC)

Can we at least agree, agr, that integer multiple is preferred in a mathematics article? I don't have time to track down published sources but I just looked at the first 10 results of a google search for "leap year" "divisible". "Evenly divisible" shows up 4 times, "divisible" shows up 5 times and "exactly divisible" shows up once. Connor Behan (talk) 20:35, 19 June 2012 (UTC)

In a mathematics article, I would have thought "divisible" was fine, unless there was some specific reason for thinking it was not fine. Sławomir Biały (talk) 22:31, 19 June 2012 (UTC)

For those of you who still think "evenly divisible" is fine, I did a Google search for "oddly divisible" and got 5 pages of hits. This is not a lot but I would have expected zero hits if "evenly divisible" were universally understood. While I find "integer multiple" to be a suitable alternative, I suspect that these are the same people who think that 7 is divisible by 3. Maybe they wouldn't think this if Wikipedia pages used terminology that did not support this conclusion. We have an opportunity to educate people here. — Preceding unsigned comment added by Connor Behan (talk • contribs) 07:07, 21 June 2012 (UTC)

It's not accidental that you're the only person to have used the adverb "universally" so far -- none of "divisible", "evenly divisible", or "integer multiple" will be universally understood. The (true) claim is that "evenly divisible" is a common English phrase, and so in widely or commonly understood. --Joel B. Lewis (talk) 12:19, 21 June 2012 (UTC)

Organizing (or "permuting"??) the List of permutation topics

I've started to organize the List of permutation topics into sections.

So far,

• Topics not yet classified into sections are at the beginning;
• A topic may appear in more than one section;
• But a topic not yet classified into one or more sections should appear only once (discuss!);
• Which section topics appear, and in what order (ha!!) they appear, and which should be sub-sections within main sections, are all debatable topics;
• There's a lot more work to do!!

Michael Hardy (talk) 21:55, 18 June 2012 (UTC)

...and now it's an organized list: everything is in a section or a subsection. Next step: the rest of you will figure out what could have been done better, and implement those ideas. Michael Hardy (talk) 20:02, 19 June 2012 (UTC)

Here's how the table of contents looks so far:

Contents

1 Particular kinds of permutations

2 Combinatorics of permutations

3 Permutation groups and other algebraic structures

3.1 Groups

3.2 Other algebraic structures

4 Mathematics applicable to physical sciences

5 Number theory

6 Algorithms and information processing

6.1 Cryptography

7 Probability, stochastic processes, and statistics

7.1 Random permutations

8 Music

9 Games

126 items are currently in the list, by my quick count. Michael Hardy (talk) 20:07, 19 June 2012 (UTC)

Yay! Leonxlin (talk) 15:27, 21 June 2012 (UTC)

Urban myth about π?

Resolved

I remember hearing that somewhere in the number that a whole bunch of 8s show up either together or in a pattern. If this is not a myth would it be worth adding to the Chronology of computation of π page?--Canoe1967 (talk) 19:14, 21 June 2012 (UTC)

No, because it has little to do with the computation of pi. Appropriate places are the final paragraph of Pi#Properties, or Feynman point, which already covers a sequence of six 8s, starting at position 222,299. --Tagishsimon (talk) 19:32, 21 June 2012 (UTC)

I think it was an an episode of Northern Exposure. I don't know if the writers made it up or actually did research on it. They may have made it up, as the plot had a couple that were trying to break the record. I do remember it as 8's though, unlike the 6s and 9s mentioned in the Feynman point article. I will resolve this section for now, and thank you for your help.--Canoe1967 (talk) 19:48, 21 June 2012 (UTC)

Bell's theorem (again)

Some more eyes on the current goings-on at Bell's theorem would be appreciated. An editor there is insistent on rewriting the nutshell version of the theorem in the lead to one that is, in my mind, much less clear than what used to be there. An attempt has been made to engage the editor on the discussion page, but it has failed to attract sufficient interest. The editor in question is (apparently) convinced that, since there are two editors on the discussion page defending the old (consensus) revision, and one editor (himself) defending the new edit, that gives him the mandate to implement his edit. I've reverted him several times already, with edit summaries indicating WP:CONSENSUS and WP:BRD, as well as menitioning these on the discussion page. Sławomir Biały (talk) 21:26, 26 June 2012 (UTC)

I reverted to your version and added a ref which supports the consensus version, also a few others in the "unreferenced" tagged sections. Hope this helps. F = q(E+v×B)⇄ ∑_ic_i 23:17, 26 June 2012 (UTC)

Category for discussion

There is a discussion for the category: Abstraction that could do with your input. Brad7777 (talk) 16:10, 27 June 2012 (UTC)

Ornstein–Uhlenbeck process

Our Ornstein–Uhlenbeck process article currently begins like this:

In mathematics, the Ornstein–Uhlenbeck process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction.

Does "friction" make sense? The Ornstein–Uhlenbeck process is supposed to tend to return to its mean. Friction doesn't do that; it only retards motion. Michael Hardy (talk) 21:14, 27 June 2012 (UTC)

Not really, it appears to be more like a Restoring force. It would also make more sense in my opinion to replace "friction coefficient" with "spring coefficient" but it depends on what can be referenced. Brad7777 (talk) 21:29, 27 June 2012 (UTC)

Tensor calculus as a disambig page?

People may think of "tensor calculus" as the content of tensors in curvilinear coordinates, but this is a redirect to the main article on tensors. I would prefer to redirect to tensors in curvilinear coordinates, but including both in a disambiguation page would also be ok (maybe better?). Opinions? F = q(E+v×B)⇄ ∑_ic_i 10:19, 28 June 2012 (UTC)

List of partition topics

I've made the List of partition topics into a somewhat more organized article than it was. More work could be done. Possibly the section on set partitions could be further subdivided. Michael Hardy (talk) 16:52, 29 June 2012 (UTC)

Jul 2012

Merge Invariant interval and Line element

The merge banners have been up for a while. I agree with merging because there is not much point in Invariant interval and is easily contained within spacetime or (my rewrite of) Line element. If there are no objections - I will merge. F = q(E+v×B)⇄ ∑_ic_i 22:21, 27 June 2012 (UTC)

Well, no response: these will be merged now. F = q(E+v×B)⇄ ∑_ic_i 15:40, 2 July 2012 (UTC)

sorry, but I'm very annoyed

I tried to build up the article Diophantine approximation starting two weeks ago (See its diff-history.) Until then it was a "dead" article no activity on a stub level (called start for politness or motivation I think). After I structured and put MUCH contents to give an overview suddenly User:D.Lazard sprang in action. He must "destroy" the things I want to build up and my thoughts how to present the topic consistently. Look at its talk-page about his justification and reasoning. Apparently he has insufficient knowledge (he doesn't know how to build up this topic he had self wrote) but could judge the importance of certain contributions by mathematicans to this subject. :-( I have waited two weeks now to see whether he is able to learn and improve the article back (or others spring in action). But it seems he is unwilling to check the material what is missing or he has deleted. :-( I withdraw from further contribution to this article and also to Mathematics in general if this is allowed/okay on wikipedia-en, you need really no experts. We(or should I say You?) will never get high quality level of contents. I will look what has happened after 1 week and then decide whether I support wikipedia-en seriously with my knowledge again. Regards, Achim1999 (talk) 20:04, 28 June 2012 (UTC)

Diophantine approximation (edit | talk | history | protect | delete | links | watch | logs | views), fwiw. I see that when you picked up on the article, it was about 9300 bytes, and now it's 21,209 bytes. Looking through the history, it's clear that you added most of that; well done & thanks. Without doing an edit by edit trawl through, it seems to me that you have been mostly successful in building up the article, and that what issues there are are surely on the margins. I don't see a 12,209 byte edit war going on. Reading the talk page, it does seem to me that you are getting emotional and being somewhat uncivil. So, your frustration comes through very loud and clear; but it's counterproductive. I earnestly suggest that you focus on staying very very calm, and discussing issue by issue with DL. It's almost certain that both of you are acting in good faith; if you avoid personalising the discussion there's a fair probability you'll make headway. --Tagishsimon (talk) 20:18, 28 June 2012 (UTC)

Sorry, you miss the point. I dislike an revision-war, thus no happend, in contrast I with-draw and now after 2 weeks looked what has happend. I will surely not teach and discuss with a person who has too less knowledge (and highly probable know this!) but whom I must/should convince. Sorry, I will not waste again my time with such people! I wonder that people (you?) here judge firstly on "uncivil"/"impolite" than on content/information and this only surficically. Bye. :-( Achim1999 (talk) 20:27, 28 June 2012 (UTC)

No, I entirely see your point. You know more than him/her, he/she should just stand out of the damned way. And yes, look at what happened: the vast majority of your changes are still there. Cataclysmic. What you seem not to be able to see, from your exulted position, is that he or she may in fact have valid points to make, despite being an intelectual pygmy; and indeed your diagnosis of DL's enfeebled mental prowess with respect to yours may in fact be incorrect. Until you see that those are fundamental problems in your approach, there really can be little progress beyond you flouncing off and wikipedia sinking slowly into the mire. We can only wait and hope. --Tagishsimon (talk) 20:38, 28 June 2012 (UTC)

This is ridiculous. Achim1999 behaved terribly impolite in several German WP discussions and now tries the same here. Back to mathematics: His style is to write “It may be remarked that, instead of the factor b², a weight-factor of a² could have been used; this would have led to effectively the same properties and insights about rational approximation.” without either showing that this is clear or giving a reference. Achim1999: why don't you make this point clear now? Thank you. -- KurtSchwitters (talk) 21:06, 28 June 2012 (UTC)

From what I can tell, whether Achim1999 and.or D.Lazard are sufficiently mathematically knowledgeable is a sideline. The problem is that the command of English of the former is insufficient to be able to make coherent sense. --Matt Westwood 05:24, 29 June 2012 (UTC)

Agreed, Achim1999's command of written English is not perfect, and his first drtafts of material can be difficult to understand. This difficulty could be overcome if he were willing to work collaboratively with other editors who could re-draft his contributions. Unfortunately, his abrasive style - as shown in his interactions with D.Lazard - makes this unlikely. It is this combination of imperfect English and confrontational interaction style that is the problem here, IMO. Gandalf61 (talk) 08:41, 29 June 2012 (UTC)

I want not enter in a discussion about who is the greatest mathematician nor about Achim1099 aggressive style. Let just recall that he has had his disruptive behavior also in Golden ratio and Line (geometry).

IMO Diophantine approximation needs further attention by memberships of the project. Before Achim1999's edit, it was a stub. Achim has introduced in it a number of relevant results, but also a number of sentences that can not reasonably be understood, a number of assertions that are pure WP:OR and, at least, one mathematical mistake (recently corrected). Moreover, the structure he gave to the article does not give a due weight to Thue-Siegel-Roth theorem. In particular he emphasizes on the use of 1/b² to measure the approximation, when other exponents are at least as important (1/b^2+ε for Thue-Siegel-Roth theorem).

I have resolved some of these issues, but a lot of work is yet needed, that I am not willing to do alone. Two points are behind my knowledge: I mention applications to Diophantine equations in the lead but I am not able to be more explicit. I believe that there are other applications (to ergodic theory?), but I have not enough information to put anything in the article.

D.Lazard (talk) 09:55, 29 June 2012 (UTC)

Not commenting on the behavioral issues, the edits to line (geometry) and Diophantine approximation over the past weeks have been net improvements. It would be ideal if Lazard and Achim could collaborate amicably, since jointly they benefit the project more than either does individually. I would be sorry to see Achim leave the project over this issue. Sławomir Biały (talk) 13:55, 29 June 2012 (UTC)

Contrarily that I have said above, I have further edited Diophantine approximation. Although I am misplaced to judge, I find decent the present version. I hope you will enjoy to read it. However there is yet many things to do in order to have a good article, in particular in the end of the article (from section "Kintchin" on). D.Lazard (talk) 17:47, 2 July 2012 (UTC)

History of Math books

This may already be common knowledge, but a fellow librarian drew my attention to the AMS's History of Mathematics: A Century of Mathematics in America set which they have made available free online -- could be a useful resource for referencing some of the history of math/mathematician articles! -- phoebe / (talk to me) 17:35, 2 July 2012 (UTC)

Recent edits from 32.173.153.198: are they vandalism

The recent edits to mathematics pages by 32.173.153.198 are puzzling. They introduce some subtle errors; most of them have already been reverted. I'd like to assume good faith here, but I think it's important to watch any further edits from that address. Jowa fan (talk) 02:08, 2 July 2012 (UTC)

See also 24.18.247.140; I can't see any way to interpret the comments by those two editors, presently at WT:Vandalism#Convince me to not vandalize as stating that he/she will vandalize unless Wikipedia can find a structural way to prevent it. (And they have now all been reverted.) — Arthur Rubin (talk) 04:20, 2 July 2012 (UTC)

Subtle this. "It is good to put mistakes in encyclopedias because that will encourage people to love their offspring." Dangerous madness that, worse even than (puke) religion. There is a structural way to stop such behaviour: block the IP address as soon as it happens. --Matt Westwood 05:11, 2 July 2012 (UTC)

Obvious troll is obvious. Sławomir Biały (talk) 13:44, 2 July 2012 (UTC)

Check the edit I just reverted on Fundamental theorem of arithmetic by some guy calling himself Shrohaneinstein. I don't know if it's vandalism or stupidity, nor do I know if it's 32.173.153.198 or 24.18.247.140. - Virginia-American (talk) 13:09, 2 July 2012 (UTC)

No, not anything like the IP edits; much more likely someone who thinks they understand more than they do. (It reads like a sort of typical proof by someone who doesn't really understand what proofs are yet.) -- JBL (talk) 14:08, 2 July 2012 (UTC)

Similarly incoherent job done by that same user on Linear congruence theorem which might also need attention. These are the first 2 edits by that user, so I suppose one ought to be gentle. --Matt Westwood 18:02, 2 July 2012 (UTC)

And likewise on trapezoid: http://en.wikipedia.org/w/index.php?title=Trapezoid&diff=prev&oldid=500455066. Obviously a well-intentioned person, but with not a lot of competence to back up the intentions :(. JBL (talk) 19:40, 3 July 2012 (UTC)

I reverted that. The result is obvious. It doesn't require a cryptic "proof". Sławomir Biały (talk) 19:53, 3 July 2012 (UTC)

Fernando Revilla

The new article Fernando Revilla has the interesting sentence "In this lecture [by Fernando Revilla], it is proven that dynamic processes assocciated with natural number characterize the Goldbach's conjecture, a characterization which is lost in an instant of time, obtaining a temporal singularity." This suggests that the article may need some attention. -- Jitse Niesen (talk) 09:25, 2 July 2012 (UTC)

Full name Fernando Revilla Jiménez, created by User:Ferejim who has only made this article and added an external link to Revilla's website to Goldbach's conjecture. Looks like an obvious WP:AUTOBIO. PrimeHunter (talk) 10:23, 2 July 2012 (UTC)

That sentence looks like WP:FRINGE flakiness to me. When I saw that this had been prodded I tried searching for his pubs in Google scholar but I saw very few citations, so I suspect he doesn't pass WP:PROF and I'm inclined to leave the prod in place. —David Eppstein (talk) 20:51, 3 July 2012 (UTC)

Motor variable

What is that article? Should it be trimmed and the non-obvious parts moved to bicomplex number. I know the article is old, but is there any evidence the term is actually used? I would rather not propose a merge tag before I understand what it is. — Arthur Rubin (talk) 15:53, 2 July 2012 (UTC)

As far as I can tell, at least some of the article concerns analytic functions of split complex numbers. Presumably this is what the article should be about, although most of it is written in a very obscure way. Sławomir Biały (talk) 17:10, 2 July 2012 (UTC)

Surely "motor variable" is merely an archaic term for split-complex number? If so, the article should be replaced with a redirect after seeing whether anything should be merged. I imagine the only mention of this term thereof should be under the history section there, which I note is already the case. — Quondum^☏ 20:33, 3 July 2012 (UTC)

Proposed GA collaboration

I was browsing WP:VITAL, and saw that Area is only start class. Would anyone be interested in collaborating to get this most important mathematical article up to GA status?--Gilderien Chat|List of good deeds 19:08, 1 July 2012 (UTC)

Ok, it has been re-assessed as B-class, any suggestions on improvements for GA?--Gilderien Chat|List of good deeds 11:18, 5 July 2012 (UTC)

help requested on merge

Hi, I'm cleaning a backlog of old merge proposals, and one of the oldest was for this article: Talk:Gödel–Gentzen_negative_translation which was proposed to be merged with Glivenko's_theorem and renamed to Double-negation translation. The consensus was to merge, so I closed the discussion and asked the involved editors to perform the merge because my math skills are too rusty to safely do this merge; since they may no longer be active, I'm also asking here if someone who understands the math can do the merge correctly. Thanks. --KarlB (talk) 13:01, 4 July 2012 (UTC)

now  Done.

