Wikipedia talk:WikiProject Mathematics/Archive/2009

Jan 2009

Quaternion (disambiguation) nominated for deletion

Silly Rabbit's mention of quaternions above reminded me that I want to put Quaternion (disambiguation) up for deletion. See the discussion at

Wikipedia:Articles for deletion/Quaternion (disambiguation).

As always, give reasons for your opinions. Ozob (talk) 09:32, 3 January 2009 (UTC)

Nomination withdrawn by Ozob. Martin 15:02, 5 January 2009 (UTC)

amscd package

I would like to shorten the vertical arrows of the diagram this (the source code is attached). Any ideas? GeometryGirl (talk) 14:50, 5 January 2009 (UTC)

Correction: It's the horizontal arrows that need to be shortened. siℓℓy rabbit (talk) 14:53, 5 January 2009 (UTC)

Two more or less stupid ideas, but probably effective: You could try typing it with \rightarrow and \downarrow etc. Or simply take a graphics program and shrink them in the processed image. Jakob.scholbach (talk) 14:56, 5 January 2009 (UTC)

Using a graphics program would either involve shrinking the whole thing, which would make the Hs look too thin, or a lot of manual realignment.

If you don't mind learning Xy-pic, it can do this sort of thing for you. Try the following code:

\documentclass{amsart}
\usepackage[all]{xy}

\begin{document}
\begin{equation*}
\xymatrix@C=1em{
\cdots\ar[r] &
H_{n+1}(X_1)\ar[d]_{f_*}\ar[r] &
H_n(A_1 \cap B_1)\ar[d]_{f_*}\ar[r] &
H_n(A_1) \oplus H_n(B_1)\ar[d]_{f_*}\ar[r] & 
H_n(X_1)\ar[d]_{f_*}\ar[r] &
H_{n-1}(A_1 \cap B_1)\ar[d]_{f_*}\ar[r] &
\cdots \\
\cdots\ar[r] &
H_{n+1}(X_2)\ar[r] &
H_n(A_2 \cap B_2)\ar[r] &
H_n(A_2) \oplus H_n(B_2)\ar[r] & 
H_n(X_2)\ar[r] &
H_{n-1}(A_2 \cap B_2)\ar[r] &
\cdots \\
}
\end{equation*}
\end{document}

A quick explanation: Each diagram entry corresponds to a matrix entry. Arrows do not get their own diagram entry. Instead, each \ar[x] creates an arrow that starts in the present entry and goes in direction x (d=down, r=right). The down arrows are subscripted with f_*s. The key spacing command is the @C=1em at the beginning, which says "Set the intercolumn spacing to 1em". Ozob (talk) 18:49, 5 January 2009 (UTC)

I was going to suggest xypic as well. Unfortunately, xypic is a brilliant piece of software with less-than-brilliant documentation. siℓℓy rabbit (talk) 22:53, 5 January 2009 (UTC)

For the most beautiful and easy to code diagrams, Paul Taylor's commutative diagrams package is hard to beat. And no, I am not Paul Taylor. Happy diagram coding :-) Geometry guy 23:09, 5 January 2009 (UTC)

Slowness, inactivity?

Is it just me, or is are the mathematics articles on Wikipedia less comprehensive than most other topics of the same importance? There are relatively few mathematics featured articles, and many of the subprojects seem to be, well, dead. Leon math (talk) 04:04, 3 January 2009 (UTC)

It may simply be that you know more about this part of wikipedia. I'm not sure how one would measure it but it seems to me that a number of other subjects I'm interested in are also fairly dead on wikipedia, then again the sales rank of books that I buy from amazon never seems to be less that some tens of thousands :) Dmcq (talk) 14:50, 4 January 2009 (UTC)

The point about FA is that the criteria are not really designed for mathematical exposition. Charles Matthews (talk) 15:32, 4 January 2009 (UTC)

The criteria still fit reasonably well, though, I think. They are: well-written, comprehensive, accurate, neutral, stable, appropriate lead, appropriate structure, consistent citations, good style in general, appropriate images, and appropriate length. I don't see anything wrong or anything missing... But if there is something that gives mathematics articles and unfair disadvantage at becoming FA's, we should go to the criteria talk page and propose changes. Leon math (talk) 21:21, 4 January 2009 (UTC)

You know, mathematicians don't really see the point of padding out articles, of adding inline citations for points that aren't important to justify (in a survey - obviously mathematics is more rigorous than anything else on the site), of adding pictures as illustration rather than really adding anything. Rather than the things that happened in the past with the reviewing, I think there is more enthusiasm for generally raising the standard over a range of articles that are really designed to cover part of a field. Certainly that would speak for me, though I'm not particularly active on mathematics articles currently. In the past I thought there was more point in driving the coverage closer to the current state of the art: that still seems to me to be the important aim. Charles Matthews (talk) 21:32, 4 January 2009 (UTC)

In addition to the above, most math articles involve subjects that are too technical and too abstract, and thus require sufficient specialized knowledge for improving them (even more so than technical articles on other scientific topics because of the abstract nature of math). This makes them ill-suited for the FA process, except for articles on the most general and basic math topics, like the recently promoted Group (mathematics). Most editors who are typically involved in the FA process have little background in math and it would be hard for them to provide informed and correct opinions as to whether a given article is comprehensive and accurate. There may be substantial ommissions and even inaccuracies in an article, but non-experts may easily miss them. E.g. take a look at Poincare conjecture - certainly a nice article on an important subject but well beyond the scope of non-experts in terms of commenting on accuracy and comprehensiveness. There are relatively few active Wikipedia editors with sufficient expert knowledge in any given reasonablty advanced mathematical topic. As Charles notes above, most of them are more interested in writing/expanding more advanced math articles in their fields rather than working on polishing existing math articles on very basic math topics that may actually have a chance to succeed in the FA process. Nsk92 (talk) 21:56, 4 January 2009 (UTC)

Articles on very basic math topics should be polished not by experts but by undergraduates etc. Right? Boris Tsirelson (talk) 15:30, 5 January 2009 (UTC)

No, I don't think either is preferred. Undergrads might not clutter up the article with allusions to advanced topics or be snobbish about presentation or metamathematics, but someone without long and broad experience might (and often seems to) also suffer from tunnel vision and think that the truth is only what they know, in the exact way they learned it. More articles should, perhaps, be read by undergrads, however. Ryan Reich (talk) 18:06, 5 January 2009 (UTC)

Probably I understand what is "snobbish about presentation"; but what do you mean by "snobbish about metamathematics"? (I ask since I like to avoid this sin.) Boris Tsirelson (talk) 02:20, 6 January 2009 (UTC)

You know, something like the argument over whether a ring should be assumed to contain a multiplicative unit. The literature is divided, and different fields will tell you different things about which one is more useful. It's basically a question of what examples of rings you consider most natural whether you think a non-unital "ring" is really a ring. I'm not sure which side is the snobbish one here (perhaps both), but it doesn't change the fact that noncommutative ring is a redirect, so this argument is comparitively a waste of time.

That could be taken to be a matter of presentation (though it has metamathematical roots). Another example of snobbish metamathematics could (arguably) be what happened at least-squares (discussion starts at Talk:Least squares#A major proposal) a while ago, when one expert vastly expanded and reorganized the article and its cousins according to what he took to be the right mathematical perspective—a perspective unfamiliar to anyone who had only learned least-squares from, say, an introductory linear algebra course, according to its detractors. Still, the article is good now and hasn't changed back. Ryan Reich (talk) 04:52, 6 January 2009 (UTC)

Yes, I saw the noncommutative ring redirect, and was very astonished. But if algebraists do it this way, I probabilist do not interfere. You ise the word metamathematics in somewhat unexpected (to me) way, but never mind. Boris Tsirelson (talk) 07:13, 6 January 2009 (UTC)

I had in mind for "metamathematics" a meaning like "not what the theorems say, but what they really mean". That's probably just mathematical philosophy, though. Ryan Reich (talk) 18:21, 6 January 2009 (UTC)

I have contributed a great deal to content review processes, and they are entirely compatible with mathematics articles, partly (in the case of GA) through my efforts. However, in my own edits to mathematics articles, I am much more interested in bringing a range of mathematics articles to B-Class, than taking any of them further. Of Wikipedia's 2.5+ million articles, less than 10000 are GAs or featured (0.4%). Improving the dross to a reasonable standard is far more important a goal than making a handful of articles exceptionally good.

The main historical failing of mathematics articles is the lack of sources. Just check out a few mathematics articles at random. Many have no sources at all. There seems to have been some idiotic belief that mathematics sources itself. I don't say this with my content review "verifiability" hat on, but as a user of Wikipedia. Wikipedia is now a great resource for looking up mathematical information. However, stubby mathematics articles would be so much more useful if they provided references (preferably online) to sources which fill in the gaps. Clicking on an article and finding inadequate content with no references is a depressing experience. Geometry guy 23:39, 4 January 2009 (UTC)

I agree wholeheartedly with your last paragraph that lack of sources is a serious problem for mathematics articles. Just yesterday I was discussing a forthcoming paper with a colleague who was eager to find some sources for a theorem due to Gaspard Monge. I suggested that he should look at the Wikipedia article (an article which I wrote, although I didn't volunteer this information). He reluctantly agreed to do so, but only after expressing a sentiment with which I was sympathetic: Wikipedia articles on mathematics tend to give fairly eclectic sources, often reflecting current trends in pedagogy or obscure areas of research, and rarely giving appropriate primary sources or good historical scholarship. Unfortunately, there also seems to be a sort of folk dogma on Wikipedia that perpetuates the notion that primary sources are bad and secondary sources are good, often to the exclusion of the former in favor of the latter. siℓℓy rabbit (talk) 23:53, 4 January 2009 (UTC)

It's not folk dogma, it's a matter of policy. See Wikipedia:No original research#Primary, secondary and tertiary sources. The policy even says, "Without a secondary source, a primary source may be used only to make descriptive claims, the accuracy of which is verifiable by any reasonable, educated person without specialist knowledge." If papers are primary sources, then we have no acceptable sources for many research-level math topics. That's ridiculous, and it's completely non-standard for a math encyclopedia.

I'm not even sure how one should interpret "primary source" in a math context. Are all those standard textbooks on abstract algebra referenced in Group (mathematics) primary sources or secondary ones? They prove everything from scratch; but they don't claim any originality. Does Borel and Serre's paper on Grothendieck-Riemann-Roch count as a primary source because it's the first publication, or a secondary one because Grothendieck had already presented it in a seminar talk? I can't tell.

My own feeling is that this is a case for Wikipedia:Ignore all rules. WP's sourcing guidelines aren't well suited to the process used in mathematics. We should source articles as well as we can with whatever sources are best suited, primary or not. Ozob (talk) 01:29, 5 January 2009 (UTC)

Yes, the policy statement is clearly problematic. Allow me to clarify: the statement of WP:OR explicitly refers to primary sources in a historiographic context, rather than a general scientific context. Our own article on primary sources adopts a much broader definition: "In scientific literature, a primary source is the original publication of a scientist's new data, results, and theories." A primary source of the latter sort is perfectly allowed, provided it meets the other criteria under the WP:OR policy. So, indeed, it is merely "folk dogma" which proscribes primary sources in mathematics and the sciences. siℓℓy rabbit (talk) 01:53, 5 January 2009 (UTC)

The notions of primary, secondary and tertiary sources are poorly understood throughout Wikipedia, and even more so at this project. First, they are not absolute: a source can be primary for one fact and secondary for another. Second, and this is Silly rabbit's point, primary sources are not a bad thing: we need primary sources in articles. This is not just because primary sources are better than no sources, but because primary sources are an important part of any encyclopedia article. Borel and Serre's paper is a secondary source for Grothendieck's contribution to the Grothendieck-Riemann-Roch theorem, but a primary source for its own novelties and presentation. Why is that so hard to understand? I have seen a case in which an article by Newton was used (appropriately) as a secondary source, even though the work of Newton is usually primary source material. Secondary sources are needed to evaluate the contributions of others. Standard textbooks on abstract algebra are obviously secondary sources for the material they detail, whether they prove everything from scratch or not. They show that original work has been accepted as standard knowledge. I am amazed that intelligent editors find this hard to comprehend. Geometry guy 02:13, 5 January 2009 (UTC)

I do not know much about the GA process; my general impression that, per individual article, GA process requires much fewer users than does the FA process. So the GA process is probably more math friendly, although even there I would imagine that a math article on a reasonably advanced topic would have a difficult time. For FA, the problem really is not with the process itself but rather with the fact that there is, at least for now, not a sufficient critical mass of active WP editors with sufficient expert knowledge for the FA process to work well for math articles on non-basic math topics. I have written a few reasonably complete math articles, such as Small cancellation theory, van Kampen diagram, Dehn function, Bass-Serre theory, and a few others. However, I think that these types of articles are completely unsuitable for the FA process and possibly even for GA process, since there are too few active WP editors with the requisite background knowledge. I agree with the Geometry guy that the lack of sourcing in WP math articles is a widespread and serious problem. I think the reason is that most mathematicians who do edit WP articles, tend to write them in a similar way as they write their regular math papers, worrying more about mathematical correctness and completeness of the presentation than about references. That is why many math WP articles read like WP:OR essays. Such articles are still quite useful, but they certainly would be more useful if properly sourced. (In my own defence I should say that I am a bit of a reference freak when I write WP math articles, and I am probably guilty of overreferencing).

I have a suggestion that is indirectly related to this discussion. I am still very uncomfortable with the idea that initial ratings are supposed to be assigned by the article's creators. This seems to represent a basic COI to me and I personally would feel very uncomfortable assigning my own article any rating above Start class; it feels like refereeing one's own paper, certainly a no-no. I prefer to keep my articles unassessed that to assign to them a B-rating myself, even in the cases where I think B-rating is deserved. It just does not feel right. I think it would be beneficial to institute a regular process where creators of new math WP articles can request their initial assessment by other members of WikiProject Math. Some other wikiperojects, like Wikiproject Biography, actually have such arrangements in place and I think we should too. There will be an added benefit of new math articles receiving substantive third-party feedback relatively quickly and, hopefully, progress to something around B class. Just a thought. Nsk92 (talk) 00:59, 5 January 2009 (UTC)

Self-assessment at the early stages works because we are our own best critics. Also a rating means "the article is at least this good", even though it might be much better, so a conservative self-assessment is better than no assessment. All four of the articles you list do not meet WP:LEAD and would stand very little chance at GAN. They are however, all at least Start class, and need maths ratings. Some might be close to B-Class, but such a judgement could be left to other editors. We can learn from content review processes even while remaining critical of them. Geometry guy 01:13, 5 January 2009 (UTC)

As I said, I am not really critical of the GA/FA review processes as such but I think that, apart from the matters of style, they need a certain critical mass of people sufficiently well familiar with a particular topic in order to work well. I believe that in most cases such critical mass is currently absent for math articles on non-basic topics. Regarding initial assessment, I still think it would be very useful to institute a regular system for requesting assessment by a third party. It would at least ensure that new math articles receive fairly quick substantive feedback. It should be easy enough to institute such a system. E.g. one could create a section of Wikipedia:WikiProject Mathematics called "Requests for third-party article assessment" (or something like that). People could add unrated or author-rated articles to a list in such a section, and, once another editor rates the article, that editor can remove it from the list. Nsk92 (talk) 02:06, 5 January 2009 (UTC)

The only way to address a perceived lack of critical mass of expert editors is to contribute. Our A-Class assessment scheme failed for the lack of contributions and is now moribund. In that respect, please contribute to WP:Featured article candidates/Mayer–Vietoris sequence. It is hard to take any editor's concerns seriously if they can't even contribute to the only current mathematics FAC. Geometry guy 02:21, 5 January 2009 (UTC)

I'll take a look at the Mayer-Vietoris nomination, although I am leaving on a week-long trip abroad tomorrow morning and I don't know if I'll have enough time to say something substantive before then. Until now I have had little interest in FAC process since it had seemed to me largely inapplicable to math articles, and also because as a matter of personal preference I find it more interesting and enjoyable to work on creating new content rather than deal with things like GA/FA (which does not mean that FA/GA projects are not important). However, I am interested in the workings of the more basic math assessment process (Start, B and maybe A, also C if it is introduced as a math rating). It seems to me that getting the more basic math rating process work more efficiently and meaningfully is a higher priority that promoting more math articles to the FA status (although the latter is, of course, good when it happens). I don't think my opinions on that are invalid or should not be considered even if I don't participate in the FAC discussion for the Mayer–Vietoris sequence. Nsk92 (talk) 02:42, 5 January 2009 (UTC)

As noted above, I have pretty much the same priorities when it comes to editing math articles. However FACs in mathematics are rare enough that it is worth contributing. Geometry guy 02:46, 5 January 2009 (UTC)

Let's not focus on what part of WikiProject Math is more important. It seems that our overall conclusion is that there aren't enough editors that possess all of the following traits: (1) have the knowledge/ability to help, (2) are willing to put information on Wikipedia, and (3) are concerned with the organization, procedures, and conventions of Wikipedia. (I fail number 1.) Hmm... this problem is not easily solved. I guess it's just like Geometry guy said; we can only do as much as we can, and there's really nothing that can be done to drastically improve the situation. Leon math (talk) 03:00, 7 January 2009 (UTC)

Track transition curve

This complex clothoid/Euler spiral is used everyday, being used in roads and on railways to blend together curves of differing radii (or straight sections). An editor recently has introduced a large amount of new material in the form of including PDF page screen shots into the article (rather than TeX notation). I have copied this material to User:Ling Kah Jai/Track transition curve for their improvement, but it would be useful to have some wider review of what is appropriate (the 8-page proof is perhaps more than necessary for a Wikipedia article).

Track transition curve, User:Ling Kah Jai/Track transition curve, Talk:Track transition curve#Formulation of Euler spiral. —Sladen (talk) 05:53, 7 January 2009 (UTC)

Category:Historical treatment of quaternions

This category, and its two current inhabitants, Classical Hamiltonian quaternions and The vector of a quaternion, should in my opinion be transwikied to WikiBooks. I feel that these are both needless and unsanctioned content forks of quaternions. They seem to be filled with the personal opinion and original research of the author, and are rather poorly written. siℓℓy rabbit (talk) 03:46, 3 January 2009 (UTC)

I've worked a lot on the quaternion article, and I agree that those two articles would be better placed at Wikibooks. You might consider contacting User:Hobojaks, who is the primarily responsible for writing those articles. As far as I can tell, he believes that classical quaternions are superior to linear algebra for most purposes. ("Classical quaternions" are distinguished from modern quaternions because the classical viewpoint is that i, j, and k are new primitive symbols, not elements of an R-vector space. At least, this is the impression that I get from Hobojaks; see Talk:Quaternion/Archive_2#A more pragmatic point of view.) I don't know how he would feel about transwikiing those two articles, but he is not always easy to talk to. (See Talk:Quaternion/Archive_2#Modern Cast system????) Ozob (talk) 04:42, 3 January 2009 (UTC)

Ok. I'm not sure what to do. I'm not good in one-on-one situations that could be potentially confrontational, which seems likely given your warning. Would it be better to take these articles to AfD? siℓℓy rabbit (talk) 02:03, 5 January 2009 (UTC)

Sorry for taking so long to get back to you. I think AfD is appropriate for both articles. They're both mostly content forks of quaternion, and the only thing they have going for them is all the historical citations. In the future it might be possible to write a real article on classical Hamiltonian quaternions which would describe how Hamilton's viewpoint differed from the modern viewpoint of H as an R-vector space. But that will have nothing to do with the present article of that name. Ozob (talk) 00:58, 9 January 2009 (UTC)

Invariants of a tensor ?

Came across invariants of tensors and noticed that it currently focuses exclusively on rank 2 tensors i.e. matrices. Matrix invariants are already covered at characteristic polynomial and related articles. Is there a more general article that could be written here about how determinant, trace etc. generalise to higher rank tensors, or is this a dead end ? Gandalf61 (talk) 17:10, 8 January 2009 (UTC)

I don't know anything about tensors, but this book: Introduction to non-linear algebra talks about generalizing linear algebra including determinants to non-linear situations, using tensors. Charvest (talk) 21:49, 8 January 2009 (UTC)

I would guess that "tensor" in that article means "tensor field", mostly because it makes a comment about a coordinate system. So there's something not entirely trivial there, I think, but the article doesn't make that clear.

There are things you can do to generalize various notions of linear algebra to vector bundles. The determinant of a vector bundle is just its top wedge power. I think EGA IV has some stuff about taking the norm of a vector bundle somewhere (sort of like taking the norm in Galois theory). IIRC it seemed to me once that there was something you could do to generalize the elementary symmetric functions, but I forget now. I don't think I found a use for it. Ozob (talk) 01:11, 9 January 2009 (UTC)

I have an incredably stupid question

An editor had earlier comment at the page Iowa class battleship that the two mathematical formulas in the paragraph below were actually the same:

That same year (1935), an empirical formula for predicting a ship's maximum speed was developed, based on scale-model studies in flumes of various hull forms and propellers. The formula used the length-to-speed ratio originally developed for 12-meter (39 ft) yachts:

${\mbox{Speed}}={\sqrt {1.408\times {\mbox{waterline length}}}}$

and with additional research at the David Taylor Model Basin would later be redefined as:

${\mbox{Capital Ship Speed}}=1.19\times {\sqrt {\mbox{waterline length}}}$.

It quickly became apparent that propeller cavitation caused a drop in efficiency at speeds over 30 knots (56 km/h). Propeller design therefore took on new importance.

Sine I have failed four separate remedial level math classes at collage, and haven't passed a math class with a grade better than C- since seventh grade, I was wondering if someone from this project could independently verify that the two formulas are in fact the same. TomStar81 (Talk) 04:08, 10 January 2009 (UTC)

$1.19\times {\sqrt {\mbox{waterline length}}}={\sqrt {1.19\times 1.19\times {\mbox{waterline length}}}}={\sqrt {1.4161\times {\mbox{waterline length}}}}$

So it is pretty close. --fvw* 04:13, 10 January 2009 (UTC)

They are indeed the same thing (except that in the second equation a lower precision is used). Specifically,

${\sqrt {1.408}}\approx 1.187$

which rounds up to 1.19. In math (or science), one would say that for the second equation one just "took out" the "1.408" from under the square root. Also, for future questions of the sort, you can go to Wikipedia:Reference desk/Mathematics. Cheers. RobHar (talk) 04:21, 10 January 2009 (UTC)

The "new articles" list on the "current activity" page

...is working again. Michael Hardy (talk) 17:48, 10 January 2009 (UTC)

A better "prime"

Look at this:

Ψ(t) = −log(π) + Re(ψ(1/4 + it/2)), where ψ is the digamma function Γ′/Γ.

In "displayed" TeX, I'd write the digamma function as

${\frac {\Gamma \,'}{\Gamma }}$

or in some contexts like this:

$\Gamma \,'/\Gamma \,$

I don't want to change an "inline" thing to TeX, since that causes comical mismatches of size and alignment, but the "prime" is barely visible. Is there a better, more legible, way to write a "prime" in non-TeX notation, and if not, can one be created? Michael Hardy (talk) 16:26, 11 January 2009 (UTC)

Well I am certainly no expert on formatting matters, one hack may be to change the font size on the prime. One simple way to do this would be:

Γ′/Γ or Γ′/Γ

But I think there are more refined ways to control the font size. I suppose neither of these look that much better. Thenub314 (talk) 16:59, 11 January 2009 (UTC)

Γ´ uses an acute accent rather than an apostrophe Γ' (too vertical) or a single quote Γ‘ (too curly). I think it's a little better as an acute accent than as the other two. If you don't know how to type it (on my Mac keyboard it's option-e space) you can copy-and-paste from this example. —David Eppstein (talk) 17:10, 11 January 2009 (UTC)

Measure (mathematics)

I am not sure how this article ever got to GA (luckliy it was demoted). I am starting a rewrite now; any help there would be appreciated (in particular, a good lede is necessary). --Point-set topologist (talk) 18:17, 11 January 2009 (UTC)

It was listed for 3 months in the early days of GA, before the criteria became more exacting. Geometry guy 19:21, 11 January 2009 (UTC)

What are you dissatisfied with? Boris Tsirelson (talk) 18:59, 11 January 2009 (UTC)

Well for a start, the article does not explain many important concepts in measure theory, nor does it include any applications to probability theory (apart from the Lebesgue integral) etc... I would think that it is fairly clear that the article is not up to par but as you are a measure theorist, it would be good to know your opinion. PST

I see. If you really feel you can do it better, then of course you should try. Yes, I know many things about measures that do not appear now in the article. However, 14 more specialized articles are mentioned in "See also". Do you want to (partially) merge them to "measure"? Or do you want to add something not present in these 14 articles? In the latter case, are you sure it should be added to "measure" rather than to these more specialized articles? Boris Tsirelson (talk) 21:46, 11 January 2009 (UTC)

I want to add some brief descriptions of these specialized concepts. In particular, something has to be there on the Lebesgue integral and the Haar measure. PST

Modulo cleanup

Go to modulo and click on "what links here".

• Some of these times should be rewritten to say [[modular arithmetic|modulo]] so that the reader sees "modulo" and clicks and sees modular arithmetic.
• Some of these times should be rewritten to say [[modulo operation|modulo]] so that the reader sees "modulo" and clicks and sees modulo operation.

In the modular arithmetic article, 63 and 53 are congruent to each other modulo 10.

In the modulo operation article, "modulo" is a binary operation and (63 modulo 10) = 3.

The modulo article is far more general than just arithmetic.

—Preceding unsigned comment added by 75.72.179.139 (talk) 22:02, 11 January 2009 (UTC)

Michael Hardy (talk) 21:51, 11 January 2009 (UTC)

......I've now taken care of the most egregious cases. Next there are the subtler cases that may require more delicate thought. Michael Hardy (talk) 23:23, 11 January 2009 (UTC)

The Princeton Companion to Mathematics

I just got the book a a preset a very pleased I am too with it. Of course I immediately dipped into he centre and also started looked up things I know about in the index. Very interesting. I didn't find much or anything about the things I thought of which indicates if it really was comprehensive it would be a bookcase of books - it is pretty huge as it is. I seem also to have been corrupted by Wikipedia, I kept thinking I should edit this to add wikilinks and better citations. Where it differs from WP mainly is it is much more chatty and readable with things like "Why should nonequivalence be harder to prove than equivalence? The answer is that in order to show....", or "For fun, one might ask a fussier question:". On further references it can say things like "For further details n sections 1-4 the reader is referred to standard textbooks such as ...". I can thoroughly recommend the book.

The book has a small section in its introduction on "What Does The Companion Offer That the Internet Does Not Offer?" (I feel like quoting WP:STYLE about the capitalization!) and I have to agree with what it says: that the internet is hit and miss, sometimes there's a good explanation sometimes not. The articles are drier just concerned with giving he facts in an economical way and not reflecting on those facts. And it doesn't have long essays on the fundamentals and origins, the various branches , biographies of mathematicians and the influence of mathematics. Not that I agree with all that, basically I think what it amounts to is one wouldn't make oneself comfortable, get a cup of coffee and curl up to read the articles in wikipedia. The book has a problem with that too as it is so heavy but otherwise it is a far better read overall.

Does a book like this have lessons for us? Should WP style be a bit more chatty? Or should we be dry and economical and just inhabit a different domain from books like this? Dmcq (talk) 12:18, 9 January 2009 (UTC)

It's more than being a little less chatty; at the moment Wikipedia's policies sometimes run counter to very standard mathematics conventions. If we can't even say "we" or "note that" in proofs, it's a while before will get anywhere near informal, comfortable chattiness. If this ever makes it to a vote, we could argue that style manuals do want prose to be "engaging"...

Unfortunately, it's difficult to write chatty prose while still covering everything in an appropriate sequence like an encyclopedia should. Leon math (talk) 03:31, 10 January 2009 (UTC)

If you ask me, Wikipedia is not suited for mathematics articles. Most of these current policies are rather useless... --Point-set topologist (talk) 18:15, 11 January 2009 (UTC)

You can still write a good article. That's what matters. Ozob (talk) 01:34, 13 January 2009 (UTC)

Additive number theory

I recently created Category:Additive number theory and I'd like help/feedback.

• What should the category name be? Additive number theory seemed best to me, but any of {arithmetic | additive} {number theory | combinatorics} would seem to be possible, and there are surely others.
• Should the category be under Category:Number theory or the narrower Category:Analytic number theory? It's usually considered one of the major branches of analytic number theory because of its heavy use of the circle method and related techniques, but they're a priori distinct.
• What other articles should be included? I just did a quick pass, but I'd expect that there are more.
• What should the category page say? I just have boilerplate text at the moment, which could be fine, but if there are any distinctions that need to be made ("not to be confused with Subtractive Number Theory") or related fields ("similar to Combinatorial Subtraction, but different because CS uses butterflies and rainbows instead of sumsets").
• Any other comments?

CRGreathouse (t | c) 20:28, 12 January 2009 (UTC)

Additive number theory sounds like a good name. IMO it should be a sub-category of Analytic number theory. That's all my opinions. RobHar (talk) 22:03, 12 January 2009 (UTC)

Something has to be done about this junky article

I am seriously concerned about the article on manifolds. First of all, it seems (from an uninvolved user's point of view) that a group of people rejected this article from becoming featured simply because they couldn't understand this. I am glad at least that it was rejected but there should seriously be some restrictions on the people who vote (some people seem to think that if they can't understand it, no-one else can) (if anyone has the time, just have a read through the article). But here is a specific section (the article is never going to be featured at this rate):

Other curves

Manifolds need not be connected (all in "one piece"); an example is a pair of separate circles. They need not be closed; thus a line segment without its end points is a manifold.

By definition, a 'closed manifold' is a compact manifold without boundary. A line segment without its end points is just R and is therefore a trivial manifold. Why mention these obvious facts? PST

And they are never countable; thus a parabola is a manifold.

????????????? For a start, they can be countable (0-dimensional manifold), and does the implication make sense (even assuming that the first statement is true)? Its like saying that X is never Y; so if Z is not Y, it must be X. PST

Putting these freedoms together, two other examples of manifolds are a hyperbola (two open, infinite pieces) and the locus of points on the cubic curve y² = x³−x (a closed loop piece and an open, infinite piece). However, we exclude examples like two touching circles that share a point to form a figure-8; at the shared point we cannot create a satisfactory chart. Even with the bending allowed by topology, the vicinity of the shared point looks like a "+", not a line (a + is not homeomorphic to a closed interval (line segment) since deleting the center point from the + gives a space with four components (i.e pieces) whereas deleting a point from a closed interval gives a space with at most two pieces; topological operations always preserve the number of pieces).

Nothing wrong with this fortunately. :) PST

I can give (if necessary) similar criticizm of almost all other sections. Recently I re-wrote the lede: I would seriously consider re-writing the whole article and deleting some of the sections there. --Point-set topologist (talk) 20:59, 12 January 2009 (UTC)

From a quick glance the article seems to be better than 98% of our articles. Deleting content is pretty delicate. What is trivial to you may not be so to other readers, so be very careful and thoughtful. Jakob.scholbach (talk) 21:23, 12 January 2009 (UTC)

From another glance at this change log it looks like most of the changes you made were unconstructive

Not true: I expanded the lede as well as made some cleanup to other sections in the article. --Point-set topologist (talk) 22:00, 12 January 2009 (UTC)

, if not harmful. For example, removing reasonable content as per "delete nonsense section" is pretty bad.

I rewrote this section in a much better manner (that is why I used 'nonsense') and merged it into the lede. So in effect, I did not delete it. --Point-set topologist (talk) 22:00, 12 January 2009 (UTC)

I have reverted your recent edits. Jakob.scholbach (talk) 21:33, 12 January 2009 (UTC)

Hi Jakob,

I did not intend my edits to manifold to be unconstructive. I deleted that section because I had already summarized it in the lede (so basically I merged that section into the lede). Maybe I should have made this more explicit (I guess this is kind of what Taku did (on a major scale) to ring (mathematics) although his intentions were good). I also rewrote the lede in the way I did after reading why this was rejected in FA; so basically I made it more accessible. I am adding that section back but if you still feel the same way you can revert it. I just feel that there has been a misunderstanding.

PST (Point-set topologist)

I reverted. It appears that you have delted a lot of my additional material in your rv. Could you please have a look at that diff (of your rv)? --Point-set topologist (talk) 21:57, 12 January 2009 (UTC)

I have to say I side with Jakob.scholbach. The introduction should be short and to the point describing what he article is about. The edits put too much into the introduction. And even if the introduction does say something it should probably be mentioned again in a more precise way later rather than stuff being removed elsewhere to put into it. The introduction should be chatty and accessible and just introduce the article so people know whether they are looking at the right place and have a quick summary. Dmcq (talk) 09:03, 13 January 2009 (UTC)

Freak software bug

I just did a minor edit to Cauchy principal value. After the edit, every line of TeX in the article looked like this:

Failed to parse (Cannot write to or create math output directory): \lim_{\varepsilon\rightarrow 0+} \left[\int_a^{b-\varepsilon} f(x)\,dx+\int_{b+\varepsilon}^c f(x)\,dx\right]

I've seen this a number of times lately. It will probably go away soon, but just when is completely unpredictable. Why is this happening? Michael Hardy (talk) 19:41, 13 January 2009 (UTC)

Because someone broke a server. For now a purge should fix it. See WP:VPT#Error_message_in_http:.2F.2Fen.wikipedia.org.2Fwiki.2FPlanetary_gearing. Algebraist 20:04, 13 January 2009 (UTC)

Shannon–Hartley theorem

There are a number of (bolded red) parsing errors in this article, related - I think - to mathematical equations. Would someone more familiar with this area take a look? Thanks! -- John Broughton (♫♫) 20:56, 13 January 2009 (UTC)

Looks fine to me. Most likely a transient server-side problem; this happens from time to time. --Trovatore (talk) 21:02, 13 January 2009 (UTC)

This sounds like the same thing as the thread above. Algebraist 21:05, 13 January 2009 (UTC)

Topic outlines

I think that these articles should be deleted: Topic outline of algebra, Topic outline of arithmetic, Topic outline of calculus, Topic outline of discrete mathematics, Topic outline of geometry, Topic outline of logic, Topic outline of mathematics, Topic outline of statistics, Topic outline of trigonometry. Charvest (talk) 20:12, 11 January 2009 (UTC)

Why? — Carl (CBM · talk) 01:07, 12 January 2009 (UTC)

Against apparent consensus here (there is a somewhat abortive thread in the archives), User:Transhumanist has gone ahead and moved all of the articles [[List of basic X topics]] to [[Topic outline of X]]. This is a bit distressing since, as far as I am aware, there is no indication anywhere in the manual of style on this massive proposed change (which has its source somewhere off in the rarely-used "Portal" namespace). This entire project appears to be Transhumanist's pet project, and has not been handled in a transparent manner. Instead of going through and changing huge numbers of articles, without attempting to obtain consensus (or disregarding a lack of consensus), an appropriate course of action would have been to draft a suggested Wikipedia guideline, and then solicit comment. The current proposal does have some discussion, but mostly in sundry talk-page archives. In this light, Charvest's request is quite reasonable, if a bit WP:POINTy. These changes should be reverted since the current articles do not follow the standard naming conventions for lists. siℓℓy rabbit (talk) 01:38, 12 January 2009 (UTC)

First of all, wikipedia is an encyclopedia, not a fixed syllabus, so "topic outline" is not appropriate - the state of art of knowledge is a constantly changing. Secondly, most of these articles are pretty rubbishy and I don't see the point in them. Take Topic outline of algebra for example. Even if this is changed back to List of ... it is still rubbishy. What does this article say that isn't already in the main algebra article ?