Hodge Dual

I've been struggling with trying to understand the Hodge dual article for a while. To be honest, I didn't get anything from it at all. I found an on-line text that explained it in a, to me at least, much more natural way. (It actually motivated the definition!) I've added a section to the article: Hodge_dual#Explanation, to hopefully add that extra clarity which I found useful. But I'm no expert and would appreciate it if someone could take a look at it. Cheers. — Fly by Night (talk) 18:31, 1 July 2012 (UTC)

• Hi, have you looked at some of the posts at math.stackexchange, in particular this one? If it doesn't address your question, I'd like to encourage you to ask your own there, because I would like to see what answers appear. Rschwieb (talk) 17:47, 2 July 2012 (UTC)

It seems bizarre to me that someone would understand the Hodge dual as one questioner at stackexchange claims to do, and yet not understand the much simpler concept of dual space. Or have I missed something? JRSpriggs (talk) 07:43, 3 July 2012 (UTC)

When the dual space is identified with the vector space through a metric, as for example in geometric algebra where the dual space is not even mentioned, it seems reasonable that someone might understand the Hodge dual without understanding the concept of the dual space. Those with familiarity of GA might prefer to study the Clifford dual and move from there to the Hodge dual. Lounesto (2001, footnote p39) indicates a subtle distinction between the two in the context of GA. I also find the Hodge dual article difficult to follow properly. — Quondum^☏ 15:55, 3 July 2012 (UTC)

@JRSpriggs With the diversity of experience out there, it's highly unsurprising that someone has a viewpoint different from the one you described. Rschwieb (talk) 17:00, 3 July 2012 (UTC)

On going through the definition in the article, it seems to me that there is a confusion between k-vectors and k-forms (or at least that the two terms are being used interchangably). This may have contributed to the problem, and should be fixed in the article. In particular, the new explanation does not seem to make this mistake, but my impression is that any reference to dual spaces can be avoided. I think anything further should be on the talk page. — Quondum^☏ 18:59, 3 July 2012 (UTC)

@Rschwieb — You seem to have misunderstood my question. I was asking for someone to review the new section that I had added. The point was that the article had been insufficient to help me understand the idea, and I had to do elsewhere. — Fly by Night (talk) 12:36, 4 July 2012 (UTC)

Relying on Hodge dual#Derivatives in three dimensions which says

$d\omega ={\frac {\partial f}{\partial x}}dx+{\frac {\partial f}{\partial y}}dy+{\frac {\partial f}{\partial z}}dz\,,$

it seems to me that the coefficients are the components of a covariant vector and thus dx, dy, and dz are the basis of a covector space (the dual space of the tangent space (vectors) of the manifold at the relevant event). So it seems to me that the W of Hodge dual#Explanation should be a covector space rather than a vector space. JRSpriggs (talk) 13:59, 4 July 2012 (UTC)

The W is any vector space. What you term "covector spaces" are examples of vector spaces. — Fly by Night (talk) 15:23, 4 July 2012 (UTC)

I agree. Sławomir Biały (talk) 15:27, 4 July 2012 (UTC)

With whom? — Fly by Night (talk) 23:18, 4 July 2012 (UTC)

With you. Sławomir Biały (talk) 00:27, 5 July 2012 (UTC)

@FlyByNight Sorry yes, I mistook what you wrote as a request for more information. What was the online text you found on the topic, by the way? Rschwieb (talk) 23:34, 4 July 2012 (UTC)

To Fly by Night: Of course, all these spaces of covectors and tensors of various types are vector spaces in an abstract sense. However, you should realize that the context here is based on the Tangent space at an point on a manifold; that is THE "vector space". Its dual space (the Cotangent space) is called THE "covector space" (although it is also a vector space). Tensor products of these spaces are called such rather than referring to them as merely vector spaces.

When speaking in the context of components and indices as at Ricci calculus, the vectors in THE vector space are also called "contravariant vectors" because their components change contrary to changes in the basis vectors of THE vector space. The covectors in THE covector space are also called "covariant vectors" because their components vary in the same direction as the the basis vectors of THE vector space. (Bear in mind that a change in the basis of THE vector space induces a change in the basis of THE covector space and their various tensor products.) JRSpriggs (talk) 04:48, 5 July 2012 (UTC)

But the article isn't about the Ricci calculus, it's about the Hodge dual. This applies to any vector space. Sławomir Biały (talk) 11:16, 5 July 2012 (UTC)

I can't shake the feeling that the added explanation refers to dual spaces unnecessarily. Tevian Dray (1999) The Hodge Dual Operator has a very similar "abstract definition" (at least its symbol choice overlaps), and it makes no use of the dual space (not counting the metric) thoughout the paper. To avoid confusion, I too agree that the Hodge dual applies to any vector space (with a nondegenerate symmetric bilinear form). — Quondum^☏ 06:27, 5 July 2012 (UTC)

I think some of the confusion stems from the fact that "dual" has several meanings in mathematics. To me this page would be clearer if it avoided any mention of the dual of a vector space. I'm not convinced that the "explanation" section actually helps, sorry to say. Jowa fan (talk) 07:17, 5 July 2012 (UTC)

@Jowa fan: The explanation is guaranteed to help some people. I know it helped me. I couldn't make head nor tail of the article as it was. Using the dual seemed much more natural and comprehensible to me. The page Quondum links to is the think I found that really helped me. — Fly by Night (talk) 12:26, 5 July 2012 (UTC)

@Quondum: Dray uses the dual just like I have. The only difference is that he doesn't explicitly name, or denote, any of the duals. You'll see that he mentions linear functions on spaces a few times. — Fly by Night (talk) 15:27, 5 July 2012 (UTC)

I retract what I said just above about no reference to the dual space in the paper. In the example Fly by Night has correctly made explicit the implicit fact in the paper that the "real-valued function on a vector space W" belongs to the dual space.

How spooky: Fly by Night, I had not read your response before I posted this retraction. I presume it was one of those copyedit phenomena, where your post occurred between my reading it and clicking edit, and I failed notice the changed text in the edit window. Nice to see such similarity in what we said. — Quondum^☏ 17:49, 5 July 2012 (UTC)

For understandability, I prefer the current "formal definition" though (and I invite comment, especially from Fly by Night), as it can be related to the following. The preferred unit n-vector can be decomposed into a (wedge product of) a unit k-vector and its unit "orthogonal" Hodge dual (up to a sign, and orthogonal in the sense that all the vectors in their decompositions are orthogonal). Require linearity (and the correct sign ignored here), and this defines the Hodge dual. So, in a sense, The Hodge dual is the "bit of an n-vector missing from" the k-vector. — Quondum^☏ 15:45, 5 July 2012 (UTC)

I really like your last sentence! I agree that the formal definition should stay; I'm in no way challenging that. That's why I created a new section with the aim of explaining the definition in context. I really like Dray's explanation because, instead of simply presenting a definition in abstract isolation, it gives some motivation and explanation for the definition. I realise that it might be superfluous for those that already know and understand the Hodge dual, but I think it's really helpful for those that don't. Maybe we should blend the two sections together. Start with, something similar, to what's in the Explanation section and build up to the abstract definition? — Fly by Night (talk) 17:40, 5 July 2012 (UTC)

The impression that I get from Dray is that the "explanation" is actually a fully fledged alternative definition, preferred by some authors. It has the advantage that it is largely by construction, and thus does not need an existence proof in addition to the definition. Perhaps it should be presented in the article as such, rather than as a motivation.

On the "missing bit of the n-vector", this would need some development; it is very hazily stated here. Where this may be clearest is given by Lounesto for GA, who states in effect (I presume his 3D statement generalizes) that ${\star x}={\tilde {x}}\omega ^{-1}$. It would be nice to be able to draw on this simplicity for general metric vector spaces. — Quondum^☏ 08:38, 6 July 2012 (UTC)

A few more eyes needed on Fano plane

An editor has been repeatedly adding a very poorly conceived section to Fano plane; I've tried to engage User:Nicolae-boicu on the talk page on how to improve the section to make it acceptable, but the editor is being evasive. (Also, someone interested in this sort of procedural detail could probably find a WP:3RR violation there somewhere.) --JBL (talk) 13:10, 5 July 2012 (UTC)

Hello, I am here Joel, trying to do my best. Just believe me, I cannot explain in several hours the Theory of Species and the techology of labeling structures. Neither the Fano article is the right place to do this. Also, I ask you to take a more constructive position; accept it as it is, Fano" = X.Klein and to work toward it and not against it. Thank you Nicolae-boicu (talk) 15:58, 5 July 2012 (UTC)

Fano plane as labeled structure

Fano" = X.Klein

Since two points determine a line, after labeling any two points in the Fano plane another point is settled. The relabeling liberty for the rest of the four remaining points is described by the Klein Group.

The Maple permutation group for Fano plane is 7T5.

The e.g.f. is

$\int \int x.6.{x^{4} \over 4!}=30.{x^{7} \over 7!}$

hence there are 30 ways to label the plane. Here 6 represents the six distinct ways of labeling the affine (Klein) corresponding plane.

here is the section that has been erased several time. I would compare this section with a Java program. The Java program requiers JRE to run. Without JRE a Java program is only an obscure text. The "JRE" of labeling is the Theory of Species, see Combinatorial species, that I will not explain inside my section. Nicolae-boicu (talk) 16:33, 5 July 2012 (UTC)

Please answer these questions, Nicolae-boicu.

1) what does Fano" = X.Klein mean? Is there a reference for it?

2) I'm assuming egf stands for "exponentional generating function." What function is being generated? Why is it an integral rather than a sum? References?

Thanks - Virginia-American (talk) 14:48, 6 July 2012 (UTC)

You're a bit late to the party (Nicolae has already been blocked for edit-warring) but the mathematics of what's written is fine, it's just a claim of marginal interest and seems to be designed to be impenetrable. The claim is a claim about exponential generating functions for labelings; "X" is the variable, "." is multiplication, and " " " is a second derivative. It has to do with the theory of combinatorial species. Why anyone would use this language to express the simple facts that there are 30 distinct labelings and that after one line has been labeled, the group of symmetries of the remaining labelings is the Klein group, is something of a mystery. --JBL (talk) 15:05, 6 July 2012 (UTC)

Five of seven points answered

Dear Ed, I have already answered to 5/7 "accusations" points. It remains the below two ones. Please be careful and read the talk before clicking an irreversible button. Thank you.

• it is poorly formatted (e.g., the use of "." instead of "\cdot" for multiplication in LaTeX, the unexplained bold text) • the language could use polishing

Nicolae-boicu (talk) 21:29, 5 July 2012 (UTC)

Just out of curiosity: where is this cryptic notation (Fano"=X.Klein etc) used? It's certainly not notable enough to be used in articles to explain things. Rschwieb (talk) 11:50, 6 July 2012 (UTC)

It's the language of combinatorial species -- it's a kind of categorical-type approach to enumerative combinatorics. While it is definitely used in the combinatorics literature, I would say that it has not widely caught on; in my (admittedly not vast) experience, Bill Cherowitzo's response at Talk:Fano plane is common. It's not clear to me what would make a person want to use that notation without mentioning that it's the notation being used, nor why a person would prefer to use that notation than to use the corresponding English sentence when dealing with a single, concrete, finite example. --JBL (talk) 13:08, 6 July 2012 (UTC)

As a guess, it's so as to appear clever. If you speak in a language which is deliberately obscure, and understood only by a few, then everyone will gasp in awe and hold you in high esteem. (Not.) I've encountered such soi-disant mathematicians before, and one of their techniques is deliberately to replace simple English with gnomic symbology, and equally deliberately remove all reference to its interpretation on the grounds that "If you need to be told what the symbols mean, you're not advanced enough to understand the truth that is being communicated." I think there's some sort of attempt to make mathematics the basis for a secret cabal of some kind, with multiple levels of initiation, to which I would respond as Belbo in "Foucault's Pendulum": "Ma gavte la nata." --Matt Westwood 16:52, 6 July 2012 (UTC)

You are right ! If someone would ask me to choose between the Latin and the language of Species, I would recommend him Latin : there are much much more to read in Latin. The species Theory ends with the syntethic aposteriori description of several multiply transitive groups. As I alse said before, the text is like a Java program, it requiers a JRE software, that is, in this case, some material distributed in one book and several articles. In that context, the text makes a lot of sense. There are not too many "initiated" of this cabalistic language; they are mainly boomers that are aging and they started to pass by. I think it would be a loos for mathematics if the art of writing or reading species equations will die with them. Nicolae-boicu (talk) 16:51, 7 July 2012 (UTC)

Good news

I continued to work on my section following the expressed requierements. I have now a new form that I cannot imagine how to improve without kidnapp the subject. Thank you all for remarks and your time. The actual variant is on my page. Dear Matt, the argument regarding the redundancy is on my talk user page.Nicolae-boicu (talk) 16:11, 7 July 2012 (UTC)

Sorry, I won't be reading it. Life's too short. --Matt Westwood 16:54, 7 July 2012 (UTC)

It's OK, I didn't wrote it for you. Thanks for your comment, after all, you help me to get a better picture. Nicolae-boicu (talk) 16:59, 7 July 2012 (UTC)

Edits by user:Nbarth

Watching edits on Hilbert's Nullstellensatz, I have reverted edits by user:Nbarth, which were out of context and not directly related to the subject of the article. Looking on the article which were linked to by these edits, it appeared that the same user has also inserted inappropriate material in Commuting matrices and Spectral theory. I have reverted, or in some cases rewritten, these edits. There may be other articles that have been similarly edited by the same editor in a way that may be viewed as some kind of subtle vandalism. Attention of the project members is thus needed. I may add that I'll be away from the net for two weeks, and I will not be able to follow the question. D.Lazard (talk) 13:31, 6 July 2012 (UTC)

I've also noticed in the past that Barth's edits can tend to go off in directions not related to the subject of the article. I think he's trying to grow the Wikipedia graph by interconnecting different mathematical ideas. However, even if ideas tend to be linked from time to time in the real world, that doesn't mean that they should be so linked in encyclopedia articles about the topics. We should try to encapsulate topics. That said, I don't think there was any harm done per se in Barth's edits. I certainly wouldn't consider them to be vandalism. Sławomir Biały (talk) 18:39, 7 July 2012 (UTC)

Forum of Mathematics on AfD

Forum of Mathematics, an article about two new journals published by Cambridge University Press, has been nominated for deletion. Here's its first paragraph:

Forum of Mathematics, Pi and Forum of Mathematics, Sigma are open-access peer-reviewed journals for mathematics licensed under creative commons which will be open to submissions from 1st October 2012 for initial publishing on 1st January 2013, published by Cambridge University Press. It is currently intended to be funded by an author-pays model with fee-waivers for those that can't afford the fees, and no fees at all for any author for the journals' first three years. Fields Medalists Terrence Tao and Tim Gowers are among the editors. Gowers is the mathematician whose blog post led to the Cost of Knowledge boycott of commercial publisher Elsevier.

An argument is that as a new journal it has not yet had time to achieve notability. Another is that it's getting mentioned in the new media in connection with the boycott and with the broader purposes of that movement and is therefore notable for other reasons.

Opine at this page. Michael Hardy (talk) 19:45, 7 July 2012 (UTC)

Cox–Zucker machine

The article titled Cox–Zucker machine suddenly showed up in our "new articles" list although it's several years old and hasn't been edited since June 30th of this year.

It is an orphan i.e. no other articles link to it.

Here's most of the article:

The Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines if a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S where S is isomorphic to the projective line.

The algorithm was first published in the 1979 paper "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker and it was later named the "Cox–Zucker machine" by Charles Schwartz in 1984.

Two tasks:

• Improve the article.
• Link to it from appropriate other articles.

Michael Hardy (talk) 18:17, 8 July 2012 (UTC)

Am I the only one who noticed the funny title? Maybe we should try to get this in shape for an April 1 DYK... Sławomir Biały (talk) 18:22, 8 July 2012 (UTC)

How do you pronounce the vowel in the second surname? It's a German name. In German, it would be something like "tsooker" (rhymes with "hooker"). Michael Hardy (talk) 19:15, 8 July 2012 (UTC)

Steven Zucker's surname is pronounced in a way that rhymes with "shucker". Sławomir Biały (talk) 19:37, 8 July 2012 (UTC)

Assistance request - quick check on Wikipedia talk:Articles for creation/Nagao's theorem

Hiyas there Wikiproject Mathematics,

A new editor recently submitted a new article trough article's for creation on Nagao's theorem. The article itself looks fine, but mathematics is most definitely not a subject that i am to knowledgeable about, which means i have some difficulty reviewing it. On a sidenote i would mention that we did receive some bogus math article's as of late so i wondered if someone could glance over it and check two things:

• If what is written sounds decent and logical.
• If the article isn't a duplicate of some other topic.

If you are familiar with the article's for creation area, feel free to handle the entire page. If not, I'll happily take care of those matters. Also - Thanks in advance for the assistance! Excirial ^{(Contact me,Contribs)} 19:14, 9 July 2012 (UTC)

I'm not familiar with the process. Go ahead and create it, though. It's a worthy article, and there are some edits I would like to make. Sławomir Biały (talk) 19:31, 9 July 2012 (UTC)

Thanks for the quick check - the article has been created and is now available at Nagao's theorem for your editing and reading pleasure. Excirial ^{(Contact me,Contribs)} 19:54, 9 July 2012 (UTC)

Wikipedia talk:Articles for creation/Penrose square root law

I just came across another mathematics article, so i fear i have to ask the same as i did above. If anyone could glance over it I'd be grateful. Excirial ^{(Contact me,Contribs)} 21:05, 9 July 2012 (UTC)

I did some editing of it and then noticed there's a notice saying not to edit it while that notice appears. My edits move it into something approximating compliance with WP:MOS and WP:MOSMATH, starting with the fact that the first sentence should be a complete sentence rather than a dictionary-style definition, and the title phrase should be set in bold at its first appearance. Michael Hardy (talk) 21:58, 9 July 2012 (UTC)

Thanks Michael, got to admit i am rather impressed with Wikiproject Mathematics response times to questions such as these two. As a sidenote; the message you saw was my own "Being reviewed" template which i added to ensure that people were aware that someone was looking into the article (Even if that someone - me - was just asking for other people's assistance over here) Excirial ^{(Contact me,Contribs)} 23:07, 9 July 2012 (UTC)

Wikipedia talk:Articles for creation/Peripheral subgroup

A lot of mathematics related article's lately - at this rate i fear i am going to have to resort to asking assistance on a regular basis. The above article is another submission, and on first glance it looks very decent for a new article. Anyone spare a moment to confirm this? Thanks in advance, as usual. Excirial ^{(Contact me,Contribs)} 18:21, 11 July 2012 (UTC)

F=q(E+v^B) exposed as puppet master

Please see Wikipedia talk:WikiProject Physics#F=q(E+v^B) exposed as puppet master. As suggested there by Christopher Thomas, I am also notifying this project. JRSpriggs (talk) 06:39, 11 July 2012 (UTC)

Though the title here makes the situation seem resolved with no doubt, let's let a little more time pass and look at the evidence another time before we write F=... off for sure. Rschwieb (talk) 13:18, 11 July 2012 (UTC)

Whitehead Professorship

We are informed that:

Martin Bridson is the Whitehead Professor of Pure Mathematics at Magdalen College, University of Oxford.

Is this professorship named after Alfred North Whitehead, or J. H. C. Whitehead, or someone else? The article about A. N. Whitehead doesn't mention his having a professorship named after him. Can the information be added to the articles with appropriate links among them? Michael Hardy (talk) 18:31, 13 July 2012 (UTC)

GA review

The GA review of the 136th most viewed mathematics article is open for comment.--Gilderien Chat|List of good deeds 18:24, 15 July 2012 (UTC)

Use of "notion" vs. "concept"

I notice the use of the term notion in a number of articles where I would have used the term concept. The former seems to have semantics of vagueness associated with it, apparently corroborated by several dictionary definitions, whereas the latter seems more appropriate for use in the mathematical context where the thing described is usually precise. Would there be any objections to me replacing notion with concept in articles when this seems to apply? — Quondum^☏ 15:33, 15 July 2012 (UTC)

To me, notion suggests a proposition (sentence) while concept could refer to a term (noun phrase). JRSpriggs (talk) 16:07, 15 July 2012 (UTC)

Excellent point. One would thus expect to see a distinction in the grammar: the notion that ... and the concept of .... I concur. — Quondum^☏ 17:05, 15 July 2012 (UTC)

The terms notion and concept are synonymous. However, the preferred term among those who study them formally is "concept". Greg Bard (talk) 18:30, 15 July 2012 (UTC)

I don't think that the distinction is particularly important in the vast majority of our articles. For example, if I write about the notion of Lebesgue measure or the concept of Lebesgue measure I mean the same thing in either case, and if there is any philosophical distinction it will not matter for the subject of Lebesgue measure. I don't see a reason to go through replacing one with the other just for the sake of it. — Carl (CBM · talk) 18:35, 15 July 2012 (UTC)

This probably arose because of some squabble over whether "concept" or "conceit" should be used in a particular place, and in order to defuse the situation whereby the protagonists were about to start beating each other over the head with their teddy-bears, someone suggested to replace it with "notion". I think that was earlier today, but I lose track of time, and I have no idea where. My own view is to use the word "concept", as "conceit" has emotional overtones and "notion" smacks of imprecision. --Matt Westwood 23:40, 15 July 2012 (UTC)

Okay, this general perception was what I was trying to gauge. My own perception is that the use of notion as a direct synonym for concept is moderately recent and regional. If this sense has gained enough mainstream global usage, its use in WP would be reasonable. And as Carl says: it is not actually important (there is no ambiguity), and wholesale replacement for its own sake is not warranted. I may still be unable to resist replacing it in text I'm copyediting for other reasons, when it feels particularly out of place to me. — Quondum^☏ 05:30, 16 July 2012 (UTC)

A classical subject of dissertation for French agregation of philosophy was "the notion of concept and the concept of notion". I do not remember if it was an actual subject or a joke. D.Lazard (talk) 08:46, 16 July 2012 (UTC)

dominant functor

Dominant functor is a orphaned article (i.e. no others link to it) and lacks references. It's also very very short. Do what you can. Michael Hardy (talk) 20:06, 15 July 2012 (UTC)

Category theory is out of my area, but it seems to me that the key word "retract" should not be linked to deformation retract (a topological concept). Perhaps it should link to retract (category theory). Although even then, I do not know how the objects in category D can be considered as morphisms (which such a retract is supposed to be).

In any case, I suspect that the "dominant functor" concept is supposed to be similar to a cofinal function. JRSpriggs (talk) 05:59, 16 July 2012 (UTC)

Presumably what is intended here is the definition of J. Adámek; Jiří Rosický C; E. M. Vitale (2010). Algebraic Theories: A Categorical Introduction to General Algebra. Cambridge Tracts in Mathematics. Vol. 184. Cambridge University Press. p. 8. ISBN 0-521-11922-7. Here a retract is defined as the target of a split epimorphism: B is a retract if e:A → B, s:B → A with e epi and e.s = 1_B. In other words, a retract is the object at the end of a retraction. Single-sentence definitions like the article in question should probably be in Glossary of category theory. Spectral sequence (talk) 12:15, 16 July 2012 (UTC)

clarification in Böttcher equation

The article titled Böttcher equation begins like this:

The Böttcher equation is a functional equation F(h) = Fⁿ, where h is an analytic function with a superattracting fixed point a, which means that

$h(z)=a+c(z-a)^{n}+O((z-a)^{n+1}),\quad z\to a$

with n ≥ 2.

I don't know if Fⁿ means n-fold composition of functions, or n-fold multiplication of the value of the function. Also, if it's supposed to be evaluated at the same point h, it wouldn't hurt to be clear about that, and if it's not, then what is meant is not clear. Then it says "where h is an analytic function with[ . . . etc . . . ]". Does that mean for every analytic function with that property, or for some analytic function with that property, or does it mean for some special analytic function with that property? Does "with n ≥ 0" mean for some n ≥ 0 (so that as long as there is some such value of n, this is an instance of the Böttcher equation, or for every n ≥ 0, or what? Michael Hardy (talk) 18:31, 17 July 2012 (UTC)

This is just a guess, so you would have to check the sources to be sure, but I think the conclusion means

$F(h(z))=(F(z))^{n}\,$

for all z. In words, ordinary multiplication, not composition.

For every n≥2, for every analytic h satisfying the hypothesis, there is an analytic F satisfying the conclusion. JRSpriggs (talk) 11:29, 18 July 2012 (UTC)

Since the article says F(a)=0, composition does not make sense (since a≠0 in general).

However, it occurs to me that just using the constant function 0 for F would work. Being thus trivial, this is unlikely to be right. I think that the intention is for

$F(z)=c^{1 \over n-1}(z-a)+O((z-a)^{2}),\quad z\to a\,.$

JRSpriggs (talk) 11:44, 18 July 2012 (UTC)

The fifth result for my Google search of "Böttcher equation" was this article: Carl C. Cowen (1982). "Analytic solutions of Böttcher's functional equation in the unit disk" (PDF). Aeq. Math. 24: 187–194. Zbl 0526.30033. This reference makes it clear that you start with an analytic function h with an n-fold zero at zero [the wiki article considers the trivial variation h(z-a)+a] and look for a function F such that F(h(z)) = F(z)ⁿ where the RHS is indeed the n-th power of F(z). In fact the reference observes that if n is fixed by the condition on h having an n-fold zero at zero, then the only value of k in an equation F(h(z)) = F(z)^k that gives an interesting result is k=n. Spectral sequence (talk) 13:59, 18 July 2012 (UTC)

Property of equivalence in gaussian primes

Property of equivalence in gaussian primes has been around for most of a year, but with a bad category that prevented it from showing up in our new article lists. It needs either a lot of help, or deletion, I'm not sure which. Please do what you can. —David Eppstein (talk) 23:40, 17 July 2012 (UTC)

I looked at it and did a few edits and moved it to Equivalence of Gaussian prime numbers. It's one of the worst-written articles I've seen in a while. I might have cleaned it up quite a lot more if I were sure I understood what it says. Michael Hardy (talk) 04:15, 18 July 2012 (UTC)

Indeed. "equivalence" is never defined or used. - Virginia-American (talk) 10:55, 18 July 2012 (UTC)

Probably makes sense to discuss with the author? (At least as far as the goal is to understand what the article is about.) I note that s/he failed twice to get this through Articles for Creation, without apparently improving it in the process. --JBL (talk) 12:46, 18 July 2012 (UTC)

Surely the discussion should take place at the article talk page? I have commented there and notified the author, which strangely nobody else has done yet. Spectral sequence (talk) 13:33, 18 July 2012 (UTC)

Without noticing this discussion I noticed the article myself on the daily new maths articles update, and also being unable to identify any notable or even comprehensible content nominated it for deletion.--JohnBlackburne^words_deeds 17:37, 19 July 2012 (UTC)

Merge help: Club filter

There is a slow-moving discussion at Talk:Club filter involving a series of merges. I was hoping some math folks could head over there and continue the discussion, and merge the article, as I know nothing of these topics. Thanks, Ego White Tray (talk) 03:39, 19 July 2012 (UTC)

I terminated the merger. JRSpriggs (talk) 14:53, 19 July 2012 (UTC)

ambiguity of "any"

Another reminder of the hazards of the word "any". This is from a new article titled Tsen rank:

We say that F is a T_i-field if any such system, of degrees d₁, ..., d_m has a common non-zero solution whenever[...etc...]

Does this mean "[...]if there is any system of degrees that has a common non-zero solution whenever[...etc...]", or does it mean "[...]if it is the case that _any_ such system, no matter which one, has a common non-zero solution whenever[...etc...]"? A reasonable person might read it either way. In the first case, changing "any" to "some" would resolve the ambiguity; in the second case, changing "any" to "every" would do it. "Any" is sometimes a hazardous word. I've changed it to "every" in the article. Michael Hardy (talk) 20:23, 15 July 2012 (UTC)

This seems to me to be a grammatical parsing ambiguity rather than any ambiguity of the word. Not being familiar with the context, I can't judge this instance, but my suggestion would be to try to solve this type of problem by using grammatically unambiguous sentence structures. Simply replacing the word does not technically resolve the grammatical ambiguity. — Quondum^☏ 05:09, 16 July 2012 (UTC)

I disagree. In mathematical usage, "... any X has property P" can mean either "for all X, P is true" or "there exists an X such that P is true". Changing "any" to "every" removes the ambiguity: the first meaning is indicated. For the case under discussion, this seems to be the only interpretation that makes sense. (I'm not a specialist in this area, but it seems clear that if the other interpretation is followed then every field would have Tsen rank zero.) Jowa fan (talk) 05:33, 16 July 2012 (UTC)

Nicely explained. I stand corrected. — Quondum^☏ 06:35, 16 July 2012 (UTC)

If the whole sentence just says "Any A is B", I would take it to mean "every". But if it says "If any A is B, then...", then it could reasonably be construed as meaning "If there is any A that is B, then...", which would be the same as "If there is some A that is B". So in that case it's ambiguous. Michael Hardy (talk) 23:05, 16 July 2012 (UTC)

Free logic

The quantifier "any" lacks existence claims.

("Any" is often used where free-logic pussyfooting is not intended, and where "every" or "some" should have been specified. Thus Halmos thinks that "any" should be avoided by mathematicians writing it gooder.)

Jaakko Hintikka has a nice article on "any" and ordinary English.

I forget whether Charles Sanders Peirce and his students considered free logical quantification. I think Mitchell has a paper on quantification in the 1878 Johns Hopkins Studies. Kiefer.Wolfowitz 17:13, 24 July 2012 (UTC)

Nomination for deletion of Template:Ring structures

Template:Ring structures has been nominated for deletion. You are invited to comment on the discussion at the template's entry on the Templates for discussion page. DH85868993 (talk) 11:07, 21 July 2012 (UTC)

Mizar system external links discussion

Members of the Mathematics WikiProject are cordially invited to chime-in in the on-going discussion of the pro and con of placing Mizar system external deep links on mathematical articles. Yaniv256 (talk) 16:19, 24 July 2012 (UTC)

Andreas Griewank

Professor Griewank is one of the principal architects of automatic differentiation, a co-founder of the theory of partially separable functions (the usage of which is an important part of the success of AMPL's modeling language and the large-scale optimization packages Lancelot and Galahad), an initiate of the mysteries of semi-analytic geometry, and an amateur guitarist:

• Griewank, Andreas (2010), Tuning guitars and reading music in major thirds (html), Matheon preprints, vol. 695, Rosestr. 3a, 12524 Berlin, Germany: DFG research center "MATHEON, Mathematics for key technologies" Berlin, Postscript file and Pdf file {{citation}}: Invalid |ref=harv (help); Unknown parameter |month= ignored (help); Unknown parameter |urn= ignored (|id= suggested) (help)CS1 maint: location (link)

His would be an interesting biography.