My opinions on these articles are:

• Topic outline of algebra - delete,
• Topic outline of arithmetic - merge with arithmetic,
• Topic outline of calculus - delete ,
• Topic outline of discrete mathematics - merge with discrete mathematics ,
• Topic outline of geometry - merge with geometry,
• Topic outline of logic - there's a lot here so keep or merge,
• Topic outline of mathematics -delete
• Topic outline of statistics - merge with statistics,
• Topic outline of trigonometry merge with trigonometry

Charvest (talk) 09:58, 12 January 2009 (UTC)

modified Charvest (talk) 21:55, 14 January 2009 (UTC)

Are you aware that these were titled List of basic algebra topics, etc., until they were unilaterally renamed a couple days ago? — Carl (CBM · talk) 12:57, 12 January 2009 (UTC)

I wasn't initially aware, but Silly Rabbit pointed this out above. A list which consists simply of the most commonly used terms is basically a glorified see also section and might as well be put in the main articles, rather than have separate pages, unless they are particularly extensive lists. Charvest (talk) 15:38, 12 January 2009 (UTC)

I would suggest that the portal is the ideal place for these pages. Martin 13:24, 12 January 2009 (UTC)

Having a look at the portals: Portal:algebra, Portal:geometry etc it seems the portals are much better presented and contain most if not all of the information in the lists. Between the main articles, the portals and the lists there is massive overlap. The lists should go. Charvest (talk) 15:38, 12 January 2009 (UTC)

I think the lists are useful, in the "List of basic topics" form. I agree they are glorified "see also" lists, but that makes them very good for including in the "see also" section of basic articles like Algebra, where it would be impractical to include a long list of links, but where naive readers are likely to be interested in a list of topics to browse. — Carl (CBM · talk) 23:52, 12 January 2009 (UTC)

Okay, so some people find them useful so they should be kept. But would a different namespace be more appropriate (i.e. Portal)? Personally I think categories do a better job of helping someone browse or find the article they want. Martin 00:03, 13 January 2009 (UTC)

I think this should be done on a case-by-case basis. Maybe most "List of basic X" really are "Topic outlines" and should be moved over to Portal namespace. I don't know. But I am definitely opposed to any blanket move from "List of basic" to "Topic outline" in the mainspace since, in principle, these denote different things. For instance, "Topic outline of geometry" ideally would contain some rather non-basic things such as differential geometry (which isn't there!) or algebraic geometry (also not there!). siℓℓy rabbit (talk) 02:13, 13 January 2009 (UTC)

I think that topic outlines for major parts of mathematics is a great idea. But to call the execution merely 'lacking' is too kind. Can these reasonably be improved? If not, I'd prefer deletion to keeping them in their present state. **CRGreathouse** (t | c) 03:59, 13 January 2009 (UTC)

To make these useful I think a greater amount of description is required. Topic outline of ecology adds a brief sentence to each term which makes it into more useful article. --Salix (talk): 08:11, 13 January 2009 (UTC)

I've nominated the worst of these articles for deletion at: Wikipedia:Articles for deletion/Topic outline of algebra Charvest (talk) 22:09, 14 January 2009 (UTC)

How to make SVG diagrams

This question sometimes comes up and it bears answering as often as possible, since a lot of people have never heard that we should be using SVG, and of those who have, few seem to have an easy way of actually accomplishing it. This is addressed at Help:Displaying a formula#Convert to SVG, but their proposed solution relies on a somewhat arcane and arbitrary invocation of two different utilities, followed by a roundabout filtration through two major software packages, which is necessitated by one of them (pstoedit) requiring a costly proprietary plugin to work properly. And the end result is still unusable if your diagram has diagonal lines. Here's the right way:

pdflatex file.tex
pdfcrop --clip file.pdf tmp.pdf
pdf2svg tmp.pdf file.svg
(rm tmp.pdf at the end)

Both pdfcrop and pdf2svg are small, free (if new and somewhat alpha) programs that work properly. I advocate pdflatex since with the alternative, you might be tempted to go the route of latex→dvips→pstopdf before vectorizing, and that runs into a problem with fonts that has to be corrected with one of the arcane invocations above. (There is a correct route, which is to replace that chain with dvipdfm, that I have never seen anyone suggest. Somehow, the existence of this useful one-step solution to getting PDFs from plain latex is always ignored.)

I have proposed at the talk page of that Help article that this procedure replace the existing one. It has been road-tested on, most notably (for the complexity of its images) Triangulated category and found to work quite well. Since the interested parties hang out here more than there, I'm soliciting feedback from whatever TeXperts and hackers might be lurking. Ryan Reich (talk) 04:23, 14 January 2009 (UTC)

Thanks for this, I'm quite happy to know this. Also, btw, on macs texshop uses pdflatex as default since pdf's are native on macs. RobHar (talk) 04:59, 14 January 2009 (UTC)

Since writing this, I have investigated Inkscape's internals and found that the following pstoedit invocation is also good:

pstoedit -f plot-svg -dt -ssp tmp.pdf tile.svg

It also makes smaller SVG files, sometimes (with the large ones) by quite a bit. This invokes the GNU libplot, and I cannot decide whether this piece of imperfect software is preferable to the one which is pdf2svg; let it be your call if you use it. Ryan Reich (talk) 20:59, 14 January 2009 (UTC)

...except that it couldn't make a nice SVG out of the pictures now at Cone (category theory), whereas pdf2svg could. I don't think I can really recommend pstoedit for this task. Ryan Reich (talk) 04:26, 15 January 2009 (UTC)

brahmagupta and Cauchy

Please see Negative and non-negative numbers. Katzmik (talk) 18:10, 14 January 2009 (UTC)

A meaningful illustration of vector spaces

Does anybody have an preferrably an illustration (or an idea for one) to illustrate the concept of vector space? I'd like to nominate that article for FA soon, but I feel without a good lead section image it's only half as beautiful. Thanks! Jakob.scholbach (talk) 20:56, 14 January 2009 (UTC)

List of mathematics categories

We have Wikipedia:WikiProject Mathematics/List of mathematics categories which is used as worklist by mathbot to fill in the list of mathematics categories.

Question: can this list of categories be also useful to Wikipedia readers, after some formatting changes or prettifying perhaps? Then we could move it to the article namespace, at list of mathematics categories, and treat it in the same way as the other mathematics topics. Oleg Alexandrov (talk) 07:08, 15 January 2009 (UTC)

Cut paste move

I tagged Krull–Schmidt theorem with {{db-histmerge}}, since there was a WP:CUTPASTE move done to it. The ndash article has no new (relevant) history to it, all of the history is in the hyphen article, which is now a redirect. Can an admin fix this? JackSchmidt (talk) 00:28, 15 January 2009 (UTC)

Done, I think. — Arthur Rubin (talk) 02:01, 15 January 2009 (UTC)

Thanks! JackSchmidt (talk) 14:22, 15 January 2009 (UTC)

What a mess

Can anyone help with Grey relational analysis? Michael Hardy (talk) 05:49, 16 January 2009 (UTC)

Gauss–Jacobi mechanical quadrature

Gauss–Jacobi mechanical quadrature is vaguely written. In particular, what does the function p_n(x) have to do with the statement that follows it? Could someone who knows the answer to these questions clarify by editing the article. Michael Hardy (talk) 05:26, 16 January 2009 (UTC)

The article was indeed vaguely written, so I rewrote it. -- Jitse Niesen (talk) 16:36, 16 January 2009 (UTC)

For me (in this article) all the equations fail to parse. GeometryGirl (talk) 16:55, 16 January 2009 (UTC)

Purging the server cache should fix that. Algebraist 17:05, 16 January 2009 (UTC)

stable module category: many formulas not rendered

http://en.wikipedia.org/wiki/Stable_module_category —Preceding unsigned comment added by 77.4.181.225 (talk) 12:33, 16 January 2009 (UTC)

Yes, there is an intermittent problem that sometimes causes a "Failed to parse ..." message to appear instead of Tex formulae. If you have a Wikipedia account, logging in seems to cure the problem. Gandalf61 (talk) 12:41, 16 January 2009 (UTC)

I've purged the cache for IPs, so it should display fine when logged out now. Algebraist 12:50, 16 January 2009 (UTC)

This occasionally happens on math articles regardless if logged in or not. Clicking on edit and preview makes the formulas render for me; then the problem may go away. I wonder if there is a simpler way. Jmath666 (talk) 01:12, 18 January 2009 (UTC)

As I stated above, purging should work as a temporary measure, but brion said this should be fixed 'pretty soon' more than five days ago now. Anyone feel like bugging him about this? Algebraist 01:18, 18 January 2009 (UTC)

Vandals again

As usual vandals are up to no good at geometry. Having scanned through the editing history for 2008, it appears that vandals were at the peak during mid year; their activity lowest around December. But since January they are back for more. I am worried about this article because everyone knows what geometry is and at least one tenth of people who come across this article are out to vandalize. So this article is never going to be safe against vandalizm. Instead of wasting our times reverting edits there every hour of the day (that article will probably fill up 80% of anyone's watchlist), can we take some action? --PST 13:59, 17 January 2009 (UTC)

There have been 5 vandalizing edits from IPs since the last semiprotection ended on 23rd December. That doesn't seem enough to require protection, and it certainly won't be filling up my 1000-page watchlist. Algebraist 14:46, 17 January 2009 (UTC)

Wow! My watchlist has only 20 pages. But the point that I am trying to make is that this is never going to stop. I stand corrected but look at the article's history in February and you are going to see only reverts and vandalizm (no improvements). Instead of wasting future time, can't we see that it stops immediately. I think that the reason that vandalizm was not there from the 23rd to the 10th is because that was the holiday season. --PST 23:36, 17 January 2009 (UTC)

One of Wikipedia's great strengths is that anyone can edit it. Wikipedia is a huge success, and its predecessor Nupedia was a complete failure, and the difference between them is that anyone can edit Wikipedia. Each protected page takes away a little bit of that great strength. —Dominus (talk) 01:01, 18 January 2009 (UTC)

Featured article nomination

The article on vector spaces is up for featured article nomination. Please opine here. Jakob.scholbach (talk) 16:00, 17 January 2009 (UTC)

bang, drum, and flag

I would be interested in comments as to the appropriateness of the following comment by Gandalf61:

Katzmik, we all know where this is going. You want to bang your non-standard calculus drum and assert calculus could be taught without the concept of limits and so they can't be central to calculus. And you could be right - in theory. However, in practice, limits play a central role in the field of calculus as it is taught and used by most mathematicians, and most mathematicians would be happy with the first sentence of this article as it stands, and your contention that this is a misconception is a tiny minority view. Now you may say that is just my opinon. But if you are really interested in what the wider community thinks, then I suggest you go ahead and flag this discussion at WT:WPM. Gandalf61 (talk) 10:23, 20 January 2009 (UTC)

— Preceding unsigned comment added by Katzmik (talk • contribs)

That (from a discussion at Talk:Topic outline of calculus seems to be an entirely reasonable, appropriate and accurate comment. Algebraist 13:12, 20 January 2009 (UTC)

I'm not certain which aspect you would like comments on.

• The idea that limits are central to calculus is a very common view. Searching google books for "limit concept fundamental calculus" shows many sources in the first few pages. Richard Courant goes so far as to say, "The fundamental concept on which the whole of analysis ultimately rests is that of the limit of a sequence".
• The "bang your drum" sentence might be viewed as strongly worded, and could have been written in a way that doesn't imply the existence of a campaign. However, you have been advocating for more coverage of nonstandard calculus in various articles, so I can understand where Gandalf was coming from. Unless there is a pattern of comments like this, I would brush it off.
• The neutral point of view policy says, "Neutrality requires that the article should fairly represent all significant viewpoints that have been published by a reliable source, and should do so in proportion to the prominence of each." The prominence of nonstandard analysis is not high in mathematics as a whole and in elementary calculus is particularly small. I think that articles like list of basic calculus topics should be written in a way that matches the majority of calculus texts, which proceed through limits to derivatives and integrals, along with applications such as Lagrange multipliers, arc length, and center of mass.

— Carl (CBM · talk) 13:37, 20 January 2009 (UTC)

I like nonstandard calculus. In fact, nonstandard analysis is the primary reason I haven't discarded (in my zeal for simplicity) the Axiom of Choice. But nonstandard calculus is not a part of the usual calculus curriculum, which always includes limits. CRGreathouse (t | c) 13:56, 20 January 2009 (UTC)

But for me the axiom of choice (beyond the countable dependent choice, of course) is rather an interesting mathematical toy (or a brave mathematical experiment), as well as all its consequences, including nonstandard analysis. Boris Tsirelson (talk) 19:43, 20 January 2009 (UTC)

No doubt. But it was nonstandard analysis that opened the door for me. CRGreathouse (t | c) 20:35, 20 January 2009 (UTC)

(Boring part) Wikipedia cannot advance an agenda. We simply reflect what reliable secondary sources say, with due weight. The NSA and constructivist viewpoints both deserve mention in some contexts, but they are most usually an aside.

(Less boring part) I don't much like the axiom of choice as it can be terribly convenient to suppose every subset of the real numbers is measurable. However, regarding NSA, I laugh at your feeble invertible infinitesimals and the fussing over standard parts :-). Real infinitesimals are nilpotent: dx squares to zero, obviously. You fools tie your hands by doing mathematics in the wrong topos :-) Geometry guy 20:59, 20 January 2009 (UTC)

What else could we do while waiting for you the genius? Boris Tsirelson (talk) 21:22, 20 January 2009 (UTC)

:-) Nobody can do much until the insights of Grothendieck and Lawvere are realised and assimilated as something comprehensible to lesser mortals. (I hope I am not giving too much away here by confirming that I am neither Grothendieck or Lawvere.) Maybe 20-30 years...? Geometry guy 22:12, 20 January 2009 (UTC)

It's not really about whether you "like" the axiom of choice. The axiom of choice is true. This I claim is self-evident, once you understand the objects whose behavior the axioms are intended to describe (the ones that appear in the von Neumann hierarchy, where the taking of subsets at the successor stages is done lawlessly).

As for having all sets of reals measurable, you have all you're likely to need of that: All sets of reals that appear in L(R) are measurable, and that's includes all the ones you're likely to encounter "explicitly" whatever that means. This claim is not provable in ZFC alone, but it follows from sufficient large cardinals. The existence of the large cardinals is not self-evident, but it has become clear, in a semi-empirical fashion, that it is true. --Trovatore (talk) 22:14, 20 January 2009 (UTC)

Those who enjoy erudite disputes will always find something to appreciate at WT:WPM. EdJohnston (talk) 22:16, 20 January 2009 (UTC)

I don't see "fun" in the title. :) --PST 22:28, 20 January 2009 (UTC)

LOL. I hope Trovatore's tongue was as firmly planted in his cheek as mine was in mine. Of course such erudite disputes should strictly be banned here as they have nothing to do with improving the encyclopedia. But my, they are at least more fun than arguing over notation or the latest AfD :-) Geometry guy 22:33, 20 January 2009 (UTC)

I was 100% serious. If you take a realist approach to sets, and understand which sets are intended, the axiom of choice is self-evidently true. --Trovatore (talk) 22:36, 20 January 2009 (UTC)

That's surely one viewpoint. Luckily I don't work in set theory or logic or category theory (neither did Grothendieck) so these things tend to make me smile rather than frown seriously. If you believe the real numbers can be well-ordered, that is fine by me. In your preferred model of ZF, they can be. But so what? Geometry guy 22:46, 20 January 2009 (UTC)

Well, the point is that "my" preferred model is the intended one, the one that takes all subsets at each stage. The only way you can make the reals non-wellorderable is to leave out some sets of reals (well, sets of sets of naturals) when you're forming V_ω+2. --Trovatore (talk) 23:00, 20 January 2009 (UTC)

(←) Hey cool, we find our way back to policy. "At each stage"? According to whom? And what interpretation of "stage"? "The only way" according to whom? "Intended model" according to whom?

No viewpoint has a right to hegemony or even undue influence on Wikipedia. There are plenty who believe that set-theoretic foundations and questions such as these are entirely the wrong approach, but there are others who dedicate their lives to resolving them. So we must try our best to keep our personal prejudices to one side, and report on what reliable sources say, with due weight. </boring> Geometry guy 23:33, 20 January 2009 (UTC)

As always, you are right Geometry guy. Except for factors of one-half. Then you're usually wrong. siℓℓy rabbit (talk) 23:51, 20 January 2009 (UTC)

Hey you must know me IRL! But don't forget the minus signs. Minus signs and factors of 1/2. Yup I'm wrong almost every time on those... :-) Geometry guy 00:27, 21 January 2009 (UTC)

OK, gg, you're conflating two things here. Of course, from a WP point of view, the realist viewpoint must be accorded its due weight, neither more nor less. No one is arguing about that. With respect to claims that go into article space, "who says so?" is an entirely appropriate question.

However, from the realist viewpoint, there is no ambiguity about the interpretation of stages. Each successor stage is supposed to consist of all subsets of the preceding one. If you have two (wellfounded) models, just find the first rank where they differ. If model M contains a subset of the preceding rank that model N omits, then model N is wrong, period. That doesn't mean model M is completely right; it might omit other subsets, but at least it's right about that one.

Following this reasoning, you can see that if V_ω+2 exists at all, then it is unique (up to a unique isomorphism), and therefore (for example) the continuum hypothesis is either really true or really false, even if we don't currently know which (and quite plausibly may never know). This was first pointed out by Ernst Zermelo. --Trovatore (talk) 00:57, 21 January 2009 (UTC)

Who is gg? And who defines what are "all subsets"? What rules are allowed to select elements from a set and call it a subset? Geometry guy 01:13, 21 January 2009 (UTC)

You don't need rules at all — that's what I was pointing out earlier. The subsets are taken lawlessly. All of them are taken lawlessly, even the ones that turn out, after the fact, to obey some law.

For example, when picking subsets of the naturals, you start through the natural numbers and start throwing some into your subset and some not, completely at whim. At the end, it may turn out, just by coincidence, that you happened to pick all the even ones, and none of the odd ones, and therefore the set of all even naturals gets into the next stage. But it doesn't get into that stage because it happens to satisfy a law. --Trovatore (talk) 01:18, 21 January 2009 (UTC)

Sounds suspiciously like second order logic to me, but whatever, I'm not a logician. Even with laws, the set of well-orderings of the reals is already an interesting example. It's a subset of something, but what subset? Geometry guy 01:27, 21 January 2009 (UTC)

(ec) And it sounds also like a presumption of choice. Any subset is okay. Even among an uncountably infinite set of pairs of socks there is a subset containing one sock from each pair. It is no wonder you believe the axiom of choice is true: it is built into your model. I'm agnostic about this question or perhaps better, my answer is: mu. Geometry guy 01:58, 21 January 2009 (UTC)

The point is that your mu position is incompatible with a realist conception of sets. If one accepts sets as real, that it becomes impossible to be indifferent to the axiom of choice (it's a well-defined question about real objects, so it must have an answer), and very difficult to avoid Trovatore's conclusion that it is obviously true. Algebraist 02:07, 21 January 2009 (UTC)

A naive question: this view of set theory tells you when something isn't the right model: when it is non-maximal, because some other model includes a set that it doesn't. But why should I be convinced that there exists any maximal model? Maybe there are plenty of models but they are all non-maximal? —David Eppstein (talk) 01:51, 21 January 2009 (UTC)

Yes, a priori, that could be. But would imply that the powerset axiom is false. I view the powerset axiom as something like a conjecture in Popper's sense — potentially falsifiable, has not been falsified, gives us useful information about the world — and so, taking a quasi-empiricist epistemological position I consider it true. --Trovatore (talk) 02:09, 21 January 2009 (UTC)

Well actually the powerset axiom is the beast isn't it? What is the set of all subsets when there is uncertainty about what a subset is? This axiom not only raises questions about the axiom of choice, but also the continuum hypothosis. Geometry guy 02:17, 21 January 2009 (UTC)

But there is nothing uncertain about what a subset is. --Trovatore (talk) 02:20, 21 January 2009 (UTC)

What are the subsets of the real numbers? Geometry guy 02:26, 21 January 2009 (UTC)

The subsets of the real numbers are those sets whose every element is a real number. What is "uncertain" about this? --Trovatore (talk) 02:36, 21 January 2009 (UTC)

There is some ambiguity about the collection of "all" subsets in first order logic, though. — Carl (CBM · talk) 02:28, 21 January 2009 (UTC)

But why do you want to limit yourself to first-order logic? --Trovatore (talk) 02:36, 21 January 2009 (UTC)

I'm sure you're familiar with the literature on that. — Carl (CBM · talk) 02:39, 21 January 2009 (UTC)

The issue of there being no maximal model was also discussed by Zermelo. The issue is not so much with V_α for any particular α, but with the issue that given any model of ZF the set of all ordinals in it is again an ordinal, suggesting that the model is just an initial segment of some larger model. Indeed, the potential axiom "every model of set theory is embeddable as a countable submodel of another model of set theory" has some aesthetic appeal to me.

Trovatore, I was just reading Maddy's "Mathematical Existence" and I'd be curious to know your personal take on "thin realism", maybe on my talk page. — Carl (CBM · talk) 02:28, 21 January 2009 (UTC)

Back to the nonstandard analysis... I did not say that the choice axiom is wrong in my favorite universe of sets. Rather, for me a proof via the choice axiom is considerably less illuminating than a choice-free proof (if exists, of course; and countable dependent choice is OK, of course). This is why I prefer to prove uniform continuity of a continuous function on [0,1] without nonstandard analysis. Boris Tsirelson (talk) 07:52, 21 January 2009 (UTC)

Whatever about non-standard or standard analysis I think the bit about limits in the article is unnecessary. What follows about differential and integral calculus describes the subject much better. Talking about limits just distracts as it is a general part of analysis and applicable to much more than calculus. And on the other hand whereas limits are I feel by far the best way to introduce calculus they really don't come into the subject much in a practical sense. Just because someone is banging a drum doesn't mean he is wrong in all circumstances. Dmcq (talk) 09:42, 21 January 2009 (UTC)

I do think it is necessary to discuss limits in the article, and I think mentioning them in the lead paragraph is appropriate. While limit proofs don't come into the subject much in a practical sense, I do think that limits do enter the subject early and often. Thenub314 (talk) 10:39, 21 January 2009 (UTC)

Percussive folks might like to work on Non-standard calculus which needs a lot of work. Not clear in intro which century the work is in. Lots of one sentence paragraphs and very bitty presentation. I could not find out from the article why the axiom of choice was important for the NSA. Also there seems to be a need for Category:Non-standard analysis.--Salix (talk): 10:40, 21 January 2009 (UTC)

Calculus just isn't about limits. The sentences saying it is about instantaneous change and areas is much closer to the mark. Calculus led to analysis because of the need to prove results rigorously and analysis with limits is now a huge subject in its own right. Non-standard analysis is another way of dealing with limits. Limits are a tool for proving results in calculus but the first statement is like saying number theory depends critically on the concept of sequence. Dmcq (talk) 11:25, 21 January 2009 (UTC)

I see your position better now. I tend to think of calculus as a small part of real analysis, comprising limits, derivatives, integrals, and applications, rather than a separate subject from real analysis. I often tell students that the thing which separates analysis from algebra is its focus on approximation and limits. — Carl (CBM · talk) 12:51, 21 January 2009 (UTC)

I tend to disagree that calculus isn't about limits. To defend my point of view let me mention that when I look at the calculus books I have had to teach from they have statements like "We could begin by saying that limits are important in calculus, but that would be a major understatement. … Every single notion of calculus is a limit in one sense or another." and "The concept of limit is surely the most important, and probably the most difficult one in all of calculus." Further Google searches also reveal several books about calculus which describe limits as central to the subject of calculus. For these reasons, I stick by the first sentence of my previous comment. Thenub314 (talk) 14:57, 21 January 2009 (UTC)

Combinatorial map and Generalized map

These two articles are in an unsatisfactory state. They look as if they could probably be phrased in such a way that any mathematician could understand them. But the author seems to assume knowledge of some related topics that most mathematicians don't have, and seems to lack knowledge of some things that most mathematicians know. I doubt that the person who wrote these two article can do what needs to be done, and I could do it only with more work than I'm going to put into it today or this week. Michael Hardy (talk) 18:23, 19 January 2009 (UTC)

I agree. From what I can make out, both articles are on the subject of topological graph theory (I have really only used graph theory in the context of algebraic topology). Combinatorics is not my strong point but I agree that it is certainly not easy to understand (too many complex terms). --PST 20:39, 19 January 2009 (UTC)

The dread words data structure suggest that the author is a computer scientist, which would account for Michael Hardy's observation. (I'll have my saucer of milk now, please, like a good cat.) Septentrionalis PMAnderson 02:23, 27 January 2009 (UTC)

I are an expert both in data structures and in topological graph theory, and I don't find the article very intelligible either. When I tried to read it I got the strong impression it referred to the same thing as a rotation system, one of the ways of encoding embedding graphs on two-manifolds, and I'm still pretty sure that's what the bulk of the article is about. But the author removed my {{mergeto}} tag, assuring me it actually referred to higher dimensional things as well, as the "general definition" section claims but never clearly describes. As for "generalized map" it seems to be a copy of only that section, making the signal-to-noise ratio even worse. —David Eppstein (talk) 02:32, 27 January 2009 (UTC)

List of topics named after Bernhard Riemann

I've created a new page titled List of topics named after Bernhard Riemann. It is of course incomplete. Please help expand it by doing two things:

• Add topics you know of that are not there.
• Add topics you can find by a systematic search of Wikipedia that are not there.

Michael Hardy (talk) 01:08, 22 January 2009 (UTC)

I've added all the wikipedia articles with Riemann in the title or in a section title that refer to a topic named after Riemann. Also added some redlinks from Google. Now somebody needs to turn the redlinks blue. Charvest (talk) 14:35, 22 January 2009 (UTC)

World Mathematics Challenge

World Mathematics Challenge is up for deletion as a possible hoax. Ben MacDui 19:43, 27 January 2009 (UTC)

Deletion proposal

See Complex argument (continued fraction) and Talk:Complex argument (continued fraction). A "prod" tag proposes deletion. The article is very clearly and cleanly written and that's quite unusual for dubious material. Michael Hardy (talk) 03:02, 20 January 2009 (UTC)

It seems to me that, assuming that there are sufficient references for the continued fraction definition of the argument function, the tag should be a proposed merge instead of a proposed deletion. However, the title is not a likely search term, so maybe a merge + delete redirect would be appropriate. — Carl (CBM · talk) 03:14, 20 January 2009 (UTC)

Sorry for not doing this myself before it was deleted, but can someone please make that article available for me to copy into userspace? It wasn't mine originally, I just wanted to check it out. Cheers, Ben (talk) 07:51, 23 January 2009 (UTC)

OK done at User:Ben Tillman/Complex argument (continued fraction). --Salix (talk): 10:19, 23 January 2009 (UTC)

Thanks Salix. Cheers, Ben (talk) 11:14, 23 January 2009 (UTC)

Did the continued fraction get merged into some other article? Michael Hardy (talk) 21:31, 31 January 2009 (UTC)

Carol number

Carol number has been nominated for deletion. Gandalf61 (talk) 11:53, 28 January 2009 (UTC)

Feb 2009

Milestone Announcements

All WikiProjects are invited to have their "milestone-reached" announcements automatically placed onto Wikipedia's announcements page. Milestones could include the number of FAs, GAs or articles covered by the project. No work need be done by the project themselves; they just need to provide some details when they sign up. A bot will do all of the hard work. Click here for more information or to sign your project up.

I thought this WikiProject might be interested. Ping me with any specific queries or leave them on the page linked to above. Thanks! - Jarry1250 ^{(t, c)} 22:01, 1 February 2009 (UTC)

Richard's principle

What should we make of Richard's principle? Someone has proposed deleting it as "original research". The topic seems similar to (maybe even the same as?) that treated in the article titled impredicativity. Michael Hardy (talk) 23:15, 4 February 2009 (UTC)

This is a clear delete. Eckerslyke isn't convinced by the proof of the uncountability of the continuum, and purports to find in Richard's paradox a reason to reject the reasoning behind the proof, although he doesn't seem to be able to identify just what's wrong with that reasoning except that it has other consequences he finds unattractive.

But that wouldn't be a reason to delete the article, if the same argument had been notably made, could be found in reliable sources, under the name Richard's principle. But it hasn't. The argument may have been notably made — it's something I wouldn't be astonished to see attributed to that crackpot Wittgenstein, if he had been aware of Richard's paradox, which I don't know whether he was or not — but not under the name Richard's principle. Therefore it must be deleted; the name, if nothing else, is original research.

What to do with the content is another matter. My guess is that any of the content that's attributable, probably already resides somewhere on WP, but I wouldn't swear to that. If it can be sourced, the content could live on under another name. But not Richard's principle, not even as a redirect. --Trovatore (talk) 23:45, 4 February 2009 (UTC)

OK, so is this actually related to the stuff at impredicativity? I think that latter article could certainly be expanded, but I'm not up on that stuff. I remember that Paul Cohen found some things to say about impredicativity in his lecture-notes book called Set Theory and the Continuum Hypothesis, but it's been a long time since I looked at that. Cohen thought impredicativity had some implications for set theory, but I seem to recall he was somewhat non-committal about its ultimate consequences. Does predicativity really mean Cantor's arguments don't work (I doubt it)? Michael Hardy (talk) 00:28, 5 February 2009 (UTC)

Not especially related as far as I can tell. The Cantor argument is predicative; given an enumeration of real numbers (whether or not it enumerates all of them), one constructs a real not enumerated. Nothing in that construction depends on the real being constructed, but only on the given enumeration.

Richard's paradox is not particularly impredicative either. The error is the assumption that there is a well-defined notion of being "definable" without further qualification (or maybe, a well-defined way of getting from a not-better-specified "definition" to the corresponding definend). Given that assumption, the reasoning that takes you to the paradox is predicative, to the extent that I understand that term. --Trovatore (talk) 00:58, 5 February 2009 (UTC)

About expanding impredicativity: I've quoted "The Princeton companion to mathematics" on its discussion page; maybe it helps, maybe not. Boris Tsirelson (talk) 19:38, 7 February 2009 (UTC)

A class nomination

Maximum spacing estimation has been nominated for A-class. Interested parties please leave comments at Wikipedia:WikiProject Mathematics/A-class rating/Maximum spacing estimation.

Also, A-class review is still ongoing for Riemann hypothesis. See Wikipedia:WikiProject Mathematics/A-class rating/Riemann hypothesis. It might need to be closed as a "no pass" but I think it's still possible to improve it in a short time. --C S (talk) 03:19, 5 February 2009 (UTC)

As for R.H., I personally think it is far from that state, but see my proposal below. Jakob.scholbach (talk) 13:39, 5 February 2009 (UTC)

I closed the RH discussion as "no pass" for now. If anyone thinks they can address the issues, of course, there is no reason not to nominate it after. --C S (talk) 22:54, 7 February 2009 (UTC)

Riemann hypothesis' 150th birthday

This year, the Riemann hypothesis will mark its 150th birthday. I think it is one of the problems that has gained some wider (i.e., beyond maths) spread, so it would be cool to get it featured. The original paper was published in November 1859, so if we make it, we could argue that it be displayed at the main page. Who is willing to join in into that effort? Jakob.scholbach (talk) 13:39, 5 February 2009 (UTC)

If the deadline is October, then I can lend a hand. --C S (talk) 22:55, 7 February 2009 (UTC)

Ongoing discussion re Boubaker polynomials

See Wikipedia:Administrators' noticeboard#Boubaker polynomials. —David Eppstein (talk) 16:03, 5 February 2009 (UTC)

old discussion at this wikiproject, for reference --Enric Naval (talk) 20:51, 7 February 2009 (UTC)

Richard's principle is up for deletion

Feel free to comment at Wikipedia:Articles for deletion/Richard's principle. --Trovatore (talk) 09:51, 7 February 2009 (UTC)

MH problem argument

I know many of you might question my sanity because of this, but I've been trying to explain the difference between conditional and unconditional probability to a user on the talk page for the Monty Hall problem. I don't know if it might be helpful, but could as many folks from this project as possible please make some sort of comment in the thread at talk:Monty Hall problem#Glkanter's objection? Thanks. -- Rick Block (talk) 19:23, 8 February 2009 (UTC)

You mean, Talk:Monty Hall problem#Glkanter's objection. No wonder if you are tired! I admire your work and patience. I am never able to make a discussion longer than 3-4 exchanges. Boris Tsirelson (talk) 20:22, 8 February 2009 (UTC)

But take it easy (and avoid the carpal tunnel syndrome!). Sometimes we fail to convince an editor, and resolve the conflict otherwise. That is the life, especially in Wikipedia. I am an expert in probability, but do not think it helps to convince... Boris Tsirelson (talk) 20:30, 8 February 2009 (UTC)

Yes, Rick, I don't know how many times you've been around this particular barn, but trust me, this sort of discussion never comes to a conclusion. If you like you can look up my old postings in sci.math and sci.logic to see how long it took me to learn that :-).

One strategy for harm reduction, when this happens at WP, is to create an "Arguments" subpage of the article's talk page, and move all these exchanges there. This expedient is not strictly speaking sanctioned by the relevant policies and guidelines (excepting WP:IAR) but it's mostly tolerated, and it can have good effects in terms of freeing up the main talk page for its intended use. See for example talk:Gödel's incompleteness theorems/Arguments. --Trovatore (talk) 20:59, 8 February 2009 (UTC)

I guess there is a history here that I'm not privy to. Have you all already determined that my proof is invalid? Or are you instead accepting at face value Rick's new argument that having been published is merit enough for inclusion AND PROMINANCE in the article, regardless of, in Rick's words, 'the Truth'?

Please be advised, that is was Rick who created the section headed 'Glkanter's objection', not Glkanter. I would respectfully request that you read the section I did create, titled 'Conventional Wisdom' before you pass judgement on the merits of my criticisms of the article.

Mr. Tsirelson, all I know about you is that you wrote you are an expert in probability. I would be especially appreciative to hear your thoughts on the matter.

Thank you for the trust. Yes, you are right: I did not read seriously your discussion with Rick. I am sorry saying so, but it is really difficult to read such a long story. It seems to me (correct me if I am wrong) that you two do not disagree on a point of probability theory, but rather, on editorial points: how to do the article better. Here I am not at all an expert. I know very well that "better to me" often means "worse for beginners". One probabilistic point that I observe is, (ir)relevance of the (un)conditional probability. I'd say that in this case they are equal not just by a numeric coincidence. Rather, the conditional probability (treated as another random variable) is constant (a degenerate random variable) in this case, due to an obvious symmetry. Taking into account the total probability formula we conclude that the conditional probability must be equal to the unconditional probability in this case. Thus I feel indifferent. Both are relevant in one sense or another. Do you agree? Boris Tsirelson (talk) 21:42, 10 February 2009 (UTC)

I'll apologize to Mr. Eppstein in advance for furthering the discussion here.

Actually, my primary disagreement with Rick is over nothing more than the validity, and relavence of, my proof. I claim it is valid, and renders 99% of the Article confusing and un-necessary. He says I am not answering the 'conditional probability' problem, which is the only fully qualified solution. It goes on from there. Please read my 'Conventional Wisdom' section.

You may have already addressed the issue with your statement "Taking into account the total probability formula we conclude that the conditional probability must be equal to the unconditional probability in this case." I think that's the point that I, and many others before me, have been trying to make.

Glkanter (talk) 22:00, 10 February 2009 (UTC)

Rather than apologizing for doing something, can you just refrain from doing it? This discussion has no place here. Algebraist 22:03, 10 February 2009 (UTC)

As for me, I like probability problems. I came to the Monty Hall Problem Article on Wikipedia to further my understanding of the puzzle and the solution. I was shocked by what I found. I did not ask for the tedium of months and months of going around in circles. Do you know there are 7 archive pages dating back to 2005? And we've already done the old 'create an "Arguments" subpage' routine. So help us out. Contribute your expertise.