Thanks! Kiefer.Wolfowitz 17:04, 24 July 2012 (UTC)

CV on Homepage. --LutzL (talk) 18:10, 24 July 2012 (UTC)

Another drive-by deletion

Help! We're getting another drive-by deletion being pushed bynon-physicists of a physics topic. Wikipedia:Categories for discussion/Log/2012 July 13#Category:Introductory physics. To express my frustration: the drive-by deletion process brings out the very worst in wikipedia behavior, and creates a huge amount of damage (remember the deletion of Category:Proof, carefully nurtured for years, here, and shot dead with only three votes?) Please help get these hooligans under control. linas (talk) 01:35, 21 July 2012 (UTC)

At least some ongoing/old CfDs are listed at Wikipedia:WikiProject Mathematics/Current activity. But it is not clear how any given category is counted as part of the project. There may be several layers of bots involved, which I can't follow. Melcombe (talk) 07:38, 25 July 2012 (UTC)

Indefinite logarithm at AfD

The article Indefinite logarithm has been nominated for deletion. Discussion is at Wikipedia:Articles for deletion/Indefinite logarithm.  --Lambiam 23:15, 25 July 2012 (UTC)

MathJax working

It looks like the bug fixes in MathJax implementation are now working so we can have less than signs $x<y$ and matrices ${\begin{pmatrix}1&0\\0&1\end{pmatrix}}$.--Salix (talk): 07:03, 26 July 2012 (UTC)

Good news! I'm trying the switch from Nageh's version to the built in support. So far it seems a little slower to render but no appearance glitches. —David Eppstein (talk) 07:39, 26 July 2012 (UTC)

Yep seems good. I just had a look at Help:Math and there are a few square boxes instead of characters for special characters and when doing \limsup and \liminf but the Nageh version does the same. Overall I'm very pleased and will use the system version of MathJax as default. Dmcq (talk) 08:36, 26 July 2012 (UTC)

Well it all depends on what renderer I've switch on. Seemingly that was with the SVG one. With the HTML-CSS they all come out okay though the special characters are half the size. And with MathML it warns me not all the features are supported by the browser. It's a hard choice, I think I'll try the HTML-CSS for a while. Dmcq (talk) 09:01, 26 July 2012 (UTC)

MathJax is excellent, but expensive. Sadly, nobody cares about such cheapie as class="texhtml", the font in which should match MathJax's one. Incnis Mrsi (talk) 09:05, 26 July 2012 (UTC)

You get that automatically if you use {{math}} and there's some ancillary templates that go with it e.g. {{mvar}} to just format a variable quickly. However some people here have a very strong dislike of serif font in the middle of non-serif. Not that MathJax will satisfy them immediately. There's also a couple of gotchas like having to put 1= in if one uses equal signs so it is another language again. As for me I'll be putting less effort into trying to use the math tempate in future and will use <math> more even if it is a little slower. Dmcq (talk) 11:43, 26 July 2012 (UTC)

Maybe we do not understand each other. I see x or x₁ markedly different from MathJax equivalents ($x_{1}$). I suppose, although not completely sure, than this can be cheaply fixed by altering texhtml's font-family to those used by MathJax. I hope, sysops just are not aware about the problem. But if someone is aware, but deliberately keeps a substandard appearance of {{math}}, then it is definitely an unfair trick to mount a prejudice against "texhtml" typesetting. Incnis Mrsi (talk) 13:07, 26 July 2012 (UTC)

You need italics as in {{math|''x''₁}} which gives x₁. I think it is fairly close but it depends on what method MathJax uses for rendering and your browser. By the way MathJax uses the STIX fonts and MathJax will run a bit faster if you install them instead of using web fonts. I guess texhtml could put the STIX fonts as the first ones to check for but they are close enough to the usual Times one for most purposes I believe, possibly the size needs to be tweaked slightly as currently it is set to match the old png render program. Dmcq (talk) 19:17, 26 July 2012 (UTC)

It was just a typo in x₁, sorry. Incnis Mrsi (talk) 09:17, 27 July 2012 (UTC)

The font of the {{math}} template could be made compatible with MathJax by adding the CSS rule span.texhtml { font-family: MathJax_Math, serif; }. You can try this in your skin.css and if we are happy with it roll it out to MediaWiki:Common.css or ask a dev to change skins/common/shared.css. I'm not sure quite how the MathJax_Math font is loaded so the font might only change if MathJax is enabled.--Salix (talk): 06:29, 27 July 2012 (UTC)

Thanks for explanations, Salix. I have MathJax's fonts locally. I will be completely satisfied if "texhtml" had to switch to MathJax's fonts if these fonts are currently available in the browser. So, do you recommend to proceed with bugzilla: and not wait for further conclusions in this discussion? Incnis Mrsi (talk) 09:17, 27 July 2012 (UTC)

P.S. apart of the problem of font-family, there is another problem with font-size in <sup>s and <sub>s. I'm afraid that, due to CSS limitation, the best solution is to supersede that explicit HTML elements by {{ssup}}s and {{ssub}}s respectively, such as x₁. Yeah, it is another language again, Dmcq is right. Incnis Mrsi (talk) 10:09, 27 July 2012 (UTC)

After yet some meditation I realized that, since class="texhtml" is defined in templates, not by the engine itself, it would be unwise to request changes to MediaWiki. So, I started small. Incnis Mrsi (talk) 11:30, 27 July 2012 (UTC)

Should we also ask for "font-size:larger" to be added. At least for me the following two match x $x$. (across multiple display settings). Not sure if this is true for all configurations of browsers/system.TR 12:36, 27 July 2012 (UTC)

I agree. Even in a browser without font-family:MathJax_Math this produces a serif text which does not looks too large. Incnis Mrsi (talk) 12:53, 27 July 2012 (UTC)

Just checked IE8 and Opera, neither of which actually pick up the mathjax font.TR 12:42, 27 July 2012 (UTC)

Did you install these fonts locally? It is useful also for the MathJax proper. Incnis Mrsi (talk) 12:53, 27 July 2012 (UTC)

Now I am in doubt again. Should font-size be better placed to {{math}} rather than to CSS? Incnis Mrsi (talk) 13:20, 27 July 2012 (UTC)

No, because then it cannot be customized by user CSS.—Emil J. 13:28, 27 July 2012 (UTC)

I see no difference between increasing font-size in CSS and doing the same in all <span>s which use the class. Both are subject to user customization. Actually, there are two templates, {{math}} and {{bigmath}}. What do you propose: To merge (effectively) these two presentations? Or to make {{bigmath}} even larger? Incnis Mrsi (talk) 13:43, 27 July 2012 (UTC)

What (I think) Emil was getting at, is that if it is conrtolled through the CSS a user/reader can specify a custom css style which changes the way math output looks. So, for example, if you detest seeing a serif font inline, you can load your own css style that set the texhtml class to a sans-serif font. As a user, you cannot load a custom version of a template.TR 15:33, 27 July 2012 (UTC)

With a bit of messing around the closes set of styles I've managed to come to is

span.texhtml {       font-family: MathJax_Main, serif; font-size: 123%;}
span.texhtml var {       font-family: MathJax_Math, serif;}
span.texhtml sup {       font-size: 70.7%; }
span.texhtml sub {       font-size: 70.7%; }

Using those styles in skin.css the following two are virtually indistinguishable.

$-3\sin(x_{2i})+\ e^{3t}$ MathJax

−3 sin(x_2i)+e^3t Using {{math}} {{math|3 sin(<var>x</var><sub>2<var>i</var></sub>) e<sup>3<var>t</var></sup>}}

MathJax uses a different font for variables, MathJax_Math, than for other content, MathJax_Main, and slightly different sizes 123% as opposed to 118%. The code is dynamically generated so it might be different in other browsers.--Salix (talk): 21:34, 27 July 2012 (UTC)

havel

what happened to V. J. Havel (see too: S. L. Hakimi) - --Rovnet (talk) 16:35, 27 July 2012 (UTC) (w:es)

It was deleted by WP:PROD in March with the rationale "Poorly-sourced BLP with questionable notability". I can undelete it for you, if you want. —David Eppstein (talk) 17:08, 27 July 2012 (UTC)

I've un-deleted it for now. I'll try to notify interested parties. Michael Hardy (talk) 17:16, 27 July 2012 (UTC)

I was the one who proposed the article for deletion. I'm not a mathematician, but at the time I found it frustrating that there was next-to-no information about the person. Havel still appears to fail WP:BLP1E and the WP:GNG, but if the article was fixed, a date of birth mentioned, and some external links offered to confirm any notability, of course I wouldn't mind if the article stayed. Jared Preston (talk) 18:42, 27 July 2012 (UTC)

He also appears to fail WP:PROF. Although I think unprodding was the right thing to do, unless more evidence comes up I'd support deletion in an AfD. —David Eppstein (talk) 22:29, 27 July 2012 (UTC)

There is also Václav Havel, a famous Czech writer who is not the same person. Sławomir Biały (talk) 18:55, 27 July 2012 (UTC)

thx . --Rovnet (talk) 04:33, 28 July 2012 (UTC)

MAJOR merger!!

What a mess! Arabic numerals and Hindu–Arabic numeral system (with an en-dash, not a hyphen) are two separate articles, and Hindu-Arabic numeral system (with a hyphen) does not redirect to Hindu–Arabic numeral system (with an en-dash) but to Arabic numerals, and Arabic numeral system does not redirect to Arabic numerals but to Hindu–Arabic numeral system.

Welcome to the earliest days of Wikipedia. In 2002 and 2003 this would be expected. Michael Hardy (talk) 16:29, 28 July 2012 (UTC)

Not-so-major merger

Is there any reason why Hurwitz quaternion order and Hurwitz quaternion should be distinct article which don't even link to each other? Deltahedron (talk) 17:16, 28 July 2012 (UTC)

The first one was linked to the second one through a redirect. I have replaced it by a direct link. However the subjects are distinct: the first article consider a subalgebra in a quaternion algebra, while the second one consider only usual quaternions. As a non specialist of non commutative algebra, I have the impression that both articles concern the integral elements in a quaternion algebra, but none of the articles make clear if the notion of integer element make sense here. I have no opinion about a merger or not. D.Lazard (talk) 19:57, 28 July 2012 (UTC)

Udita fractional operator

The article Udita fractional operator is at AfD. Please comment there. Sławomir Biały (talk) 13:56, 28 July 2012 (UTC)

In related news, more eyes would be appreciated on Fractional calculus and Erdelyi–Kober operator, where a gang of SPAs are POV-pushing to include mention of the so-called "Udita fractional operator". Sławomir Biały (talk) 17:05, 29 July 2012 (UTC)

These three SPA, namely MathProff, MathBuddy and Uditanalin lock like sockpuppetts. Can someone investigate this? D.Lazard (talk) 09:37, 30 July 2012 (UTC)

Holomorphic function

If I recall correctly, a function $f:\mathbb {C} \to \mathbb {C}$ is holomorphic in a neighbourhood of $z_{0}$ if $(\operatorname {d} \!f/\operatorname {d} \!{\overline {z}})(z_{0})=0$. There is no mention of this in the article. I'm assuming that this is a well known fact. Should we add something to the article? — Fly by Night (talk) 21:33, 29 July 2012 (UTC)

It is not sufficient that the Wirtinger derivative vanish at $z_{0}$, rather it should be zero in a neighborhood. Vanishing of the Wirtinger derivative is equivalent to the Cauchy-Riemann equations (and is mentioned in that article). Sławomir Biały (talk) 22:31, 29 July 2012 (UTC)

Elementary Algebra GA candidate

If anyone is interested, I've recently made what I consider to be a number of improvements throughout the article on Elementary algebra, and submitted it as a Good Article nominee (see the article Talk page template for details). --Iantresman (talk) 16:29, 30 July 2012 (UTC)

Aug 2012

History of the function concept

The new article bearing this title is perhaps interesting. Some people implicitly believe that the concept of function that we know today is axiomatic and coeternal with the Father, but the true story is complicated and messy. Michael Hardy (talk) 12:28, 1 August 2012 (UTC)

Formalized form infobox experiment

A

Correct me if I am wrong in summarizing that the discussion we had at the Mizar system talk page raised two main concerns. The first is one of bias in favor of a particular formalized math system, in this case the Mizar system, violating WP:NPOV with respect to other competing systems. The second concern is that by granting permission to place these links we will be sanctioning en masse changes to almost all mathematical articles, which while may benefit a minority of readers, will probably not be of any benefit to the typical reader in the near future. One additional secondary concern was that if we want to expose the readers to formalized math it is better to develop it inside Wikimedia than sending the users to outside sources.

Before addressing these issues please allow me one personal note: I have an agenda. My agenda is to have formalized math accessible from Wikipedia mathematical articles. No more and no less. This is driven by a view that for some readers, like myself, reading code is more instructive than reading descriptive text. I am not here to write articles, but I am here to help build the best encyclopedia the world has ever seen.

I am not affiliated with any proof assistant and in fact my knowledge of Mizar is rather slim. My choice to promote the Mizar system was based on considerable groundwork I made in preparation for this initiative, but truth be told I like Coq much better. Without much understanding of how Wikipedia works, I made the judgment that the Mizar system is the one which is best suited to the task. I believe this choice can be defended on objective grounds, but seeking to avert single-purpose-account charges I will not attempt to do so here.

Next, the issues. Indeed, I realize now that Wikipedia cannot provide access to one particular formalized system, no matter its benefits, at the expense of other systems. Nor should it be in the business of picking winners. It must be either all in or all out. This does make the choice of inclusion much harder, but should not warrant, by itself, automatic submission to the deletion impulse. My answer to this concern is two-fold: yes, we will have to link to more than one system, and no, we cannot do so in the external links section. We will have to come up with some kind of infobox or an addition to an existing infobox that will accommodate these links and help keep the typical reader away from clicking them.

Second, clearly the initial scale of deployment is not to be left to individual decision making, but should result from the formation of consensus here, in the math project discussion forum. But consensus is built by discussion, so we will probably have to spend some time in deliberation. Thus, a measure of patience will be required and yes, a willingness to learn enough of a foreign formal language that it stops reading like gibberish. It is however not in the spirit of Wikipedia established policy to brush this initiative aside by not being willing to engage the other side.

Seeking compromise, I suggest that we limit the initial deployment to a small number of key non-trivial mathematical constructs, where access to a reference of formal definitions and properties can be most helpful to undergraduate math students who are working on problem sets. I further suggest that we try and measure take-up quantitatively and by field, by contacting professors and asking that they mention the links in class and ask students to make a note if they used them in the solution of a problem set. This experiment should be limited in time as well as scope, guaranteeing that the typical Wikipedia reader does not suffer too much.

Which brings us to the final concern of internal vs. external development of formal math structures. Frankly, I do not have much to say here. I wish I was in the position to help work on the developer side, but I am not. It does however seem odd to me to suggest that Wikimedia developers should put much efforts into something for which it is not clear if there is any need. First we need to establish that there is some demand for the product, then we go about building it. This seems common sense to me and provides additional impetus to running this experiment.

I thank you for taking the time to read this lengthy post and hope that I was able to address the main issues raised. Yaniv256 (talk) 21:12, 1 August 2012 (UTC)

If we are going to include Mizar system, Coq, or Metamath proofs by reference, then I think we should make sure that those proofs are available under the CC-BY-SA 3.0 License and the GFD License as are proofs contributed by other means.

I think that proof assistants are the wave of the future, but not the present or near future. They need to develop to the point that they can read proofs in English+TeX and translate them into their internal format (perhaps asking questions of the person running the program in the process). They do not appear to be there yet. JRSpriggs (talk) 04:34, 2 August 2012 (UTC)

Metamath is in the public domain, which is CC-BY-SA compatible. I can't speak to the others. CRGreathouse (t | c) 05:16, 2 August 2012 (UTC)

Formalization links
Structure	sigma-algebra
Definition in
Metamath	Coq	Mizar
Proof of properties
Metamath	Coq	Mizar
See automated proof checking for more information.

I know that Coq-Corn and the MML are open-source but I don't know much about which kind and if it is compatible. I'll have to look into it. Yaniv256 (talk) 06:26, 2 August 2012 (UTC)

To make the discussion concrete I am posting a prototype for the purposed infobox. Currently only the Mizar links will work, the others will just send you to Google. Yaniv256 (talk) 06:26, 2 August 2012 (UTC)

I am against the inclusion of formalized proofs in WP. Unless for "trivial" results they use to be too long to be read by humans. This is similar to the case of programs. On the other hand, for pages containing results that have been formally proved, we has to mention this with references (the non trivial computer aided proofs are usually published in scientific journals and/or conferences). D.Lazard (talk) 09:48, 2 August 2012 (UTC)

It's unclear to me exactly what is being proposed. Yaniv, are you suggesting that we add an infobox to lots of mathematics articles containing links to various proof assistants? I oppose this. The input to proof assistants is really not human readable, and adds nothing to the article. If you truly find it easier to read this kind of code than plain prose, and to understand its mathematical intent, then I applaud you. But that probably makes you one of a kind. Moreover, I should add that the consensus at Talk:Mizar system was decidedly against adding links to articles, largely because such links add nothing of value to the article. Now it is being proposed that a large infobox be added, taking up more valuable real estate with the same useless information. It seems most peculiar to me that you would think the consensus at Talk:Mizar system would support such an initiative. Sławomir Biały (talk) 12:03, 2 August 2012 (UTC)

That's pretty much my position too. It would be different if these systems were widely used and understood. That is if all, or at least a large number of mathematics educators used them to teach mathematics. But that would be reflected in mainstream sources: they should be used in many textbooks, and on many courses, in the same way. But this was not true when I was at university and I've seen nothing to suggest this has changed. These links are only relevant to the particular formal systems, not general mathematics articles.--JohnBlackburne^words_deeds 13:23, 2 August 2012 (UTC)

What I said on that talk page was I was against it as a general thing and pointed to WP:NOTDIRECTORY but would support such external links where formalized logic or proof seemed relevant, for example for things like variants of the axiom of choice. Sigma-algebra doesn't sound like something like that to me. 'Deployment' sounds exactly the opposite to what I was thinking of. Dmcq (talk) 14:26, 2 August 2012 (UTC)

I would support a small-scale experiment once the template is constructed. Add the template to a small number of articles where (as Dmcq says) formalized logic or proof seems relevant. CRGreathouse (t | c) 14:36, 2 August 2012 (UTC)

Please excuse my poor choice of words as I am not native to English. Let me be more precise: 7-9 pages, determined by consensus, for a period of 6 months. My choice to use sigma-algebra was probably misguided. Can I suggest that we defer the discussion of which pages to select until after we establish a consensus that running such an experiment would be desirable, in theory? Yaniv256 (talk) 19:17, 2 August 2012 (UTC)

I really don't see what all this is about. The articles in Wikipedia are all independent and there isn't really such things as experiments like this except to test out new Wikipedia features. I think you have some picture in your mind about Wikipedia that it is monolithic and organized. It isn't. Of course some people can discuss something but I think your best bet is just to go ahead and try it out, we'll all have forgotten whatever was here in six months, or at least I will as I have a dreadful memory and I don't suppose many others will care. Dmcq (talk) 20:02, 2 August 2012 (UTC)

Before attempts to try this, though, the box needs to be improved. In particular links to Wikipedia namespace (especially a redlink) from article space are not a good idea. —David Eppstein (talk) 20:41, 2 August 2012 (UTC)

Yes, that is true. Thanks! I changed it from WP:Formal math links to Help:Formal math links, which of course I will need to create before we will be done here. Any other suggestions? Yaniv256 (talk) 21:05, 2 August 2012 (UTC)

Still not good enough. Help: namespace is for help editing Wikipedia, not for explaining Wikipedia content, and should also not be linked from article space. See WP:SELFREF. —David Eppstein (talk) 21:28, 2 August 2012 (UTC)

What should I put then? Yaniv256 (talk) 21:36, 2 August 2012 (UTC)

Since we can only work in article space I think that the best we can do then is to just send readers to a page like Automated proof checking. They will have to work out the details by themselves. Formal proof and proof assistant are two other viable landing sites. Now that I took another look at these pages I see that I'll have to attend to them anyway, so don't judge them by their current form. Yaniv256 (talk) 00:39, 3 August 2012 (UTC)

Just link the title to one of those and remove the explanation at the bottom. People can click on things to find out. Dmcq (talk) 18:02, 3 August 2012 (UTC)

Sure, if you think that is better, thanks. Opening a new page and pasting prototype B. Yaniv256 (talk) 18:15, 3 August 2012 (UTC)

Maybe whats needed is a reference template like thouse at Wikipedia:WikiProject_Mathematics/Reference_resources#Citation templates?--Salix (talk): 04:26, 3 August 2012 (UTC)

I considered this option, but read in one of the guidelines that citations should only be used to support the text to the degree that one uses them in editing the text, and not as a way to hide external links. I could work on each page and edit it so as to find a way to place these links as citations, since they do count, in my mind, as quite reliable secondary sources. My concern, however, is that this might cause confusion to the typical reader, due to the fact that such citations would have to be placed in a way that somewhat obscures their nature and will not be consistent across pages. For this reason, in case someone would revert my citations, I fear that I will have little to say in defense, as I will probably agree with most of what they would have to say. Yaniv256 (talk) 16:32, 3 August 2012 (UTC)

The citation guidelines are irrelevant, as you note, as these are not being used as sources to what's already there. The relevant guidelines are the external links ones and those suggest that not even one of these should be added, never mind six, for the same reasons as given at Talk:Mizar system. If individual links are not appropriate then box highlighting them is especially so.--JohnBlackburne^words_deeds 18:34, 3 August 2012 (UTC)

B

Formalization links
Structure	sigma-algebra
Definition in
Metamath	Coq	Mizar
Proof of properties
Metamath	Coq	Mizar

Please excuse me. I thought the matter of legal compliance with the external links guidelines was behind us. My answer to these claims was and still is here. I fail to see a meaningful response to my arguments in the discussion we had, but then again I may be missing something. Since if this proposal is to fall due to legal objections we are all just wasting our time discussing it, I suggest we stop here and assert if John's argument does have consensual support. Yaniv256 (talk) 19:49, 3 August 2012 (UTC)

You just don't get it do you? Just because you think you are right does not mean others do. You have not convinced people of your case and those references would be removed if stuck on things like sigma algebra. The reason it would be okay for things like axiom of choice is because a person reading that might not know about it and would find it a useful link. A person reading about sigma algebra is very unlikely to find it of interest unless they were already deeply into that sort of business. Wikipedia is not a directory to other web sites or software or books, it is an encyclopaedia. We do not list every single book that defines sigma algebra so why on earth should we list Mizar? Dmcq (talk) 21:54, 3 August 2012 (UTC)

Thank you for making it clear. I will not waste your time any longer. Yaniv256 (talk) 22:17, 3 August 2012 (UTC)

Real-valued function prodded

Deletion of the article titled Real-valued function has been proposed on the grounds that it's been only a dictionary definition for several years and it's unclear what to redirect it to. A problem I see with this is that a large number of articles link to it. So: (1) Is there some appropriate redirect target; or (2) Can it be expanded so that it becomes a proper article? Michael Hardy (talk) 16:57, 31 July 2012 (UTC)

I don't see any problem with letting those links go red, and removing them bit by bit. Maybe someone could get them all with AWB? --Trovatore (talk) 17:42, 31 July 2012 (UTC)

That's a difficult question okay. I think developing real analysis and redirecting there might be best. The real question is what do we actually mean by real-valued function is it instead the old idea of smooth functions including 1/x which is actually a partial function? I guess real analysis would be better for covering more classical stuff too. Dmcq (talk) 17:59, 31 July 2012 (UTC)

I just don't see much value in linking the phrase real-valued function, in most cases. I think these links probably should be removed, independently of whether there's a canonical place to redirect the search term. --Trovatore (talk) 20:16, 31 July 2012 (UTC)

Why shouldn't "partial functions" be considered real-valued if their values are real numbers? Michael Hardy (talk) 12:38, 1 August 2012 (UTC)

I think expansion would be difficult (if someone had something to say, it probably would have been said by now). A reasonable redirect would be to function (mathematics)#Types of functions. The current definition is the first line of that section.Bill Cherowitzo (talk) 18:10, 31 July 2012 (UTC)

And by the way, I didn't do the redirect I suggested because I think that Trovatore is making a good point. I've seen far too many useless wikilinks in the math pages and I would count this one as one of those. I'm sure that some discussion of standards for wikilinks in mathematics pages has already occurred - so if someone could dig it up for review I would appreciate it. Bill Cherowitzo (talk) 02:38, 1 August 2012 (UTC)

Is there such a thing as a "cross-reference page" (or should we call it by some other name?) that links to various pages that may be of interest to those who follow a link like this one? I.e. Someone clicks on real-valued function and they see a page that might look something like this:

In mathematics, a real-valued function is a function whose values are real numbers. See:

• Function (mathematics)
• Real number
• Real analysis

This is a cross-reference page.

If such a thing doesn't exist, should we invent it (along with a template for the footnote, a style manual for them, and mentions and links within the other appropriate style manuals)? Michael Hardy (talk) 12:38, 1 August 2012 (UTC)

I've raised the topic of multiple-cross-reference pages here. Michael Hardy (talk) 13:37, 1 August 2012 (UTC)

For now I've made the article into a multiple-cross-reference page and created this manual, which currently has "essay" status. Michael Hardy (talk) 00:18, 3 August 2012 (UTC)

The Real analysis article has a heading called "Key concepts." Adding a short section there on Real-valued functions, perhaps covering some of the issues mentioned above, would seem appropriate and would make a good redirect target. --agr (talk) 00:36, 3 August 2012 (UTC)

But remember that real-valued functions occur not only in real analysis, but also in other areas of mathematics and the sciences, so that can't be the whole account of real-valued functions. Michael Hardy (talk) 19:37, 4 August 2012 (UTC)

What about adding Random variable as another entry?--Kmhkmh (talk) 03:18, 5 August 2012 (UTC)

There is some similarity in these two cases. "Real-valued function" is a function to real numbers from an unspecified domain. "Random variable" is a function from the sample space to an unspecified codomain. But these are not the same. "Random variable" is a historically important concept, discovered well before modern probability space approach, and must be retained as an article. Moreover, a half of probability theory is explained with various random variables (actually, even with random events as a special case of Boolean-valued random variables), with little consideration about codomains. Contrary, "real-valued function" is not anything historically significant, nor is it important in modern mathematics. BTW, I do not see much sense in these bizarre "multiple-cross-reference pages" and would prefer to see just a red link to avoid careless inbound links, rather than such an explanation of a trivial notion. Incnis Mrsi (talk) 12:42, 5 August 2012 (UTC)

My point was not to equate those 2 concepts, but rather that a random variable is one of the most important and most examples of a real valued function. That aside I'm not sure why you'd s real valued function si historically insignificant. There would be no calculus or real analysis without it and historically it actually stand for the development of the function/map concept itself. In fact many books simply treat function as a synonym for real valued function (or a subset of them since the domain is restricted to the reals as well), i.e. if some calculus or analysis primer speaks of functions, they usually mean real valued functions.--Kmhkmh (talk) 17:18, 6 August 2012 (UTC)

The phrase real-valued function appears to be nothing more than the sum of its parts: the two links real number and function (mathematics) should in effectively every case be sufficient. To allow articles, disambiguation pages, redirects or cross-reference pages for such phrases that have not acquired a distinct notable meaning seems to be inviting a proliferation of valueless pages. (I've also seen redirects for "common misspellings" that I feel should be removed.) I am not arguing against the concept of a Wikipedia:Multiple-cross-reference page, but to me it seems that real-valued function does not qualify. — Quondum^☏ 13:25, 5 August 2012 (UTC)

Why would you delete redirects from commonplace misspellings? Michael Hardy (talk) 16:25, 6 August 2012 (UTC)

A course like "Real functions", "functions of a real variable", "real analysis", etc., has been standard in U.S. mathematics for 80 years. A disambiguation page is useful, as Michael Hardy stated. Kiefer.Wolfowitz 17:08, 6 August 2012 (UTC)

+1--Kmhkmh (talk) 17:19, 6 August 2012 (UTC)

@Quondum : It's more than the sum of its parts in that (1) there are lots of existing links to the phrase; and (2) Someone who knows that "real" should redirect to "real number" and who also knows what a "value" of a function is might not know how locutions like "real-valued" are used, and "real-valued" is not a suitable article title.

When I create a new article, I always immediately create redirect pages from (1) alternative names, (2) alternative spellings and capitalizations, (3) common misspellings, (4) common misnomers. I also add hatnotes to other articles with similar names saying "This is about X. For Y, see [[Y]]." or the like.

@Kieffer : Of course I agree, except that "disambiguation page" isn't quite what this is, since links to it are appropriate and it's not about unrelated things bearing the same name. It more like a redirect but with multiple targets for the reader to choose among. Michael Hardy (talk) 15:50, 7 August 2012 (UTC)

Fundamental theorem of ideal theory in number fields

I created the article Fundamental theorem of ideal theory in number fields because this theorem is mentioned in Wieferich prime. Do others feel that this theorem should have an own article, or should I better include that information in Wieferich prime via a footnote? -- Toshio Yamaguchi (tlk−ctb) 07:10, 7 August 2012 (UTC)

This theorem appears in Dedekind domain#Some examples of Dedekind domains. Therefore a redirect to this link suffices. By the way, the Dedekind domains are just the rings in which this theorem hold and have mainly been introduced for the case of the integers in a number field. Therefore the lead of Dedekind domain should be expanded to mention this important example. D.Lazard (talk) 09:30, 7 August 2012 (UTC)

links to Hermite's identity

I deleted the "orphan" tag from Hermite's identity. Three articles link to it. But one of those is only a hatnote and otherwise the linking to it seems on the thin side. If someone can think of other articles that could appropriately link to it, could they add those links?

Also, it currently lacks references. Michael Hardy (talk) 15:21, 7 August 2012 (UTC)

I linked it from one other article that immediately came to mind. -- Toshio Yamaguchi (tlk−ctb) 15:53, 7 August 2012 (UTC)

Knights and knaves

The lead for this article credits Raymond Smullyan with the invention of "this type of puzzle". Not knowing much about history of logic puzzles, and suspecting that the puzzle has been around a lot longer than Smullyan's books, I thought this sounded like a rather generous claim. Can anyone check into how important Smullyan's contribution to the topic is? He is pretty old, and my sense that this is a problem from antiquity could just be wrong. Rschwieb (talk) 16:46, 7 August 2012 (UTC)

I have a book by Maurice Kraitchik ("Mathematical Recreations") dated 1943, well before Smullyan appears to have committed his Knights and Knaves to print, in which one of the first problems is one of exactly this type. Although I remember as a child finding something similar in one of my grandmother's Arthur Mee encyclopedias (which was old-fashioned even before she acquired it: 1870-ish I believe) which also had a puzzle along the same lines. So no way did Smullyan invent such a puzzle, although he may well have been a pioneer in giving an exhaustive workout to the genre. --Matt Westwood 21:34, 7 August 2012 (UTC)

Thanks for taking the pains to clear that up! Rschwieb (talk) 12:28, 9 August 2012 (UTC)

Proofs and sourcing of proofs in WP-articles

There is currently a developing discussion at WP:NOR which might be of interest/importance for editors here. It is at Wikipedia_talk:No_original_research#Original_mathematical_proofs_are_not_interpretations and in the next section as well.--Kmhkmh (talk) 15:31, 8 August 2012 (UTC)

Jitse's bot

Jitse's bot has done nothing in more than three days; the "current activities" page has not been updated. I don't see a lot of expression of alarm about that here. Is that because everyone else has directed their comments about it to Jitse Niesen, as I have, or could it be that I'm the only one who notices? Michael Hardy (talk) 18:36, 9 August 2012 (UTC)

I suspect there is not as much appreciation of the "current activities" page as would be useful. Once things get back to normal here, I may start posting a few highlights from that page here as they appear, along with a link to the page. Michael Hardy (talk) 00:41, 10 August 2012 (UTC)

August 9, 2012

Here are some new articles that do not (yet?) appear on the "current activities" page since Jitse's bot is down:

Added Douady–Earle extension

Added Perfectly orderable graph

Added Schizophrenic Number

Added Sumner's conjecture

Mathematicians:removed I. Bacharach

Mathematicians:removed Isadore M. Sheffer (is a redirect to Isador M. Sheffer)

Mathematicians:removed Jake Brown

Mathematicians:removed Peter Montgomery

Mathematicians:removed Robert Bryant

Mathematicians:added Isador M. Sheffer

Mathematicians:added Peter Montgomery (mathematician)

Mathematicians:added Robert Bryant (mathematician)

Michael Hardy (talk) 00:48, 10 August 2012 (UTC)

....and now the page has been updated for the first time since August 5th. Here's the list of new articles:

9 Aug: Christian of Prachatice, Cohen ring, Combining dimensions, Cone, Curta, Deal.II, Dedekind group, Douady–Earle extension, Equidissection, Isador M. Sheffer, J. W. Bruce, Matrix similarity, Mirsky's theorem, N. U. Prabhu, Orthogonal array, Perfect graph theorem, Perfectly orderable graph, Peter Montgomery (mathematician), Proper base change theorem, Regular tunings, Robbins' theorem, Robert Bryant (mathematician), Schizophrenic Number, Semiregular polytope, Smooth morphism, Sumner's conjecture, Trilinear polarity, Vizing's theorem, Zero order.