Glkanter (talk) 21:17, 10 February 2009 (UTC)

Please let's keep this discussion on Talk:Monty Hall problem where it belongs. You've already gone on for pages and pages and pages expressing your point of view there; there's no need to do so here as well. —David Eppstein (talk) 21:33, 10 February 2009 (UTC)

Thank you for the gracious encouragement, professor. You are a shining example for the rest of us.

Glkanter (talk) 22:09, 10 February 2009 (UTC)

Policy on references/citations in math related articles

I have notice that many math related articles have little to no referencing. Therefore, I wanted to know if you had any policies or guidelines concerning referencing and citing information in math related articles, and, if not, would people be interested in developing one? kilbad (talk) 19:51, 13 February 2009 (UTC)

There are the Scientific citation guidelines. I think that's the most specific thing we have. Algebraist 20:52, 13 February 2009 (UTC)

I don't think that it's worth the effort to develop a long and drawn-out policy in addition to the scientific citation guidelines that Algebraist already pointed out. It's true that there are many math articles that could use some additional referencing, but also true that many facts in math articles are covered perfectly well by general references instead of footnotes.

There are a few simple rules of thumb that can be helpful for editors who are starting to edit math articles on WP:

• When you add material to articles, only add stuff that agrees with the general consensus of published texts in the field. In general, this means that you know it would be possible to give a few references that cover the point in the way you're covering it.
• If you see something in an article that you think is probably right, but you wish it had a source, ask on the talk page or mark it with a {{fact}} template.
• If you see something that you feel is probably wrong, move it to the talk page and ask about it. Of course you should have some sort of good reasoning, not merely "I don't know whether this is right."
• Remember that some others here are experts in the topic you are editing, and others are complete novices. So take a balanced approach to editing and talk page discussion.

— Carl (CBM · talk) 21:57, 13 February 2009 (UTC)

It might be worth revisiting and revamping the scientific guidelines to ensure that they reflect current best practice. I think the attitude that "it would be possible to give a few references" (without actually giving any) has become increasingly untenable with the enormous improvements, wider use, and increased respectability of the encyclopedia since the guidelines were first drafted. If you know it would be possible to give references, then provide some! I say this primarily as a user of Wikipedia. It is frustrating to read a weak article on an interesting topic, only to find that it has no useful references. Geometry guy 21:57, 14 February 2009 (UTC)

Alleged WP:Ownership Violation on the Monty Hall Problem Article

On the Monty Hall Problem talk page I have been documenting what I believe is an Ownership violation by Rick Block.

Viewed by themselves, I think Rick's edits today are indicative of such a problem. Glkanter (talk) 20:58, 14 February 2009 (UTC)

I have interacted with Rick Block several times on this article over a period of nearly 2 years, disagreeing with him substantially and/or proposing significant changes. I have seen no evidence of article ownership, only a desire to maintain the high quality of an article that tends to attract well-meaning but less than well-informed contributions. Geometry guy 21:47, 14 February 2009 (UTC)

Glkanter has taken a look at the responses and decided they verify his accusations of ownership (he wrote "All these other Wikipedia Math gurus already knew about Rick's MHP article Ownership issues!") If you are interested in your response not being misused, I suggest leaving a comment on the MHP talk page. I left a comment in the most recent section created by Glkanter, "WP:Ownership Allegation Update." --C S (talk) 03:22, 15 February 2009 (UTC)

This is the original post from the Monty Hall Problem talk page, verbatim:

Here's where Rick first asked for assistance to aid in Resolving our Conflict.

http://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mathematics

All these other Wikipedia Math gurus already knew about Rick's MHP article Ownership issues!

I'm a first-timer here. It's been way too long, but is has been instructive as to how horribly mishapen things get when an editor claims ownership of an article.

Glkanter (talk) 19:25, 12 February 2009 (UTC)

You are 100% correct. Two days ago, before I ever brought the topic of Ownership to your attention, I was guilty of pre-judging you all. I apologize for that. When I took a leap from your being aware of Rick's fondness for the Article, to the conclusion that you would therefore have already identified a WP:Ownership situation, that was wrong on my part. I'll post my apology on the MHP talk page immediately. Glkanter (talk) 03:41, 15 February 2009 (UTC)

Proposed addition to Monty Hall problem

In hopes of ending a continuing series of arguments at talk:Monty Hall problem, I am proposing adding additional text to the article, perhaps in a new section, please see Talk:Monty Hall problem#Conditional or unconditional, once again. I know the problem is of little mathematical interest being essentially trivial. However, as this is one of only 23 Featured Articles about mathematical topics I would hope several folks from this WikiProject could take a few moments to express an opinion about this proposed addition. Thank you very much. -- Rick Block (talk) 19:16, 14 February 2009 (UTC)

Maybe it is better to make a pair of articles, "Introduction to Monty Hall problem" and "Monty Hall problem" (in the same spirit as Introduction to entropy and Entropy, etc.)? Boris Tsirelson (talk) 20:25, 14 February 2009 (UTC)

Surely we can do this in one article - or are you saying the distinction between unconditional and conditional probability is so technical there is no point in discussing it in a general encyclopedia article? It seems to me this distinction is the essence of several popular "paradoxes". Boy or Girl paradox is another one. I think the bottom line is that the Monty Hall problem is clearly a conditional probability problem and our article here about it should mention this. -- Rick Block (talk) 20:57, 14 February 2009 (UTC)

I am suggesting, that in the one article we consider the 'simple fully defined problem' as an unconditional one (since the condition is a null one) and the 'real world problem' conditionally. What is your view on this Boris? Martin Hogbin (talk) 23:54, 14 February 2009 (UTC)

Yes, this approach, or something in this spirit. My hope is that then one group of editors will edit intensively one of these two articles, another group — the other article, and so, the amount of wikihate will decrease substantially. Boris Tsirelson (talk) 18:49, 15 February 2009 (UTC)

What you're suggesting is a POV fork. And yes, that does decrease the "wikihate" substantially. But it is in direct opposition to policy. The distinction between an introduction/advanced split and a POV fork here is that an introductory article is supposed to be an introduction to the topics in the advanced article. Here you are proposing that the "advanced" article be created so that people who don't believe its contents can stick with the "introductory" article, which will only contain a POV consistent with their misunderstanding. And in practice, if what you suggest happens, where everyone that understand the problem edits one article and people unwilling/unable to understand edit the other, that is undeniably a POV fork. --C S (talk) 12:01, 17 February 2009 (UTC)

Many people really need an interesting article (on this subject) accessible to them. Other people really need a deeper insight. Why should they fight each other? No more free disk memory on Wiki servers? Boris Tsirelson (talk) 18:54, 15 February 2009 (UTC)

And then hopefully the next section (below) will become obsolete since "the ownership problem" will dissolve smoothly. Boris Tsirelson (talk) 18:57, 15 February 2009 (UTC)

To be honest, while I think things like introduction to general relativity are regrettably probably necessary, an article called introduction to the Monty Hall problem would strike me as ridiculous. General relativity is a massive subject consuming entire careers; the Monty Hall problem is a cultural meme cum amusing little paradox. It's — perhaps not borderline, but at least somewhere in the borderlands — whether the Monty Hall problem should have even one article.

Splitting articles is dangerous in even the most justified situations. Take a look at the Boolean algebra articles. I was behind the split into what are now called Boolean algebra (logic) and Boolean algebra (structure). This split, I continue to maintain, was absolutely necessary, because these are very distinct notions, and there was no end of confusion from editors who didn't understand that.

However I can't honestly say that the outcome has been happy. Rather than the justified two, there are now at least five articles covering the space of the original (confused) article, and restoring order to them appears to be a lost cause.

Compare to the present case, where there is no different subject matter being proposed for the two articles, but only a different level of treatment, and with nothing very difficult proposed for the more "advanced" article. The right way to handle that is just to put the more difficult material later in the article. Splitting should be done for compelling reasons inherent to the material, never simply to resolve disagreements between editors.

I hope my frank language does not offend Boris Tsirelson, a highly valued contributor for whom I have great respect as a mathematician. --Trovatore (talk) 21:04, 15 February 2009 (UTC)

OK with me, why not. You are much more experienced wikipedian. I support the "put the more difficult material later in the article" in a sincere hope that editors will then coexist piecefully. Boris Tsirelson (talk) 17:23, 16 February 2009 (UTC)

Check references at AfD talk

For those of you who have participated in the recent AfD that has been so polluted with false statements by sock puppets, can I ask that you look at the list of references on the AfD's talk page once again. I (and a few others) have tried to clean them up to the point that verifying enough of them is trivial.

• I think many of the claimed citations are not reliable sources, but enough of them are.
• I think a journal is independent of its contributing authors.

Combining these two yields that the mathematical concept (not the scholar) has received significant coverage in reliable, independent sources, and so should be presumed notable.

Obviously, each of you should make up their own mind if the concept really meets wikipedia's notability criteria, but I think many of us have been tricked into not even reading over the references. The ones with DOIs on the talk page are almost all "good". JackSchmidt (talk) 03:20, 16 February 2009 (UTC)

What AfD is this? Algebraist 03:22, 16 February 2009 (UTC)

Kind of a nasty one, so feel free to steer clear. It is just that most of the active WP Math people have already commented, and I wanted to ask each of them to reconsider the "reliable" part of the proposed sources. However, I guess it makes sense to link WP:Articles for deletion/Boubaker polynomials (3rd nomination) and WT:Articles for deletion/Boubaker polynomials (3rd nomination)#Reference list. Myself, Plclark, Arthur Rubin, and perhaps David Eppstein have based our votes in the (un)reliability of the source (providers). I suspect many others who gave short reasons also based their decision on the behavior of the "keepers" and of the the original author. JackSchmidt (talk) 03:32, 16 February 2009 (UTC)

Oh, that thing. I've been steering well clear for a while now. Algebraist 03:34, 16 February 2009 (UTC)

Very wise. I verify sources as a hobby. This one is intriguing, but I suspect demoralizing. JackSchmidt (talk) 03:40, 16 February 2009 (UTC)

Thank goodness that has all gone away, hopefully for ever this time. I tried reading one of the papers and it just didn't make much sense for me, it was like a Chinese paper about making insulin where they had a whole bit on it being due to the thoughts of Chairman Mao. He put a lot of work into publicizing it,I was wondering if there could be some other reason like selling a journal or something - or do people really go to that trouble just to get their name in some rather obscure lights? 19:31, 17 February 2009 (UTC)

Generalised circle

user:Jim.belk has proposed merging generalised circle into inversive geometry. I have the impression the material now there may have been taken entirely from Hans Schwerdtfeger's book. I don't know why the word "generalised" is used, so if it doesn't get merged, maybe the title should be changed, although I'm not sure what to change it to. Opinions? Michael Hardy (talk) 02:37, 18 February 2009 (UTC)

....and now I find this page: User:Paul Murray/Geometry of Complex Numbers. This appears to be a draft of an expansion of the article. Michael Hardy (talk) 02:41, 18 February 2009 (UTC)

There's some material on circles with imaginary radius in Apollonian circles, by the way. I think that's essentially the same thing as these generalised circles, and when I put some of that material into Apollonian circles I sourced it to Schwerdtfeger's book. —David Eppstein (talk) 02:52, 18 February 2009 (UTC)

The merger is appropriate. Generalised circle may refer to a variety of different constructions in geometry. The more common contemporary usage is a curve along which a cartan connection is Lie derived. This includes, for instance, the "conformal circles" of conformal differential geometry. Acannas (talk) 03:16, 18 February 2009 (UTC)

Math2English

I ran across this template, Template:Math2english, on Kepler's_laws_of_planetary_motion. If the laws didn't have English equivalents included in the article), I would understand the purpose of it, but as the article stands with the template, I'm at a loss to see how something like

$\ {\dot {X}}={\frac {dX}{dt}}={\frac {dX}{d\theta }}\cdot {\frac {d\theta }{dt}}={\frac {dX}{d\theta }}\cdot {\dot {\theta }}={\frac {dX}{d\theta }}\cdot \ell p^{-2}u^{2}.$

is supposed to be translated into English beneficially or have a picture. Has anyone seen this template before? It is not mentioned on Wikipedia:Make_technical_articles_accessible. The addition of this template to an article also has the side-effect of adding it to category: technical and circumventing the explicit instructions at Wikipedia:Make_technical_articles_accessible to leave an explanation. --C S (talk) 03:36, 18 February 2009 (UTC)

It's pretty clear-cut. Something like this appears to be called for: "the time derivative of X is equal to the theta derivative of X multiplied by the time derivative of theta, and the time derivative of theta is equal to ell times the square of u divided by the square of p." Remember, the blind have an especially difficult time with typeset formulas. Acannas (talk) 03:41, 18 February 2009 (UTC)

What is clear-cut? It is definitely not the standard to write that kind of translation for equations on Wikipedia. Nor does the wording of the template in any way suggest this is for visually impaired readers. Quite the contrary. --C S (talk) 03:45, 18 February 2009 (UTC)

Wikipedia does provide a way for the blind to access content in mathematics formulas, who cannot otherwise view the rendered LaTeX. Acannas (talk) 03:51, 18 February 2009 (UTC)

From Wikipedia talk:Make technical articles accessible/Archive 1, it looks like this template was once mentioned in WP:Make technical articles accessible but was removed because it was stupid. Algebraist 08:51, 18 February 2009 (UTC)

Ok. Thanks for pointing that out. Well then, I'm removing the template from the handful of articles it's on. I can see no good reason for any of the templating on them. Should this template be deleted? It seems to see almost no use. --C S (talk) 06:07, 19 February 2009 (UTC)

I'd like to see it deleted. CRGreathouse (t | c) 02:51, 20 February 2009 (UTC)

Agree. Paul August ☎ 03:04, 20 February 2009 (UTC)

Continuous game

Could you chaps and chapettes please take a look at the intro to this article and tidy it, so it at least states that it's discussing maths (as opposed to a game that is continuous, like some kind of eternal Timeless Test or marriage).

I note also that the link to discrete game points to Game Theory. Perhaps it could have its own article?

Cheers! --Dweller (talk) 11:58, 18 February 2009 (UTC)

Reminder: We have a conventions page

There are a few proposals at Wikipedia:WikiProject Mathematics/Conventions, the latest one being two months old. Unless someone protests I am going to promote them by moving them downwards. I think the page is still quite incomplete, and it would be nice to have some new proposals and overall more activity on the page. Last year there were only 5 edits to the page and 3 to the talk page! --Hans Adler (talk) 13:41, 19 February 2009 (UTC)

I started the page, and still think it is a good idea to have a single, central page where such matters are discussed. There seemed to be a little resistance to the concept, but that was some time ago. Charles Matthews (talk) 17:31, 21 February 2009 (UTC)

Notification of Science FAC symposium

• See Wikipedia:WikiProject Featured articles/Science FAC symposiumLing.Nut ^{(talk—WP:3IAR)} 13:10, 20 February 2009 (UTC)

Failure to parse

At power of a point I've been seeing this for the past hour or so:

Failed to parse (Cannot write to or create math output directory): \overline{\mathbf{PT}}^{2} = \overline{\mathbf{PM}}\times\overline{\mathbf{PN}} = \overline{\mathbf{PA}}\times\overline{\mathbf{PB}} = \left(s - r \right)\times\left(s + r \right) = s^{2} - r^{2} = h

Michael Hardy (talk) 18:41, 20 February 2009 (UTC)

OK, never mind. I purged the server cache. That worked. Michael Hardy (talk) 18:43, 20 February 2009 (UTC)

Failure to parse

Wait! This is a problem. Over the last 48 hours, this has been happening with unusual frequency. I've just run into several cases today, and I found another user complaining of it on a talk page within the past few hours.

Purging the server cache works, but it's suddenly needing to be done with unusual frequency. Michael Hardy (talk) 16:11, 21 February 2009 (UTC)

I've had this problem quite frequently, over the last few months. And recently (a few hours ago) I couldn't get the contents of a <math></math> to show up at all. (The image wasn't generated, so Firefox showed the bare contents and Safari a missing image icon.) It was fixed by forcing Safari to download the image. Might be related? Shreevatsa (talk) 16:39, 21 February 2009 (UTC)

Connected space/Proofs

Could someone help out with this article? I am working on wikifying articles and this one is tagged for wikification. It currently has no lead. Also I think the title has to be changed, to avoid the slash. Would Proofs of theorems relating to connected space make sense? Someone who knows a bit about topology and is used to editing maths articles could probably sort it all out quite quickly. Thanks. Itsmejudith (talk) 23:15, 16 February 2009 (UTC)

Do we even need this article? It is textbook textbook content; students prove these sorts of things on their point-set topology homework. Ryan Reich (talk) 23:57, 16 February 2009 (UTC)

No, I think we do not need it. All this content and more appears already in locally connected space. Plclark (talk) 00:11, 17 February 2009 (UTC)

I have proposed it for deletion. Ozob (talk) 21:51, 17 February 2009 (UTC)

User:Dcoetzee has removed the prod tag. I won't put it up for AfD at least until the present discussion is done. Ozob (talk) 02:18, 19 February 2009 (UTC)

On a closely related subject, can we do something with Distributive lattice/Proofs? I removed two of the lemmas from there since they were better covered in Birkhoff's representation theorem, and now there's just a sad lonely lemma claiming that min/max in a total order forms a distributive lattice. It doesn't seem very encyclopedic to me: it's an important fact, but not an important proof, and I don't think it deserves its own article. But I'm not sure what to do with it. —David Eppstein (talk) 22:12, 17 February 2009 (UTC)

I think these pages are part of the "article proofs" project, with the aim of including proofs of all the claims that are made in the corresponding main article. I don't have any strong opinion about them, but I agree that they are not independent articles. — Carl (CBM · talk) 22:45, 17 February 2009 (UTC)

It might be considered as a specific way, proper to mathematics, to ensure Wikipedia:Verifiability. This is not encyclopedic in its own way, but a mention like "Otter Example if.in, retrieved on 2007-09-21" (random quotation from First-order logic) is not very encyclopedic either. Both are useful though, as satellits of encyclopedic informations whose purpose it to make these infos verifiable. Though this is something very special to maths (I can't imagine other places where a similar way to proceed could be adopted) these pages don't seem pointless ; of course it could be argued, not wrongly, that not everything has to be sourced, and that there is no more reason to help verifiability for A locally path-connected space is path-connected if and only if it is connected than for Glasgow is the largest city in Scotland since both can be very easily checked without help by somebody with a level of knowledge adapted to the article where they are to be found. All in all, I don't think efforts to eradicate such trivial proof pages are well directed, though I shall not fight to keep them. French Tourist (talk) 23:03, 17 February 2009 (UTC)

Using "article proofs" as instruments of verifiability seems to me to be always wrong. According to WP:V, one needs a source for anything "challenged or likely to be challenged", so there are three kinds of situations we could be talking about.

• First, a given theorem (or lemma, or computation) might be unremarkable, in which case no proof need be given or cited. This especially includes anything which is "obvious" or routine, depending of course on the context.
• Second, the statement might be questionable, but fortunately, a proof exists in the published literature. Great! It can be cited like any other fact on Wikipedia. Math doesn't become less true just because the proof is not visible, any more than primary sources are untrue because you have to trust the author's word.
• And third, the statement might be both questionable and lacking a published proof. If it's questionable it is unlikely to be trivial, and therefore any proof is likely to be somewhat creative. Even though the verification of any rigorous proof is a mechanical process, and therefore the proof itself need not be cited for verifiability, if it can't be cited and it's nontrivial it looks to me like original research. And honestly, if we have a mathematical statement of questionable veracity that lacks a published proof, how can we include it (unconditionally) in this encyclopedia?

It seems to me also that Planet Math is the right place for proofy articles. They like that sort of thing and their model may be better suited to including them. We don't have to be the one-stop shopping destination for all math on the internet.Ryan Reich (talk) 04:20, 18 February 2009 (UTC)

The inclusion of proofs in Wikipedia is a difficult and complex question, and it isn't lost on me that contributors often make small changes in good faith that invalidate the correctness of proofs. I think in the long term a much better place for proofs will be a wiki attached to a formal theorem prover backend for verification. However, my argument is that proofs in math articles serve the same purpose as "examples" or "demonstrations" in other articles; they show, for example, how the axioms of a system might be used together in proving a result, or what kind of properties of a system are useful in simple proofs. They should never be creative or prove complex results; they should be trivial and obvious, but we're not proving them in order to demonstrate the correctness of the theorems (that would be silly), but in order to demonstrate the proof method, which is something worth documenting in an encyclopedia. Dcoetzee 05:52, 18 February 2009 (UTC)

I disagree that proofs “should never be creative or prove complex results.” A properly sourced but highly creative proof can be perfectly appropriate to an article. For instance, I've included several examples of such in double counting (proof technique), in some cases creative enough to justify a new journal paper for a proof of an old result. And if a proof doesn't require any creativity to come up with, what's the point of including it when the readers could come up with the same thing on their own? I'm a little torn about including unsourced novel and somewhat creative proofs of known facts, though: on the one hand, it seems to be a violation of WP:OR, but on the other hand they're self-verifying and if I were writing a survey paper that's the sort of thing I would do without any concern. —David Eppstein (talk) 23:59, 18 February 2009 (UTC)

Apologies for being unclear; of course anything can be included if it's sourced and relevant. As for "what's the point of including it when the readers could come up with the same thing on their own?" - well, like I said, the point isn't to establish the correctness of the theorem; it's to demonstrate the proof technique, which the reader may not be familiar with, even if the result is intuitive. For example, I think in an introduction to group theory, it's perfectly sensible to prove some basic results (it doesn't matter what they are) to demonstrate how the group axioms are used together in a simple proof. I challenge the statement that proofs are self-verifying, just because there really isn't enough expertise available on Wikipedia to verify that all proofs are accurate and remain accurate over time (particularly proofs that use advanced ideas from a particular subfield). Dcoetzee 02:30, 19 February 2009 (UTC)

Would you agree that the introduction of Grothendieck universe, which proves a trivial proposition, is a good example of what you're talking about? I have to admit that when I first encountered Grothendieck universes I was a little surprised at how few axioms there were and how much immediately followed from them, so I think the proposition is good or at least not inappropriate.

Looking at the very next section of the article, however, we find a sketch of a more involved proof. It ought to be possible to present most of the facts of that proof outside the context of the proof itself: The cardinality of c(U), the universe function u, and the main theorem can all be presented without proof. In this case I'd say the proof is bad because it obscures some of the underlying facts: In order to learn about c, u, and the main theorem, you have to read the proof section, which shouldn't be necessary. That could be fixed with better presentation, but what's left is either trivial or punted to the references.

I suppose that's the really worrying problem for me: It's very easy to hide important facts in the middle of proofs, and we want to avoid that if at all possible. I think a straightforward proof should be presented if it's a good way of suggesting something deep. Otherwise it's not interesting; including too many straightforward proofs amounts to either a textbook presentation (which is inappropriate for our goal to be an encyclopedia) or to undue weight (on trivial details). And, as David said, what's the point? Ozob (talk) 02:41, 19 February 2009 (UTC)

(undent) I think I see here that we are talking about two different things at the same time. One of them is the issue addressed by my long post above: using proofs as in-place sources for mathematical statements. The other is including proofs as part of the content of the article, as discussed by all replies to that comment. My opinion is still that proofs should never be used here as proofs, because that would be either textbook or OR content, and anyway we are not generally in the business of convincing the reader of anything, except of course (like in the infamous Monty Hall problem) if the proof or the question of the truth of what it proves are themselves notable. I think that trying to include proofs for completeness' sake is a failure to keep our collective eye on the ball and falls into an easy trap of mathematical exposition where a theory's narrative is contained in the flow of the logic itself without synthesis or external motivation. The argument that proofs are self-verifying and thus suitable for inclusion is a perfect example of its own incorrectness: it puts the burden on the reader to do the job of the author in making what is (when sufficiently rigorous to be actually self-verifying) a logical tautology, that is, an objective truth, into a truth that is also subjective. As Ozob said, doing this can obscure important ideas inside the proof, and in my opinion perhaps actually encourage the migration of such ideas into proofs, where they "make sense" better.

I don't have this objection to using proofs as examples because this implies a conscious decision for the proof argument to complement prose material in the rest of the article. If done well, it surely improves the article by presenting a more complete mathematical picture, but this requires writing the proof in a way which is different from "journal style" because the focus is not on correctness but on technique. However, just like examples can be excessive and degenerate into textbook pedagogy, so can the proliferation of trivial exemplary proofs return the article to an arid classroom format. For instance, in an article on calculus, examples of epsilon-delta proofs should not aim to instruct the reader in writing them, but to show how the formalism reflects the very intuition that is presumably discussed in the surrounding text.

Anyway, Connected space/Proofs and all other articles of similar genesis should be frowned upon. No article here should require the knowledge of particular details of the layout and contents of a specific other article even for its existence to be justified. Something like the proof of Bertrand's postulate is of independent interest; the proof that a locally path-connected space is connected if and only if it is path-connected is just not. Ryan Reich (talk) 05:18, 19 February 2009 (UTC)

I think the comment about survey articles says it for me: include a proof iff someone writing a survey on that particular topic would at least consider it as content. Generally sketches of proofs are much superior, anyway: if the proof depends on the Widget Lemma, saying that is a helpful guide to prerequisites, but the details are usually not so valuable. Charles Matthews (talk) 18:00, 19 February 2009 (UTC)

I have tagged Connected space/Proofs for merge into Connected space, as that seems to reflect the consensus of the discussion here. It opens the vote, anyway. Itsmejudith (talk) 01:14, 23 February 2009 (UTC)

If people here prefer AfD then could someone initiate it. And if the article survives, then can a project member undertake to wikify it. It's a bit difficult for non-mathematicians. Itsmejudith (talk) 16:55, 23 February 2009 (UTC)

Implication

Is it just me or you also see the difference between

$\implies$ and $\Longrightarrow$

what's about

$a\Longrightarrow b$ and $a\implies b$

(Igny (talk) 17:58, 18 February 2009 (UTC))

I see it too. When I type \Longrightarrow on my own LaTeX installation it's not ugly like the above. Ozob (talk) 02:14, 19 February 2009 (UTC)

Same here. Looks like a bug. Michael Hardy (talk) 05:38, 19 February 2009 (UTC)

I see $\implies$ as the proper character, $\Longrightarrow$ as a broken one, and both $a\Longrightarrow b$ and $a\implies b$ as having the same fuzzy character (different from the previous one) but with different spacing. Shreevatsa (talk) 13:50, 19 February 2009 (UTC)

Whoa, I see <math>a \implies b</math> as the broken fuzzy one too! I always use the unicode ⇒ so hadn't noticed this. This is a reasonably big problem, as that broken fuzzy one looks pretty awful. JackSchmidt (talk) 19:10, 23 February 2009 (UTC)

If you look closely, this has always been like that in any LaTeX-Installation, at least with the standard fonts. The "parallel" lines are somewhat wider at the point, probably to counteract some visual illusion where exactly parallel lines would appear narrower at the point. But the antialiasing settings seem to worsen this slight slant incredibly.--LutzL (talk) 19:27, 23 February 2009 (UTC)

Hrm, I don't exactly see this, though I do see some weird rendering anomalies in moderate sizes. They disappear when the implies is full screen though. I use "\documentclass{article}\usepackage{amsmath,amssymb}\begin{document}$$a \implies b$$\end{document}" and pdflatex (from tetex 3.0-1006) and apple's preview.app. I agree there is a problem in vanilla latex, and the antialiasing makes it look much, much worse. Guess that makes it almost impossible to file a mediawiki bug report for this one. JackSchmidt (talk) 19:44, 23 February 2009 (UTC)

"Fixing" math displays

user:Wikid77 has been "fixing" various TeX displays to allow articles to fit windows of certain sizes, and he has no understanding of the conventions of Wikipedia:Manual of Style (mathematics) for non-TeX mathematical notation, and also doesn't seem to understand the effects of what he's doing—how to get math displays to look the way he intends (e.g. he seems to do some attempts at spacing that don't work). In one case, logarithmic distribution, I entirely undid his work but then changed the display into two lines by using "align" within TeX, in the hope that that would address whatever his concern was. How shall we try to help him? Michael Hardy (talk) 18:01, 23 February 2009 (UTC)

TeX offers no facilities for line-breaking within equations. Knuth says somewhere in the TeXBook that line-breaking in equations is impossible to do mechanically, because there are too many things to consider, foremost among them being the underlying mathematical content (which TeX does not understand in the slightest).

User:Wikid77 does not seem to notice the damaged spacing. (See, for example, his comment on Talk:Matrix normal distribution.) He also seems unaware that he's introducing MoS violations. I'm inclined to mass revert all of these changes. Ozob (talk) 18:34, 23 February 2009 (UTC)

TeX does allow line-breaking by use of the "align" environment. That's what I did with logarithmic distribution. I don't know if that addresses "Wikid77"'s concerns or not. Michael Hardy (talk) 22:08, 23 February 2009 (UTC)

I failed to be clear. TeX offers no facilities for automatic line-breaking. That is, in some sense, the ultimate progenitor of this issue.

Wikid77 has attempted to respond to our concerns at User_talk:Wikid77#Confusion_over_math_formulas. Ozob (talk) 13:05, 24 February 2009 (UTC)

I tend to agree with Ozob that these changes should be reverted, the do more harm the good. Thenub314 (talk) 14:19, 24 February 2009 (UTC)

User:Wikid77 seems to discuss things only on his talk page. He suggests formatting things as follows:

$\displaystyle X+Y=$ $\displaystyle A+9$

which is generated by

<math>\displaystyle X + Y =</math>&nbsp;<math>\displaystyle A + 9</math>

That is, he wants to insert manual line breaks in equations, then correct the spacing with  s, that is, HTML non-breaking spaces. This produces slightly uneven spacing: Compare the first line, which has no line break, to the second, which uses Wikid77's method: (You may have to get really close to your screen to see this)

$\displaystyle X+Y=A+9$

$\displaystyle X+Y=$ $\displaystyle A+9$

It does not work so well when you try to break along a math operator:

$\displaystyle X+Y=A+9$

$\displaystyle X+Y=A+$ $\displaystyle 9$

Here the second line is generated by <math>\displaystyle X + Y = A +</math>&nbsp;<math>\displaystyle 9</math>. I don't think Wikid77 has considered this problem. (After all, breaking along a binary operator is usually less desirable than breaking along an equals sign or inequality anyway.) I'm going to leave another reply on his talk page; but he doesn't seem to listen to objections very well. Ozob (talk) 13:40, 25 February 2009 (UTC)

Radius-invariance of the volume of a band around a sphere

I've just created the article titled Radius-invariance of the volume of a band around a sphere, about a bit of folklore in elementary geometry. Sometimes the proof of this is assigned as an exercise in sophomore calculus.

Concerns:

• Which articles should link to this?
• Which books or articles should it cite? This is decades or maybe centuries old. I wouldn't be surprised it it originated in some piece in the American Mathematical Monthly or the like in about 1900 ± a few eons. Or could it be some 17th-century French geometer? Or even older? Ancient Greece?
• Is there a more efficient title for the article?

Michael Hardy (talk) 00:48, 25 February 2009 (UTC)

The title is long and awkward. I suggest, following the Devlin and Lines references I added, that we move this to Napkin ring problem. Any thoughts? —David Eppstein (talk) 01:12, 25 February 2009 (UTC)

Devlin does this by a cumbersome method, and MathWorld does it the same way Devlin does (did they get it from Devlin? If you look at this edit, you will see that I did it by a far less cumbersome method, more straightforward, but still needlessly far too complicated by comparison to what I finally put there. It was while doing that that it occurred to me that Cavalieri's principle would probably work. That being the case, one could present this in a high-school geometry course. Do you happen to know if any of the books you cited do it that way? Michael Hardy (talk) 04:11, 25 February 2009 (UTC)

I guess someone found Devlin's column just by random google searches or something. If you read the column a few months later, he explains that his cumbersome method was a setup for his followup article on "Lockheart's Lament" [1]. And yes, he does provide a different non-calculus method. The Lockheart article is pretty interesting too. I recommend reading it. --C S (talk) 08:29, 25 February 2009 (UTC)

I wasn't checking very carefully what proof techniques they used, but Howard Eves' Two Surprising Theorems on Cavalieri Congruence mentions this briefly as being solvable using Cavalieri. I didn't add that citation because he doesn't go into any detail. —David Eppstein (talk) 04:42, 25 February 2009 (UTC)

By the way, it's another known and similar fact (also Cavalieri, I think, but maybe more easily by Pythagoras) that the area of an annulus is πL where L is the length of the longest line segment that can fit inside the annulus, independently of the inner and outer radii. For each annular cross-section of the napkin ring, this line segment is the intersection of three shapes: the cross-sectional plane, the sphere, and a tangent plane to the inner hole. But the intersection of two of these shapes, the sphere and the tangent plane, is a circle with diameter equal to the hole's height, independent of the sphere radius. Therefore the line segment length, the annulus area, and the napkin ring volume are independent of the sphere radius. —David Eppstein (talk) 04:55, 25 February 2009 (UTC)

On a related topic, don't they teach geometry in high school any more? Our article titled sphere derives the volume of the sphere only by calculating integrals. Michael Hardy (talk) 06:53, 25 February 2009 (UTC)

On that note how about a Proof without words? The result for an annulus can be see as obvious from a VISUAL Approach to CALCULUS problems and then if you look at Sphere picture. A cylinder has the same volume as a sphere plus two cones. When a hole is put through the centre of the sphere and that is added to a shortened pair of cones it is equivalent to a shortened cylinder with a hole down the centre, and that is the same as a cylinder with the same width as the shortened cone. The smaller cylinder and shortened cone then together make a sphere with th same diameter as the length of the hole. Um, well, perhaps I did put in a lot of words there ;-) Dmcq (talk) 15:08, 25 February 2009 (UTC)

Proofs

I was recently looking at Fundamental theorem of calculus, and I again was asking myself how appropriate proofs are on wikipedia. The two proofs in this page (in my opinion)

• are not short
• are not especially easy
• don't clarify the theorems greatly

But I feel that this is an increasing trend with pages on wikipedia. Even after reading the looking at the MOS I am left with the following questions. When do we include proofs? (Some pages need them, for example 0.999...) How many proofs? (Some pages that I feel don't really need any proof have multiple proofs)? Do proofs blur the boundary between wikipedia and wikibooks? (Some pages are in fact only a proof.)

Overall, I was just curious to hear other peoples thoughts on the subject. Thenub314 (talk) 09:37, 25 February 2009 (UTC)

If a proof is short and easy to understand, then would you allow it because it makes it clearer that the theorem is, in fact, true? JRSpriggs (talk) 09:53, 25 February 2009 (UTC)

I think we just have to allow them but they need some rules and better control so they don't mess up the flow, e.g. put them at the bottom of articles if of any size or as separate articles if important. One thing that annoys me and really needs to be guarded against is people sticking in erroneous proofs. Too any people come along being mathematical and sticking in what they think is a proof rather than checking. I think they should all refer to some publication, no proof should be allowed without a citation. Dmcq (talk) 10:22, 25 February 2009 (UTC)

Though I shall not move a finger in defence of the second proof in your example, I quite disagree with you as concerns the first one : it is not very short indeed, but mainly because it is written in a slow expository mode (probably best suited to many readers) -indeed it is not very long either. It is not especially difficult or intricate (I don't see any significantly easier way to do). More important, it clarifies quite a few things as concerns the theorem proper : when I look at this proof, I understand quickly that the theorem is an easy subproduct of the mean value theorem, and why the question of "which integration theory is used ?" is irrelevant.

I really think proofs are quite often useful and worth including (of course this is to be judged individually for every article).