(Some may be newly recategorized articles rather than actually new articles.) So see if they need further work. Michael Hardy (talk) 02:44, 10 August 2012 (UTC)

Wikipedia:Featured article review/Infinite monkey theorem/archive2

This is a notification to interested editors that the article Infinite monkey theorem has been put up for featured article review for referencing and prose issues. — Crisco 1492 (talk) 03:56, 10 August 2012 (UTC)

Batrachion

AfD discussion at Wikipedia:Articles for deletion/Batrachion. Gandalf61 (talk) 21:16, 12 August 2012 (UTC)

Not a maths textbook, but an encyclopedia

The FAQ at the top of the page, asks "Why is it so difficult to learn mathematics from Wikipedia articles?", and suggests that it is because "Wikipedia is an encyclopedia, not a textbook [..] and not supposed to be pedagogic treatments of their topics".

To me, nearly every other subject in Wikipedia does read like a textbook summary. They all teach someone the basics of a subject. The one exception is maths, which despite my confidence to tertiary level, I find Wikipedia useless, because any attempt to include pedagogic examples are frowned upon.

Textbooks include 20 examples of a problem, and laboriously step through them. Surely this does not mean that we should exclude all examples? We readily include an image too illustrate a fact, but there can be no reason to exclude a stepped-through example, that also illustrates a fact.

Wikipedia is different to most other encyclopedias where space is not at a premium. I don't expect an article on, for example, Elementary algebra to be equal in length to a 500-page book. But I also don't expect it to exclude a couple of pages of examples, because a pedagogic approach is supposed to be bad. Maths articles are supposed to educate people, not exclude 95% of the readership who are expected to be able to learn something. --Iantresman (talk) 00:17, 13 August 2012 (UTC)

Do you have a particular example you were hoping to add to a particular page that was removed? If not, I'm not sure what sort of responses you're looking for. The number 1 reason that wikipedia math articles are not very accessible is that they tend to be written by specialists or other people with a relatively advanced math background, but as far as I can tell there's no organized campaign to prevent people from making math articles more accessible. --JBL (talk) 00:33, 13 August 2012 (UTC)

It also requires a specialist to make an advanced mathematics article accessible to lay persons. Most of the pedagogy we get is from WP:RANDY, and is of poor quality. I think this makes our more experienced editors believe that all pedagogy is bad. But I think we should aim for the quality of pedagogy in the Princeton Companion to Mathematics, written by specialists and aimed at a general audience. Sławomir Biały (talk) 12:41, 13 August 2012 (UTC)

Some math articles do include examples. But there are several reasons their use is limited.

1. Examples usually fail a strict reading of WP:V and WP:NOR. Making up our own examples to illustrate things leads to complaints when people demand specific sources for everything that is written. For lower level articles we might be able to directly quote some examples, although extensive copying would cause other complaints about excessive direct quotations.
2. The tone of examples tends to be nonencyclopedic. If we add an example with no explanation, people may not understand it at all. If we add the detailed explanation to help them, the article begins to read like a math textbook instead of an encyclopedia article - and the explanations again fail WP:V.
3. Even ignoring the verifiability problems, it's very hard to get agreement on which examples would be included. Everyone has their own pet way of presenting topics, and there is no easy way to find the "best" one. Even two authors of the same book have to go through lots of argument about how to phrase things. Finding agreement on unsourceable content in a wiki setting would be utterly impractical.
4. There's an entirely separate project, wikibooks, which is intended for pedagogical writing.

As a general principle, it is much more straightforward for us to focus on giving summaries of material, and leaving pedagogy to textbooks. — Carl (CBM · talk) 01:12, 13 August 2012 (UTC)

Comment: this type of issue has been raised a few times before. For example: Wikipedia_talk:WikiProject_Mathematics/Archive_69#wikipedia_is_a_great_source_of_info_for_just_about_anything.2C_with_one_exception:_mathematics., Wikipedia_talk:WikiProject_Mathematics/Archive_70#Accessibility_of_WP:Math_.28or_.22No.2C_I_don.27t_have_Dyscalculia_but_WP:Math_is_just_facts_and_proofs..22.29, Wikipedia_talk:WikiProject_Mathematics/Archive_18#General_Comment_about_Math_articles_from_a_non-mathematician, Wikipedia_talk:WikiProject_Mathematics/Archive_16#Request_from_Non-math_Person. Jowa fan (talk) 02:25, 13 August 2012 (UTC)

It may help the OP to realize that maths (and other specialist subjects, such as physics) are simply different from most other topics in an encyclopedia: the depth of coverage is far greater and more precise, and the average person has very little familiarity with the concepts. The overall result is that making a maths article pedagogical generally unavoidably detracts from it as a reference and vice versa. A bit like writing English articles for non-English readers would detract from them. — Quondum^☏ 04:24, 13 August 2012 (UTC)

Probably also worth suggesting that those who are wizards at mathematics are often not so good at writing encyclopedia articles to explain their knowledge. As a fairly frequent visitor to another (mathematics specialist) wiki, I hav seen the phenomenon whereby a page is written succinctly and smartly, so as to be readily understood by a newcomer (with solidly maintained links to concepts referenced), and then someone turns up who remarks, "This work is not rigorous and the examples are misleading" and replaces it with a much more difficult-to-follow exposition based on an axiomatic framework which is far from clearly explicated. This is not because the topic can not be explained in an easily-assimilable manner, so much as the fact that as the mathematician is so clever he can not believe that everyone in the world is so badly educated as not to understand a particular obscure symbology or terminology. When asked "Please explain your language," the answer that comes back is "Why should I, only a mathematician of my standing is clever enough to (be allowed to) know this." This (in my usually rubbish opinion) is not fully optimal.

Finding the balance is difficult, but not so difficult as to be impossible. Just because you can't do it doesn't mean to say it can't be done, however clever you think you are. --Matt Westwood 06:06, 13 August 2012 (UTC)

Imho editors often still thinking old print categories, when they treat this as an either-or-scenario. Since WP is not paper it is often possible to offer various approaches to the article's subject in different section, which have different levels of abstraction and accessibility.--Kmhkmh (talk) 13:06, 13 August 2012 (UTC)

Thanks for all the comments and links. Perhaps I'm over-reacting, or I misinterpreted the guidelines which I took to mean that articles should mostly exclude material that is (a) pedagogic, (b) textbook-like. Maybe the guidelines could be improved to suggest how an article can (i) be accessible (ii) include examples, without becoming a textbook, POV etc. --Iantresman (talk) 10:16, 13 August 2012 (UTC)

I think a balance is possible, but of course not so easy to achieve as there are many tradeoffs. I think most editors strive for this, but the primary value as a reference must not be sacrificed. The assumption of flexibility in an electronic medium may be a little misinterpreted: an article's length is severely constrained, and consequently pedagogy must in general be linked rather than included an added section. — Quondum^☏ 13:18, 13 August 2012 (UTC)

I guess that the more general an article (eg. algebra), the more problems we will have with space. But subdividing an article (eg. Solving a linear equations in two variables), should give us more space for explanations. So are we saying that in other words, divide and conquer? --Iantresman (talk) 17:05, 13 August 2012 (UTC)

It is not the place in an encyclopedia to teach how to solve a linear equation or a system of linear equations in two variables. This is done in high-school textbooks. In elementary algebra, the relevant information is that

• there are general methods to solve linear equations and systems in any number of variables,
• there are algorithms and computer programs that do that efficiently,
• if there are more variables than equations, then either there is no solution or an infinity
• etc.

The detailed explanation of the methods have to be referred to the articles on linear equations and systems. D.Lazard (talk) 17:45, 13 August 2012 (UTC)

Now I'm confused again. We have an article on the quadratic formula, which teaches people how to derived the quadratic formula, and even refers people to another article on how to do so using the Completing the square method, and articles on Solving quadratic equations with continued fractions. A strict reading of "Wikipedia is not a textbook" would exclude their approach.

So what I think you are saying, is that we don't go into detail in a general article like elementary algebra, but we might include that detail in separate relevant article. In which case we are not saying strictly that Wikipedia is not a textbook and can't teach like a textbook, but we may "teach", if follow the appropriate structure and style that does not read like a textbook. For example, L'Hôpital's rule includes just the kind of examples I would describe as pedagogic and textbook-like. --Iantresman (talk) 22:46, 13 August 2012 (UTC)

We can include an example as an illustration and it can include editor generated data just like an image but we need to be sure we don't include any new material - that they really are just illustrations and clearly seen to be such. We don't provide them in the sense of 'this is how you do it' but more as in 'here is an example illustrating what is being discussed'. Dmcq (talk) 23:11, 13 August 2012 (UTC)

I agree with Iantresman that many, if not most, articles on elementary math are written in a textbook-like style and do not follow the recommendations of MOS:MATH. This does not really bother me, if the reader may easily find the relevant information that an encyclopedia must provide. But it is frequently not the case. An example is the case of the division of the integers, there are the articles division (mathematics), long division, division algorithm, now moved to Euclidean division, remainder and modulo operation. The first article is overly detailed on notions that anybody, which is able to read Wikipedia, should know, but does not state clearly that there are two divisions between integers, the division that produces a rational number and the Euclidean division which produces a quotient and a remainder. The four other articles are related to the same notion of Euclidean division, but, although it is an ubiquitous notion, the reader can not have any idea of its main applications. As a consequence, all these articles are much less useful that they should be. Maybe a section on elementary math should be added to MOS:MATH? D.Lazard (talk) 09:54, 14 August 2012 (UTC)

I also think that an encyclopedia must provide certain information, but that some textbook-style examples may improve them. I'm certainly not suggesting that we replace the encylopedia style with textbook style. I would envision an article on division (mathematics) to be more "encylopedic" than an article on long division, which I would argue, can not avoid but include an example.

Since I am sure that no-one is suggesting that we never include examples, the question then becomes, how do we improve accessibility and include examples, without contravening "Wikipedia is not a textbook". --Iantresman (talk) 10:27, 14 August 2012 (UTC)

This is not a complete answer, but links to pages in Wikiversity and similar sites should be considered for filling this purpose when examples etc. start detracting from the main purpose as a reference. In all, I think the principle of retaining an article's utility as a reference could act as a guide for what level of examples/explanation is suitable. Within this constraint, accessibility should be maximized, possibly more in the sense of style of presentation (using more commonly understood definitions, avoiding unnecessarily obscure concepts, accessible language, etc.) than in the sense of pedagogy. As D.Lazard points out, articles have a tendency to morph in the direction of pedagogy at the expense of reference value of the topic. This is most acute in the articles that are elementary or topical enough to attract a large amount attention (e.g. Speed of light, Higgs boson, Division (mathematics)). The article Elementary algebra falls squarely in this zone. — Quondum^☏ 12:43, 14 August 2012 (UTC)

Gunther Schmidt

Deletion of Gunther Schmidt has been proposed on the grounds of lack of references. Can someone improve the article to the point where that objection doesn't apply? Or is it not worth keeping? Michael Hardy (talk) 00:21, 14 August 2012 (UTC)

David Eppstein did an edit on this after I posted what you see above, but he didn't delete the "prod" tag, and the article got deleted.

Two questions:

• Can references be added to support what the article says?
• Is it worth keeping as an article?

If so bit of further work might make it possible to restore it. Here's what the article said:

copied from deleted article:

Gunther Schmidt (born 1939) is a German mathematician whose research ranges from informatics of mathematics to mathematical logic. After studying mathematics at the University of Göttingen and the University of Munich, he worked from 1962 to 1988 at TU Munich (TUM) and 1988 until his retirement 2004 at Universität der Bundeswehr München.

Books

• Gunther Schmidt, 2010. Relational Mathematics. Cambridge University Press, ISBN 978-0-521-76268-7.
• Gunther Schmidt, Thomas Ströhlein, 1993. Relations and Graphs – Discrete Mathematics for Computer Scientists. Springer Verlag, ISBN 3-540-56254-0.
• Gunther Schmidt, Thomas Ströhlein, 1989. Relationen und Graphen – Mathematik für Informatiker. Springer Verlag, ISBN 3-540-50304-8.
• Manfred Broy, Gunther Schmidt, Eds. 1982. Theoretical Foundations of Programming Methodology. Reidel Publishers, ISBN 90-277-1460-6.

References

Weblinks

• Gunther Schmidt's web page in the Faculty of Informatics
• [35]

Category:German mathematicians Category:Living people Category:1939 births Category:University of Göttingen alumni Category:Ludwig Maximilian University of Munich alumni Category:Technical University Munich alumni Category:Bundeswehr University Munich alumni Category:German academics

end of copy of deleted article

I think that blpprod was the wrong reason to delete this article (almost certainly it could have been sourced adequately for verifiability) but the reason I didn't fight harder for it was that I was not certain he passed WP:PROF. Being a full professor with several books is suggestive but not conclusive. The strongest case for WP:PROF seems to be criterion #C1, significant impact within his discipline (as measured by citation counts, for instance) but in his case I was having a difficult time finding good citation counts because his name is so common. —David Eppstein (talk) 17:07, 14 August 2012 (UTC)

Mathematical Manuscripts of Karl Marx | References

Dear Members of the concerned community, I request you to consider adding the following to the References part of <http://en.wikipedia.org/wiki/Mathematical_manuscripts_of_Karl_Marx>:

Marx, Karl (1994)[1968], Yanovskaya, Sofya, ed.,Mathematical Manuscripts[complete English translation]together with a Special Supplement <http://cfcul.fc.ul.pt/varios/Karl_Marx_FINAL.pdf> Calcutta/Kolkata: Viswakos Parisad, I S B N 81-86210-00-8.

Regards. Pradip Baksi — Preceding unsigned comment added by 223.180.185.44 (talk) 03:58, 4 August 2012 (UTC)

I would have thought the ideologues in Soviet Russia and China would have gone out of their way to destroy pure mathematics with their Gradgrind type outlook, but it seemed to survive very well. Is there a story to be or already told about that? Dmcq (talk) 17:41, 6 August 2012 (UTC)

There's already a link. Why would we need another? Why is a Kolkata link hosted in Portugaul? What's Kolkata got to do with it anyway? What's the "special supplement"? linas (talk) 15:55, 18 August 2012 (UTC)

Elementary algebra GA review

I was reviewing Elementary algebra and then I found that the editors used textbook language, such as "Let's" which would be changed to "Let us," but that means let me teach you. Article sounds a lot like a Wikiversity page. I would appreciate a second opinion on this. Obtund^Talk 04:39, 4 August 2012 (UTC)

I think ""lets/let us" is unencyclopaedic. linas (talk) 15:57, 18 August 2012 (UTC)

How about the use of "we" as used in the Encyclopedia Britannica article on Elementary algebra --Iantresman (talk) 18:27, 18 August 2012 (UTC)

It's allowed by WP:FIRSTPERSON but the MOS says that "often rephrasing is preferable" and avoiding it is usually not difficult. For past discussions see e.g. Wikipedia talk:Manual of Style/Archive 95#"We" in mathematics. —David Eppstein (talk) 19:19, 18 August 2012 (UTC)

SVG output from graphics tools

Hi, not an official part of this project (yet), but what you think of these SVG images I made based on MATLAB source code:

Exemplified in the Gaussian function article: New images:

• 
• 
• 

Old images:

• 
• 
• 

If you have any feedback (prefer the SVG or old versions) please let me know.