As Wikipedia is supposed to be "an encyclopedia incorporating elements of general and specialized encyclopedias, almanacs, and gazetteers", and as we have not to reinvent how to write an encyclopedia, my opinion is that proofs can be included as long as a specialized encyclopedia might reasonably include one. Of course, this means we have to decide which texts are or are not "specialized encyclopedias" which is not always obvious. For a similar discussion on :fr (the same questions are asked everywhere...) I opened a (more or less) random volume of the Encyclopedia of Mathematics and its applications (volume 71, Special functions) at a random page : [2]. I find proofs there, absolutely similar indeed to proofs to be found in "ordinary" textbooks in maths. After this experience, I see no reason to forbid ourselves to include such kind of proofs in our articles. French Tourist (talk) 16:50, 25 February 2009 (UTC)

I would generally prefer forking the content to blah/Proof. This lets the proof go into more detail, if needed, and leaves the main article cleaner for users who don't want to (or can't) follow the proof. CRGreathouse (t | c) 18:14, 25 February 2009 (UTC)

As someone commented, the two proofs have been written in an extremely pedantic, long way. But they are quite short proofs. The first, as has been mentioned, is more or less the obvious way to do it. At the least, a novice mathematician would be able to understand what the statement is, that is to be proven, and why you would start the proof that way. As for the second proof, it is written in an obfuscatory fashion, but the essence of the idea is that it mimics a classical proof of Stoke's theorem in this more elementary context. So I do think it adds insight. I expect many calculus instructors don't even realize the connection between Stoke's theorem and the fundamental theorem of calculus. --C S (talk) 19:22, 25 February 2009 (UTC)

Ernst Snapper

• (diff) 18:27, 4 November 2007 . . Parslad (Talk | contribs | block) (899 bytes)
• (diff) 21:16, 21 June 2007 . . Kane5187 (Talk | contribs | block) (888 bytes)
• (diff) 16:13, 21 June 2007 . . Fabrictramp (Talk | contribs | block) (656 bytes (internal links; added uncat people)
• (diff) 17:14, 30 October 2006 . . Amalas (Talk | contribs | block) (stub sorting, Replaced: mathbio-stub → mathematician-stub using AWB)
• (diff) 01:39, 25 May 2006 . . Akriasas (Talk | contribs | block) (created article)

Deleted for lack of an assertion of notabilityat 18:34 on 4 November 2007 by user:Sandahl. Should we rewrite the article, making the assertion of notability clear, and then restore the edit history? Michael Hardy (talk) 06:58, 26 February 2009 (UTC)

Inertia tensor of triangle

Inertia tensor of triangle has been proposed for deletion via WP:PROD 76.66.193.90 (talk) 07:16, 26 February 2009 (UTC)

Mar 2009

A-Class

An initiative has just been launched to try to breathe more life and kudos into A-Class and A-Class review activities. Project members are warmly invited to participate. See: Wikipedia:WikiProject Council/Coordinators' working group. Geometry guy 19:32, 23 February 2009 (UTC)

Wikiproject Council? This is news to me. As I suspected, they have now fallen to squabbling on the talk page.

Does "kudos" mean badges, awards, medals? I would think just working to improve math coverage would be a suitable reward for most of us. After all, it's not as if math editors get much praise anyway, usually we just get people demanding we explain things simply and not in the self-gratifying manner we usually explain things so we can feel good about having math degrees.

"more life" would be good, but as always, that's always an issue in everything. I don't see what more there is to do, and I think in terms of overall progress, we are doing better than most projects. Do you disagree? --C S (talk) 13:21, 28 February 2009 (UTC)

New contributor in numerical analysis

I noticed four or five new articles today from the same contributor on the topic of fast numerical algorithms, especially classical 18th century work. The content is reasonably high quality and contributed in both English and Russian, but the wiki style and wiki integration is poor. I tried to fix some things, but probably this could use some more help, especially from people who can link to these articles from our existing relevant articles or even just merge them into topically identical existing articles:

Added Complexity of computation (bit)

Added Fast algorithms

Added The AGM method of Gauss

Added The FEE method

Added The Karatsuba multiplication

If anyone is comfortable editing in Russian, I think some of the same issues are in the Russian versions. I suspect English is not the new contributor's native language, but the English in the articles is usually good. JackSchmidt (talk) 13:18, 26 February 2009 (UTC)

Four color theorem nominated for A-class review

This is an old A-class article, one that attained its rating before the system went into effect. The nomination is here. I went through and fixed what I thought were the biggest issues: lack of citations, some errors, and just cruft. More eyes would be helpful. --C S (talk) 10:44, 28 February 2009 (UTC)

Cfd

There is a cfd for Category:Second wranglers currently going on here. Some informed views would be useful. Occuli (talk) 14:08, 1 March 2009 (UTC)

Does it seem strange to anyone else that User:Black Falcon participated in the prior discussion for Category: Senior Wranglers (influencing some later comments) and then closed it as a delete, based on apparently the strength of his/her own argument? After all, all of the delete arguments before his weren't clear either and based on the notion that this is like being a valedictorian from some college. Then his became an argument that the only good reason to keep was not sourced. --C S (talk) 23:52, 1 March 2009 (UTC)

It seems strange to me. There was the other far-fetched comparison with Eagle scouts, the last comment, made 2 weeks after the penultimate comment. I feel a drv coming on. Occuli (talk) 01:14, 2 March 2009 (UTC)

The relist, in which he changes the focus from miscapitalization to outright deletion, makes him effectively the nominator for the CfD, making it highly inappropriate for him to close. Additionally, as comments on the new CfD make clear, some participants who would have argued for keeping didn't take it seriously based on the fact that they thought it was only about capitalization and didn't find out about the later change of focus. DRV seems like a good idea. —David Eppstein (talk) 01:31, 2 March 2009 (UTC)

Since I closed the discussion, I think it would be appropriate for me to comment here. My thoughts on the matter are as follows:

1. The discussion for Category:Senior Wranglers stopped being just a renaming discussion when the first user suggested deletion. Once a category is nominated at WP:CFD, the course of the discussion rather than the initial nomination determines what will be done with it.
2. My participation in the discussion was limited to relisting the discussion and posting what was intended to be my closing rationale (I relisted it instead of closing it due to the fact that both categories were not tagged at the time), so as to hopefully stimulate additional discussion. It is a mistake to equate evaluating of the merits of the arguments with the actual making of an argument one way or the other.
3. The discussion was open for more than one month, which is significantly more than the 5 days spent on most category discussions.

I do not object to having my close evaluated at deletion review and I am perfectly happy to see the outcome overturned if there is agreement that I failed to properly evaluate the consensus or that there was not sufficient opportunity (either due to time or confusion regarding the scope of the nomination) to properly discuss the category. –Black Falcon ^(Talk) 02:25, 2 March 2009 (UTC)

Weird edit!!

This is weird. This was an article about an Australian combinatorialist, who is not the same person as the American mathematical physicist at the University of Toledo, who was born in Connecticut. A couple of edits earlier, someone added the "University of Toledo" category, although the Australian mathematician was never affiliated with that institution. Then this edit changed the article to be about a different person. Michael Hardy (talk) 16:34, 3 March 2009 (UTC)

PS: The AfD discussion was about the Australian. Michael Hardy (talk) 16:34, 3 March 2009 (UTC)

Perhaps we should create two new articles: Geoffrey Martin (Australian mathematician)

and Geoffrey Martin (American mathematician). Charvest (talk) 18:20, 3 March 2009 (UTC)

The American one (ie the present one) could be moved to Geoffrey K. Martin (supported by genealogy.math) and the Australian one restored. Occuli (talk) 20:27, 3 March 2009 (UTC)

That sounds like a good solution to me. I'll see if I can do that in a way that splits the history properly. It will likely involve some temporary deletion of the article. —David Eppstein (talk) 21:07, 3 March 2009 (UTC)

Having searched Google, I now reckon both articles should be deleted. Charvest (talk) 21:45, 3 March 2009 (UTC)

But the deletion discussions should be separate. Michael Hardy (talk) 21:48, 3 March 2009 (UTC)

I've started a deletion discussion on the Australian one (I'd have used prod but for the previous afd). I'm less certain that the other one should go, though, so someone else can start that. —David Eppstein (talk) 22:14, 3 March 2009 (UTC)

Possible plagiarist

There's a discussion going on about some possible plagiarism by Lantonov (talk · contribs) at WP:ANI#Plagiarist caught red-handed and refusing to cooperate. Among his contributions are some math articles: Hewitt–Savage zero-one law, Rook polynomial, Projective geometry, Eigenvalue, eigenvector and eigenspace, Hölder's inequality, Curvilinear coordinates, Pseudotensor and maybe others (I didn't go back through his whole edit history). It may be worthwhile for some project participants to check whether there are any problems with his additions to these articles. —David Eppstein (talk) 21:54, 3 March 2009 (UTC)

Hölder's inequality is fine; he just added a ref. (Hope it is ok to strike it off as done.) JackSchmidt (talk) 22:10, 3 March 2009 (UTC)

Most of his "AWB" edits that I have looked at are fine; they appear to just be letting the tool do its automatic cleanup. These are the 2008-02 ones. JackSchmidt (talk) 22:18, 3 March 2009 (UTC)

An article with a lot of edits from 2007 was Laplace transform. It looks ok to me, but I would not be able to recognize the problem there. He cites a book by Korn that might make it easy to check. Here are 10 or 20 consecutive edits. JackSchmidt (talk) 23:06, 3 March 2009 (UTC)

Hewitt-Savage zero-one law is okay. Rook polynomial is almost all Lantonov. On Projective geometry he made only one non-trivial edit, [3]. His contributions to Curvilinear coordinates are substantial. He has a few non-trivial contributions to pseudotensor, notably [4] and [5], but that's not an exhaustive list. He has lots of contributions to Eigenvalue, eigenvector, and eigenspace, but all the ones after 16:49, 25 March 2008 were either reverted or are okay. History of geometry is okay. Clifford bundle is okay. Manifold is okay. Cartesian coordinate system is okay. Covariant derivative is okay. Standard basis is okay. Lie derivative is okay. Loewner's torus inequality is okay. The relevant part of Laplace transform has been rewritten since his questionable additions. Aleph number is okay. Combinatorial proof is okay. Combinatorial species is okay. I think those are all of his math contributions which are not marked "AWB". Ozob (talk) 23:39, 3 March 2009 (UTC)

BTW, User:Gareth Owen should be thanked for his tireless corrections to Lantonov's edits at Eigenvalue, eigenvector, and eigenspace. Ozob (talk) 23:41, 3 March 2009 (UTC)

AfD for "History of quaternions"

Resolved

I've nominated the article "History of quaternions" for deletion. The discussion page is Wikipedia:Articles for deletion/History of quaternions. --A. di M. (talk) 13:50, 28 February 2009 (UTC)

I would appreciate the opinions of mathematical editors on this topic. I see little accuracy, and much eloquence, on how quaternions are Good, but Oppressed, by modern vector analysis; if someone can read this and see more virtue, please do so. Septentrionalis PMAnderson 21:24, 2 March 2009 (UTC)

I would also appreciate more eyes on Classical Hamiltonian quaternions. It begins with a summary of Hamilton's own notation, which may well be sound, but continues into the same Quaternions Good, Vector Analysis Bad, as the article considered for deletion (it wasn't, but I redirected it - this may or may not hold). Septentrionalis PMAnderson 01:20, 5 March 2009 (UTC)

"Show new selections"

What is the link "Show new selections" on the mathematics project page good for? It links to the same site, but with an "action=purge" attached. Ringspectrum (talk) 15:52, 4 March 2009 (UTC)

"action=purge" forces the server to refresh the page. There may be some content on the page that isn't smart enough to refresh itself. In this case, it appears that asking the server to refresh the page causes a new article to be showed in the "Selected article". However, refreshing the browser does the same thing. It seems weird to force the server to refresh for such a process... hmm... Whereas simply refreshing your own browser will not change this. It does seem like a strange thing to have as such a process as a prominent link on the page... hmm... And just to be clear you're talking about the Math Portal, right? RobHar (talk) 16:02, 4 March 2009 (UTC)

"And just to be clear you're talking about the Math Portal, right?" Yes, thanks for the explanation. Ringspectrum (talk) 17:19, 4 March 2009 (UTC)

For the maths portal there quite a lot of content is selected at random, but the random numbers are only regenerated when the page is purged. --Salix (talk): 18:31, 4 March 2009 (UTC)

Cavalieri's principle

We finally have an article titled Cavalieri's principle. Happy editing! Michael Hardy (talk) 17:45, 5 March 2009 (UTC)

Nice. Should Method of indivisibles redirect there? —David Eppstein (talk) 18:47, 5 March 2009 (UTC)

OK, it now redirects. Michael Hardy (talk) 00:52, 6 March 2009 (UTC)

The vector of a quaternion

The vector of a quaternion has been sitting there for months. The article has obvious issues in regard to some of the usual Wikipedia conventions. Maybe it has other issues too. Michael Hardy (talk) 17:14, 6 March 2009 (UTC)

Lune of Hippocrates

Another new article for elementary geometry buffs to work on: Lune of Hippocrates. Michael Hardy (talk) 03:57, 7 March 2009 (UTC)

Manual of Style questions regarding TeX, displaystyle, and scriptstyle

Your collective comments and opinions would be greatly appreciated here: Wikipedia talk:Manual of Style (mathematics)#Using scriptstyle to make in-line symbols "fit". Thank you. -- Avi (talk) 18:59, 6 March 2009 (UTC)

<ping> Anyone have any comments? -- Avi (talk) 00:13, 9 March 2009 (UTC)

Infinite matrices

Is anybody knowledgeable in infinite matrices? In matrix (mathematics), I wrote a little section on that, but that may all well be POV, so I'm trying to find a good source for this topic. Who knows a book/book chapter on infinite matrices? Thanks, Jakob.scholbach (talk) 13:09, 7 March 2009 (UTC)

You might want to add a link to Hilbert space#Operators on Hilbert spaces to that section. JRSpriggs (talk) 15:40, 7 March 2009 (UTC)

In my opinion, your text is accurate, free of POV. Boris Tsirelson (talk) 18:43, 7 March 2009 (UTC)

Paul R. Halmos, "A Hilbert space problem book", ed. 2, Springer 1982. Chapter 5 "Infinite matrices". A quote from page 23: "Many problems about operators on finite-dimensional spaces can be solved with the aid of matrices; matrices reduce qualitative geometric statements to explicit algebraic computations. Not much of matrix theory carries over to infinite-dimensional spaces, and what does is not so useful, but it sometimes helps." Boris Tsirelson (talk) 18:46, 7 March 2009 (UTC)

Encyclopedic dictionary of mathematics, Second edition, ed. Kiyosi Itô, Math. Soc. Japan, 1993. Article 269 "Matrices" item K "Infinite matrices". Boris Tsirelson (talk) 18:51, 7 March 2009 (UTC)

love of digits

I hope this is the right place to mention — User:76.120.151.113 has been going through the polyhedron articles and changing every number-word (such as "one") to a numeral, as well as adding some strange alternate names such as "Heptagonal Deltahedron" for the triaugmented triangular prism. Can something be done? Should something be done? Am I getting over-excited about a petty matter of style? —Tamfang (talk) 04:01, 8 March 2009 (UTC)

usually the topic most likely to excite people on this page is style related. Who can forget the slanted and non-slanted d in derivative discussions? I would just revert all such edits. It's well-established to not use numerals in those cases, and any alternate names should be verifiable in some source. --C S (talk) 04:37, 10 March 2009 (UTC)

Boubaker polynomials (yet again)

Resolved

See WP:ANI#Boubaker's polynomials (again) — it appears the same sockpuppets behind the mess in Wikipedia:Articles for deletion/Boubaker polynomials (3rd nomination) are back, again attempting to game Wikipedia:Notability (numbers) by inserting language implying that mentions of a sequence in unreliable web sources such as OEIS and PlanetMath is relevant to judging the notability of the subject here. In this diff, the editor in question asserts that ”Michael Hardy, Elehack , Robinh , Mazca , Troogleplex , Reyk ,VolkovBot, Jkasd, Popo le Chien and Asenine” are all in favor of the change (how the group in favor can include at least one bot is beyond me). The two socks in question have also made a number of edits to math articles but when I checked all were at the level of harmless punctuation changes. —David Eppstein (talk) 21:50, 8 March 2009 (UTC)

I was never consulted about the change and had no suspicion that that edit was to be done, so any suggestion that I am in favor of it is based on nothing. Michael Hardy (talk) 22:34, 8 March 2009 (UTC)

Some blocks and WP:Numbers has been semi-protected. I think that resolves it. --C S (talk) 04:34, 10 March 2009 (UTC)

Euclidean algorithm

Hi, I'm thinking of bringing the Euclidean algorithm to Good Article level. The topic seems small enough to be feasible, but has wide applications; it might make a good "cornerstone" article from which readers might begin to understand more advanced topics, especially in algebra. I was thinking of organizing the topic stepwise, beginning with integers (which many non-mathematical readers will understand) and advancing gradually to rationals, reals, polynomials, quadratic fields and then to general Euclidean domains. We might add applications such as some factorization algorithms and Sturm chains, and some generalizations such as Gröbner bases. If anyone wants to help, I'd appreciate it; thank you! Proteins (talk) 17:40, 11 March 2009 (UTC)

This is off-topic, but what is the Euclidean algorithm for real numbers? — Carl (CBM · talk) 01:58, 12 March 2009 (UTC)

In general, Euclid's algorithm applied to two real numbers a and b yields an infinite continued fraction (or equivalently an infinite series of convergents that are ever better approximations) to a/b. If I recall correctly, Euclid's second presentation of the algorithm in Book 10 of the Elements concerned real numbers, not integers. You might be interested in the article on integer relation algorithms. Proteins (talk) 04:31, 12 March 2009 (UTC)

If a > b are nonzero real numbers, the remainder of dividing a by b is 0, so I still have no idea what you are saying. Indeed, the section of that article that talks about continued fractions doesn't make sense, because there are no quotients in the Euclidean algorithm, only remainders. I'll leave a note on the talk page of the article. — Carl (CBM · talk) 05:11, 12 March 2009 (UTC)

I think what is meant is the Euclidean algorithm gives a way to generate the continued fraction of a rational number a/b. This process essentially consists of taking the integer part (if the rational is > 1) and then taking 1 over the reciprocal of the fractional part and then repeating with the reciprocal. This can of course be done with an arbitrary real number, not just a rational. So given a real r, take the integer part, then take the fractional part and then take 1/reciprocal and repeat (take integer part...). --C S (talk) 05:48, 12 March 2009 (UTC)

Ditto rational numbers. They are both fields, so surely the idea of a gcd doesn't make sense - everything is a divisor of everything else (give or take 0). I've done the Euclidean Algorithm for integers, polynomials and the general case (I'm not sure what is meant by a "quadratic field" in this context - a quadratic extension of the integers (which wouldn't be a field), perhaps? Is that significantly different to the general case?). The EA is a very important topic and certainly deserves a good article written about it, but let's be clear about what it does first! --Tango (talk) 02:13, 12 March 2009 (UTC)

You can apply it with real inputs, insisting that the quotients be integers, and then the remainders are real and smaller than the divisor. It then runs forever iff the ratio of the two inputs is irrational. Michael Hardy (talk) 05:46, 12 March 2009 (UTC)

Sorry, I was careless in using the term "quadratic field"; I meant the ring of quadratic integers.

I'm glad you agree that the EA is an important article to be improved, and I hope that you'll contribute. I'm afraid you'll have to expect a few mistakes from me, since I'm not a mathematician, and I'm just beginning to think through the topic. If you can be patient with my mistakes, I'll be patient with your corrections. ;) More generally, I'll be grateful for the help of anyone at this WikiProject in bringing the article to GA. Proteins (talk) 04:31, 12 March 2009 (UTC)

Concept algebra

It has been raised in an AfD here that this article could do with an expert eye so I am asking for an editor to give it the once over thanks. BigDunc^Talk 20:27, 12 March 2009 (UTC)

Dyson's transform

Dyson's transform has been tagged for deletion 76.66.201.179 (talk) 05:51, 13 March 2009 (UTC)

Indeed. It's a badly written article. An article should not be deleted because it's badly written; it should be re-written. Should this article be kept? I can't tell, because I don't know what Dyson's transform is, and whoever wrote the article is evidently unable to explain it. If someone here knows something, could they rewrite it if it's worth keeping and then remove the "prod" tag? Michael Hardy (talk) 13:47, 13 March 2009 (UTC)

Done! I rewrote it and removed the PROD and the other maintenance tags. I'm not sure it deserves its own article, but it's not clear what it might be merged into. Several related topics are in Schnirelmann density but don't really belong there. --Uncia (talk) 20:03, 13 March 2009 (UTC)

Helping Simple English With Maths?

Hello there, I know that the Simple English Wikipedia does not have a good standing with many EnWP editors; I just tried to make the article on the Riemann hypothesis (on Simple) better, but I am not from hard-line, pure mathematics (but applied maths). Anyway, we would like to welcome any editors wanting to help us with mathematics-related topics. --Eptalon (talk) 12:55, 13 March 2009 (UTC)

WikiProject Council

Does anyone here have any interest in Wikipedia:WikiProject Council or Wikipedia:WikiProject Council/Assessment working group? Michael Hardy (talk) 16:41, 12 March 2009 (UTC)

I sometimes look at the council page, but I haven't participated much in the recent assessment discussions. I suppose I should find out what is happening with them and then make a summary here. — Carl (CBM · talk) 14:09, 15 March 2009 (UTC)

Template: WikiProject Mathematics

{{WikiProject Mathematics}} is broken after a recent bot update. 76.66.201.179 (talk) 05:50, 13 March 2009 (UTC)

It seems fine now. Template:WikiProject Mathematics should not be used; the correct name is Template:Maths rating (or Template:Math rating). The idea is to subtly remind people that the point of these is to assign quality and importance ratings. — Carl (CBM · talk) 14:07, 15 March 2009 (UTC)

Categories of categories

Perhaps someone could have a look at this cfd. There is some abuse of notation involved in the category structure – putting a category C at the bottom of an article X means 'X is a member of C'; putting a category C at the bottom of a category D usually means 'D is a subcategory of C'. However when we put A = Category:Categories named after criminals at the bottom of B = Category:Al Capone the meaning can only be 'B is a member of A' (not 'B is a subcat of A'). Of course I may be wrong about this and if so perhaps someone could explain my error to me. Occuli (talk) 16:32, 13 March 2009 (UTC)

What does this have to do with mathematics? Algebraist 20:24, 13 March 2009 (UTC)

If it spills over from criminals into Category:Category-theoretic categories it might start affecting us. —David Eppstein (talk) 21:12, 13 March 2009 (UTC)

I don't see any "named after" categories in the List_of_mathematics_categories. — Carl (CBM · talk) 00:23, 15 March 2009 (UTC)

We could always try starting Category:Categories named after category-theoretic categories... —David Eppstein (talk) 00:25, 15 March 2009 (UTC)

Article alerts

This is a notice to let you know about Article alerts, a fully-automated subscription-based news delivery system designed to notify WikiProjects and Taskforces when articles are entering Articles for deletion, Requests for comment, Peer review and other workflows (full list). The reports are updated on a daily basis, and provide brief summaries of what happened, with relevant links to discussion or results when possible. A certain degree of customization is available; WikiProjects and Taskforces can choose which workflows to include, have individual reports generated for each workflow, have deletion discussion transcluded on the reports, and so on. An example of a customized report can be found here.

If you are already subscribed to Article Alerts, it is now easier to report bugs and request new features. We are also in the process of implementing a "news system", which would let projects know about ongoing discussions on a wikipedia-wide level, and other things of interest. The developers also note that some subscribing WikiProjects and Taskforces use the display=none parameter, but forget to give a link to their alert page. Your alert page should be located at "Wikipedia:PROJECT-OR-TASKFORCE-HOMEPAGE/Article alerts". Questions and feedback should be left at Wikipedia talk:Article alerts.

Message sent by User:Addbot to all active wiki projects per request, Comments on the message and bot are welcome here.

Thanks. — Headbomb {^ταλκ_{κοντριβς} – WP Physics} 09:23, 15 March, 2009 (UTC)

I know this is an automated announcement, but people may not know that that this is essentially a duplicate of Wikipedia:WikiProject Mathematics/Current activity, except that the article alerts system relies on having talk page tags while the current activity system uses the ordinary category system on the articles themselves. So we probably do not need to subscribe to the article alerts system. — Carl (CBM · talk) 14:05, 15 March 2009 (UTC)

Knot theory FAC

Knot theory has been nominated for Featured Article. See Wikipedia:Featured_article_candidates/Knot_theory. --C S (talk) 10:45, 15 March 2009 (UTC)

recent edit to Wedderburn's little theorem

Can someone help me with this Talk:Wedderburn's little theorem, please? Ringspectrum (talk) 18:15, 15 March 2009 (UTC)

WAREL/DYLAN LENNON

The unmistakable behavioural patterns of Katsushi in Riemann hypothesis, as well as the choice of the topic, makes me believe that the user is a sockpuppet of our friend User:WAREL. Shall we do something about it? — Emil J. 12:36, 12 March 2009 (UTC)

I came to the same conclusion. Unfortunately, I can't block him myself since I reverted one of his edits. -- Jitse Niesen (talk) 13:11, 12 March 2009 (UTC)

Some editors are under the impression that Warel is a banned user. This doesn't seem to be the case (although I had thought so too). --C S (talk) 02:42, 13 March 2009 (UTC)

It doesn't seem so, although he has been blocked long-term multiple times. See Category:Suspected Wikipedia sockpuppets of WAREL, Wikipedia:Requests for comment/WAREL, Wikipedia:Administrators' noticeboard/IncidentArchive88#Indef block of WAREL/DYLAN LENNON, Wikipedia:Administrators' noticeboard/IncidentArchive126#User:WAREL is back, and Wikipedia:Administrators' noticeboard/IncidentArchive138#User:WATARU, etc.. —David Eppstein (talk) 03:08, 13 March 2009 (UTC)

Over at WP:Sockpuppet investigations, my impression is that accounts that cause this much trouble are usually blocked indefinitely. Are there diffs to show Katsushi acting like WAREL, for instance on Riemann hypothesis? Can anyone collect a set of diffs here that would be complete enough to justify a block by any random admin? (so that they don't have to go through all the talk archives of this page). Or, as an alternative does anyone have the patience to make a filing at WP:SPI? EdJohnston (talk) 04:12, 13 March 2009 (UTC)

Since peculiar edits to math articles have continued after a warning, with no response at all, I've blocked Katsushi indef as a sock of User:WAREL. I welcome review of this block. Other admins may modify the block as they think appropriate. EdJohnston (talk) 06:14, 19 March 2009 (UTC)

I found Katsushi basically easy to work with, and that his edits always had merit (but that a revert always left the article in a better state). His contributions to the Riemann hypothesis article both pointed out a deficiency in the given sources (though one that was trivially fixed with other common sources) and a useful source for the expansion of the divisor function article. In particular, I believe he did read talk pages and did modify his actions accordingly. I don't think many editors tried to discuss things with him, but those that did (either on his talk page or on the article talk page) did not get any easy to read response. I don't disagree with the block or the ban (especially of repeatedly editing the article without discussion), but I would caution that his edits do not appear malicious or horribly ill-informed. They are merely "peculiar", sometimes of questionable style, but most importantly unexplained. JackSchmidt (talk) 07:13, 19 March 2009 (UTC)

LaTeX to Wiki conversion

I haven't had a chance to try it yet, but this blog post (from the maintainer of the polymath wiki) concerning an automated tool for converting LaTeX-formatted documents to wiki-formatting looks like it could be of interest to editors here. —David Eppstein (talk) 21:08, 19 March 2009 (UTC)

mistake in Perfect map

"if the perfect image (image under a perfect map) of a certain space X is connected, then X must be connected." A counterexample is given in Examples and properties, 6.

Does anyone know if the statement becomes true if we add "the preimage of every point of Y is connected" (or something like that) as a hypothesis? Ringspectrum (talk) 06:10, 20 March 2009 (UTC)

Help wanted: documenting divergences between constructive and classical maths

On the talk page for Constructivism (mathematics) I wrote:

I have an idea that the article would benefit immensely from a more hands-on account of where classical and constructive mathematics diverge, organised on a thematic basis. The kind of thing I have in mind is to say that, say, in measure theory, how the accepting or rejecting AC gives different worlds, where classical measure theory is interested in the complexity of constructions of non-measurable sets, and constructive measure theory is concerned with things like integration of functions over notions of the computable real line. Doing this properly is well beyond my mathematical-recreations pay grade, though. I'd appreciate some help in coming up with a good set of topics. My initial ideas are:

1. The above bit on measure theory and Lebesgue integration;
2. Analysis and Specker's theorem;
3. Maybe there's something interesting in ideal theory and Buchberger's computable algebra?

This little enterprise might be of interest to folks not orbiting the constructive maths-think bubble. All help appreciated. It's probably best to reply on Talk:Constructivism (mathematics) — Charles Stewart (talk) 14:44, 20 March 2009 (UTC)

Manifold

There is an attempt to introduce mathematical jargon into the first line of our A-class article Manifold. Please, comment at Talk:Manifold. Arcfrk (talk) 17:58, 20 March 2009 (UTC)

Donsker's theorem

Can someone address the question I raised at talk:Donsker's theorem? Michael Hardy (talk) 11:58, 21 March 2009 (UTC)

I did. You are right (as usual). Please look now. Boris Tsirelson (talk) 17:11, 21 March 2009 (UTC)

A small lesson in math typestetting

Look at the way this article appeared BEFORE this edit. Someone intended a period at the end of the "displayed" TeX, which consisted of several lines in the "align" environment. The period was OUTSIDE of the <math> tags, and was slightly above one of the lines in the MIDDLE! Moral: TeX on Wikipedia doesn't work like TeX in NORMAL use. Michael Hardy (talk) 23:12, 21 March 2009 (UTC)

Duality (mathematics) collaboration

I remember an attempt -- quite successful, IMO -- to bring an article with more involved mathematics, namely homotopy groups of spheres, to a decent (GA) standard. I'd like to propose another such collaboration, and would be glad if many people join in. The topic I propose is duality (this is waiting as a COTM, too), so something (m)any of you will have encountered, but it looks like a subject where having contributors from many mathematical backgrounds is highly beneficial (more so than as usual). Who is willing to join in? I think a reasonable aim would be Good Article level. Jakob.scholbach (talk) 17:37, 10 March 2009 (UTC)

I think it's a great aim, I will try to help. But I have a question. It's currently a bit like a list of subjects under the heading "duality". It seems one main goal should be to explain how all these dualities are really coming from the same idea, namely that a linear functional can be identified with a vector. At least I think I haven't seen any duality theory where the main idea was not this. Has anyone? --GaborPete (talk) 17:20, 17 March 2009 (UTC)

Sets are dual with their complements, and the set intersection and union operators are dual; this is analogous to the logical duality of ∧ and ∨. This duality does not seem to me to have any obvious connection with vectors and functionals. The article mentions dualities between high- and low-dimension components of polyhedra, graphs, and planar configurations. I wonder if explaining these in terms of vector spaces and functionals would really be to the point. Not mentioned on the page are logical dualities between ∀ and ∃, and between certain pairs of modal logical operators such as ⋄ and □. I would be fascinated and astonished to see these explained in terms of vector spaces.

I happened to read (Gowers, Timothy (2008), "III.19 Duality", The Princeton Companion to Mathematics, Princeton University Press, pp. 187–190) last night, and was interested to see that Gowers presented no general theory or explanation of duality either. —Dominus (talk) 19:05, 17 March 2009 (UTC)

There is a (non-obvious and somewhat tenuous) connection between logical/Boolean duality and vector space duality, via linear logic. But even so, it is quite a stretch to claim that De Morgan's laws "really come from" linear algebra ... –Henning Makholm (talk) 20:28, 17 March 2009 (UTC)

There might be an interpretation of set-theoretic duality via vector spaces using the field with one element. But I'm kind of doubtful because duality in the sense of vector spaces never changes the dimension, whereas the complement of a set usually has a different cardinality from the original set. (It doesn't help that the foundational stuff surrounding F₁ is still very mysterious.) Ozob (talk) 21:40, 23 March 2009 (UTC)

It also occurs to me that the relationship between provability and satisfiability has probably also been considered a duality. —Dominus (talk) 20:56, 17 March 2009 (UTC) (Addendum: it has. —Dominus (talk) 21:02, 17 March 2009 (UTC))

Panos Papasoglu on AfD

I don't know why Jitse's bot hasn't been picking this one up for the current activity page, but: Panos Papasoglu, an article on a Greek geometric group theorist, has been up for deletion for a few days now already. There's still time to comment before it closes, but probably not for much longer. Discussion is here. —David Eppstein (talk) 03:43, 23 March 2009 (UTC)

Jitse's bot seems to have been asleep for a few days. Michael Hardy (talk) 07:06, 23 March 2009 (UTC)

Logarithmically-spaced Dirac comb

Logarithmically-spaced Dirac comb has been prodded for deletion . 76.66.193.69 (talk) 06:07, 24 March 2009 (UTC)

Catalog of articles in probability theory versus List of probability topics

In the end of 2008 I have found the List of probability topics in a somewhat neglected state; see Talk:List_of_probability_topics#A:_Articles_missing_from_the_List_of_probability_topics and Talk:List_of_probability_topics#Organize_the_list. I tried taking care of it, but was still unhappy. Thus, in December 2008 I have created a new version named Catalog of articles in probability theory. Just look on both and see the difference. It was suggested once (in December 2008) to merge the new list into the old one, but this did not happen, still.

It seems clear to me that this new experimental format has some advantages (at least in this case); however, it has an important drawback: it is computer-assisted, thus, it should not be edited manually. Instead, one should edit its source (for now, see User:Tsirel/Catalog source; ultimately it should be "Talk:Catalog_of_articles_in_probability_theory/Source") and call a bot that formats the source and rewrites the "Catalog". Such a program is written (see the source User:Tsirel/Bot code and parameters User:Tsirel/Bot parameters); for now, I run it myself. Ultimately it should be callable by anyone, similarly to the "mathbot" by Oleg Alexandrov, instrumental to both lists of probability articles, "traditional" and experimental (and to many other mathematical lists, of course). See also my exchange with Oleg Alexandrov User_talk:Oleg_Alexandrov#Another_bot_needed?