Zerodamage (talk) 19:20, 8 August 2012 (UTC)

Those look like nice improvements. One thing: in your images, there is a transparent background. I think for accessibility purposes people like there to be a solid background. Though I think this may have been a contentious point. You should check it out. RobHar (talk) 19:41, 8 August 2012 (UTC)

I agree that this is an improvement. I noticed that the svg makes the grid quantization visible (e.g. in the solid blue area) while the old png doesn't; I assume this is a deliberate choice, and I think it's a good idea e.g. to make it clearer why the central red-orange area has some jagginess. —David Eppstein (talk) 20:17, 8 August 2012 (UTC)

It is usual and easy to make a solid appearance of a transparent image. There are several more ways to do it via setting HTML/CSS background or superimposing of images. But it is, generally, impossible to make a transparent appearance of an opaque image. Do not add any background. The only thing I advice to change is width="100%" heignt="100%". Not so good in the context of Commons' web interface. Use concrete dimensions (such as 1050×787.5), please. Incnis Mrsi (talk) 20:18, 8 August 2012 (UTC)

Actually the jagedness is a sideeffect of the tools used. I looked at correcting it but decided it actually was advantageous for the images to preserve it. As for size code (100%), I'm assuming your referring to the SVG code; I will look into correcting that. Zerodamage (talk) 09:29, 9 August 2012 (UTC)

The images are annoyingly tiny. It would be great if all of the whitespace were removed, and they were rotated by 45 degrees so that the corners would not poke out and take up space. Make the central item, the point of interest, as large as possible! linas (talk) 16:22, 17 August 2012 (UTC)

List of reciprocity laws

Yet another link farm. -- Taku (talk) 20:32, 13 August 2012 (UTC)

The reciprocity law article seems like it is worth having to me. I don't see the need for a separate list of reciprocity laws. Sławomir Biały (talk) 00:22, 14 August 2012 (UTC)

I don't understand what is meant by calling it a "link farm", but in view of the content of the article titled reciprocity law, it's a duplicate that should redirect to the older article, as it now does. Michael Hardy (talk) 00:35, 14 August 2012 (UTC)

Sorry. It was a mistake. It has been corrected. -- Taku (talk) 02:01, 15 August 2012 (UTC)

Change the subject slightly, but I have been working on an article about Eisenstein Reciprocity, should be ready in a week or so. - Virginia-American (talk) 19:24, 17 August 2012 (UTC)

nLab cross-pollination

Anyone have any experience with movement of content between WPM and nLab? I notice that nLab has deeper/more extensive coverage of cat theory topics than WPM, and so I'm tempted to do some cut-n-paste effort from there to here, but am stymied slightly by the license, or rather lack there-of. The de facto license at nLab seems to be this, quoting from the home page: "Using content obtained from the nLab in your publications is free and encouraged if you acknowledge the source". That's it; I can find nothing more explicit. As far as I can tell, this hasn't been discussed on WPM before... Comments? linas (talk) 16:49, 17 August 2012 (UTC)

FYI, I've just created a template to help w/ ncatlab citations: so:

* {{nlab|id=simplex+category|title=Simplex category}}

will create the following text:

• Simplex category at the nLab

linas (talk) 19:22, 17 August 2012 (UTC)

Some parts of n-lab does seem to have original research. But if we're careful, the content dumping sounds like a good idea, only if we can do it as you noted. There is some discussion [36]. -- Taku (talk) 11:37, 18 August 2012 (UTC)

Apparently, the springer EOM has a CC-BY-SA/GFDL policy now, too, as long as one provides attribution. Someone dumped the whole contents of Neil Hitchin's 'magnetic monopole' into Magnetic monopole#Appendix... I am looking for an attribution template.... linas (talk) 14:13, 18 August 2012 (UTC)

Wait, you have to be careful. The only new content is unde cc-by-sa. From the main page:

"The original articles from the Encyclopaedia of Mathematics remain copyrighted to Springer but any new articles added and any changes made to existing articles within encyclopediaofmath.org will come under the Creative Commons Attribution Share-Alike License"

-- Taku (talk) 14:25, 18 August 2012 (UTC)

I had to read that 4 times, but I think they are actually saying that *all* content is CC-BY-SA/GFDL. The first few sentences make it sound like its only the new material, but later, they state that its all of the material. Or at least, that's what I got out of it after reading it over and over... So, FWIW, there is now a Template:SpringerEOM attribution. If this is wrong ... well, time for the wiki-lawyers to step in, as otehrwise, magnetic monopole is now in copyvio land ... linas (talk) 15:31, 18 August 2012 (UTC)

Finitely generated ring

I think I know enough algebra to know that there is no such thing as finitely generated ring (or every ring is finitely generated, namely by 1). Google search disagrees. I think people mean finitely generated k-algebras; so this should be redirected to finitely generated algebra in my opinion. But maybe someone knows better. -- Taku (talk) 20:46, 17 August 2012 (UTC)

Generally, when there is a term that can be used with R-algebra at the end, and is used with ring at the end instead, it's that one is speaking of Z-algebras. Similarly, a scheme is just a scheme over Z. Anyway, here the term "finitely generated ring" is defined on page 30 of Atiyah–Macdonald as indeed being a finitely generated Z-algebra. RobHar (talk) 04:08, 18 August 2012 (UTC)

Ok, this is very helpful. This answers my problem exactly; especially, the AM part. I will probably add a discussion f-gen in f-gen algebra unless someone else beats me do it. -- Taku (talk) 13:32, 18 August 2012 (UTC)

And just to preempt another conceivable use in the future: someone might use this term while working in a ring without unity. I think Rob's right though that most often it's going to be one of these screwy uses of "finite" that have been invented. Rschwieb (talk) 23:38, 19 August 2012 (UTC)

Stefan Banach

Volunteer Marek (talk · contribs) has been working hard on improving our article on Stefan Banach. The coverage of his education, mentorship, and life is now much better than it was, but the coverage of his mathematical contributions is still weak. Perhaps some project members whose interests run towards that kind of mathematics could help? —David Eppstein (talk) 00:11, 21 August 2012 (UTC)

His contributions section does seem short, but it looks like a good start to me. Maschen (talk) 14:42, 21 August 2012 (UTC)

List of zero terms

List of zero terms is also at AfD. Please comment there. Sławomir Biały (talk) 19:08, 28 July 2012 (UTC)

The treatment of zero in mathematics on Wikipedia is more generally a bit of a jumble. We have:

• 0 (number)#In mathematics,
• Zero (disambiguation)#Mathematics,
• Zero element,
• List of zero terms,

each giving a list of zero terms, each incomplete, with a lot of overlap.

Note also this curious pair of redirections:

• Non-zero → 0 (number),
• Nonzero  → Nonzero: The Logic of Human Destiny.

 --Lambiam 15:52, 29 July 2012 (UTC)

Now closed as merge to Zero element. I've done the merge but it could do with some eyes. I also had to split off Zero order as a seperate article which is very stubby.--Salix (talk): 11:33, 7 August 2012 (UTC)

See Talk:Zero order for some comments. Deltahedron (talk) 19:48, 18 August 2012 (UTC)

I have updated the article Zero order process to distinguish two separate meanings. Deltahedron (talk)

Normally when the same phrase is used for two different and unrelated meanings, we have two articles, with a hatnote linking one to the other. See WP:NOTDICT, in the last line of the table under "Major Differences". —David Eppstein (talk) 17:32, 22 August 2012 (UTC)

Feel free ... Deltahedron (talk) 19:01, 22 August 2012 (UTC)

New article feed

I've noticed your project was listed at User:AlexNewArtBot but was missing the ruleset, so the search was not carried out. I'ved added the rule (list all new articles with the string "math" in it, and hopefully that's all that was needed. If so, you should see this link turning blue soon, and then you may want to add it to your main page. See how we did it at our WP:SOCIOLOGY: Wikipedia:WikiProject_Sociology#New_article_feed. --_{Piotr Konieczny aka Prokonsul Piotrus| reply here} 18:18, 22 August 2012 (UTC)

Thanks, but mostly we depend on Mathbot (talk · contribs), Jitse's bot (talk · contribs) and Wikipedia:WikiProject Mathematics/Current activity instead. Rather than using syntactical analysis like that, it is based on the categories of the articles, so the two efforts may be complementary (both picking up ones missed by the other). —David Eppstein (talk) 18:22, 22 August 2012 (UTC)

Must y be an integer?

Take a look at this edit. If one adopts the definition

${\binom {n-y}{n}}={\frac {(n-y)(n-y-1)(n-y-2)\cdots (n-y-n+1)}{n!}}$

then this is well defined even if y is not an integer, and I'd have guessed the whole identity would still hold then. Maybe when I'm feeling less lazy I'll check it.

A good edit? Or not? Michael Hardy (talk) 16:38, 7 August 2012 (UTC)

If n > y >1 are integers, this binomial coefficient is null. Thus the series involved by this edit is finite. For small values of n, all factors are negative. It is not clear to me what the notation "choose" means in this case. On the other hand the formula you have written is clearly a polynomial in y, and thus defined for any n. Thus the edit is certainly not good. But it reveals that the involved formula has to be checked, as binomial coefficients are rarely used when all factors of the numerator are negative. D.Lazard (talk) 17:28, 7 August 2012 (UTC)

The last sentence is not entirely correct. For instance, the binomial series

$(1+x)^{\alpha }=\sum _{k=0}^{\infty }{\binom {\alpha }{k}}x^{k}$

is valid for any $\alpha \in \mathbb {R}$ and $|x|<1$.--LutzL (talk) 18:15, 7 August 2012 (UTC)

The expansion in question follows formally by expanding one factor of the integrand defining the beta function in a binomial series and integrating term by term. This would not require y to be an integer, though there would be some natural constraint on y to ensure convergence. Sławomir Biały (talk) 19:14, 7 August 2012 (UTC)

Yes, it uses ${\binom {y-1}{n}}=(-1)^{n}{\binom {n-y}{n}}$. Uniform convergence does not extend to the upper bound 1 of the integral, but I don't see a dependence on y. If convergence follows as some variation of the alternating harmonic series, then the argument should be valid for all y.--LutzL (talk) 19:55, 7 August 2012 (UTC)--Number of negative factors stabilizes.--LutzL (talk) 07:54, 8 August 2012 (UTC)

Well, the problem is that ${\binom {n-y}{n}}$ all (ultimately) have the same sign for fixed real y, so the series never converges on the real axis, except at $y\in \mathbb {N}$, where it's zero. Sławomir Biały (talk) 20:51, 7 August 2012 (UTC)

They all have the same sign, but it doesn't follow that the sum diverges. For example, if I'm not mistaken, ${\binom {n-1/2}{n}}$ grows like $c\cdot n^{-1/2}$, which certainly yields a convergent sum (as long as x isn't a negative integer). --JBL (talk) 22:52, 7 August 2012 (UTC)

Ah yes, of course. In general ${\binom {n-y}{n}}\sim n^{-y}/\Gamma (1-y)$. Sławomir Biały (talk) 00:50, 8 August 2012 (UTC)

Indeed, and convergence follows directly from the Raabe or Gauß tests, as long as $x,y>0$. For non-positive x or y even the defining integral would have a non-integrable singularity at t=0 or t=1.--LutzL (talk) 07:54, 8 August 2012 (UTC)

Presumably the formula in question is taken from a reliable source? What is that source and what does it say? Deltahedron (talk) 06:47, 8 August 2012 (UTC)

Knuth somewhere has a discussion of the binomial formula, perhaps in Volume One or Concrete Mathematics.... Sedgewick and Flajolet's 2-volume Analytic Combinatorics used to appear on the internet in draft form.Kiefer.Wolfowitz 10:01, 8 August 2012 (UTC)

2-volume ?? Their book, which is 1-volume, is available where it's been for years by following the link at Analytic combinatorics. — Preceding unsigned comment added by 2.97.22.242 (talk) 11:12, 8 August 2012 (UTC)

They wrote an earlier, simpler book on enumerative combinatorics (with a view towards algorithm analysis), perhaps as part of the same project. Kiefer.Wolfowitz 18:02, 21 August 2012 (UTC)

Mmm, Ok, I'll give you that one. 89.241.231.98 (talk) 03:33, 24 August 2012 (UTC)

Behrens–Fisher distribution

I've written this somewhat hastily scrawled user-space draft. I have in mind that with some further work it can evolve into something to be moved into the article space under the title Behrens–Fisher distribution (currently a redirect). In its early stages that will be maybe two or three times as long as the present draft. I'll be back to do more work on it. In the mean time, maybe others can improve it as well. Michael Hardy (talk) 03:40, 24 August 2012 (UTC)

Is there a mechanism for people to advertise userspace drafts of mathematical articles that they want others to look at (other than posting here of course)? It might be quite helpful. Deltahedron (talk) 03:45, 24 August 2012 (UTC)

Deltahedron: Probably not. Why not just link from here to there?

Michael Hardy: Good start to the article, though I probably will not be much help... Maschen (talk) 06:33, 24 August 2012 (UTC)

To Deltahedron, actually Wikipedia was supposed to be a place where you put your draft. But maybe nowadays it is more of a place for articles waiting for a peer review. One way to provide a mechanism (which doesn't exist to my knowledge) is to create a tag and ask people put it on their drafts. -- Taku (talk) 13:38, 24 August 2012 (UTC)

Sometimes with a fairly complicated article, one wants to make the draft somewhat complete before moving it to the article space. I might move it there soon with some tags saying some sections should get expanded. Michael Hardy (talk) 22:51, 24 August 2012 (UTC)

OK, it's moved to the article space. For now, it's an "orphan". Michael Hardy (talk) 23:35, 24 August 2012 (UTC)

Semi-Simplicial Sets and problems with that article

The whole thing with semi-simplicial sets is quite messy, so I'll start with a short history wrap-up

• 1950 Eilenberg and Zilber published the paper Semi-Simplicial Complexes and Singular Homology, where they defined a Semi-simplicial set as a collection of elements together with dimension and face-maps, which is what nowadays is commonly called a Delta set, and a Complete Semi-Simplicial Set as a Semi-Simplicial Set with degeneracy maps, which correponds to what today is most commonly called a Simplicial set
• 1967 Gabriel and Zismann published the book Calculus of Fractions and Homotopy Theory, where they used the term Simplicial Set to denote what Eilenberg and Zilber called complete Semi-Simplicial Set (they didn't use Semi-Simplicial- or Δ-Sets in this book).
• 1969 Rourke and Sanderson published the paper Δ-Sets I: Homotopy Theory. where they used the term Δ-Set for what Eilenberg and Zilber called Semi-Simplical Complex, css-set to describe what Eilenberg and Zilber called Complete Semi-Simplicial set, and Semi-Simplicial Complex as an umbrella term for Δ- and css-sets.
• 1997 Gelfand and Manin published the book Methods of Homological Algebra, where they refered to Semi-Simplicial sets as Triangulated Spaces (well, technically they call the geometric realization a triangulated space, and the combinatorial object the Triangualtion)
• 2008 Kozlov published the book Combinatorial Algebraic Topology, where he used the term trisp for Semi-Simplicial Sets, which is an abbreviation of Triangulated Space.

So, I think all this should be somehow incorporated into the Δ-Set article, though I'm not sure really sure what might be the best way to do so (and I don't know who coined which term originally). Moreover I'd say the article should be named after it's original name, i.e. Δ-Set should refer to semi-simplicial set, and not the other way round. And last but not least the article needs to be generally improved, e.g. by including the categorial definition (as a functor from Δ to Sets) for a semi-simplicial set. I'll might very well do that sometime, though. --Roman3 (talk) 12:19, 24 August 2012 (UTC)

The better math articles have a History section to them. I see nothing wrong with copying the above, more or less verbatim, into one of the two articles. Just make sure terms like trisp are not redlinks. linas (talk) 04:12, 25 August 2012 (UTC)

Suggested merges with dyadic product and outer product, into tensor product...