Thus, I am asking approval of my new bot, CataBotTsirel, see Wikipedia:Bots/Requests_for_approval/CataBotTsirel. Naturally, the Bot Approvals Group is wondering whether WikiProject Mathematics finds my experiment interesting, or not. Your comments are welcome! Boris Tsirelson (talk) 08:37, 16 March 2009 (UTC)

The bot is already approved for trial (7 days); I use it, see User talk:CataBotTsirel. You are welcome to edit the "Catalog", but indirectly, as explained in its lead. It may happen that you want edit some headings etc; in this case, edit User:Tsirel/Bot parameters (respecting the syntax). Boris Tsirelson (talk) 20:59, 16 March 2009 (UTC)

I find your catalog well designed (somewhat complementary to the old list; I'd oppose a simple merger). I'd support using the bot on regular basis. At some stage, however, you may want to devote some time to document the "protocol" to assure that anyone can understand it and modify the page (via the source) and anyone can easily understand the codes/abbreviations used on the page. ptrf (talk) 09:21, 18 March 2009 (UTC)

Thank you. Indeed, the explanations should be better. But I guess that you do understand all that, and maybe you can write the explanations better than me! (Not that I am so lazy, but really, the developer is often not the best person to explain.) I am the initiator, not the owner of all that. (Except for the bot, of course; regretfully, for now I am its owner.) Boris Tsirelson (talk) 09:38, 18 March 2009 (UTC)

I'll think about it (please be patient, though). ptrf (talk) 10:53, 18 March 2009 (UTC)

The bot is on trial for 7 more days. Boris Tsirelson (talk) 11:44, 25 March 2009 (UTC)

Help explain proof of Fermat's Last Theorem

Please help with Wiles's proof of Fermat's Last Theorem. I am trying to use Wikipedia's strengths to make this a really useful article for the non-professional.--Lagelspeil (talk) 09:36, 16 March 2009 (UTC)

Looks basic enough to me without removing the really important bits. To write a really good article, you probably have to know the proof and understand it deeply. That is to say, you know the crucial bits and can explain them in a relatively easy manner (without going into complicated algebraic geometry). But really, many professionals want to get something out of the article so try not to make it too trivial. --PST 11:53, 16 March 2009 (UTC)

I suspect that the professionals are not in need of Wikipedia. They can get through the Wiles paper on their own. It is really for the college scientist or engineer (or bright and determined high school student) that Wikipedia should aim for. The problem is that the Wiles style aims for the professional and leaves the non-professional to grope around in order to recognize this or that notation. Between that, the NOVA/Horizons program and other on-line resources, what the next level (downwards) of reader needs is a key to explain that when you encounter this or that notation, it points to a specific English-word subject area and WP page. Of course, it is the very rare layman who has any new feedback to offer the article, but I am trying to play to Wikipedia's strengths in helping one to actually plough or at least skim through the entire paper and develop, if not a sense of mastery, then a least a sense of familiarity. That is one thing that an encyclopedia should do: ask the young or flexible reader: should perhaps you become a professional in this subject area? That is what sharing knowledge should be about. The implied message should be: "Don't stop. Keep going. Here is some help."--Lagelspeil (talk) 04:30, 17 March 2009 (UTC)

Believe it or not, many professionals whose expertise is not in precisely the same area of mathematics find Wikipedia useful, as a gentler way of starting to learn about subjects that they are not already familiar enough with to read the technical papers easily, and also as a way of finding out which technical papers to read and which ideas in a subject are the important ones. Please don't make it less useful for them in your attempts to make it more useful for others. You are not the only target audience. —David Eppstein (talk) 05:10, 17 March 2009 (UTC)

Indeed; and I am an example. However, what about peaceful coexistence of an "easy" part and a "hard" part of an article? Boris Tsirelson (talk) 06:40, 17 March 2009 (UTC)

Not unlike the "progress of previous decades" and "Wiles proof" sections already present in the article? —David Eppstein (talk) 07:02, 17 March 2009 (UTC)

I most certainly agree. If professionals are not in need of Wikipedia, then who writes the articles around here? --PST 23:42, 17 March 2009 (UTC)

Lagelspeil, although I like your aim, I think there are some serious problems with your edit. First of all, that paragraph in Wiles proof is certainly not at the right place: the paragraph after it is a direct continuation of the paragraph before it, so your paragraph is very disruptive. Then, I'm not sure that the list you are providing is helpful for anyone. It is a quite random collection of links to some of the basic notions used in the article. lt's something like having a link to every single English letter in the middle of an article on a Shakespeare drama. I would say that a more natural way for a non-professional reader to explore the math background of such an article is to read the leading paragraph, follow the links from there to larger and more basic topics, and so on. Of course, the leading paragraph has to be carefully written for this. And, of course, it still would be very valuable to provide a good popular science account of the proof, for example explaining how geometry comes into the proof and what type of geometry that is. --GaborPete (talk) 07:32, 17 March 2009 (UTC)

Let me add that my analogy with the Shakespeare article makes sense only if it's on the Chinese wikipedia, say. There the English letters would contain non-trivial information, but still, it wouldn't be the right place for them. --GaborPete (talk) 17:10, 17 March 2009 (UTC)

Well, this issue could more readily be settled if an arithmetic geometer were available to comment on the article (rather than on the overall state of Wikipedia). Maybe User:RobHar? The article in question is worthy, and could use improvement on both the "high" and "low" ends. Acannas (talk) 00:47, 18 March 2009 (UTC)

I have incorporated some of your feedback. Yes, some of the text was choppy because it was a cut-and-paste merge of the text we had in the FLT and Wiles articles. Both of those other two articles now have a much more focused feel to them. I have put in a final section called a "Reading and notation guide" so that the motivated reader can ramp up to the 100-pager with some expert reviews. Still, it is justified to give the naive reader some warning that they are embarking on a somewhat long road from knowing little-to-nothing about abstract algebra and getting to understand some parts of the proof. Some know-it-alls will attempt it, just like Mt. Everest.--Lagelspeil (talk) 14:39, 25 March 2009 (UTC)

AfD Elegant Exponents

I nominated Elegant Exponents for deletion. A couple of people on te discussion in WP:Articles for deletion/Elegant Exponents have talked about merging the useful content into exponentiaion. I don't think there is any useful content and wonder why a person expended effort on it in it first place, but I'm raising it here as stranger things than my being wrong have happened before now. Dmcq (talk) 18:23, 24 March 2009 (UTC)

Calculus on manifolds (disambiguation)

Calculus on manifolds was until moments ago a redirect to differential geometry. I"ve changed it to a disambiguation page listing that and also differentiable manifold and Calculus on Manifolds (book). Michael Hardy (talk) 13:43, 25 March 2009 (UTC)

.....and then I found that Calculus on Manifolds (with a capital initial "M") redirected to differential geometry, despite the fact that capitalization of the "M" matches the book title. I've now redirected it to calculus on manifolds, the new disambiguation page. Michael Hardy (talk) 13:46, 25 March 2009 (UTC)

Problematic article

The article on supernatural numbers confuses two very separate notions (formal products of infinitely many primes, versus elements of nonstandard models of arithmetic). Not sure what is the best course of action. --Trovatore (talk) 17:10, 26 March 2009 (UTC)

Take out the stuff on generalized natural numbers, if that's what the formal products are actually called, and make a separate article. Both will be stubs, but so be it. Septentrionalis PMAnderson 22:58, 26 March 2009 (UTC)

Actually I think it's the other way around — Hofstadter's terminology (for nonstandard natural number) is apparently unique to him (and those quoting him), whereas Algebraist finds that the infinite-formal-product meaning is actually in use. --Trovatore (talk) 00:06, 27 March 2009 (UTC)

Going by Google Books, 'generalized natural number' seems to not be much used, while most authors just call all the formal products supernaturals (even the ones that correspond to naturals). Algebraist 00:16, 27 March 2009 (UTC)

Frequently viewed math articles

The list Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Frequently_viewed/List is quite interesting, I think, but outdated by roughly a year. Could somebody update that list? Jakob.scholbach (talk) 12:40, 28 March 2009 (UTC)

That somebody would probably have to be me. I do know it's somewhat outdated. I'll see what I can do, but it may be a few days. I have a sense that the vast majority will stay the same, which is why I don't think there's a need for any sort of automated updates. — Carl (CBM · talk) 12:57, 28 March 2009 (UTC)

Thanks muchly; and do take your time. You are right, it's not at all urgent. Jakob.scholbach (talk) 13:32, 28 March 2009 (UTC)

Frank Grosshans

The article titled Frank Grosshans is

• a near-orphan (only two other articles link to it); and
• being considered for deletion.

If you offer an opinion in the deletion discussion, don't just say Keep or Delete; also give your arguments. The discussion is here: Wikipedia:Articles for deletion/Frank Grosshans. Michael Hardy (talk) 03:34, 31 March 2009 (UTC)

Just barely not a disambiguation page?

In the article titled Mollweide's formula, I wrote:

Mollweide's formula can be used to check solutions of triangles.

I wanted to link to solution of triangles or whatever the suitable title is, but we had no such article.

Why should there be such an article when we already have law of sines and law of cosines, and those two cover it all, and in addition we have law of tangents?

A new article just to link to all of those seems a bit like a disambiguation page, since the articles it links to are where the substantial material is.

But it seems to me there could be a dozen or so articles that refer to the concept of solution of triangles, where it would be appropriate to link to an article explaining what that is, so the new not-quite-disambiguation page should be there. And now it is. Michael Hardy (talk) 23:36, 31 March 2009 (UTC)

Definition of curl

There is an ongoing dispute in the Curl (mathematics) article over the proper definition of the curl (see Talk:Curl (mathematics)#Definition of Curl). I imagine that an outside opinion would be helpful. Jim (talk) 05:33, 1 April 2009 (UTC)

Apr 2009

Wranglers

The 2nd wranglers cfd has been closed as delete and the closer has declined an invitation to re-open. Perhaps someone would like to start a DRV on both the wranglers categories. The first was deleted on the argument '1. This is a valedictorian category. 2. We have deleted a valedictorian category (risible cfd). 3. So we must delete this one.' Occuli (talk) 14:49, 23 March 2009 (UTC)

There is now a DRV on the categories for Wranglers, a travesty mathematicians will doubtless wish to remedy. Occuli (talk) 13:55, 24 March 2009 (UTC)

It was closed, with the decision being to restore the categories. They now exist again at Category:Senior wranglers and Category:Second wranglers. One could quibble about the capitalization, but it was a quibble of that nature that led to the original deletion... —David Eppstein (talk) 00:03, 1 April 2009 (UTC)

Is there a central discussion for these categories somewhere? Moving them to the capitalized names is a trivial task that only requires a template to be set up. Bots will handle the actual category changes on the pages. Tothwolf (talk) 19:40, 1 April 2009 (UTC)

Yes, Categories for Discussion. That's exactly what set off this whole situation — a trivial recapitalization request two months ago for these two categories morphed halfway through into a suggestion that they be deleted, because the people who regularly participate in the discussions at CfD are not mathematicians and didn't understand the difference between this honor and being selected as valedictorian of one's local high school. And they probably still don't, so I would urge caution in trying it again. —David Eppstein (talk) 20:37, 1 April 2009 (UTC)

While we're on the topic, I see we have a page List of Wranglers of the University of Cambridge. This is not in fact a list of Wranglers (of whom there are a great many, most of whom, such as myself, are not notable) but rather a list of Senior and Second Wranglers. Should it be moved to List of Senior and Second Wranglers of the University of Cambridge, or would that be too clunky? Algebraist 20:45, 1 April 2009 (UTC)

Well, yes, but I meant is there a central discussion location outside CFD/DRV? I could set up the templates to move the articles over to the capitalized names but I wouldn't want it to catch anyone off guard or anything. Tothwolf (talk) 20:48, 1 April 2009 (UTC)

No, I don't think there is. Algebraist 20:51, 1 April 2009 (UTC)

(break)
Ok, here are links to the various CfD and DRV discussions that I could find:

• CfD 2008-01-16 – proposed deletion, relisted 2008-01-16
• CfD 2008-01-29 – relist of 2008-01-16, keep
• CfD 2009-01-27 – proposed rename/delete, relisted 2009-02-05
• CfD 2009-02-05 – relist of 2009-01-27, delete
• CfD 2009-03-01 – proposed deletion, delete
• DRV 2009-03-24 – restore

I also uncovered this discussion:

• CfD 2008-01-16 – Category:Tripos Wranglers

I can't help but wonder if the Tripos Wranglers category should have gone to DRV as well?

If no one here objects, I'll be WP:BOLD and point the soft redirects the other way so the bots will recategorize articles under Category:Senior Wranglers and Category:Second Wranglers.

--Tothwolf (talk) 23:23, 1 April 2009 (UTC)

I'm not sure if we really need to go through another round of discussion for a simple renaming. Is there any controversy about the capitalisation change? If not then an application of WP:IAR could be appropriate. Total number of articles is within the scope of WP:AWB so don't need to get bots involved. --Salix (talk): 16:32, 2 April 2009 (UTC)

Tothwolf: I don't think Category:Tripos Wranglers should be restored. Being a high-ranking wrangler is important (or was, while they were still ranked). Being a plain wrangler is no more important than getting a first in any other degree, and as far as I know this has always been the case. Algebraist 17:16, 2 April 2009 (UTC)

Algebraist, well, I wondered about it because it was deleted in pretty much the same manner as the other two categories and was listed in the 2008-01-16 CfD which was also where Senior wranglers and Second wranglers were first listed. The Wrangler (University of Cambridge) and Wooden spoon (award) articles both cover the third degree and just going by Wrangler (University of Cambridge) being in the top 3 was a very high achievement. Tothwolf (talk) 20:13, 2 April 2009 (UTC)

The top three, maybe, but all of them? I'd want to see some sources for that being important. Algebraist 00:30, 3 April 2009 (UTC)

I'm out of my element here with the terminology and your reply has me confused. Based on what I saw in the CfD archives I thought Category:Tripos Wranglers had previously been used for third-ranking wrangler articles but maybe this wasn't the case? Was this category actually used much more broadly? Tothwolf (talk) 01:32, 3 April 2009 (UTC)

See Cambridge Mathematical Tripos. My understanding: "tripos" is the name of the exam; a "wrangler" is anyone who takes the exam. A "third wrangler" would be someone who places third in the exam, but a "tripos wrangler" is just a redundant way of writing "wrangler". —David Eppstein (talk) 02:51, 3 April 2009 (UTC)

Ah, it would seem to be redundant to Category:Senior Wranglers and Category:Second Wranglers then. Unless there happen to be lots of existing articles that wouldn't fit into those two categories I can't really see a need for it. A Third Wranglers category might be useful for navigational purposes depending on the number of articles though. Tothwolf (talk) 03:56, 3 April 2009 (UTC)

Salix, exactly. I just wanted to make sure I wasn't misreading or overlooking something before I made any changes and I also wanted to make sure people involved with these knew what was going on so no one would be surprised. Tothwolf (talk) 20:13, 2 April 2009 (UTC)

 Done Now we just have to wait for the bots to recategorize the articles. Usually it only takes a day or two but sometimes it takes a little longer. Tothwolf (talk) 00:24, 3 April 2009 (UTC)

Euclidean algorithm and Fermat's Last Theorem

I'm still hoping to interest the talented mathematicians here in improving the Euclidean algorithm article. I've had a few nibbles, but basically I've been alone in transforming this into this. Does anyone want to help significantly before I submit it to GAN, and thence to FAC? I've more that I want to add, of course, but a fellow editor or two would make it more fun. It's an important article, don't you agree?

It's wonderful to see that Wiles's proof of Fermat's Last Theorem is getting attention, but please let me call your collective attention to Fermat's Last Theorem itself? It seems as though it could be improved significantly with relatively little effort from the people here. It's a rewarding article, since the problem is one of the most engrossing of the last four centuries, one that has inspired much of algebraic number theory (the current WPM collaboration) and captured the public's imagination. I'll be glad to work on it myself, in a few weeks, but as a biochemist, I feel poorly qualified, especially relative to the many mathematicians here. Proteins (talk) 07:41, 28 March 2009 (UTC)

Recently Lagelspeil has been undertaking the huge task of working on an article on the mathematics of Wile's proof. As part of his/her work, he unfortunately deleted significant chunks of the FLT article, including the story behind Wiles and his proof, and a brief overview of his approach. Whether or not there is a separate in-depth article on the Wiles proof, it is clearly inappropriate to remove this content. I have restored these deletions and provided a link to the more in-depth math article. --C S (talk) 08:17, 28 March 2009 (UTC)

I don't think anyone will be ashamed if you bring up the FLT article to FA status. Rather, I would imagine many (including myself) would be highly pleased. Indeed, I don't seem to have as much time as I thought for the knot theory FA nom and had to withdraw it. One thing it lacks is a brief section on applications in biology (including understanding actions of enzymes on DNA and using knot invariants as protein shape descriptors). I wish someone with a good knowledge of biochemistry would add one. --C S (talk) 08:33, 28 March 2009 (UTC)

I'll be delighted to help you as best I can with the knot theory article. By lucky coincidence, I have a little collection of knot-theory articles on proteins and nucleic acids. (I'm not sure whether anything has been published on polysaccharides.) Give me a few days to dig them up. And thank you for taking my unhappily critical comments about the FLT in the best possible way; I'll be happy to help in making FLT a good article, hopefully with your and others' help. Proteins (talk) 19:32, 28 March 2009 (UTC)

Misc. comment: Lagelspeil has been blocked as a returning banned user, so don't expect any further work from him/her on Wiles' proof of the FLT. --C S (talk) 00:40, 3 April 2009 (UTC)

Indefinite sum and indefinite product

Does anyone have a view on the two new articles List of indefinite sums and List of indefinite products ? I have found some (minimal) sources that use the term "indefinite sum" to mean the inverse of the forward difference operator - enough for me to give this article the benefit of the doubt - and added them to the article. But I can't find any useful sources for the term "indefinite product", and I am beginning to wonder whether this is a neologism/OR. I have left a note on the author's talk page. Gandalf61 (talk) 15:55, 1 April 2009 (UTC)

This is definitely not original research; I've seen it in the context of computer algebra. For example the Mathematica documentation for the Sum and Product functions uses the respective terms "indefinite sum" and "indefinite product". Googling gave this hit in a book about Maple. Fredrik Johansson 16:51, 1 April 2009 (UTC)

Thanks for the reference. I've added it to the article. Charvest (talk) 17:11, 1 April 2009 (UTC)

The term "indefinite sum" seems self-explanatory, in view of the way the term "indefinite integral" is used. Just do for sums what "indefinite integral" does for integrals and that's it. Michael Hardy (talk) 15:05, 2 April 2009 (UTC)

Agreed, but being self-explanatory does not, AFAIK, obviate the the requirement to conform to WP:V by providing reliable sources. Happily, this requirement has now been met for both articles, and they have also been given better titles and some context. Thanks to everyone who helped. Gandalf61 (talk) 09:05, 3 April 2009 (UTC)

Complexity

I find maths very interesting, I am trying to understand many more complex aspects of maths and in my mind this is the best website to use. However, sometimes I feel you need a Masters degree in Calculus to understand many of the pages. Somehow even the most simple articles are turned into mind blowing formulae and all sorts of complicated explanations. On many articles, there are no examples that actually involve numbers to demonstrate somethings use. For example, I find functions hard to understand, I thought I had the grasp of it after reading a book so I came onto here and after reading I am now more confused. It's easy to forget this is an encylopaedia and sometimes behind all of the info there still needs to be a simple, easy to understand description. 95jb14 (talk) 18:21, 2 April 2009 (UTC)

That's a fair criticism. I also think that many articles could use more/better illustrations.

Did you have any particular examples in mind?

CRGreathouse (t | c) 19:05, 2 April 2009 (UTC)

Thanks for responding. These are a few examples: Integral (too complex in intro, lacks example), Function (mathematics) (same reason) and Limit (mathematics). I won't be on in about ten minutes after writing so feel free to reply but I probably won't respond before tomorrow. If need be, leave a comment on my talk page - this could be a long discussion!!!! 95jb14 (talk) 19:56, 2 April 2009 (UTC)

Readability for basic mathematics articles is something that we need to work on. It can often be difficult in an article to strike the right balance between formalism and intuition, between generality and important special cases, and between advanced and elementary viewpoints. The authors of the function (mathematics) article have clearly worked very hard to strike a balance between all of these competing objectives, and they've done an admirable job, but the result is a huge conglomerate of competing ideas and viewpoints struggling for attention. I'm not sure that anyone reading that article would be able to understand it unless they were already familiar with all of the different concepts of a function.

My attitude towards these problems is that it often works well to have an elementary article and an advanced article on the same topic. For example, about a year and half ago I wrote an article entitled Euclidean subspace that covers subspaces of Rⁿ from an elementary standpoint. This makes it possible for the article on linear subspaces to be primarily about subspaces of an abstract vector space, while still having an article that is accessible to non-mathematicians.

I suspect that the same thing would work for the function (mathematics) article: some of the content could be split off into a function (calculus) article, which would present functions from the elementary standpoint common in calculus classes. In addition to providing a readable article for those who don't know anything about sets, I imagine the main function (mathematics) article would be better off if it didn't have to struggle so much to include both elementary and advanced ideas. Jim (talk) 18:44, 5 April 2009 (UTC)

I like the idea of two (or even more) levels. But I wonder, could these levels coexist in a single article? (Simple - first, of course.) Boris Tsirelson (talk) 19:12, 5 April 2009 (UTC)

Splitting an article into an "easy" and "hard" version is often a bad idea. Here are some reasons:

• It leads to duplication of effort to maintain both
• It makes it hard for other people to figure out which article to link to. Readers following links are likely to end up in the wrong place.
• The "easy" version often ends up reading more like a textbook than an encyclopedia article. We aren't supposed to "teach" like a textbook would.

It's often better to just make the introductory parts slightly more accessible and put the truly general or esoteric stuff at the end, even if it means that the initial parts are not fully general. — Carl (CBM · talk) 00:38, 8 April 2009 (UTC)

In general, I don't think it's reasonable to expect that a reader with no idea whatsoever about a topic can pick up an article in an encyclopedia and understand exactly what is going on. This has never been true in other encyclopedias, like Brittanica, and those have a much more elementary presentation than we do. it is not our role to provide numerous worked-out examples; even proofs should only be included when there is really encyclopedic interest in them.

Of course articles, like function (mathematics) should be written to be as accessible as possible – but not any more accessible than that. Readers should not expect wikipedia to replace a good textbook, because the role of any encyclopedia is to provide an overview for people who have a vague idea what is going on, and provide a reference for people who know a topic but need to check a particular fact. — Carl (CBM · talk) 00:38, 8 April 2009 (UTC)

I recall an engineer that told me: some engineers succeed to do, others succeed to explain convincingly, why they could not do. :) That was rather a joke, but seriously: Wikipedia is not a firm; if no one volunteers something (say, examples or explanations), it cannot be enforced. On the other hand, given that Wikipedia has no deadline and a lot of volunteers, assume that some want to explain. Should they be discouraged? Or even prevented? Boris Tsirelson (talk) 05:47, 8 April 2009 (UTC)

Speedy deletion

The article Steven Roman has been tagged for speedy deletion if anyone wants to comment. Charvest (talk) 22:36, 5 April 2009 (UTC)

I've untagged it. It looks reasonably likely to pass a full AfD if it comes to that. —David Eppstein (talk) 23:13, 5 April 2009 (UTC)

thankyou Charvest (talk) 09:28, 6 April 2009 (UTC)

On a related subject, Yousef Alavi has been proposed for deletion. I'm not certain he passes WP:PROF, so I haven't unprodded his article myself, but others may want to take a look. —David Eppstein (talk) 20:57, 7 April 2009 (UTC)

Unprodded. "Yousef Alavi" OR "Y Alavi" "graph theory" gets a high number of hits on google web, google books and google scholar. Charvest (talk) 21:16, 7 April 2009 (UTC)

Herbrand's theorem

I stumbled upon this article and noticed it is missing a math ratings template. Thanks! momoricks (make my day) 07:10, 8 April 2009 (UTC)

Aliquot

I've been engaged with a bit of a dispute with Milo Gardner on Aliquot regarding whether his additions concerning Egyptian fractions are sufficiently relevant to include in the article. More eyes would be welcome. If there's discussion of the issue it should probably be on the talk page there. —David Eppstein (talk) 17:36, 8 April 2009 (UTC)

J. Michael Steele

Is he notable enough? He claimed that he invented shattering, which is not true. At best, he and his advisor were the first who used the term shattering in his PhD dissertation in 1975 in relation to the process defined by V&C 6 years earlier. Are there any other accomplishments which necessitate presence of the article about this mathematician? (Igny (talk) 17:02, 10 April 2009 (UTC))

The named professorship is an automatic pass of WP:PROF #5. We don't have to look for notability ourselves; the committee that gave him that title has already done the looking for us. But if you want a better answer, his six books and papers with over 100 citations in Google scholar (ignoring the antipyrine one which appears to be by someone else) would probably be a good place to start. Judging by my past experience with AfDs of academics, those publications would very likely be enough to give him a pass of WP:PROF #1, and the presidency of IMS #6. Any single one of those criteria would be enough to keep the article. —David Eppstein (talk) 17:07, 10 April 2009 (UTC)

Ok, ok you convinced me. Two points: this article is more of a stub then because it lacks details about his accomplishments. Second point, there is a significant number of professors who got honorable titles of various degrees, likely numbered in thousands in USA only. I could name a few from my department who are distinguished enough and who do not have an article on WP. (Igny (talk) 17:29, 10 April 2009 (UTC))

So why not write more articles on equally-deserving academics who are not properly represented here, and/or fix up this one to better represent his accomplishments? —David Eppstein (talk) 17:41, 10 April 2009 (UTC)

(a)I do not know much about Prof. Steele. to contribute, (b) I did not want to fight AfDs which I expected to follow. (Igny (talk) 18:05, 10 April 2009 (UTC))

History of matrices

I'm currently trying to write a good article on matrices. One of the still weak points is the history section. Does anybody know a good reference for this topic? Thanks, Jakob.scholbach (talk) 20:09, 10 April 2009 (UTC)

Try Matrices and determinants and Thomas Muir: History of determinants r.e.b. (talk) 20:28, 10 April 2009 (UTC)

Jakob, I think you can read French-language texts. Try Les matrices : formes de représentation et pratiques opératoires (1850-1930) which seems complete, with a lot of sources, some of them in English. --El Caro (talk) 07:16, 11 April 2009 (UTC)

Poll: autoformatting and date linking

This is to let people know that there is only a day or so left on a poll. The poll is an attempt to end years of argument about autoformatting which has also led to a dispute about date linking. Your votes are welcome at: Wikipedia:Date formatting and linking poll. Regards Lightmouse (talk) 11:45, 11 April 2009 (UTC)

Save this article!

Please forgive my complete lack of familiarity with mathematics on Wikipedia, but the article Internal_-_Proof:_Orthogonality_of_Solutions_to_the_General_Sturm-Liouville_Equation looks like it could be deleted, even though it (looks to me like) it contains some salvageable information. Could someone more familiar with the area take a look? Cheers, - Jarry1250 ^{(t, c)} 16:07, 11 April 2009 (UTC)

I moved this to Orthogonality of solutions of the general Sturm–Liouville equation, and then someone deleted the new redirect. Michael Hardy (talk) 16:24, 11 April 2009 (UTC)

• Assume user mistake. Now at User:Dnessett/Proof: Orthogonality of Solutions to the General Sturm-Liouville Equation. — RHaworth (Talk | contribs) 16:27, 11 April 2009 (UTC)

I am working on the markup for this proof (I am new to Wikipedia and forgot to prepend the page with my account name). This proof is not yet properly typeset, but is closer than the material mistakenly put into the general Wikipedia namespace. When it is ready to go, I will make a proposal to create a page for the proof and link the Sturm-Liouville page to it. I am also working on the markup for a proof of the orthogonality of Associated Legendre Functions for fixed m. (see separate entry on this talk page). Dnessett (talk) 17:32, 11 April 2009 (UTC)

Polynomial recurrence

Polynomial recurrence has been prodded for deletion 76.66.193.69 (talk) 06:54, 25 March 2009 (UTC)

I added a little to the article mentioning Somos sequences (a different subject, one that I think we should have an article but don't now, and one that is an example of the type of recurrence described by the polynomial recurrence article). However I haven't unprodded it yet because I'm not convinced this is important terminology. —David Eppstein (talk) 18:27, 26 March 2009 (UTC)

A big problem with this article is its title. "Polynomial recurrence" is a well-known non-trivial notion in Ergodic Ramsey Theory. Look at Vitaly Bergelson's website (math.ohio.edu), for example. In contrast, the definition of this article is a trivial one, probably not deserving a separate name and article. At least, the title should be changed. Polynomial recursion would be much better, I think. A bit of a problem is that I see there exist some more papers using the term "polynomial recurrence" in this meaning... So maybe a disambiguation page is necessary? --GaborPete (talk) 06:01, 3 April 2009 (UTC)

"Recursion" would be quite incorrect. This is about recurrence relations. But whether it deserves to be separate from the main recurrence relation article is not obvious to me; I'm leaning towards a merge. —David Eppstein (talk) 06:50, 3 April 2009 (UTC)

Wow. I have used "recursion" for recurrence relation in all my life, without having heard (or noticed?) the expression "recurrence relation"... It might be the influence of my Hungarian mother tongue (rekurzió), but it's still strange, given that I have been working in North America for 8 years now (with degrees from Cambridge, UK, and Berkeley, CA). Anyway, I vote for this article to be merged into recurrence relation. But is it OK to do it without a redirect? "Polynomial recurrence" should really be about Ergodic Ramsey Theory, I think, but I'm biased, since I'm interested in that area. --GaborPete (talk) 09:00, 3 April 2009 (UTC)

To David Eppstein: A recurrence relation is one way of defining a primitive recursive function. So the use of "recursion" is appropriate. JRSpriggs (talk) 12:56, 3 April 2009 (UTC)

I too have encountered "recursion" in this sense often; in particular the terms "recursion equation" and "recursive sequence" seem fairly frequent. My impression was that it's old-fashioned, and "recurrence" is more common and what we should call it now. Shreevatsa (talk) 13:16, 3 April 2009 (UTC)

Perhaps my greater care at distinguishing "recursion" from "recurrence" comes from my computer science background. But to me, "recursion" is a computer programming concept involving subroutines that call themselves. There are no computer programs, no subroutines, in a recurrence, only an equation relating certain values of a sequence to certain other values of the same sequence. One can trivially construct a recursive algorithm to compute the values of a recurrence, but it's usually the wrong way to compute them (dynamic programming is much more efficient). —David Eppstein (talk) 14:20, 3 April 2009 (UTC)

Yes, I know — I should have mentioned that I too, since learning programming, have always hated the use of "recursion" for recurrence (but that I've encountered it sufficiently often to hate it!). In my experience, this use of "recursion" (which is not a reference to the computer programming concept, or to a method for computing the values) is mostly found in old books written long before computer programming was common (and in some translated books). I agree that Wikipedia (and everyone else) should, to avoid confusion with computer programming (but note that the recursion article talks of other things too), not use "recursion", but the more current term "recurrence" — was only explaining why "recursion" might be familiar to User:GaborPete and yet seem incorrect to modern US readers. Shreevatsa (talk) 15:03, 3 April 2009 (UTC)

Well, I find it quite strange that although recurrence relations are much closer to algorithmic recursion, recursive definitions and recursive sequences than to recurrence in dynamical systems and probability, this closeness for you is a reason for calling them differently, rather than similarly. Also from the point of view of English word endings: recursion is a product of something recursive, while recurrence is the state of being recurrent. Of course, one could equally say that the defining relation of a recurrence relation is 1. a recursive relation, or 2. a recurring relation, but then why "recurrence relation" and not "recurring relation"? Anyway, I know I won't change this. But according to google, my version also seems well-established (both in research papers and textbooks), so you shouldn't forbid "linear, polynomial, non-linear recursions". --GaborPete (talk) 03:53, 13 April 2009 (UTC)

Given all this discussion, what should we do with polynomial recurrence? Merge the article to recurrence relation, then a disambiguation page? I volunteer to write the ergodic theory version. --GaborPete (talk) 03:53, 13 April 2009 (UTC)

Merge and dab seems like a fine solution to me. —David Eppstein (talk) 04:16, 13 April 2009 (UTC)

Proposal for adding proof to Associated Legendre Function article

I spent 2 weeks searching the web, trying to find a proof of the orthogonality of Associated Legendre Functions for fixed m without success. So, working together with a theoretical physicst (retired) we developed one. Some of the proof relies on logic I found on the web and some we developed on our own. We would like to contribute this proof to the Associated Legendre Function wiki page (using a link to a separate page for the proof). It was suggested to me by RHaworth (who seems to be a Wikipedia administrator) that I work with an established editor on this. I am happy to do so. Please contact me if you are interested in working on this. Dnessett (talk) 17:32, 11 April 2009 (UTC)

Please see WP:OR. Wikipedia is not the place for publishing original proofs. It's ok to have proofs in some articles (especially to the extent that it contributes to the reader's understanding, rather than merely supplying a mechanical verification of some fact) but it would be best if you could point to something in the mathematical literature as a published proof of the same fact that you're simply rewording. —David Eppstein (talk) 18:01, 11 April 2009 (UTC)

I am not proposing an original proof. The proof is an amalgamation of steps I found on the web, these fragments being hard to follow. The proof contains a reference to a book that is partially available on Google:books. The reason I am making this proposal is I am learning Quantum Mechanics (with the help of a Theoretical Physicist) and could not find anywhere on the web a proof that the Associated Legendre Functions for fixed m are orthogonal. This is stated on the Associated Legendre Function Wikipedia page, but it is not easy to demonstrate (there are a few calculus tricks that are non-obvious). So, providing a proof would help others who find themselves in the same position understand why these functions are orthogonal. A draft of the proposed proof is at: User:Dnessett/Legendre/Associated Legendre Functions Orthogonality for fixed m. Dnessett (talk) 18:26, 11 April 2009 (UTC)

Since Wikipedia isn't really the best place for proofs, it might be better to put the proof on PlanetMath, and put an external link to the proof in the appropriate Wikipedia article. --Zundark (talk) 18:33, 11 April 2009 (UTC)

I disagree that Wikipedia isn't the place for proofs. We shouldn't insist on proofs for every mathematical fact stated here, but I think it's reasonable to include a proof (or maybe better a sketch of a proof) when it conveys more to the reader than just the validity of the proposition being proved — often a proof will contain important ideas that have more general applicability, and are best expressed in the context of the proof. Alternatively, another reasonable standard is whether a survey article in the Monthly would be likely to include the proof. And some proofs are notable in their own right (for instance, most or all of the proofs in Aigner and Ziegler's "Proofs from the Book" could be considered to meet WP:N, as they are explicitly discussed by a third-party reliable source). My biggest concern with proofs is (as I know from experience) it's easy to commit original research rather than following previously published steps, but it sounds like that's not an issue in this case. —David Eppstein (talk) 19:20, 11 April 2009 (UTC)

I don't know much about PlanetMath, but when I went to its web site and searched for "Associated Legendre Function" I found nothing (there was some material on Legendre Polynomials, but they are a limited subset of Associated Legendre Functions). There is a Wikipedia article on Associated Legendre Functions and it would seem to me appropriate to provide a subpage of that article that proves the orthogonality of those functions (right now it is just stated). These functions are components of Spherical Harmonics, which are used extensively in the solutions of differential equations expressed in spherical coordinates. Speaking from personal experience, I found it hard to accept by fiat that the Associated Legendre Functions are orthogonal. So, I would argue that others who are investigating subjects that use these functions would find a proof of orthogonality beneficial. Dnessett (talk) 18:52, 11 April 2009 (UTC)

For those who may be interested, a first draft of the proposed proof page is found at User:Dnessett/Legendre/Associated Legendre Functions Orthogonality for fixed m Dnessett (talk) 19:07, 11 April 2009 (UTC) [Sorry, I already stated this above. I'm not sure what is the proper etiquette here. Should I remove this redundant comment or leave it, since it is part of the historical record?] Dnessett (talk) 19:20, 11 April 2009 (UTC)

It has been pointed out that the proposed proof not only shows orthogonality of the Associated Legendre Functions, but also provides the normalization constant. Consequently, I have created a new page User:Dnessett/Legendre/Associated Legendre Functions Orthonormality for fixed m that is properly labeled. The old page will remain, but all my future work on the proposal will occur on the new page. Dnessett (talk) 14:28, 12 April 2009 (UTC)

Honorable titles for Professors

It is somewhat connected to the previous section. There are many honorable titles in academics of various degrees. I wonder which are worthy of inclusion here. In my personal opinion, many of these titles should not be notable enough. In fact, from the experience of people who I know, earning the title is akin to becoming a member of an elite club, not quite notable enough on its own merit. In many cases it says more about the person as a politician rather than as an academician. I am talking about various named professorships, distinguished professors, etc. How about professors who gained other types of recognition/ achievements, like publishing 100+ papers, or 10+ books, or getting a million dollar grant? Where should we draw the line? What do you think? (Igny (talk) 18:33, 10 April 2009 (UTC))

If you don't think that having a title should be sufficient, you should suggest that on WP:PROF.

It's worth pointing out that what's considered a large number of published papers varies depending upon the field. And quality is generally more important than quantity. If someone has published 100+ papers or even 1,000+ papers, but not a single one is interesting, then that person should not have an article. Whereas someone who doesn't like to publish and publishes only interesting work (such as Ofer Gabber or Mariusz Wodzicki) should have an article. (Unfortunately, neither of them do!) Ozob (talk) 20:34, 10 April 2009 (UTC)

I personally haven't met any titled math professors that seem to have achieved their distinction from politics. Rather, I see a number of such people who generally avoid politics and have hefty mathematical reputations. I'd like to know if Igny's assertions are based on either plentiful experience, academic studies, or perhaps s/he has experience in other subjects and certain countries. --C S (talk) 23:28, 10 April 2009 (UTC)

Well, I am not trying to diminish achievements of mathematicians in any way. Any of the recognition is quite an accomplishment, and I actually did not mean to judge it. However, I would like to discuss the inclusion threshold for WP articles of thousands of science professors. The reason of this discussion is actually to avoid AfD battles before they even start. Case in point, article on Estate V. Khmaladze, existence of which was questioned soon after it was created. (Igny (talk) 19:41, 11 April 2009 (UTC))

I agree with Igny's comment. I strongly believe that developing a set of meaningful criteria for inclusion of living mathematicians into Wikipedia is a serious issue that we need to discuss at length. Refering to WP:PROF is a non sequitur. We need to come up with guidelines, or better yet, clear criteria that are suitable specifically for mathematicians, that are consistent with Wikipedia's mission, and that make sense from the practical point of view. So far I mostly see a knee-jerk reaction on a part of a few people ("who are you to question professional merit of my peers"?), which is off the mark, with some overtones of inclusionism, and only occasional rational arguments. I personally prefer to err on the side of caution and not create articles unless there is a good reason to do so (it's not a secret that removing material from WP is harder than adding it, and that many reasonable AfDs fail in the face of entrenched resistance of only a few persons or due to general apathy). Further, it would be nice if we can reach consensus on the kinds of information that should and should not be included into the math biographies.

I will list some things to consider in developing the criteria, and I hope that more than the usual two or three people will contribute their perspectives. Arcfrk (talk) 21:22, 11 April 2009 (UTC)

• We are not in the business of evaluating scientific merit of anyone's work. The committees that oversee appointments for named chairs and professional awards base their judgment on confidential reports that cannot be cited on Wikipedia.
• There is a large number of mathematicians who have made impact within their fields and/or have been recognized through academic honors but who lack significant secondary source coverage. Although notable according to WP:PROF and other guidelines, their inclusion will contradict Wikipedia's policies on sources and verifiability (apart from the obvious difficulty of coming up with encyclopaedic information in the first place).
• There are mathematicians with significant impact on major areas of mathematics who presently lack wikipedia bio articles (shockingly, this includes several winners of Leroy P. Steele Prize for lifetime achievement). Should we, therefore, engage in systematic creation of articles on mathematicians deemed notable according to a certain set of criteria? This seems already to be happening eg with members of national academies and presidents of professional societies.
• Wikipedia is not a directory or indiscriminate collection of information. On the other hand, there are electronic databases, such as MathSciNet and Zentralblatt der Mathematik, that are "closed source" and are viewed both as authoritative and as accurately reflecting the publication record in mathematics.
• Thousands of mathematicians have published articles in the leading mathematics journals such as Annals of Mathematics, Inventiones Mathematicae and a few others (it would be hard to even come up with a generally agreed upon list, but I note that some of the leading journals themselves do not have a WP article yet!). Any attempt to create articles for all of them is bound to result in thousands of stubs with no reason or mechanism for further development.
• Any biographical article is a liability to maintain and a potential source of aggravation for its subject, as evidenced by continuous debates relating to WP:BLP.
• Should the practice of creating red links for mathematicians whose contributions are mentioned in topical articles on Wikipedia or whose work is cited be encouraged or discouraged?
• What is a reasonable quantity of publications in a biographical article? Should monographs or textbooks be given more weight than articles? All too often, the publication list appears to be a fairly random hack (not even based on MathSciNet in some cases). Should we strive to create annotated lists? Or would a link to the person's own publication list on the web be a better solution?

Since Arcfrk asked for contributions from other than the usual suspects, I'll keep it brief, but (1) if there's a problem here, it's true generally of professors rather than specific to mathematicians, so I don't see the point of math-specific standards other than some obvious points such as that MathSciNet is a more appropriate database to use than the alternatives; (2) there's a related recent discussion at Wikipedia_talk:Notability (people)#WP:ATHLETE needs updating in which WP:PROF is cited as appropriately restrictive compared to the situation in professional sports in which walking on the field once counts as being sufficiently notable; (3) I think verifiability is a much bigger problem than notability for our current academic biographies. —David Eppstein (talk) 21:54, 11 April 2009 (UTC)

Here's a proposal. New list: List of basic details for notable mathematicians. It is proposed that redlinks for mathematicians are redirected to their section in this list. The list will eventually include links to each mathematicians homepage, their Mathematics Genealogy Project page, other biographical sources as they are found, list of awards etc. Charvest (talk) 18:29, 12 April 2009 (UTC)

It looks like a useful aid to editing math biography articles, but shouldn't it be in Wikipedia project space rather than in article space? —David Eppstein (talk) 18:43, 12 April 2009 (UTC)

RHaworth thought similarly but chose user space instead. It's now at User:Charvest/sandbox. —David Eppstein (talk) 19:46, 12 April 2009 (UTC)

Now at Wikipedia:WikiProject Mathematics/mathing missematicians. — RHaworth (Talk | contribs) 19:51, 12 April 2009 (UTC)

A funny name! Boris Tsirelson (talk) 20:09, 12 April 2009 (UTC)

At the moment all the redlinks from Euler medal, Godel prize, Polya Prize, Leroy P. Steele Prize and EMS prize are included. The list was formatted and sorted in alphabetical order using Textpad with regular expressions, with some manual adjustments. I can do the same again to incorporate lists of redlinks from other prizes for every prize deemed suitable. Would you say that all mathematicians getting any of the prizes in the category Category:Mathematics awards are automatically notable ? Using textpad was a workaround. It would be better to use a database I suppose. Any recommendations ?Charvest (talk) 21:26, 12 April 2009 (UTC)

Ahem, all? What about Richard Kadison (Leroy P. Steele Prize, 1999)? Also, maybe seeing all these red links will cool down some heads thinking of including more prizes. Arcfrk (talk) 21:46, 12 April 2009 (UTC)

Ok, I missed some. Now added. Charvest (talk) 23:43, 12 April 2009 (UTC)

I've moved the page to Wikipedia:WikiProject Mathematics/missing mathematicians; hope the new name is less funny. Boris Tsirelson (talk) 15:25, 13 April 2009 (UTC)

Artinian ideal

Artinian ideal has been proposed for deletion via a "prod" tag. It gets 30 hits in google books and 78 hits in google scholar. I have qualms about its deletion because Wikipedia's coverage tends to be broad. But algebra is not my field.

I added the identification of the eponym as Emil Artin. Is it possible that it's actually Michael Artin? Michael Hardy (talk) 16:22, 11 April 2009 (UTC)

If it is, the whole section needs work; we imply that these are named for Artinian rings, which come from the Artin-Wedderburn theorem. Septentrionalis PMAnderson 14:28, 13 April 2009 (UTC)

I figured it out: the article intends to talk about "Artin monomial ideals" in (free) polynomial rings. I just haven't gotten around to correcting it. Arcfrk (talk) 16:34, 13 April 2009 (UTC)

Continuity property

Should this article exist? Is this a common name for this theorem? Jim (talk) 02:14, 13 April 2009 (UTC)

The name is almost certainly ambiguous. By me, this is a trivial consequence of the Heine-Borel theorem, but I'm not sure our readers will think so. Septentrionalis PMAnderson 03:09, 13 April 2009 (UTC)

The real content of this theorem is expressed in the statement that the continuous image of a compact set is compact and the image of a connected set is connected; everything else follows immediately from the Heine-Borel theorem, as PMAnderson points out. The name looks like a neologism, so it seems better to me to delete this article. I have prodded it. Ozob (talk) 15:28, 13 April 2009 (UTC)

It's not just Heine-Borel: you also need the fact that intervals are connected. Even the compactness part can be done without open covers. When I was an undergraduate we did all this with sequential compactness. Algebraist 16:08, 13 April 2009 (UTC)

Good point, thanks for the correction. Ozob (talk) 00:58, 14 April 2009 (UTC)

I went there and read it and my reaction was to see if it could be redirected to Heine-Borel theorem. But after I looked at Heine-Borel theorem, I decided I'd better not. The H-B theorem article is too technical. I think there is room in the encyclopedia for an article that highlights the special case of H-B that says that the image of a closed interval under a continuous function f ; R → R is a bounded set. That could be a new article, or it could be a section at the top of the article on H-B. The H-B article as it is has a number of pedagogical problems. For example, it launches almost immediately into a discussion of pseudocompactness. But pseudocompactness is only interesting in case cases that the H-B theorem does not cover!

I think a good approach would be to fix up H-B suitably, and then redirect Continuity property to there. I'll take a stab at that if nobody else does something sooner. —Dominus (talk) 15:39, 13 April 2009 (UTC)

There are two natural questions here: firstly, how commonly in the literature is the result covered by this article treated as a single result, rather than two separate results (one to do with compactness and one with connectedness)? Secondly, of the sources that do treat this a single result, what name do they give to it? I do not know the answer to either of these questions. Algebraist 16:08, 13 April 2009 (UTC)

I don't know the answers. But I will speculate: I think that the special case I noted above predates the formulation of compactness, and provided the initial motivation for both compactness and for the H-B theorem. Was H-B really discovered in the context of arbitrary metric spaces, as the current Heine-Borel theorem article suggests? I imagine that it was originally a theorem of analysis, not topology, and was generalized later. I will try to do some research on this, and I suggest that we take this part of this discussion to Talk:Heine–Borel theorem. —Dominus (talk) 16:28, 13 April 2009 (UTC)

The compactness-related stuff isn't the issue here: it's covered in our article extreme value theorem. The problem with continuity property is that it is (more or less) a combination of the EVT with the IVT, and this combination may not be notable. Algebraist 16:34, 13 April 2009 (UTC)

Neither Baby Rudin nor Ross's Elementary analysis seem to state this in quite the way the article has it. In Baby Rudin, it's proved in the middle of theorem 4.23; in Ross, I guess corollary 18.3 is the closest, but it doesn't include compactness of the image. Ozob (talk) 00:58, 14 April 2009 (UTC)

Infobox

Hello, everyone. Does anyone think having an infobox in a math article is a good idea? What I have in mind is something like this (see right):

Principal ideal domain

Technical level	Undergraduate
Commutative?	Yes
noetherian?	Yes
Domain?	Yes. (Dedekind)
Dimension	≤ 1
Examples	Field, Polynomial ring in one variable, Set of integers
Generalizes	Euclidean domain
Special case of	UFD, Bézout domain
R[X]	UFD
If localized	Discrete valuation ring
Applications	Finitely generated modules over a PID

(This is something I prepared for the purpose of the discussion, so the details are not my concern right now.) If there was a similar proposal before, I'm not aware of it.

Part of the reason I'm proposing this is that I think infoboxs are inherently more accurate than those chains of rings we have in some articles; e.g., one in principal ideal domain article. I understand the motivation behind those chains: to put a topic in a large context. I believe infoboxs can do a better job. -- Taku (talk) 11:26, 11 April 2009 (UTC)

No, I don't think that's a good idea, for several reasons. I don't see the issue with the lede of principal ideal domain; it's easy to read. Here are some reasons I don't support that sort of box:

• Foremost, mathematics is best communicated through the same language we ordinarily use to communicate, which is English sentences. It's not actually any easier to read the infobox than it is to read sentences; in fact, it's harder, because I have to read each line, decide what phrase on the left is actually supposed to mean, and then read the right, and decode any abbreviations there.
• Because of the lack of context and space, it's very hard to convey any subtlety via an infobox. This tends to generate lots of questions and confusion when readers cannot figure out what something in the infobox is supposed to mean. It also leads to erroneous edits by well-meaning users who think something in the infobox is correct, because it is too brief to explain fully.
• Some over-zealous editors tend to put far too much in the infobox. Not having the infobox at all is a good way to avoid this. For example, if we have a "examples" section, I predict some editor will copy all the examples into the infobox. It's very difficult to get agreement on exactly which subset of the examples to include in the infobox, and the time taken for that discussion is better spent on other things.
• More generally, the information in the infobox only duplicates what is in the article, and so it just adds to the difficulty of maintenance.
• Because there is no good reference for the technical level of a part of mathematics, we shouldn't try to assign it one. Is metacompactness a graduate or undergraduate topic? The Gauss–Bonnet theorem?
• Infoboxes are nice for Chemicals, where there is certain data (such as the chemical name and molecular formula) that we know each chemical will have. And they are OK for people, because again there is certain data (birth and death, nationality) that all people will have. But there is no simple collection of bullet points that all mathematical topics share.

— Carl (CBM · talk) 12:09, 11 April 2009 (UTC)

I think it's a very good idea. I don't agree that "infoboxes are inherently more accurate" or that they "can do a better job" than anything, but I do feel that adding infoboxes can be useful. (In addition to the text of the article, not as a replacement.) In particular, the "Examples", "Generalizes", and "Special case of" would be useful to have quickly visible in an infobox for any article. To answer some of CBM's points:

• Everything is best communicated through English sentences, and yet we have infoboxes everywhere on Wikipedia,
• Readers who care will read more than just the infobox, so it's okay if it misses some of the subtleties,
• The question of what is "far too much" for an infobox can be resolved through discussion and consensus as usual,
• I don't see a problem with the infobox duplicating what is in the article (that's what it's meant to do),
• I agree that "technical level" should not be one of the fields of the infobox (but this a detail, let's not discuss this right now),
• It's OK that there isn't a simple collection of bullet points for all mathematics topics, really Shreevatsa (talk) 15:07, 11 April 2009 (UTC)

Let me clarify a few things first. I never meant to suggest we replace text by infoboxes. (I though that was obvious...) I never said the lede of the PID article has a problem, and my infobox idea is going to solve it. All I meant was that an infobox is probably a better idea than a chain of rings currently we have. I never meant to claim infoboxes are "inherently" superior forms of describing math. I agree that an infobox cannot convey some important subtlety, which text can provide better. But that's basically the point of an infobox. While the article can discuss a topic in depth, infobox can provide a summary of the article; they work complementary to each other. I also don't believe math is best communicated via prose. Why do you, for example, put examples in bullet points on a white board when you teach a class? Because, apparently, sometimes leaving some technical details out help students remember essential points. infoboxes duplicate information, but that's exactly the point: putting the same information in different forms help readers digest information. I think this is why infoboxes are popular throughout Wikipedia. We are in bussiness of conveying information after all and we seek to maximize the effectiveness.

As to "technical level" section in my muck-up, I thought that's important because, often, math articles are often accused of not clearly specifying the background necessary to understand them. It is inevitable that some math articles are simply unreadable without proper prior-training. Also, it is important that an article clearly states if the topic that the article discusses is of interest only to researchers or something every math major learns in college. Of course, "technical level" isn't a good way to do. A possible alternative would be "prerequisite". Does anyone have suggestion? -- Taku (talk) 18:25, 11 April 2009 (UTC)

In the article principal ideal domain there is already a bullet point list of examples - in the section titled "examples". But most of the other things in your mock up would only apply to algebraic structures (commutativity, etc), not to arbitrary articles on mathematics.

The idea of having article list "prerequisites" has been discussed many times, and the outcome of the discussions has always been that the lede section should establish the context, and that there is no need to list prerequisites otherwise. — Carl (CBM · talk) 18:41, 11 April 2009 (UTC)

I should have been more specific. I didn't propose to put an infobox that exactly looks like one I put above to every math article. No. Obviously, not every math article needs an infobox, and each article needs a different kind of infobox. The one above should be called "Template:Infobox ring" or something and should be put to articles on rings or rings-like structures. I was interested how people feel about infoboxes in math articles in general, not specific one above. If "prerequisites" is not a good idea, then that's ok. As I said above, I only made that mock-up to generate discussion about infobox. The details could be worked out later if people are for infoboxes. -- Taku (talk) 18:52, 11 April 2009 (UTC)

I don't have a strong opinion about this, but I think the infoboxes may lead to crappier pieces of information than a usual text would. Also, the information you have put in the box up there should mostly be covered by an adequate lead section. (E.g. commutative, Noetherian, domain, a few examples, applications). Jakob.scholbach (talk) 19:57, 11 April 2009 (UTC)

My general feeling is that infoboxes are a very bulky way of conveying very little information, and that they discourage editors from putting the same information in a more readable form into the prose of the article. Also, when placed prominently in an article they get in the way of illustrations. —David Eppstein (talk) 20:01, 11 April 2009 (UTC)

I think infoboxes are really a matter of taste. Obviously the example doesn't work; it would take quite a bit of work to get this right. But done right, they could make our articles a bit more appealing to a wider audience. I don't really see them getting in the way of illustrations – typically we don't have any, and this is unlikely to change any time soon. In that case infoboxes can work as a substitute. What I see as a potential problem is that infoboxes may discourage merging of articles.

E.g. the articles prametric space (could someone comment on the talk page whether that's a translation error for premetric?), pseudometric space, quasimetric space, semimetric space could profit from an infobox for generalised metrics. But it would probably be better to merge the whole bunch. --Hans Adler (talk) 21:54, 11 April 2009 (UTC)

I've moved the article to premetric space, and I agree that all these articles should be merged. Charvest (talk) 22:55, 11 April 2009 (UTC)

I have a religious dislike for infoboxes. Paul August ☎ 03:21, 13 April 2009 (UTC)

I don't have anything in particular against Taku's infobox over other infoboxes...but to echo Paul's comment: I have never seen an infobox in an article improve the article. Articles on chemical elements is an interesting example and one I may be easily persuaded are useful. However, looking at the cluttered infobox in carbon, I wonder how useful it really is. --C S (talk) 05:35, 14 April 2009 (UTC)

For what it's worth, mathematics articles on probability distributions already have infoboxes (that's Template:Probability distribution), see e.g. Exponential distribution, Cauchy distribution etc. And I have found the infoboxes useful on several occasions (well, I don't know what skewness and excess kurtosis are, but all the rest have been useful at least once). Not all mathematical topics have similar facts about them that might be looked up often, but for ones which have them, infoboxes are useful. Shreevatsa (talk) 05:58, 14 April 2009 (UTC)

Shreevatsa made a good point; I was completely unaware of infoboxes in probability articles (probably because I don't edit them.) This led me to believe that I didn't start the thread with a right question. Let me ask a slightly different question. Does anyone can think of any math articles that can be benefited from having infoboxes? In particular, do you think ring articles (e.g., PID, UFD, Bezout domain, GCD domain, ...) can use infoboxes to improve the convenience of readers? -- Taku (talk) 11:58, 14 April 2009 (UTC)

I have found the infoboxes on elements and statistical distributions to be useful. I don't think they would be useful in many math articles. For the algebra articles I prefer more of a breadcrumb "monoid - semigroup - group". CRGreathouse (t | c) 14:25, 14 April 2009 (UTC)

Infoboxes seem to be most useful when the item falls into a well defined classification scheme, and have a few well defined properties which people want to look up. Towns, species fit well with this, I certainly find it easier to find the population of a place from the infobox rather than having to parse the text. Polyhedra (eg) is another grouping of mathematical objects where infoboxes prove useful.

I'm undeiced about whether specific rings really fit. Most properties are fairly esoteric which will be of little interest to most readers. --Salix (talk): 15:29, 14 April 2009 (UTC)

Infoboxes are useful for examples of a general phenomenon. All chemicals share certain properties such as the existence of a boiling point and the existence of a freezing point. Similarly, all probability distributions share certain properties such as the existence of a mean and a median. Just where the boiling point or freezing point is depends on the chemical, and just where the mean or the median is depends on the probability distribution. That's where infoboxes are useful: They collect data on examples. If you can find another type of mathematical structure that has many, many examples, then it might be worthwhile to have an infobox for examples of that structure. For example, you might have a group infobox: It would have information such as whether the group is abelian, simple, nilpotent, solvable, and so on. The trouble with this is that in order for it to be useful, you'd have to find a lot of interesting information for all the groups on Wikipedia; if you had only very basic information, such as whether the group is abelian and whether it's simple, then the infobox would be a waste of time and space.

Another thing to consider is that sometimes our articles cover topics where an infobox may not be workable. Consider group of Lie type, for example. There are lots and lots and lots of groups of Lie type. If you wanted to put a group infobox in that article, for just about every entry you'd have to say "Depends on the group". For specific families of these groups, you may be able to answer this question (e.g., most groups of the form PSL_n(F_q) are simple), but in general there's nothing to say. So you'd have to pick which articles get the infobox very carefully.

On the whole, I'm not sure infoboxes are worth the effort. It doesn't seem like they would be for rings since classifying rings is an impossible project. Ozob (talk) 15:59, 14 April 2009 (UTC)

copyvio

The page Talk:Method of lines says it is a copyio. Charvest (talk) 05:38, 15 April 2009 (UTC)

It looks like the writer tried to paraphrase, but failed to do so very well. They also added information not present in the MathWorld article. I have copyedited it some more and trimmed a sentence or two; I think it is OK now. The best way to make it look less like the MathWold demo would be for someone knowledgeable to expand the article on WP. — Carl (CBM · talk) 11:48, 15 April 2009 (UTC)

New collapsible auto collapsible template for calculus

Topics in Calculus

Fundamental theorem Limits of functions Continuity Mean value theorem Differentiation  Product rule Quotient rule Chain rule Change of variables Implicit differentiation Taylor's theorem Related rates Identities Integration  Lists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order Vector calculus  Gradient Divergence Curl Laplacian Multivariable calculus  Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian

For practice with templates, I rewrote a calculus template that was collapsible and that you can have open to the correct category. I did add some articles as well to help from a physics perspective. (Being collapsible, the space issue is diminished quite a bit.) I stole the autocollapse mechanism from Template:PhysicsNavigation but I tried to keep the calculus style.

If there is no objections, I am likely to replace this current calculus template with the one I rewrote soon. I don't know enough about the math projects style to push the button without some warning, though. TStein (talk) 19:15, 17 April 2009 (UTC)

Go ahead. I know not much about Wikipedia templates but I see nothing wrong with your changes. --PST 03:23, 18 April 2009 (UTC)

WAREL back?

See Special:Contributions/Motomuku, Category:Wikipedia sockpuppets of WAREL, Category:Suspected Wikipedia sockpuppets of WAREL, and Wikipedia_talk:WikiProject_Mathematics/Archive_47#WAREL/DYLAN LENNON. —David Eppstein (talk) 20:58, 17 April 2009 (UTC)

I am not familar with WAREL, but it seems clear that Motomuku is a reincarnation of User:Katsushi. --Hans Adler (talk) 10:19, 18 April 2009 (UTC)

Strange articles

Valya algebra and Commutant-associative algebra — both created by a single purpose account (no other substantive edits), appeared to be hoaxes at the first glance, since I'd never heard these terms before. After investigating a bit, I found out the following.

• Neither of the two EOM articles quoted (devoted to certain non-associative structures) mentions anything related.

• MathSciNet has exactly one instance of "Valya algebra", in a review of an article of some V.E.Tarasov from 1997, the review quotes from the author's introduction. The same review is also the only occurrence of "commutant-associative algebra" in MathSciNet.

• Zentralblatt has no instances of either term.

• Books of Kurosh quoted do not contain references to these structures.

• The book of V.E.Tarasov quoted has not been reviewed either by MathSciNet or Zbl (in fact, it's not even listed there).

I strongly suspect that the other books quoted (e.g. Malcev) contain nothing on the subject and have only been put in in order to lend an air of legitimacy to the topic. The terms appear to have been used by a single author (and possibly, only on a single occasion); as such, I would think that they are not notable, in spite of having appeared in an established (non-mathematical) journal. It is entirely possible that these articles were created with a purpose of promoting a fringe topic. Whether or not that is the case, what would be an appropriate course of action? What are the specific policies that these articles violate that can be quoted in filing AfD? Arcfrk (talk) 02:52, 18 April 2009 (UTC)

WP:V#Burden of evidence says "The source cited must clearly support the information as it is presented in the article." and "Any material lacking a reliable source may be removed, ...".

WP:V#Reliable sources says "Articles should be based upon reliable, third-party published sources with a reputation for fact-checking and accuracy." and "In general, the most reliable sources are peer-reviewed journals and books published in university presses; university-level textbooks; magazines, journals, and books published by respected publishing houses; and mainstream newspapers.". JRSpriggs (talk) 07:01, 18 April 2009 (UTC)

If this is fringe in the sense of something that only the author works on, then perhaps the definitions can be mentioned in an existing article on a related topiic? Of course, if it is fringe in the stronger sense it's probably better to simply prod it and send it to AfD if necessary. Commutant-associative algebra seems to give two definitions for the same term. I am not used to this type of algebra; does the first imply the second? --Hans Adler (talk) 10:12, 18 April 2009 (UTC)

Proposal to add proof to Sturm–Liouville theory page

I propose to add a subpage to the Sturm-Liouville namespace that proves solutions to the Sturm-Liouville equation corresponding to distinct eigenvalues are orthogonal. I am asking for help from an editor who works on this namespace to work with me on this. The proposed proof is found at Orthogonality proof. To avoid unnecessary suggestions, let me state that this proof is not original research and there does not seem to be consensus whether proofs belong on Wikipedia or not. On the latter issue, I have contacted established editors asking for their views, but have not yet received a response. If I do not hear from anyone by next week, I will just add the subpage and see what happens. Dnessett (talk) 15:31, 15 April 2009 (UTC)

Why not just add it to the article? Shreevatsa (talk) 15:36, 15 April 2009 (UTC)

I am new to Wikipedia and so am being somewhat cautious in adding pages to the main Wikipedia namespace. It was earlier suggested (when I made a mistake that placed an unwelcomed page in the main namespace, see [Internal?]) that I work with an established editor of the Sturm-Liouville namespace. I have attempted to do this, but no one has stepped forward. Dnessett (talk) 16:01, 15 April 2009 (UTC)

After rereading your question, I now realize I didn't understand it on first reading. I am proposing a subpage so that readers uninterested in a detailed proof need not wade through significant text in order to get to the next point. Dnessett (talk) 17:35, 15 April 2009 (UTC)

What is the value of this. The Sturm–Liouville theory article already gives an effective sketch of how to prove this. A detailed proof on this matter seems of very little encyclopic value. If you still decide that this is useful then that proof should be much better explained. (For example explain before hand what the idea of the proof is.) (TimothyRias (talk) 15:56, 15 April 2009 (UTC))

Value: I and another collaborator were motivated to add this proof when I spent two weeks searching the web looking for a proof that Associated Legendre Functions are orthonormal. I failed to find anything except a Google Books excerpt that made significant jumps in logic. When I contacted my collaborator (a Theoretical Physicist helping me to learn Quantum mechanics), he showed me how the orthogonality of these functions follows from the fact that they are solutions to the Sturm-Liouville equation. He then explained why solutions with distinct eigenvalues are orthogonal and noted that this information was also missing on the web. So, we decided to make a contribution to Wikipedia. Effectiveness of sketch: The sketch might be effective for someone experienced with Sturm-Liouville equations, but for me it was not. I expect other students also would have trouble following the sketch. Better explanation: I am open to doing this, although the sketch in the main article serves that purpose. Why would you repeat that in the subpage? Dnessett (talk) 16:25, 15 April 2009 (UTC)

My general feeling is that any article should stand on its own in terms of notability of subject matter, verifiability, etc. So if you are going to have an article solely about a proof (whether it be called a subpage or "Proof of..." or whatever) you need to justify that the proof itself is notable. This seems difficult to do in this case, given your earlier statements that you had trouble even finding a clear writeup of the proof. If it's not notable in itself, and the details of the proof are not central enough to the topic of the main article to include there, then maybe a Wikipedia article isn't the right way to publish this writeup. —David Eppstein (talk) 17:44, 15 April 2009 (UTC)

The situation is this. I (and others, for example, see physics forum discussion, although that discussion is about the sub problem of Legendre polynomials) have found it difficult to understand why the Associated Legendre Functions are orthonormal. This can be shown directly or by noting they are solutions to the Sturm-Liouville equation, which solutions are orthogonal if they have distinct eigenvalues (which then only demonstrates orthogonality, not orthonormality). The proof of the orthogonality of solutions to the Sturm-Liouville equation is non-obvious, even when sketched as it is in the main article. Is it the role of Wikipedia to help people understand the fundamentals of a theory? I don't know. I only know that when I searched for some help on the web, nothing useful showed up. So, if it is the consensus of the Wikipedia community that this doesn't belong here, fine. I will try to find somewhere else to put it. However, I am not sure how an understanding of consensus is developed. So far, only a couple of editors have responded to this proposal. Would someone give me some guidance on the criteria I should use to simply give up on Wikipedia and go elsewhere? Dnessett (talk) 18:27, 15 April 2009 (UTC)

New Thought: After some thought, I wonder if the following would satisfy your objection. As I understand it, you are uncomfortable with articles that are not self-contained. How about creating a section at the bottom of the Sturm–Liouville theory page that contains the proof. This keeps the proof with the material with which it is associated (so there is no problem with self-containment), but it also doesn't disturb the flow of the reader who isn't interested in the detailed proof. A link to the bottom of the page where the proof resides could be put into the main article. Would this answer your objection? Dnessett (talk) 20:24, 15 April 2009 (UTC)

Your proof is a combination of two proofs: (1) eigenvectors of a symmetric operator, corresponding to different eigenvalues, are orthogonal; and (2) the Sturm-Liouville operator is symmetric. Right? Each one separately is available in many textbooks (I guess so). What is really a problem here? Boris Tsirelson (talk) 19:08, 15 April 2009 (UTC)

You make a legitimate point, but your general argument applies to all Mathematical articles on Wikipedia. Wikipedia Mathematical articles are not supposed to contain original research. They are summaries of knowledge already existing in textbooks, papers and other written sources. So, by your criterion all Wikipedia Mathematical (perhaps all Wikipedia) articles would be unnecessary. Also, let me point out that the proof is a summary of that given in the reference at the bottom of the proposal page. That source provides the explicit proof and does not simply state that orthogonality follows from the two properties you note. Dnessett (talk) 19:33, 15 April 2009 (UTC)

To all proofs, not to all math articles... Proofs are included in Wikipedia only if they are especially interesting (more than usual). But even if this statement should be proved in Wikipedia (assume for now that it should), why in the "combined" form? Surely you do not want to prove specifically that (a-3)(a+3)=a²-9. Instead you'd prove that (a-b)(a+b)=a²-b², and that 3²=9. Boris Tsirelson (talk) 19:53, 15 April 2009 (UTC)

Well, I think your argument that: "Each one is separately available in many textbooks..." applies to just about everything on Wikipedia, but leave that aside for the moment. The reason for not dividing the proof into two parts, as you suggest, is it moves the reader away from the main concern. It requires the reader to suspend his/her interest in why solutions are orthogonal and take up the higher level issue of symmetric operators and their properties. Of course, in the final analysis the form of a proof is a matter of taste. But, presenting the proof in the form as it stands in the proposal has precedent (in the referenced book), which argues for keeping it in its current form. Dnessett (talk) 20:12, 15 April 2009 (UTC)

To reply to your earlier question about self-containment, I think that your proposal of making it a section towards the bottom of the article (but above the references) would be an acceptable solution in that regard. However now I'm finding the later concerns about modularity very cogent. If the result can be made to follow in a straightforward way from two mathematical facts that are each independently so important, what is the value added in merging those separate facts into a single combined proof that doesn't mention them? —David Eppstein (talk) 20:34, 15 April 2009 (UTC)

As I suggested to Boris Tsirelson, the value in presenting the proof as an integrated whole is pedagogical. Factoring it into two parts requires the reader to suspend his/her interest in the orthogonality question and move the focus of attention to the theory of symmetric operators. If, as I was, the reader is interested in why solutions to the S-L equation are orthogonal, but not particularly interested (at least at this point) in delving into the theory of symmetric operators, then the separation frustrates his/her interest. If the reader is a graduate student in Physics or Mathematics, then perhaps forcing him/her to consider the general issue would be healthy. But, not every reader of the article will be in this position (e.g., I am not). My interest is convincing myself that the solutions are orthogonal and then returning to my real interest, which is studying Quantum Mechanics. Let me once again admit that the form of a proof is a matter of taste. Some may find the bifurcation of a proof into two parts a cleaner and clearer way of presenting the proof. But, again as I stated previously, the form of the proof in the proposal is similar to that in the reference, which provides some evidence that this approach has merit. Dnessett (talk) 21:01, 15 April 2009 (UTC)

As a side note. Since your interest is learning Quantum mechanics, you should be primarily concerned with learning the simple fact that the eigenvectors of a Hermitian/Self-adjoint/symmetric are orthogonal if there eigenvalues are different. This fact is central to QM since Hamiltonians are suppossed to be Hermitian operators hence solutions of the time-independent schrodinger equation with different energy eigenvalues are orthogonal. (This little fact is presented in any undergrad textbook, although seldom proven rigorously) From a physics perspective it is then clear that legendre polynomials are orthoganal as they appear as (part of) solutions of the Hydrogen atom.(TimothyRias (talk) 20:59, 15 April 2009 (UTC))

I am using Shankar in my studies. The place where the orthonormality of Spherical Harmonics (and therefore the subsidiary issue of the orthonormality of the Associated Legendre Functions) is introduced is in Chapter 12, which covers rotational invariance and angular momentum. The Hydrogen atom is covered in the next chapter. Spherical harmonics are introduced before we get to the section that covers the solution to rotationally invariant problems (which is section 12.6). So, while your point is valid, I (as an example of a student) am in the process of learning the facts you mention. However, since I prefer to understand things as I go along, I dived into the orthonormality question as soon as Shankar stated it (without proof). That may be more detail about my situation than you desired, but it does provide an example of why people reading Wikipedia might desire the proof provided in the proposal. Dnessett (talk) 21:14, 15 April 2009 (UTC)

Another reason to use the existing proof, rather than breaking it up into two parts: The proof in the proposal elaborates the sketch given in the article. To provide a different proof approach would confuse the reader. Dnessett (talk) 03:32, 16 April 2009 (UTC)

Where is the "monolithic" sketch you mean? I fail to find it. Just the opposite: in Sturm–Liouville theory#Sturm–Liouville equations as self-adjoint differential operators I see: "Moreover, L gives rise to a self-adjoint operator. This can be seen formally by using integration by parts twice, where the boundary terms vanish by virtue of the boundary conditions. It then follows that the eigenvalues of a Sturm–Liouville operator are real and that eigenfunctions of L corresponding to different eigenvalues are orthogonal." Just a sketch of a "split" (rather than "monolithic") proof. Boris Tsirelson (talk) 06:00, 16 April 2009 (UTC)

To my regret, I did not find in Wikipedia this important fact: eigenvectors of a symmetric operator, corresponding to different eigenvalues, are orthogonal. Someone should state it in an article about operators (or spectra etc); and the "Sturm–Liouville" article should link there. As a rule, proofs do not appear in Wikipedia, but statements do. Boris Tsirelson (talk) 06:06, 16 April 2009 (UTC)

Have a look at Compact operator on Hilbert space. And I'd like to add that I don't personnally enjoy very much reading pure lists of facts. What I like in math is seeing the properties in action, and to be told WHY things are true, when it can be done in a reasonably short and nice way. --Bdmy (talk) 07:52, 16 April 2009 (UTC)

I see, thanks. However, this one is not immediately applicable to the Sturm–Liouville operator, since the latter is unbounded. It is applicable indirectly, since (roughly speaking) the inverse operator is compact, but the direct way is preferable. In fact, the needed statement "eigenvectors of a symmetric operator, corresponding to different eigenvalues, are orthogonal" is of the sort you like: "can be done in a reasonably short and nice way"; the proof is short (one line, maybe two). In order to keep the argument short and clear, however, one should avoid self-adjointness (irrelevant here) and use only symmetry (weaker than self-adjointness when operators are unbounded). One should also avoid existence of eigenvectors (this is a harder problem). Boris Tsirelson (talk) 08:37, 16 April 2009 (UTC)

Actually I wrote my post before (and I was wrong about that) looking at the article on Sturm-Liouville theory. Now that I saw both the original article and the proposed adjonction, I must say that I am not in favor of adjoining the proposed proof to the article: there is a too strong difference of level and tone between the two. --Bdmy (talk) 08:43, 16 April 2009 (UTC)

There is a larger issue at hand in this discussion that directly affects the proposal. That is, should Wikipedia include proofs? Subsidiary to this question (if it is decided that proofs are legitimate material in a Wikipedia article) is: when is the inclusion of a proof allowable? This is something the Wikipedia community must decide and perhaps there should be a discussion of this issue at some "higher level" before proceeding with discussions about this particular proposal. However, given that such a "higher level" discussion does not yet exist, I would like to contribute the following thoughts. Wikipedia is used by a large number of people for different reasons. At least three categories of Wikipedia users are relevant to the proof question: 1) those who understand the subject intimately, 2) those who basically understand the subject, but need a place to find details in order to refresh their memory, and 3) those who are learning the subject. Users in the first category tend to be those who write articles. Those in the second and third categories tend to be those who read articles. Discussions about what to include and what not to include in Wikipedia articles are dominated by those in the first category, since they are the Wikipedia editors who do the work. Those who intimately understand a subject many times are interested in eloquence and elegance, rather than in transparency. Since they understand the subject, many details seem to them obvious and therefore unacceptable as material in Wikipedia articles. Readers (those in the second and more importantly the third category) are underrepresented in discussions about Wikipedia content. Many if not most don't even know such discussions exist. So, I think it is prudent for those writing the articles to attempt to take the perspective of users in the other categories. What is obvious to Wikipedia article writers in many cases is not obvious to Wikipedia readers. Dnessett (talk) 16:09, 16 April 2009 (UTC)

However, note the distinction between Wikipedia and Wikiversity. Boris Tsirelson (talk) 17:34, 16 April 2009 (UTC)

In regards to the "monolithic" sketch (a term I don't recall using), if you look at the proof sketch and then at the detailed proof in the proposal, you will see that the latter elaborates the former. So, if you think the sketch is in two parts, then it seems to me you would judge the detailed proof to be in two parts. Dnessett (talk) 16:29, 16 April 2009 (UTC)

The sketch explains (shortly) why this operator is self-adjoint, and says: the orthogonality follows. In this sense it is explicitly split. The "monolithic" (or "combined", if you prefer) proof need not mention the notion of self-adjoint operator at all, and indeed, it does not. Boris Tsirelson (talk) 17:40, 16 April 2009 (UTC)

There has been considerable discussion, off and on, as to whether, when, where, and how to include proofs, some of which is archived on these two pages:

• Wikipedia talk:WikiProject Mathematics/Proofs/Archive 1
• Wikipedia talk:WikiProject Mathematics/Proofs/Archive 2

I believe that the consensus has been though, that in most cases, proofs are not appropriate. There are exceptions, notable proofs for example (with references) can be appropriate.