See talk:outer product, Dyadic Product and talk:Dyadic product. Opinions? At least a merge of dyadic product into outer product seems sensible to me and a few others. Maschen (talk) 14:30, 21 August 2012 (UTC)

Partial oppose. Outer product is concrete while tensor product is heavy on abstract nonsense. Kiefer.Wolfowitz 14:35, 21 August 2012 (UTC)

I was expecting this response, I'm not so fussed about merging outer into tensor product, but dyadic into outer could be done... Also Kronecker product should be left alone IMO. Maschen (talk) 14:38, 21 August 2012 (UTC)

"Dyadic product" is certainly the same thing as the article "outer product" currently describes. "Tensor product" is an operation on spaces (objects), not elements, but it is hardly possible to understand one without another. IMHO all content has to be merged, and outer product is about to be made a disambiguation page. Incnis Mrsi (talk) 14:39, 21 August 2012 (UTC)

Partial oppose, per Kiefer.Wolfowitz. I also think that the term "dyadics" is almost entirely obsolete, only appearing in very old textbooks. Sławomir Biały (talk)|

"Dyadic" is a very obsolete term, but that doesn't mean it can't be mentioned briefly in the merged articles (if they are), for historical awareness and completeness. It may be difficult to pull tensor product and outer product together, but certainly not dyadic and outer (also for which there is plenty of favour to merge on that talk page). Maschen (talk) 20:35, 21 August 2012 (UTC)

Let's summarize different merging possibilities:

1. Dyadic product + Outer product + Tensor product
2. Dyadic product + Outer product leaving Tensor product alone,
3. one proposal for: Dyadic product + Dyadics + Outer product,
4. everything on dyadics into one article, for pure historical interest: Dyadic tensor + Dyadic product + Dyadics, and optionally Outer product + Tensor product,

Which one(s)?... By all means we can't fall into the trap of pulling everything into one article... Maschen (talk) 20:56, 21 August 2012 (UTC)

I would say leave Tensor product and outer product articles alone for now, and merge all of the dyadic articles as you suggest in option 4. Sławomir Biały (talk) 22:35, 21 August 2012 (UTC)

P.S. Another thing to think about is how the article Kronecker product fits in with outer product. Sławomir Biały (talk) 22:35, 21 August 2012 (UTC)

Ok - that's reasonable. Kronecker product is a bit long and heavy to merge into anything though, and I think it should have its own article. If merged it will need a significant trim to just the lead definition and properties. Maschen (talk) 05:45, 22 August 2012 (UTC)

The term tensor product evidently refers not only to the tensor product of spaces, but also to the tensor product of elements (e.g. tensors such as vectors) within those spaces, as specifically addressed by section 2 of the article. (The tensor product of the spaces is the linear span of the tensor products of their elements.) The dyadic product and outer product are also mentioned in that article.

So I respectfully disagree with Incnis, Kiefer.Wolfowitz and Sławomir, and feel that Dyadic product, Outer product should be merged into and made into redirects to Tensor product#Tensor product of two tensors. Dyadic tensor and ***Dyadics should be merged into and redirected to Tensor as minimal historical notes. Note that outer product is equivalent to tensor product (i.e. it applies to an arbitrary pair of tensors over the same field, not only vectors), whereas dyadic product seems to refer specifically to vectors.

I do no know whether Tensor product or Outer product is the dominant term, but some reputable people use the first (e.g. Pertti Lounesto).

Dyadic is a disambiguation page, and so should not be merged.

The Kronecker product is in some sense the tensor (or outer) product of two order-2 tensors (the components are the same, except rearranged), put into the notation of matrices. It seems to me to be a clumsy way of representing a 4th-order tensor (product) using a rectangular matrix, and I think that link, the detail thereof in Tensor product should be trimmed to a mention and a link.

In summary, I think Tensor product already says mostly what it should, but should mention that the terminology and notation of dyadics and polyadics generally is obsolete, possibly in a historical section.

Disclaimer: I'm no expert, but browsing internet sources led me to this picture some while ago. — Quondum^☏ 08:48, 22 August 2012 (UTC)

Sorry I meant Dyadics - not the disambig page, links have been fixed. Fair points, although I prefer Sławomir's suggestion.

Out of interest, the tensor product article uses links in its headings, contrary to this guideline...

Should also add: I'm not going to actually merge anything (until consensus), but trying it out... Maschen (talk) 09:37, 22 August 2012 (UTC)

Even though outer products are an example of tensor products (assuming that a matrix is a rank-2 tensor), I think the Wikipedia articles outer product and tensor product serve different audiences. The outer product between vectors can be understood by people familiar with vectors in R^3 and matrices, while to understand tensor products you need to know some abstract algebra. I think it will be unnatural for one article to take both these audiences into account, so I prefer to have separate articles.

On dyadics, I don't see any harm in having an article on it, even though it's historical. In my opinion, all the dyadic articles should be merged into one. In particular, I see little reason for having a separate article on dyadic product. But I note that User:Crowsnest opposed this and I don't feel strongly about it either. I alerted this editor to the discussion here. -- Jitse Niesen (talk) 11:08, 22 August 2012 (UTC)

Due to a lack of time, I will not participate in the discussion. I expect there are enough knowledgeable editors around here to come to a nice solution. Wishing you a fruitful exchange of ideas, Crowsnest (talk) 20:46, 23 August 2012 (UTC)

I would like to voice my agreement with those who think that not everything should be merged to tensor product on grounds of different levels of concreteness/different audiences. (Of course these articles should link each other prominently.) Options 2 and 3 both seem like fine ideas to me. --JBL (talk) 13:50, 22 August 2012 (UTC)

As expected - there are conflicting views... All options 1-4 are in favour, although the slightly dominant consensus is 4 minus the merge outer product + tensor product...

The dyad articles are effectively merged, just waiting for more responses which may contain more valuable and subtle perspectives before inserting this into dyadic tensor... Maschen (talk) 06:01, 23 August 2012 (UTC)

It seems to me that there is actually disagreement on the meaning of the respective terms, and that the existing articles (esp. Outer product) misleadingly define simpler versions of what they really are. But since no-one seems to agree with me, I guess I should keep quiet. Besides, some of you may have direct experience in the field. — Quondum^☏ 09:53, 23 August 2012 (UTC)

I agree that all the articles dealing with dyadics, dyadic tensors, and dyadic product should be merged. The natural target for this merge would be (IMHO) dyadics, since the common factor here is the notation. The objects, and operation themselves are simply specially cases of tensors and tensor products, but what sets them aside is the historical notation and terminology surrounding them.

As for outer product that should probably be a disambuigation page, since that term can refer to a number of loosely related operations including the one currently described in outer product, exterior product, and even is some case cross product.

The tensor product article should be kept separate since that is a much more general operation than any of the others. (Which can be applied pretty much to anything which has some sort of module structure.)TR 12:51, 23 August 2012 (UTC)

I'll support TR. An article that focusses on dyadic terminology and notation (and related terms e.g. "polyadics" if notable) makes sense with an explanation of its relationship with more modern notation and terms, with a single "see also" to it link in Tensor and Tensor product. I'll need some study to comment properly on "outer product". Tensor and Tensor product can have these aspects offloaded if desired — Quondum^☏ 21:42, 23 August 2012 (UTC)

So there is no opposition to merge the dyadics articles... time to do it - see dyadics. Maschen (talk) 23:20, 23 August 2012 (UTC)

Here is a possible basis for turning outer product into a disambig page. By all means take, leave, and/or change it, just thought to give a head-start if anyone would like to actually reform the article in to a disambig page. Maschen (talk) 23:42, 23 August 2012 (UTC)

Support TR's position. Don't make the mistake of confusing "conceptually identical if you're trained in math" with "content is accessible to the lay audience". Insofar as the article serve different audiences, let them be. Also, be aware: the simpler the article, the more frequently it attracts incorrect edits from younger/inexperienced editors. Patrolling large articles is difficult. linas (talk) 03:53, 25 August 2012 (UTC)

As to DAB pages, please note: product (mathematics) already does the job; I don't see why we'd need another one. linas (talk) 03:59, 25 August 2012 (UTC)

On the potential DAB of outer product, we still need to resolve what to do with that title. Are you suggesting that product (mathematics) be expanded to give links to the various meanings of the term, and that outer product should become a redirect to it? (I'm not objecting). — Quondum^☏ 05:11, 25 August 2012 (UTC)

Another summary:

1. The point of changing outer product to this was to listify all of the links, then everything related to "outer product" people may expect from the title could be clicked to.
2. Redirecting outer product to product (mathematics) means outer product can't be linked in product (mathematics), but could still of course be listed/explained very briefly.
3. Linking from product (mathematics) to outer product would be wasteful.
4. Expanding product (mathematics) may not gain much, except for

• inserting the statement: "Some authors use the expression "outer product of tensors" as a synonym of "tensor product". The outer product is also a higher-order function in some computer programming languages such as APL and Mathematica."
• and link: Bra-ket notation for outer product.

Most of the other links in my draft are just "see also" links.

I'd say 2 and 4. Opinions? Maschen (talk) 18:44, 25 August 2012 (UTC)

Projective variety

Someone has to start the article someday and I just thought why not me today. I'm posting this since I don't mean to do it covertly. Right now, most of materials there overlap other elsewhere and it's not a balanced account, but I think it's not a good start, either.

About the title: "algebraic" is missing. It's because, in my real life, I never say "projective algebraic". The only concern would be ambiguity with "projective analytic". But by Chow's theorem this is actually not ambiguous. Right? -- Taku (talk) 00:33, 24 August 2012 (UTC)

More links could be added, right from the start "algebraic geometry" is not linked nor "topology" etc., I'll do that now. There is concern that if lots of effort goes into rewriting it this article, and it doesn't grow much, and still has plenty of overlap with other articles, then a similar event to recently merged dyadic articles (see above) could happen in the future - i.e. merged back into algebraic variety or whatever. At least a start though, good work. Maschen (talk) 06:30, 24 August 2012 (UTC)

Good going. It will be necessary to address the overlap with Algebraic geometry of projective spaces. Is there an article anywhere on the projective Nullstellensatz? Deltahedron (talk) 06:39, 24 August 2012 (UTC)

Maybe there isn't but see Hilbert's Nullstellensatz and Differential Nullstellensatz, probably close as can be... Maschen (talk) 06:50, 24 August 2012 (UTC)

To me, Algebraic geometry of projective spaces appears bizarre. What is it doing? Projective space seems like a natural space for the topic. Projective space shouldn't just focus on the topological and differential-geometric aspects, that's not balanced if more elementary and pedagogical. Some parts of it also overlap the Proj construction. Finally, the section "Morphisms to projective schemes" should move to projective variety. -- Taku (talk) 11:53, 24 August 2012 (UTC)

Are you sure that we don't already have a bunch of articles on this topic? Don't create a situation, where, like outer product and tensor product, someone will want to merge them all back together again in a few years. linas (talk) 04:07, 25 August 2012 (UTC)

There are some overlaps for sure. For example, Proj construction gives a very nice scheme-theoretic constriction and so there is no need to get into details in projective varieties. Also, some other subtopics (say GAGA) is covered adequately in its own article. On the other hand, I don't see this as an argument against having this article. It's an overview. To me, it's no brainer that this is an important topic and deserves its own article. In short, I believe it survives AFD :) -- Taku (talk) 11:47, 25 August 2012 (UTC)

Actually maybe some more concrete constructions could be useful (the red book does coordinate-non-free construction with explicit examples and something like should be included.) -- Taku (talk) 11:51, 25 August 2012 (UTC)

Just to provide an analogous situation to balance my previous view: there are many articles related to generalized dynamics - Analytical mechanics is the overview of many articles: principle of least action, Hamilton's principle, Lagrangian, Lagrangian mechanics, Hamiltonian, Hamiltonian mechanics, equations of motion, generalized coordinates, Euler-Lagrange equations... and all have plenty of mutual overlap (there are more physics examples, though will not clutter the space here). There is nothing wrong with an overview article, just be sure to reduce all overlap using WP:summary style, so it may be better to keep all concerete examples/derivations/details in whichever main articles are appropriate... and summarize everything in the overveiw. Maschen (talk) 21:17, 25 August 2012 (UTC)

Disambiguation help needed

Kernel (mathematics), Lie bracket, Adjoint representation, Generating set, and Covariant are currently among the disambiguation pages with the largest numbers of incoming links. Please help fix these. Cheers! bd2412 T 17:24, 23 August 2012 (UTC)

Kernel (mathematics), Lie bracket, Adjoint representation look fine, Generating set and Covariant need tidying up. I'll do that now. Maschen (talk) 20:21, 23 August 2012 (UTC)

Well generating set probably shouldn't be a dab page, it should probably be renamed to something like generator (mathematics) and turned into a real article. There is a fine line between being a DAB page, a list of related topics, and an article that explains why they are all related. Everything there is dealing with exactly one and the same concept of a generator, and not a bunch of unrelated things that happen to have the word 'generator' in them, yeah? So I am not at all convinced that "fixing" the incoming links is even the correct thing to do. linas (talk) 01:33, 26 August 2012 (UTC)

For generating set (now redirected to generator (mathematics)) - I extended slightly into article format and added the wikiproject maths/physics banners to talk:generator (mathematics) (change the settings if inaccurate). Maschen (talk) Maschen (talk) 09:16, 26 August 2012 (UTC)

I had looked at a few of them and it did seem to me that in many cases a link to a disambig or similar page was appropriate, i.e., there wasn't actually anything to be "fixed" in many cases. --JBL (talk) 02:06, 26 August 2012 (UTC)

Steiner point (disambiguation)

Steiner point now redirects to Steiner point (disambiguation). Should the title of the disambiguation page be changed simply to Steiner point? Michael Hardy (talk) 03:26, 26 August 2012 (UTC)

According to Wikipedia:Disambiguation#Naming the disambiguation page, yes. Deltahedron (talk) 06:01, 26 August 2012 (UTC)

 Done —David Eppstein (talk) 06:15, 26 August 2012 (UTC)

OK, next problem with this page: Which of the pages in the article space that link to it (other than redirects) are from hatnotes (so those links should remain intact) and which should get disambiguated? Michael Hardy (talk) 17:44, 26 August 2012 (UTC)

image:Shing-TungYau.jpg

File:Shing-TungYau.jpg is missing sourcing, and will be deleted soon. Does anyone know about this photo  ? -- 76.65.128.252 (talk) 12:50, 26 August 2012 (UTC)

Euclidean algorithm

There is a proposal to move Euclidean algorithm to Euclid's algorithm at Talk:Euclidean algorithm#Move?. Johnuniq (talk) 01:34, 28 August 2012 (UTC)

Daviddaved

Please look at this discussion. User:Daviddaved appears to be a mathematician. He is totally clueless about Wikipedia conventions and possibly about Wikipedia's purposes. _Some_ of his new articles may be worth keeping after some cleanup. Some may have copyright problems. He doesn't seem to notice things people post on his user talk page. Members of this WikiProject may be able to figure out which of his pages are worth keeping after cleanup. Michael Hardy (talk) 18:04, 30 August 2012 (UTC)

Isovolume problem

Isovolume problem is an "orphaned" article, i.e. no other articles link to it. If you know of other articles that ought to link to it, work on it. Michael Hardy (talk) 00:54, 31 August 2012 (UTC)

if isoperimetric inequality (section Isoperimetric inequality in higher dimensions) were not so technical, I would say, merge it there. Especially since the article is called 'isovolume problem' (= minimal surface given volume), but is actually about the isosurface problem (maximal volume given surface). The two are mathematically equivalent, but as the latter is really just a high-dimensional isoperimetric problem, the justification for a separate article is not so clear. Sasha (talk) 03:49, 31 August 2012 (UTC)

Merger proposal Equidistributed sequence

I suggest that Equidistribution theorem and Weyl's criterion could both be merged into Equidistributed sequence. I have just boldly merged Van der Corput theorem. Deltahedron (talk) 17:02, 26 August 2012 (UTC)

methinks, equidistributed sequence is already a bit long. Equidistribution theorem is a nice article with a historical overview which will be too long for a section of equidistributed sequence, why merge it?

As to Weyl's criterion, my objections are less firm (the main objection is that it is has connections beyond the field of equidistributed sequences, but perhaps it is not so crucial: if you succeed to make it a nice section of e.s., I will probably rescind my objections.

Sasha (talk) 19:18, 31 August 2012 (UTC)

Totally positive matrix

Totally positive matrix is a surprisingly neglected article. Work on it. Michael Hardy (talk) 02:47, 31 August 2012 (UTC)

Slightly expanded (emphasis on "RELIABLE" was to discourage pop sites like planetmath). Maschen (talk) 14:00, 31 August 2012 (UTC)

Sep 2012

Wikipedia talk:WikiProject Mathematics/Archive/2012/Sep

Oct 2012

Wikipedia talk:WikiProject Mathematics/Archive/2012/Oct

Nov 2012

Wikipedia talk:WikiProject Mathematics/Archive/2012/Nov

Dec 2012

Wikipedia talk:WikiProject Mathematics/Archive/2012/Dec