Paul August ☎ 18:07, 16 April 2009 (UTC)

The topic has occurred here at WT:WPM, too. The original poster may be interested in the discussions Wikipedia_talk:WikiProject_Mathematics/Archive_46#Proofs and Wikipedia_talk:WikiProject_Mathematics/Archive_46#Connected_space/Proofs. But I suggest that further discussion take place at Wikipedia talk:WikiProject Mathematics/Proofs. Ozob (talk) 18:38, 16 April 2009 (UTC)

I looked at the pages you referenced and again found no clear consensus on the issue. However, I have added an entry to Wikipedia talk:WikiProject Mathematics/Proofs asking for clarification. Before my own, the last entry was 28 Dec 2008. This suggests the discussion page is not very active. So, if the discussion on the larger issue takes off there, then I will pursue it before returning to this discussion. However, if that page turns out to be a black hole, then I would like to continue the discussion here. Dnessett (talk) 19:21, 16 April 2009 (UTC)

I briefly read through the two archives you (Paul August) referenced. It seems to me that there was overwhelming support for providing proofs on Wikipedia. Only one or two users objected to doing so. In addition, there seems to be a category devoted to proofs Article Proofs. So, I am puzzled why you believe that the consensus is most proofs are inappropriate. Dnessett (talk) 18:51, 16 April 2009 (UTC)

I googled "Wikiversity Sturm-Liouville". One of the hits is a page on ordinary differential equations Wikiversity ODEs. This page is in a chaotic state, which means adding a proof of S-L orthogonality to it would be premature. So, there seems to be three choices: 1) wait for the page to become coherent enough to contribute the proof, 2) work on the page myself and get it into sufficient shape to add the proof, and 3) continue pursuing the proposal for adding it to Wikipedia. Choosing the first option would mean there would be a significant amount of time before the proof is available to readers. Choosing the second option isn't practical, since I am not an expert in differential equations, nor do I want to put in the significant amount of time it would take to become one. Choosing the third option has the advantage that the proof would be available relatively soon (if the proposal leads to the proof's inclusion), but has the disadvantage that it is not clear that inclusion is either certain or likely. So, I would appreciate some feedback on these options or suggestions of other options. Dnessett (talk) 18:16, 16 April 2009 (UTC)

Make a PlanetMath page? —David Eppstein (talk) 18:34, 16 April 2009 (UTC)

There is a page on PlanetMath that mentions S-L problems (see Eigenvalue problem). However, they are given as examples. There is no page that I could find that addresses the S-L problem directly. Of course, I could work on creating such a page, but I don't feel I have sufficient depth of expertise to do so. Consequently, this option is very much like option 2 in the entry above. Dnessett (talk) 19:21, 16 April 2009 (UTC)

Well, I don't want to sound hostile, because I'm not, but we're here to build an encyclopedia, not to solve your internet hosting issues. If you can't find better places to publish your writeup, that's irrelevant to inclusion here — what's relevant is what it adds to the article here. So I'd prefer to see discussion continue on the basis of whether adding this proof would be an improvement to our S-L article rather than on how quickly the proof could be made available to readers via one option or another. —David Eppstein (talk) 20:49, 16 April 2009 (UTC)

Fair enough. Dnessett (talk) 21:52, 16 April 2009 (UTC)

I wonder if those who hold that a proof must provide significant improvement to an article might suggest some criteria by which this is judged? It's pretty hard to come up with arguments for inclusion when no objective standards for those arguments exist. Dnessett (talk) 23:22, 18 April 2009 (UTC)

First a comment about Wikipedia_talk:WikiProject_Mathematics/Proofs, where I noticed Ozob left a pretty good summary of the state of the consensus. That subpage isn't actually watched by a lot of people. It sounds kinda bad, but it is there simply to appease people who would like more proofs, particularly the instructive kind I think you wish. There is a pretty set "house" style to writing Wikipedia math articles, and it simply does not include writing details of little lemmas. It's going to take more than a discussion here or there to change it. This style is in fact the de facto consensus. Any time someone deviates from this style, their edits will be reverted/discussed/moved to a subpage (which is the reason there are more than a few such subpages). This has been happening for quite a while (probably at least 4 years), so it's fair to call it the consensus. One interesting aspect of all this is that if you invite the consensus of the rest of wikipedia, you may find something quite different: that a great number probably want all proofs deleted ("not a textbook!" he said), even the famous ones. This leads to the situation where people from this wikiproject have to stridently argue for proofs in AFDs (another place to look for the elusive consensus smoking guns). Thus there is a natural relectance to speak out too strongly against proofs (I know this is true for me and a couple others). We don't want to give "them" too much fodder for arguments to delete proof articles.

As for objective criteria, what Ozob write is correct. Different people have ideas of what good summary writing is. I think in a recent discussion somewhere Charles Matthew commented it would be appropriate to include a little proof of even a trivial fact, if it were the case that this little proof would be included in a typical survey article on the subject. An example might be deducing the uniqueness of the inverse for a group from the group axioms (I haven't read any surveys on group theory but I notice group (mathematics) includes this). For the specific example under discussion, I think what you suggest shouldn't be included. It reminds me of math classes where someone might hand in like 30 pages for math homework while someone else turns in one page. First person gets half the points, second person gets full credit. The lesson here is that when one is learning, particularly at the beginning, one is prone to include all kinds of "important points" that are, in the end, not so primary. --C S (talk) 01:32, 19 April 2009 (UTC)

I'm going to avoid the immediate temptation to defend my proposal in light of the opposition expressed by C S, because as David Eppstein correctly writes, the objective of this discussion is to determine whether the inclusion of the proof in that proposal "would be an improvement to our S-L article", "not to solve (my) internet hosting issues." Unless I am mistaken, C S thinks there are no objective criteria that indicate when a proof will improve an article. It's a matter of taste. Is that what others think? Dnessett (talk) 14:18, 19 April 2009 (UTC)

I'm jumping in here without reading the above discussion, which is always risky. But just responding to the last paragraph above — of course there are no objective criteria as to whether a proof, or practically anything else for that matter, would improve an article. How could there be?

I would call it a matter of judgment rather than "taste".

The fetish for objectivity is harming Wikipedia in general. The most important questions about an article, like does it convey its information effectively? and is it a pleasure to read? are all judgment calls. When objectivity is overvalued, so are less important questions like how many inline citations does it have?. --Trovatore (talk) 19:02, 19 April 2009 (UTC)

The comments by Trovatore suggest he advocates the "Bring Me A Rock" approach to developing articles. For those not familiar with this approach it conforms to the secular parable named (not surprisingly) "Bring Me A Rock," which goes something like this. A King tells one of his servants, "bring me a rock." The servant leaves the castle, goes to the river and selects a rock from its bank. The servant thinks it is a nice rock, it is smooth, pleasantly colored and not too big. He brings the rock back to the King. The King looks at the rock, frowns and says, "not that rock, bring me a different rock." Even if the standards for judging what should and what should not go into Wikipedia articles are subjective, it is only fair to articulate them. This allows those who "aren't in the know" to have some way to judge what they should attempt to insert into an article and what they should not. Dnessett (talk) 00:56, 20 April 2009 (UTC)

Generalisations of metrics

We had lots of stubby articles on generalisations of metrics: pseudometric space, quasimetric space, semimetric space, hemimetric space, premetric space, inframetric. Except for the first I have boldly merged them all into the pre-existing section Metric (mathematics)#Generalized metrics. --Hans Adler (talk) 00:27, 17 April 2009 (UTC)

Nice. Boris Tsirelson (talk) 04:38, 17 April 2009 (UTC)

Thanks – great that the first response was positive. I still half expect to be lynched. --Hans Adler (talk) 10:13, 17 April 2009 (UTC)

Good work. There has been some research going on lately in the theory of such "generalized metrics". In particular, the question asking for necessary and sufficient conditions for a space to be quasi-metrizable is unsolved. I think that soon we probably would have to allocate each concept to its own article but for now I think what you have done looks good. As far as point-set topology is concerned, these are some of the interesting unsolved problems. --PST 14:56, 17 April 2009 (UTC)

Yes, I agree we may have to spin them out again later. But for the moment there just isn't enough information, the confusing naming issues can only be understood when everything is in one place, and merging allowed me to move some of the examples to the most logical location.

I am not sure what to do with Metric (mathematics)#Important cases of generalized metrics, which I am currently not motivated to understand. It would be great if somebody could find a better title for this subsection, or even a home in one of the other subsections.--Hans Adler (talk) 15:12, 17 April 2009 (UTC)

Does anybody have definite information about the intended meaning of the MSC category 54E23: Semimetric spaces? As it is under 54 (General Topology), I expect that it is for semimetric spaces, but last time I looked the annotated MSC didn't make this clear, and many publications on pseudometric spaces (which are also often called "semimetric spaces") were in this category. I asked the MSC2010 team, but never got a response. If we can be sure about the intended meaning it should go into a footnote, to discourage incorrect categorisation. --Hans Adler (talk) 15:12, 17 April 2009 (UTC)

There seems to be enough information on the various generalized metrics to warrant a split from Metric (mathematics). I'm thinking Generalized metric space; what do you say? CRGreathouse (t | c) 03:45, 18 April 2009 (UTC)

Initially I was going to collect everything in User:Hans Adler/Generalized metric spaces. As you can see I went as far as creating the page in my userspace. But then I noticed that we have two articles metric space and metric (mathematics) which need distinguishing features, and when I started it was already one such distinguishing feature that metric (mathematics) discussed generalised metrics. The other reason for not pursuing this was a naming problem: Lawvere coined "generalized metric space" for extended pseudoquasimetrics, and Stephen Vickers and probably others are still using this term. I believe sooner or later they will have their own decent-sized article, and generalisations in an orthogonal direction don't really seem to belong there. This is just an explanation for why I approached it this way. I have no strong opinion either way. --Hans Adler (talk) 07:48, 18 April 2009 (UTC)

I also don't have a strong opinion. I just noticed that the article on metrics was, after merging all the information, mostly about certain generalizations, and that seems a little but too much. CRGreathouse (t | c) 22:53, 19 April 2009 (UTC)

Unbounded operator

You are kindly invited to see and expand my new stub Unbounded operator (which was redirected to Closed operator, Operator norm, Bounded operator and what not). Boris Tsirelson (talk) 09:04, 17 April 2009 (UTC)

Nice work. It's amazing that we didn't have an article on such an important topic before. -- Taku (talk) 11:19, 18 April 2009 (UTC)

Thank you. I agree that it is amazing. However, see my comments to your edits. Boris Tsirelson (talk) 16:33, 18 April 2009 (UTC)

Good work. It is nice that we have someone knowledgeable about functional analysis around here - many articles in this topic are under-developed as it appears. --PST 14:01, 20 April 2009 (UTC)

Talk pages of articles

When we post on talk pages of mathematics articles, we are usually unlikely to get a response within a fixed period of time, unless of course the article is frequently viewed. Sometimes however, we may make important comments at talk pages of articles, which might play a role in improving its quality. In this case, I feel it reasonable to create a certain page that is linked to from WikiProject mathematics (page X, for example). When we post an important comment on the talk page of an article, we write the name of the article, along with out signature on page X. And those who watch page X, will be notified of the article at which a comment has been placed, and will be able to reply. This will allow much more progress for even the more specialized articles, and will give us some place to notify people without piling up comments on this page. Of course, if the comment is highly important, it would be best to post here, but any comment which may improve an article is important, and it is best therefore to have a page which notifies people of such comments. Any thoughts? --PST 07:14, 21 April 2009 (UTC)

I think you are addressing a real problem with this question, but I am a bit reluctant to start a new page on this. We can't force people to post there, and we can't force people to watchlist the new page. This problem could be addressed by using this page for your proposal. We could have a perennial thread "Links to discussions" consisting of entries like the following:

• Talk:Solid of revolution#Template a very old question which I found when looking at random articles --Hans Adler (talk) 07:58, 21 April 2009 (UTC)
• Talk:First-order logic#Clarification resolved --Hans Adler (talk) 07:58, 21 April 2009 (UTC)

Everybody would be encouraged to add new or stalled talk page sections. (Within reason this happens already.) When the list gets too long we can start a new one in a new section, so that the old one is archived automatically. If the experiment fails, at least we don't have additional pages lying around. If it's successful but clutters this page too much, we can still move it to a new page. --Hans Adler (talk) 07:58, 21 April 2009 (UTC)

First of all, it is certainly true that we can't force people to post on "page X" and nor can we force them to watch it. But at least some people will do so, yes? And "some" is probably better than nothing (at least the dedicated members of this project would do so). On the other hand, I agree that we should first test it out on this page to see if it works because this page would be more seen than "page X", in any case. So I believe that we should do as you say. I'll start a new section below to allow people to note any old discussions that they may remember, or any current important ones, and we will base the decision on the result. --PST 09:09, 21 April 2009 (UTC)

OK, I've created the section below. --PST 09:13, 21 April 2009 (UTC)

The other thing to note is that since it will take time to catch up with the old discussions, it would be of great help if people could note down any current discussions they notice that have been neglected. --PST 09:33, 21 April 2009 (UTC)

I have reservations about the suggestion above, but I think one thing that could work is to have a bot check talk pages of math articles and see which ones have recent comments. Then a page, like the current activity page, could be updated. It could have info like how often during a recent span some talk page is updated. I think this is simple and sufficient for the problem being discussed. --C S (talk) 09:44, 21 April 2009 (UTC)

I don't think that would work for the observed problem. Such a list will be dominated by the very active/high traffic talk pages while the problem was with issues raised on very low traffic talk pages. (TimothyRias (talk) 10:39, 21 April 2009 (UTC))

I'm not sure what you mean. Adding automation by a bot means talk pages will get listed regardless of being low traffic or high traffic. Indeed, in a way, if someone lists an entry on a manual list, as initially suggested, that article can't really be truly low traffic. Each entry (whether high traffic or not) would only show up once after the bot detects a recent talk page comment, so it couldn't dominate the others. Each entry would have additional info that could be useful, such as when the comment was made and whether the talk page was updated during a recent span. This would, I expect, even help entries not "dominate" others. The real problem, as I see it, is that people who know enough about this page to be part of this kind of listing project, usually have ways of gaining the attention from experts needed to improve the page. There may be an infrequent contributor who makes an enlightening comment on an article talk page, but since nobody watches that article, it doesn't get noticed at all. A central location that would note a comment was left on such and such talk page is better than nothing at all.

The bot would pick up such comments, from people who may not be aware of a central location to make such listings. With a manual list, once say, people are drawn to that page, will the entry then be removed? And when is it ok to remove? I expect that's problematic. With bot listed info like, "talk page entry made on such-and-such date, and 5 responses during the recent month", it'd be clear to people reading the list that there is perhaps enough traffic to that page, and others can be looked at. Indeed, the bot could do something like shuffle entries according to different sections like "talk page entry within the last 6 months but no response" and "talk page entry within last 6 months with more than 10 responses". Of course, this is a hypothetical bot, but I don't think it really requires a superbot to be able to do this.

One advantage a manual list offers is summaries, but here again, i see no reason why some human helping maintain the list could not add summaries too. The bot could as a default, list the section heading (if any), and this can be further edited and revised by a human if need be. --C S (talk) 11:25, 21 April 2009 (UTC)

I should add that just because I made a suggestion here doesn't mean I think this is a problem that should be addressed, given our limited resources. Consider things like tags that are already added to articles and listed on the current activity page. I don't really see more than a handful of people going through and fixing the problems indicated by the tags. A lot of these tags are added by non-math people which strongly indicates that those are important articles to fix so that non-math people can read them. Rather than creating more mechanisms so that people interested in the intricacies of some advanced topic (of which only a couple people know enough and are motivated to edit) can be notified of it, I'd suggest it's more important to just do the plentiful work that is already available, namely the tagged articles. --C S (talk) 11:37, 21 April 2009 (UTC)

We are having the same trouble, like everyone I suspect, at physics. I will be keeping a close eye to see if this works. Should we not also try to find ways to make the existing mechanisms work as well such as RfC or the cleanup tag? — Preceding unsigned comment added by TStein (talk • contribs)

Thanks User:C S for your comments. I am not sure how to operate a bot (although I have not really looked at them in detail). On the other hand, the procedure below seems to be going well (User:Hans Adler is contributing as well as some other editors). We'll see what other people think and how this goes but if you have an idea using a bot, feel free to get it started. --PST 02:17, 22 April 2009 (UTC)

proposing deletion of additive map

I feel that the recent article additive map should be deleted. Before taking formal action, let me explain myself and see whether others agree.

1) What is called here an additive map of rings $R_{1}\rightarrow R_{2}$ would be referred to by most mathematicians as a homomorphism $(R_{1},+)\rightarrow (R_{2},+)$. Since the multiplicative structure of the ring is not being used, it is somewhat strange that the article requires the objects to be rings: why not groups, or semigroups?

2) There is almost no actual content in the article. It is mostly an unmotivated definition.

3) The section on additive maps on a division ring is so incoherently written that I cannot understand it. Moreover, it is easy to show that an additive map from a division ring of characteristic zero to itself is simply a linear map of the underlying $\mathbb {Q}$-vector space. (Similarly, an additive map on a division ring of characteristic p is a linear map of the underlying $\mathbb {F} _{p}$-vector space.)

4) There are two "references" given to justify that the article is not orginal research. However, the references do not cite anything in the sources but simply list two entire texts, the first of which is 1400 pages long. This is not acceptable bibliographic practice.

Plclark (talk) 15:06, 21 April 2009 (UTC)

We already have an article additive function. Anything worthwhile in additive map should be merged to there. Algebraist 15:14, 21 April 2009 (UTC)

OK. I don't find any material in additive map which is worth merging into additive function. Anyone else? Plclark (talk) 21:22, 21 April 2009 (UTC)

I can't either. I've boldly redirected additive map to additive function. --Tango (talk) 21:35, 21 April 2009 (UTC)

Looks good to me. I'll go ahead and leave my comment anyways:

(ec)I don't see anything worth saving. I think the division algebra thing is trying to say additive maps between division rings can be represented as sums of "rank one tensors", except that if the destination division algebra is commutative, then it is claiming all additive maps are scalar multiplication, which is clearly false. I wonder if they mean to claim that every K-linear map between two central simple K-algebras, is a sum of such "rank one" maps. I wonder if that is true?

Someone might check Lyndon-Schupp to see if it mentions anything like this. I don't see why it would, but if it did, it might be some interesting math. Also it is a much shorter book. Google books does not think it mentions anything about division rings or algebras (or division really!), and while it does discuss some ring theory, I didn't see anything while searching for "additive" either. JackSchmidt (talk) 21:41, 21 April 2009 (UTC)

Links to discussions (current or ongoing) - see above section

Links (provide a link to the talk page in question, a comment on the discussion in question if the discussion is long, and your username if possible - otherwise just the link will do):

• Talk:Sylow_theorems#Third_part_of_Theorem_3 - --PST 09:24, 21 April 2009 (UTC)

• Talk:Compact_space#What_should_be_done_here.3F - quality rating of the article and a suggestion regarding the addition of another concept - --PST 09:27, 21 April 2009 (UTC)

• Talk:Compact_space#Compact_space_vs._complete_algebraic_variety - question that should have been posted at the reference desk - --PST 09:27, 21 April 2009 (UTC)

• Talk:Connected_space#Graphs - criticizm of an assertion that was/is in the article - --PST 09:30, 21 April 2009 (UTC)

• Talk:Locally_connected_space#New_revision - request for further input and suggestions for further improvement - --PST 09:30, 21 April 2009 (UTC)

• Talk:Discrete_mathematics#Article_rewrite - a significant effort was made to improve the article and was successful but of course further improvements are welcome - --PST 09:36, 21 April 2009 (UTC)

• Talk:Compact_operator#Finite_spectrum - criticizm of an assertion what was/is in the article - --PST 02:24, 22 April 2009 (UTC)

• Talk:Boolean algebra (structure)#Possible move to Boolean lattice – should the article be renamed to Boolean lattice? --Hans Adler (talk) 19:12, 22 April 2009 (UTC)

• Talk:Baire_set - a request (by me) that an expert help improve the article - also there have been some (recent) improvements to Baire set - --PST 06:57, 24 April 2009 (UTC)

Red Links

For the red links that start with the character "0", why are there so many numbers?Math Champion (talk) 03:18, 24 April 2009 (UTC)

Numbers don't normally start with "0". What special page are you using to see the list? — Arthur Rubin (talk) 05:31, 24 April 2009 (UTC)

My guess would be User:Mathbot/List of mathematical redlinks. Cheers, Ben (talk) 06:20, 24 April 2009 (UTC)

Most of those start with "-" or "−". Only five or so actually start with "0". — Arthur Rubin (talk) 06:27, 24 April 2009 (UTC)

My exhaustive sample of two of these -1284 and -1805 both came up with the links relating to Saros cycle. -1284 is on 54 (number)

The Saros number of the solar eclipse series which began on -1284 July 25 and ended on 32 September 3. The duration of Saros series 54 was 1316.2 years, and it contained 74 solar eclipses.

similar to -1805. So it seems that a lot of these are really years of questionably notability. --Salix (talk): 08:09, 24 April 2009 (UTC)

Sorry, I wasn't clear. I mean the numbers in the list that goes from 0 to 9. Math Champion (talk) 00:44, 25 April 2009 (UTC)

Alan Turing Year

The new page titled Alan Turing Year is moderately orphaned: probably more pages should link to it. Michael Hardy (talk) 17:12, 24 April 2009 (UTC)

Matrix (mathematics) and Euclidean algorithm for GAN

 Done

Matrix (mathematics) is now a Good Article Nominee. Please consider reviewing the article. Jakob.scholbach (talk) 12:31, 18 April 2009 (UTC)

The Euclidean algorithm is also up for GAN, and I would likewise appreciate a review. But please consider "Matrix" first, especially since Jakob helped a lot with improving the EA and I owe him a debt of gratitude. Proteins (talk) 13:21, 18 April 2009 (UTC)

TimothyRias is nearly done with his review of matrix (mathematics) as a Good Article; would someone else be willing to review the Euclidean algorithm? It'd be much appreciated. There's also a request for a peer review in preparation for nominating the EA as a Featured Article, asking especially for advice on the writing (criterion 1a). Proteins (talk) 18:14, 24 April 2009 (UTC)

I passed matrix for GA just now. Congratulations to Jakob and all others editors that were involved with this articles. (TimothyRias (talk) 07:25, 27 April 2009 (UTC))

Trisk

Resolved

Mathematical eyes would be welcome at Wikipedia:Articles for deletion/Trisk to confirm (or refute) my view that this article is codswallop. Regards, JohnCD (talk) 21:03, 25 April 2009 (UTC)

• Thanks to all who commented, article has been deleted per WP:SNOW as a hoax. JohnCD (talk) 12:32, 27 April 2009 (UTC)

Epsilonics

Resolved

Could someone with the requisite knowledge ascertain whether this is a suitable topic for an article, if it is a "translation" might be in order. Guest9999 (talk) 23:33, 25 April 2009 (UTC)

It's certainly not a well-written article. What's much worse (since it can't be remedied by re-writing) the definition is not standard (unless unbeknowst to me, I've been on Jupiter for a few decades; I can't entirely rule that out). I'd seriously consider merging it into (ε, δ)-definition of limit. Michael Hardy (talk) 03:59, 26 April 2009 (UTC)

....also, to speak of "finding the right epsilon" sounds weird. Usually, definitions say "for every epsilon, there exists delta,....". So epsilon is given; the problem is to find the right delta, not the right epsilon. Michael Hardy (talk) 04:00, 26 April 2009 (UTC)

The article goes through the proof that

$\lim _{x\to c}(f(x)+g(x))=L+M$

BEFORE mentioning that that is what is to be proved. Moreover, it phrases the beginning of the argument as if that is already known. As I said: badly written. Whoever wrote it seems to have some idea what the proofs are, but doesn't know how to write them and explain them. Michael Hardy (talk) 04:02, 26 April 2009 (UTC)

A.k.a. "epsilon-delta gymnastics". If it was a homework I'd give it a C. The real question is, is a simple example of this proof technique proper contents for WP? Jmath666 (talk) 07:26, 26 April 2009 (UTC)

I have made significant improvements to the article as well as included some context of this concept in mathematics. The mistake that I have made was to correct the previous version rather than erasing it and re-writing it completely. As a result, there are still possibly some incorrect logical implications within the proof of which I do not know. Therefore, I would probably leave the article as it is now, and let others polish it to perfection. --PST 12:31, 26 April 2009 (UTC)

I see that User:Point-set topologist has made some significant changes to the article. However, the future of the article remains unclear. No one has yet given any justification for the existence of an article whose content is entirely contained in another, more established article. My recommendation, following Michael Hardy, is that the article be merged with (ε, δ)-definition of limit. Plclark (talk) 16:17, 26 April 2009 (UTC)

This concept is also know as "epsilontics" and also includes the epsilon-N definition of a limit. However, reliable sources are thin on the ground and I agree with merging or replacing by a redirect until sufficient sources are found to support an article on the math culture associated with this. Geometry guy 20:07, 26 April 2009 (UTC)

I also think this should be merged into (ε, δ)-definition of limit, since they are on the same topic. The more general topic, of course, is the use of approximation and estimation techniques; that topic is mathematical analysis. — Carl (CBM · talk) 21:45, 26 April 2009 (UTC)

Looking over the discussion here, I went ahead and redirected the article. — Carl (CBM · talk) 15:15, 27 April 2009 (UTC)

Note that there is some information in that article that could be added to the redirect article or at least to some other articles. --PST 00:09, 28 April 2009 (UTC)

Ideal ring bundle

Ideal ring bundle is an orphaned article. It it's a valid topic, then it needs work. Michael Hardy (talk) 21:04, 27 April 2009 (UTC)

Base-27 numeral system

Is a base-27 numeral system septemvigesimal or heptovigesimal ? Both articles are unsourced. Clearly a merge is required - but under which title ? Gandalf61 (talk) 10:06, 28 April 2009 (UTC)

Don't know what is actually being used, but the Latin-based "septemvigesimal" makes more sense, as "heptovigesimal" mixes Greek and Latin roots. — Emil J. 10:13, 28 April 2009 (UTC)

Orphaned article

I've just stumbled across the orphaned article Generating set of a topological algebra. In addition to being linked from somewhere it needs a proper introduction at the very least. Thryduulf (talk) 09:56, 29 April 2009 (UTC)

I have boldly merged the article into topological algebra, which I have also expanded a bit. Incidentally, "topological algebra" might be a better title for the theory. E.g. such an article could discuss the principle of reading the definition of groups, rings, algebras in the category of topological spaces to get topological groups, topological rings, topological algebras. I could not verify the claim about van Dantzig. Because of the general issues around associativity and units for algebras, this claim might be slightly misleading even if basically true. --Hans Adler (talk) 12:43, 29 April 2009 (UTC)

"Probabilistic interpretation of Taylor series" on AfD

Probabilistic interpretation of Taylor series has been nominated for deletion. I wondered if this should be considered another case of a badly written article being mistaken for a bad article. I've done some cleanup and organizing, but more can be done.

So help improve the article if you can, and opine at Wikipedia:Articles for deletion/Probabilistic interpretation of Taylor series. As usual, don't just say Keep or Delete; give arguments. Michael Hardy (talk) 15:20, 29 April 2009 (UTC)

May 2009

Moves to inappropriate names?

Recently, Nbarth (talk · contribs) has moved some articles to new names which are inappropriate according to Wikipedia:Naming conventions. In particular, I noticed that he moved Lambert quadrilateral to Ibn al-Haytham–Lambert quadrilateral and Saccheri quadrilateral to Khayyam–Saccheri quadrilateral, saying "full term, credit original discoverer". JRSpriggs (talk) 13:52, 20 April 2009 (UTC)

Looking at the link, some of the moves did conform to the Wikipedia conventions, however some did not. In my opinion, it would be in the best interests of the user to notify him/her about the issue. --PST 13:58, 20 April 2009 (UTC)

OK. I left a message on his talk page. JRSpriggs (talk) 14:13, 20 April 2009 (UTC)

I think these are the wrong names for those articles and they should be moved back. This is English Wikipedia. Nbarth has argued that Wikipedia:Neutral_point_of_view#Article_naming is in conflict with naming convention guidelines but actually, that section of the NPOV policy explicitly states:

Where proper nouns such as names are concerned, disputes may arise over whether a particular name should be used. Wikipedia takes a descriptive rather than prescriptive approach in such cases, by using the common English language name as found in verifiable reliable sources. Where inanimate entities such as geographical features are concerned, the most common name used in English-language publications is generally used. See Wikipedia:Naming conflict for further guidance.

It couldn't be any clearer. Even Nbarth has stated the common English names are Lambert quadrilateral and Saccheri quadrilateral resp. --C S (talk) 01:02, 1 May 2009 (UTC)

I moved the pages back per the above reason. I have notified Nbarth to this discussion thread. --C S (talk) 01:08, 1 May 2009 (UTC)

I've also reverted Saccheri quadrilateral back to the previous version not only to revert the terminology but because I think it reads slightly better. Regarding the terminology issue, however, it's not appropriate for use to try and rectify historical wrongs by using terminology less likely to be familiar to the reader. Khayyam is actually given plentiful credit in the article (there's more on him than Saccheri). --C S (talk) 01:31, 1 May 2009 (UTC)

Recursion

Resolved

Someone is once again adding circular links from recursion to itself. Could someone else deal with it this time? — Carl (CBM · talk) 14:43, 27 April 2009 (UTC)

It seems to have stopped after Carl reverted him Incidentally I don't see what's wrong with a little joke under the "see also" section, but I understand jokes aren't for everyone :-). --C S (talk) 01:16, 1 May 2009 (UTC)

Euclidean algorithm at FAC

I have nominated Euclidean algorithm at FAC. Please consider reviewing the article. Thank you to the several mathematicians here who helped to improve the article over the past few weeks. It was much appreciated and the favor will be returned. Proteins (talk) 16:28, 27 April 2009 (UTC)

A gentle reminder to the mathematicians here that the Euclidean algorithm is still at FAC, and would benefit from their reviewing it. Several mathematicians have helped to improve the article (thanks, all!), but more reviewers would be welcome. Thank you, Proteins (talk) 15:27, 1 May 2009 (UTC)

Another Weisstein neologism?

Please comment at Talk:Sexy prime#neologism.3F. --Trovatore (talk) 23:29, 3 May 2009 (UTC)

Articles in need of attention/cleanup/something

Equipossible and Equiprobable could really need some help:

Equiprobability is a philosophical concept in probability theory that allows one to assign equal probabilities to outcomes that are judged to be equipossible or to be "equally likely" (in some sense).

Equiprobability "allows" one to assign probabilities? Etc. etc.

CRGreathouse (t | c) 17:27, 7 May 2009 (UTC)

Loyer's paradox on AfD

I've nominated the article titled Loyer's paradox for deletion. I hesitated for a few weeks before doing this because the article's author had said he would replace the content. Some time has gone by with no progress on this. I'll withdraw the nomination if he can do that. But for now, see the discussion at Wikipedia:Articles for deletion/Loyer's paradox. Don't just say Keep or Delete; give your arguments for your position. Michael Hardy (talk) 00:27, 8 May 2009 (UTC)

Treatment of tensors

Apparently there are nearly half a dozen articles treating tensors:

• Tensor
• Classical treatment of tensors
• Intermediate treatment of tensors
• Tensor (intrinsic definition)
• tensor field

and maybe even more.

Besides the awful naming of these articles (what is 'classical' about the component treatment of tensors), is it in anyway useful? It seems to me that there must be a better way of organizing these articles. Any thoughts? (TimothyRias (talk) 11:21, 22 April 2009 (UTC))

Oh my gosh, this is awful. It looks like these are all content forks of the same material. Something has to be done with this. There's also a tensor product article which covers the same material again! What a mess. Ozob (talk) 15:11, 22 April 2009 (UTC)

It does seem like a lot of work to cobble all these articles together! On a hunch, I also noticed dyadic tensor, dyadics, symmetric tensor, antisymmetric tensor and pseudotensor. I've a soft spot for axiality and rhombicity since I published on that in protein NMR, but they should probably be integrated into another article as well. On the other hand, it might be good to separate tensor and tensor field. Proteins (talk) 17:57, 22 April 2009 (UTC)

I'm in full agreement. On top of the (mis)organisation of these articles, for instance the main tensor article is in quite bad shape. Can anyone get any view on what a tensor is from that one? I met this mess of articles more than a year ago, I think; what kept me from getting involved was that these articles seem to be subject of frequent and unproductive disputes. Tensors (in all their meanings) could be among those entities where the mathematical and (undergrad?) physical / engineering usage and customs are very far from each other. Full clean-up is in order, but could be resisted, I'm afraid. Stca74 (talk) 17:59, 22 April 2009 (UTC)

You know, this is a pretty old mess. I seem to recollect that there should be a simple, concrete article explaining basic tensor stuff like sum convention, raising/lowering indices, etc., without using abstract algebra. I don't know what happened to it (if it ever existed), but the "classical treatment" version is clearly inadequate. The problem seems to be that tensors are a subject that a wide variety of people are interested in reading about, undergrad engineers, people studying relativity, etc. Due to frequent complaining about articles being unreadable (understandable and justified in my view), some kind of compromise was arranged with different level articles. Unfortunately, the above organization doesn't seem to be how I remember things (some of "intermediate treatment" seems to have been at "classical treatment" before...). It might be worthwhile asking User:Kevin_Baas what happened; he's one of the few people, I think, that has been there through the entire history of these articles. --C S (talk) 18:30, 22 April 2009 (UTC)

From the standpoint of someone who learned tensors in order to study general relativity, I think that the Classical treatment of tensors is much easier to understand than the other articles. Also, you missed Tensor density, a closely related generalization. JRSpriggs (talk) 09:56, 24 April 2009 (UTC)

It might be easier to understand, but only because there's hardly anything there. That's why I call it inadequate. Not to mention, the only explanation of what's going on is the "abstract" one, talking about bundles and such. --C S (talk) 15:57, 24 April 2009 (UTC)

I don't understand why I "missed" that article, but thanks for bringing that to our attention. --C S (talk) 16:00, 24 April 2009 (UTC)

Also related are Covariant transformation and Covariance and contravariance of vectors.

To C S: Physicists and engineers do not care what a tensor really is, they only want to know how to use it. That is, how to transform them, add them, multiply them, etc.. For that purpose, the classical treatment (which I learned from one of Eddington's books on relativity) is quite sufficient. JRSpriggs (talk) 00:34, 1 May 2009 (UTC)

Yes, I understand what it is you're saying. But I wasn't saying that Eddington's treatment was insufficient. I think nobody could learn how to use tensors from classical treatment of tensors. --C S (talk) 00:37, 1 May 2009 (UTC)

I don't know what your comment about what tensors "really is" is in response to. What I said was that classical treatment of tensors doesn't give sufficient explanation of what is going on, only giving some abstractions. I didn't mean something abstract like "what tensors really are" (whatever that means), but rather I don't think sufficient explanation is given for engineers to understand their computations. Even engineers need to understand some basics of what they are computing, otherwise the computer would replace them. I seriously doubt any engineer is going to be able to work out any tensor computations after reading that article. It is considerably spare compared to the usual "how to use" treatments I have seen. --C S (talk) 00:41, 1 May 2009 (UTC)

Just a quick comment that Hamilton's ideas, and the quaternionists point of view, have somewhat of a claim on the right to share the tensor name space with those of the matrix algebra point of view. Tensor of a quaternion being an example of a defunked article on the subject.130.86.76.31 (talk) 23:24, 4 May 2009 (UTC)

The "mess" is largely caused by incompatible ideas of pedagogy in this area. Being a mathematician I would prefer to discuss what a tensor is, rather than what someone else thinks is the right way to teach tensors to the people he or she has to teach, for whatever purpose that will be. And I would argue that an encyclopedia (rather than a textbook) has an obligation to address that question. The social fact is that there were in the past plenty of people agitating for their version of a suitable pedagogy of tensor products to be in Wikipedia. Hence the forking. If anyone wants to re-run the whole discussion, go ahead; but I would be unsympathetic to involving certain people from the past of the article, and to hearing once more what the article ought to contain. These days we should ask for reliable sources, starting from the very definitions. Charles Matthews (talk) 22:11, 7 May 2009 (UTC)

Unfortunately I think you'll run into a lot of resistance insisting on what a tensor is. Classically, as far as I can tell tensors were treated as new primitive quantities that were not describable in terms of other quantities. What a tensor is (in this case, a section of a tensor product of tangent and cotangent bundles) was never specified; indeed, it couldn't be specified until the language of tensor products of vector bundles had been developed. As far as I can tell, this approach to tensors is still universal in engineering and the physical sciences. I have even heard a prominent applied mathematician say derogatory things about the incomprehensible way in which algebraists approach tensors.

My own view is that the main tensor article should begin with the history, and I mean a thorough history, not one that stops a little after 1900 like the present tensor article's history does. A thorough history would introduce both the viewpoint that a tensor is a quantity that transforms in a certain way as well as the viewpoint that a tensor is a section of a certain vector bundle; it would even mention that a tensor is in general an element of a tensor product of modules (or a section of a tensor product of sheaves). I think that gives a foundation to discuss all the aspects of tensors, classical, modern, or whatever. Ozob (talk) 17:10, 8 May 2009 (UTC)

Well, we do have content policies here, and they are not suspended when there is disagreement on the type of treatment. Rather, that is exactly the context where they should be brought into play. The normal view isn't that you start the article with a thorough history, because we believe in a 'concentric' treatment. We don't make the article group (mathematics) start with a history that has to include the odd order theorem; we start with information about what a group is, and why groups matter in mathematics, as well as some relevant history.

It is also valid to bring into the discussion what other encyclopedias do. The big Soviet encyclopedia, the basis of the Springer encyclopedia, has articles: tensor algebra, tensor analysis, tensor bundle, tensor calculus, tensor density, tensor on a vector space, tensor product. As well as related ones such as multilinear algebra. The Japanese Encyclopedic Dictionary of Mathematics takes a different approach, with one main article tensor calculus from a differential geometer's point of view, but about 50 different sections in articles spread over the encyclopedia treating different aspects of tensors. Neither of those models starts with the assumption that a 'killer' article is the ideal.

By the way, bringing up sniping of applied mathematicians is about as unhelpful a comment as can be made here. There is the whole traditional pedagogic issue of 'methods of mathematical physics' courses. (I learned tensors, if you could call it that, from Eddington and then a DAMTP treatment following Jeffreys.) But that is not for here. Anyone who wants to write 'methods' material can do a wikibook that way. The mission statement for Wikipedia is clear: articles about tensors compile verifiable facts about tensors. Charles Matthews (talk) 19:03, 8 May 2009 (UTC)

Algorithmic Lovász local lemma

The new article titled Algorithmic Lovász local lemma has no introductory section. This raises two questions:

• Can someone do something about it?
• I thought there was a template for such occasions. Where is it?

Michael Hardy (talk) 04:21, 9 May 2009 (UTC)

Template:Intro-missing? --El Caro (talk) 11:30, 9 May 2009 (UTC)

I've added that template—thank you. Michael Hardy (talk) 17:08, 10 May 2009 (UTC)

GAR for Rubik's Cube

The article Rubik's Cube is tagged as being a part of this WikiProject, so I am letting the members know that I have started a Good Article Reassessment as part of the GA Sweeps process. You can find a list of my concerns on the article's talk page. Thanks and good luck! Nikki♥311 00:39, 13 May 2009 (UTC)

PlanetMath

Just to let you know, looks like the PlanetMath undergoes an extensive editing. If so, the more eyes the better... ptrf (talk) 13:08, 14 May 2009 (UTC)

Amazing. After about 80 edits by Bci2, the article seems to have undergone absolutely no improvement. Quite the contrary. --C S (talk) 14:10, 14 May 2009 (UTC)

TeX question

${\begin{aligned}{\frac {1}{N_{e}^{(F)}}}={\frac {1}{4T}}\left\{{\frac {1}{N_{0}^{f}}}+{\frac {1}{N_{0}^{m}}}\right.&{}+\sum _{i}\left(\ell _{i+1}^{f}\right)^{2}\left(v_{i+1}^{f}\right)^{2}\left({\frac {1}{\ell _{i+1}^{f}}}-{\frac {1}{\ell _{i}^{f}}}\right)\\&\left.{}+\sum _{i}\left(\ell _{i+1}^{m}\right)^{2}\left(v_{i+1}^{m}\right)^{2}\left({\frac {1}{\ell _{i+1}^{m}}}-{\frac {1}{\ell _{i}^{m}}}\right)\right\}.\end{aligned}}$

The sizes of the left and right curly braces above do not match, and in fact, the one on the left isn't big enough for the last set of fractions on the first line. Can something be done about this while retaining the format the breaks the whole display into two lines? Michael Hardy (talk) 11:11, 14 May 2009 (UTC)

Is this what you want?

${\begin{aligned}{\frac {1}{N_{e}^{(F)}}}={\frac {1}{4T}}\left\{{\frac {1}{N_{0}^{f}}}+{\frac {1}{N_{0}^{m}}}{}+\sum _{i}\left(\ell _{i+1}^{f}\right)^{2}\left(v_{i+1}^{f}\right)^{2}\left({\frac {1}{\ell _{i+1}^{f}}}-{\frac {1}{\ell _{i}^{f}}}\right)\right.\;\;\,&\\\left.{}+\sum _{i}\left(\ell _{i+1}^{m}\right)^{2}\left(v_{i+1}^{m}\right)^{2}\left({\frac {1}{\ell _{i+1}^{m}}}-{\frac {1}{\ell _{i}^{m}}}\right)\right\}.&\end{aligned}}$

--Hans Adler (talk) 12:07, 14 May 2009 (UTC)

That seems to do it. I've now used (approximately) that format in effective population size.

Thank you, Hans. Michael Hardy (talk) 11:20, 16 May 2009 (UTC)

Normally you would use \vphantom, by inserting

\vphantom{\sum_i\left(\frac{1}{P_1^f}\right)}

inside the first set of delimiters. However, this does not work with Mediawiki's tex engine; the vphantom command is not recognized. So you must either set the sizes manually (big, bigg, etc) or use an alignment hack like Hans suggests. — Carl (CBM · talk) 13:19, 14 May 2009 (UTC)

Template:SpecialChars

There is an edit war brewing at convolution over the placement of the {{SpecialChars}} template. There seems to be no precedent for placing this at the top of maths articles, and there is no editing guideline as far as I can tell either — certainly nothing at WP:MOSMATH. My chief objection is that the template is ugly and pushes the meaningful content further down the page. Sławomir Biały (talk) 12:34, 15 May 2009 (UTC)

In general I do not think we need to use this template on math articles at all. Perhaps if the special characters were unexpected, it would help, but for a math article people should expect them. — Carl (CBM · talk) 10:39, 16 May 2009 (UTC)

Strange page

János Komlós is, as of a few minutes ago, a disambiguation page. Before that, it said this:

János Komlós is an American mathematician, working in probability theory, discrete mathematics. He is a professor at the Rutgers University.

He was also (Budapest, 9 February, 1922–Budapest,18 July, 1980): an influential writer, journalist under the Kadar political era in Hungary.

Several years ago, we used to frequently see pages putting unrelated topics on the same page like this because they were known by the same term (see the edit history of tar, which was about computer software and viscous gooey stuff), but I don't recall seeing this odd way of using the word "he" (or "she", or maybe even "it") before. I'd use that word only if referring to the same person.

The page on the mathematician needs something added about notability. Michael Hardy (talk) 18:44, 15 May 2009 (UTC)

I've added some information which I think shows a pass of WP:PROF #1 and likely #3. —David Eppstein (talk) 01:07, 16 May 2009 (UTC)

Wolfram Alpha and possible use as for reference on mathematics articles

The issue of whether or not Wolfram Alpha can be used for reference on WIkipedia has been raised several other places on WIkipedia. It seems to me that the place is it most likely to be desirable for reference is within WikiProject Mathematics. WIkiProject Mathematics already makes extensive use of Wolfram's other web resources and is familiar with the computational abilities of Mathematica.

So, what guidelines should apply? --Pleasantville (talk) 15:40, 18 May 2009 (UTC)

I do not believe it is a useful source for mathematics articles. The key things we want in a source are additional context and additional depth compared to the Wikipedia article. I looked at Wolfram Alpha briefly, and all it ever gave me was a glorified infobox; less information than a Wikipedia article would provide. — Carl (CBM · talk) 18:23, 18 May 2009 (UTC)

Fractional part and equation rearrangement

I'm involved with a dispute with an anonymous editor over how to write the fractional part of a number and whether it is permissable or desirable to make some minor rearrangements to an equation rather than copying it directly from a source, and I'd welcome additional opinions on this dispute. See Talk:Calkin–Wilf tree#Newman's formula, and please leave responses there rather than here. —David Eppstein (talk) 16:24, 18 May 2009 (UTC)

New Featured Article for WPM

A top-priority, frequently-viewed article, Euclidean algorithm, has just been promoted to Featured Article — thanks very much to everyone who helped in that effort!

No article is perfect, so of course I'll continue to (try to) improve this one. I appreciate your keen criticisms and I'll do my best to incorporate them.

I've begun a rudimentary sketch of an article at Fermat's Last Theorem, and I'd be grateful for your suggestions and ideas. If anyone is interested in helping out there, I'd appreciate that as well. The article is still quite primitive, however. Proteins (talk) 05:05, 20 May 2009 (UTC)

GA Sweeps invitation

This message is being sent to WikiProjects with GAs under their scope. Since August 2007, WikiProject Good Articles has been participating in GA sweeps. The process helps to ensure that articles that have passed a nomination before that date meet the GA criteria. After nearly two years, the running total has just passed the 50% mark. In order to expediate the reviewing, several changes have been made to the process. A new worklist has been created, detailing which articles are left to review. Instead of reviewing by topic, editors can consider picking and choosing whichever articles they are interested in.

We are always looking for new members to assist with reviewing the remaining articles, and since this project has GAs under its scope, it would be beneficial if any of its members could review a few articles (perhaps your project's articles). Your project's members are likely to be more knowledgeable about your topic GAs then an outside reviewer. As a result, reviewing your project's articles would improve the quality of the review in ensuring that the article meets your project's concerns on sourcing, content, and guidelines. However, members can also review any other article in the worklist to ensure it meets the GA criteria.

If any members are interested, please visit the GA sweeps page for further details and instructions in initiating a review. If you'd like to join the process, please add your name to the running total page. In addition, for every member that reviews 100 articles from the worklist or has a significant impact on the process, s/he will get an award when they reach that threshold. With ~1,300 articles left to review, we would appreciate any editors that could contribute in helping to uphold the quality of GAs. If you have any questions about the process, reviewing, or need help with a particular article, please contact me or OhanaUnited and we'll be happy to help. --Happy editing! Nehrams2020 (talk • contrib) 06:23, 20 May 2009 (UTC)

Allegation of error in a peer reviewed source

Over at Talk:Monty Hall problem/Arguments#Error in Morgan et al? there's a claim that the primary academic source about the Monty Hall problem computes the conditional probability of winning by switching using the wrong Bayesian prior. The source is Morgan, J. P., Chaganty, N. R., Dahiya, R. C., & Doviak, M. J. (1991). "Let's make a deal: The player's dilemma," American Statistician 45: 284-287. Are there any Bayesians here who could comment on this? The specific issue is whether the probability of winning by switching (which is 1/(1+q) where q is the host's preference for the door that has been opened, i.e. door 3 in the usual problem setup) given the noninformative prior should be computed using:

1) a uniform distribution of q in the conditional case, i.e. q is uniformly distributed in the conditional case where the player has picked door 1 and the host has opened door 3. This makes the probability of interest

$\int _{0}^{1}{\frac {1}{1+q}}dq=ln(2)\approx .693$

or

2) a uniform distribution of q in the unconditional case, so the distribution in the conditional case must be computed as a conditional distribution

$\int _{0}^{1}{\frac {1}{1+q}}f(q)dq=2/3$

where f(q) is the conditional distribution of q given the host has opened door 3.

The paper uses #1. Several users are claiming #2 is correct. -- Rick Block (talk) 16:53, 16 May 2009 (UTC)

Note that the in the paper in question, it is clearly the prior distribution of q that is taken to be uniform. They say, '..the noninformative prior in the vos Savan scenario makes this probability...'. Martin Hogbin (talk) 08:38, 20 May 2009 (UTC)

Ron Larson

We've had a well-written submission at WP:AfC on this person, and would welcome opinions on whether he meets WP:PROF. It can be found at Wikipedia:Articles for creation/Ron Larson (mathematician). Thanks, — Martin (MSGJ · talk) 10:17, 20 May 2009 (UTC)

Having a textbook that goes to nine editions looks like a pass of WP:PROF #4 to me. I don't see the case for the other criteria, but it only takes one. As for the article, it could stand some form of inline citation so we can tell which information which comes from which source, but that's a cleanup issue rather than one of whether it should be kept. —David Eppstein (talk) 16:33, 20 May 2009 (UTC)

The textbook also caught my eye. If there was any doubt, the quality of the article sold me. Most newly-created articles are much less informative and well-written. CRGreathouse (t | c) 19:26, 20 May 2009 (UTC)

There's a fair amount of subjective sentences, verging on peacock, but I agree that it's in a fine state for a new article. It's created; thanks for the comments. — Martin (MSGJ · talk) 20:34, 20 May 2009 (UTC)

Links to discussions

The section started by PST was archived due to inactivity, so I am starting another one.

• Talk:Triadic relation#Article rewritten; proposed move to ternary relation over redirect --Hans Adler (talk) 23:09, 14 May 2009 (UTC)
• Talk:Relation (mathematics)#Merge directed relation – Relation (mathematics) is a strange tiny content fork of finitary relation/binary relation. What do we do with it? --Hans Adler (talk) 23:42, 14 May 2009 (UTC)
• Talk:Order theory#GA Reassessment - Several important points were made by User:Geometry guy here, but to no avail. --PST 09:17, 24 May 2009 (UTC)

I've moved triadic relation to ternary relation. Michael Hardy (talk) 00:13, 15 May 2009 (UTC)

Codomain definition

An editor is trying to change the definition of a codomain to say a function is the same if the codomain changes. I believe it is a problem from the way logicians handle functions and then trying to go to the way it is normally done in maths. Anyway discussion at Talk:Codomain#Reverted? Dmcq (talk) 10:15, 23 May 2009 (UTC)

Efficient arithmetic

Below is my adaptation of something that an anonymous reader added to the article titled complex number recently. user:Paul August deleted it from the article. He's probably right that it doesn't belong in such a prominent place, but it should be somewhere within Wikipedia. Is there a suitable article to insert it into? Then maybe a see-also link from complex number to link there. Michael Hardy (talk) 20:10, 22 May 2009 (UTC)

Complex multiplication in only three real multiplications instead of four

In computing the product (a + bi)(c + di), one can reduce calculations in the following way.

Let

${\begin{aligned}k_{1}&=c(a+b),\\k_{2}&=a(d-c),\\k_{3}&=b(c+d).\end{aligned}}$

Then the real and imaginary parts of (a + bi)(c + di) are as follows:

${\begin{aligned}{\text{real part}}&=k_{1}-k_{3},\\{\text{imaginary part}}&=k_{1}+k_{2}.\end{aligned}}$

This method has been used by computers to reduce the number of multiplications by adding a few additions. This is most commonly used in fast Fourier transforms where one uses only three multiplications and three additions.

end of excerpt

Multiplication algorithm I suppose. I guess it might be used in a fixed point integer implementation. The scaling needed for addition with floating point tends to offset any speed gains addition should have compared to multiplication. Dmcq (talk) 20:25, 22 May 2009 (UTC)

In fact it can be useful for the complex multiplication in FFT because the twiddle factors can be precomputed so one only has three adds and three multiplies. So there's a choice between FFT, complex numbers and multiplication algorithms. I'm not sure who discovered it - that would be good for a citation. The article Arithmetic complexity of the discrete Fourier transform gives some amazingly low minimum numbers of multiplies. Dmcq (talk) 12:23, 23 May 2009 (UTC)

I recall hearing that this was discovered by Gauss. But I heard that in a seminar talk, and I don't know a written reference. Ozob (talk) 21:55, 26 May 2009 (UTC)

It would be good to have a reference that this numerical method is used in practice, and is not just a teaching example. At first glance, the method seems susceptible to a loss of precision when ac or bc is large compared to the other terms. Proteins (talk) 16:59, 24 May 2009 (UTC)

These formulas are given as the solution of an exercise in Knuth, although he does not claim they have any practical value and he does include the warning "Beware numerical instability." He doesn't give a reference for this particular formula but does give references for other alternative formulas. See Knuth, Seminumerical Algorithms, 3rd edition (1998), section 4.6.4 exercise 41 (pp. 519, 706). --Uncia (talk) 22:35, 26 May 2009 (UTC)

Added a bit to Multiplication algorithm about it thanks. Dmcq (talk) 22:58, 27 May 2009 (UTC)

Binomial theorem

I have put a cleanup tag on binomial theorem. It's a typical page about a basic topic which has just grown up in a straggly way: it has duplication, poor structure, an "in popular culture" section, and other indicators of a lack of TLC. Needs a general taking in hand. Charles Matthews (talk) 12:40, 27 May 2009 (UTC)

Pointer to discussion: Propositional logic or sentential logic?

We currently have an article Propositional logic and a category Category:Sentential logic. I have started a discussion at WT:WikiProject Logic#Propositional logic or sentential logic? --Hans Adler (talk) 13:53, 27 May 2009 (UTC)

Logarithmic differentiation

Logarithmic differentiation seems to lack good concrete examples, and maybe it's somewhat disorganized. I'll be back.... Michael Hardy (talk) 17:37, 26 May 2009 (UTC)

I would say that log differentiation is used whenever it is easier to differentiate $\ln f(x)$ than the original function, $f(x),$ which is true when

$f(x)=\prod (f_{i}(x))^{\alpha _{i}(x)}$

And the function has to be non zero, not positive, because

${\frac {d}{dx}}\ln |x|={\frac {1}{x}}$

(Igny (talk) 23:26, 26 May 2009 (UTC))

@MH: shortly after the origination of this article, some complained about it being too textbook-like because of the examples it incorporated. They were therefore removed and taken to Wikibooks. —Anonymous Dissident^Talk 02:34, 30 May 2009 (UTC)

Unrendered TeX

For several hours now, when I save a page or preview a page, some of the lines of TeX fail to get rendered. Wikipedia usually works well in that regard, but not today. Have others had that experience? Michael Hardy (talk) 19:40, 26 May 2009 (UTC)

Do you mean they just render as normal HTML but not image? You can change that in your preferences. --Visit me at Ftbhrygvn (Talk|Contribs|Log|Userboxes) 01:50, 29 May 2009 (UTC)

No—I meant I just saw the TeX code.

It hasn't happened today, though. Michael Hardy (talk) 01:57, 29 May 2009 (UTC)

I saw it few times in the past few days. It went away after few seconds by itself, or on page reload. Jmath666 (talk) 04:56, 29 May 2009 (UTC)

I've seen it before. The reason you see the TeX code is that the browser (Firefox?) shows the alt-text of an image when it fails to load. Shreevatsa (talk) 12:58, 29 May 2009 (UTC)

Surface area

This article is currently shocking. I'd write it myself, but do need feel comfortable in my ability to be rigorous enough. Any help would be fantastic. —Anonymous Dissident^Talk 02:31, 30 May 2009 (UTC)

OMG! The rating is completely wrong! It should be a top-priority stub! It MUST be improved! Unfortunately, I am currently busy for my exam and improvement works on Matrix. I will start working on this when I have more spare time. Visit me at Ftbhrygvn (Talk|Contribs|Log|Userboxes) 03:47, 30 May 2009 (UTC)

Looking through the history, there used to be a lot more to this article. For some reason it was pared down to a bare four sentences. I'm not really sure why. —Bkell (talk) 04:10, 30 May 2009 (UTC)

I have restored the seemingly last complete version, I had to go more than a year back for that. This article gets shocking amounts of juvenile vandalism, in addition to some unscrupulous edits and edits whose motivation escapes me as well. I suspect the reasons for vandal's attention are similar to the situation at Geometry. Given its history and difficulty of maintaining an article under such circumstances, I propose to semiprotect it indefinitely. Arcfrk (talk) 06:11, 30 May 2009 (UTC)

References -> Further reading crusade

User:TedPavlic seems to be intent on changing "References" sections into "Further reading". This seems quite unwarranted. As far as I know, there is no rule that References sections must contain only footnotes. Indeed, most mathematics articles on Wikipedia seem to do just fine without an enormous proliferation of footnotes. I'm going to be undoing most of these changes, unless there are significant objections here. Sławomir Biały (talk) 19:42, 30 May 2009 (UTC)

Fair enough but I couldn't see anywhere on his Talk page where you've told him you disagree with what he is doing. Have I missed something or were you just coming here to see what other people thought first? Dmcq (talk) 20:48, 30 May 2009 (UTC)

I have posted a message on the user's talk page, per your recommendation. My reason in posting here first is that it seems to me that editorial decisions like this that potentially effect a great number of articles should be made in the open rather than in users' talk pages. Sławomir Biały (talk) 22:29, 30 May 2009 (UTC)

Zero element or zero elements or.....?

What shall we do with this situation? Michael Hardy (talk) 04:56, 31 May 2009 (UTC)

I believe the parenthetical there would make the change correct.Julzes (talk) 05:12, 31 May 2009 (UTC)

OOPS. Hold on the parenthetical should be removed from the original!Julzes (talk) 05:14, 31 May 2009 (UTC)

I didn't manage to find the phrase "semigroup with zero element(s)" in the Grillet reference, so I'm not convinced this isn't a neologism, in which case its probably just poor grammar. I suggest changing it to "Empty semigroup" or "Semigroup with no elements" unless it can be shown that "semigroup with zero element(s)" is actually a way it is referred to. RobHar (talk) 05:18, 31 May 2009 (UTC)

Yes (e/c), that's something like what I was trying to say. It seems that the old definition of semigroup is being brought in line with category theory type thinking.Julzes (talk) 05:23, 31 May 2009 (UTC)

And, furthermore, I would check whether a categorical framework might not be common modern practice for the possibility of improving the semigroup and perhaps other articles.Julzes (talk) 05:33, 31 May 2009 (UTC)

I WP:BOLDly moved it to empty semigroup. "With zero elements" is not typical English usage (it would more idiomatically be "with no elements" or "without any elements") and the "zero element" phrasing made it too easily confused with a monoid (a semigroup that, using additive notation, has an element that acts like the number zero). I haven't done anything about the contents, though. —David Eppstein (talk) 07:32, 31 May 2009 (UTC)

That seems like a good way to start, but the whole category theory approach might find a regular place in the algebra articles generally.Julzes (talk) 07:35, 31 May 2009 (UTC)

The group (mathematics) article is a good case in point. It looks like a beautiful article, but mentioning categories might be a good thing in the introduction, say after mention that groups are a kind of algebraic structure.Julzes (talk) 07:42, 31 May 2009 (UTC)

Should Semigroup with one element also move to Trivial semigroup? —Dominus (talk) 21:25, 31 May 2009 (UTC)

Yes, that seems better.Julzes (talk) 02:14, 1 June 2009 (UTC)

PR

I have requested a PR for Matrix. Please comment on the article so that I can improve it to FA. Visit me at Ftbhrygvn (Talk|Contribs|Log|Userboxes) 13:05, 31 May 2009 (UTC)

Jun 2009

References to Non-Newtonian calculus

References to Non-Newtonian calculus are being added to to the 'See also' section of various articles related to the exponential function. They don't seem relevant enough to warrant inclusion, but what should I put into a comment when removing them - is there a guideline please? Or do you think they are reasonable? Dmcq (talk) 16:01, 30 May 2009 (UTC)

The guideline is WP:SEEALSO, although it leaves it mostly up to the judgment of the editor. "See also" is slightly deprecated, in the sense that it is better to weave the items into the narrative. My opinion is that this subject is irrelevant to the exponential function, so I would be bold and delete the links with the comment "remove irrelevant wikilink". --Uncia (talk) 16:36, 30 May 2009 (UTC)

Non-Newtonian calculus is the pet project of User:Smithpith. He's identified himself as Michael Grossman, one of the inventors of non-Newtonian calculus, and consequently he has a WP:COI every time he writes about it. In my opinion, the "theory" is a non-notable piece of quackery, but unfortunately the article survived AfD. I would love to see it go away, though. Ozob (talk) 15:32, 1 June 2009 (UTC)

Looking for help with mathematical coincidence

There is current and threatened editorial action on the article mentioned. The article is primarily a list, and I would like to improve its nature. I would also categorize it as a part of mathematics education, if such is possible. I have one citation to "attempted" work by a CalTech Ph.D. at zhurnaly.com/cgi-bin/wiki/CoincidentalTaxonomy that I would like to use or suggest as being used in the article. I also think the article might be re-directed to a larger article on mathematical curiosities. I have my own original results that I deem not to be research that I also would like to place in the introduction or body of the article as well. This is the subject matter you can find at User:Julzes/365.25. The results were found by happenstance, this being my explanation for not regarding them as research, and I have no interest in staking a claim to them.Julzes (talk) 04:40, 31 May 2009 (UTC)

Somebody's (or several somebodies) have been having a lot of OR fun. I wouldn't be displeased if it was just deleted. --C S (talk) 06:05, 31 May 2009 (UTC)

Well, I can understand that point of view from someone interested in 4-dimensional topology, but you have to acknowledge that users of lower levels might benefit if such an article were really well-written rather than in its current pathetic state.Julzes (talk) 06:44, 31 May 2009 (UTC)

I have no idea what you are going on about. The article is in violation of Wikipedia policies, which is why you've been getting different people commenting likewise on the talk page. You haven't been around for too long, so you should consider that you aren't really understanding what's viable content or not. In particular, I recommend thoroughly reading and digesting WP:OR. And I mean, really trying to understand it, not trying to parse it in a way that justifies your article -- that's a mistake a lot of newcomers make, and not surprisingly, they always parse the policies in a way that justifies their articles that a lot of experienced Wikipedians who have long familiarity with policies don't agree with. --C S (talk) 06:54, 31 May 2009 (UTC)

I've been down this road, and I'm trying to get the exception on routine calculations clarified. You're no help, and it's not "my" article.Julzes (talk) 07:06, 31 May 2009 (UTC)

Thanks for pointing out the article. I'll have a quick search with google books if any of the 'fact' ones strike me as interesting but otherwise Wikipedia can't be used as a repository for odd bit of numerology people dream up, it has got to satisfy notability. If nobody can find citations then they should be removed. Dmcq (talk) 07:48, 31 May 2009 (UTC)

Don't rush it, though, if that's your attitude. BKell set a two-week deadline a few days ago.Julzes (talk) 10:45, 31 May 2009 (UTC)

By the way, in the current article the fact that the square root of 2 plus the square root of 3 is a fair approximation to pi has been arbitrarily removed ahead of schedule (along with one that is more precise but also more complex), and the article does not even contain the coincidence involving simply e and its base-ten representation or that of the common logarithm of 2. All these things should be in a wikipedia article somewhere, and if not this article then where? Finding sources for notability's sake should not be top priority. Fixing things like this should.Julzes (talk) 10:53, 31 May 2009 (UTC)

Not all things should be in Wikipedia. It is not an attempt at forming The Library of Babel. Notability is a basic requirement. There's places and in Wikipedia to discuss changing basic things like this but |I don't think you'll get far with this one. Dmcq (talk) 12:17, 31 May 2009 (UTC)

Some things are a kind of mathematical common knowledge. Consider if instead of the article in question saying that log₁₀2= 0.30103 it were corrected to show how close it is to this.Julzes (talk) 12:48, 31 May 2009 (UTC)

How about transferring this to our sister project Wiki Books? They are using the same software and probably have a lot more tolerance for this type of thing. Of course sometimes the worst things are turned into a fine article by some genius, but I have no idea how this should work in this case. --Hans Adler (talk) 15:21, 31 May 2009 (UTC)

Am new and only so far familiar with the encyclopedia.Julzes (talk) 20:31, 31 May 2009 (UTC)

I'm surprised h2g2 doesn't have an article on numerical coincidences what with the infinite improbability drive. Dmcq (talk) 13:27, 1 June 2009 (UTC)

Certain external links

user:MrOllie recently deleted these two links from Circumscribed circle, calling them "linkspam" in the edit summary:

• Triangle centers by Antonio Gutierrez from Geometry Step by Step from the Land of the Incas.
• Circumcenter, Circumcircle, and Circumradius Theorems and Problems.

(In the course of doing this, he left fully intact the previous edit, which was vandalism.) The pages appear to be well written and relevant, unlike cases of linkspam I've seen where the page merely links injudiciously to other places on the web that superficially seem relevant to the topic, for the purpose of advertising. It looks as if they supported by advertising but not created for the purpose of that advertising, again unlike sites of the other sort I've seen. Some of MrOllie's recent edits leave the impression that he spends a lot of time removing linkspam, but may not be capable of judging the quality of the pages that he deletes the links to.

In some cases of this kind, the person deleting the links on these grounds asserts that the person who put the links there has a conflict of interests. In such cases, reinstatement of the links by someone with no such conflict is then found inoffensive, so that it is held there is no grounds for considering them "linkspam". MrOllie has recently deleted lots of links to various pages on geometry on that particular site. It appears that MrOllie may lack either the ability or the willingness to judge the difference between two sorts of sites:

• Those that are supported by advertising and are competently and professionally done pages on topics unrelated to the thing being advertised, maintained for purposes other than advertising;
• Those that are created for the purpose of advertising and include either material on some other topic of interest, crudely copied from other web pages, or links to other web pages superficially appearing to be on that other topic of interest, but without professional or competent judgment, or any judgment, as to what material is good and what is worthless crap.

If those whose primary concern is getting rid of linkspam, and any WikiProjects or the like concerned with that, lack the ability or willingness to make this sort of distinction, then people like the denizens of this present WikiProject need to intervene to help them. Michael Hardy (talk) 16:43, 31 May 2009 (UTC)

I see no problem with restoring these two external links in the article. An editor who had knowledge of the topic and did not personally have a COI would certainly be justified in putting the links back, under WP:BRD, provided he left a comment on the article Talk and ideally with a notification to the person who had removed them. If MrOllie is doing this all across the geometry articles then he shouldn't keep doing these removals without joining a discussion like the present one. EdJohnston (talk) 17:58, 31 May 2009 (UTC)

I removed many links to this site because they are links to an ad supported site and linked by the site owner, Agutie (talk · contribs · deleted contribs · logs · filter log · block user · block log) who operates a single purpose account for the purpose of adding these links. If anyone who is independent of the site would like to add them back, go ahead and please do so, since we would then be developing a consensus in favor of inclusion. I would request that they be considered case by case - please don't blanket add them all back. - MrOllie (talk) 20:43, 31 May 2009 (UTC)

May I ask any editor who restores a link (removed as spam) to please make sure to include an edit summary indicating that you have checked the linked site and believe it to be helpful for the article (and not redundant).

Re the issue raised above, I checked the edit claiming "linkspam" and would like to thank MrOllie for taking the time to remove the promotional links added by what is clearly a single purpose account. I wanted to put that on the record here, but may I suggest that further discussion on the general spam issues should take place at WT:Spam. Johnuniq (talk) 11:07, 1 June 2009 (UTC)

You also raised this issue at Wikipedia talk:WikiProject Spam#Seeking expert help to judge suspected spam (permanent link); I have responded to you there. --A. B. ^{(talk • contribs)} 18:11, 1 June 2009 (UTC)

Trivial or relevant?

I would be interested in hearing people thoughts about this. Articles such as 6 (number) generally attract lots of trivia.

• Six is the name of a character on Blossom.
• In football (soccer), the number of substitutes combined by both teams, that are allowed in the game.
• The number of cans of soda or beer in a six-pack.

etc. etc. etc. What are the relevant guidelines on what should be included in such an article? Are there any good or featured articles of this kind that can be used as a model? The most recent inclusion

• It is the only even perfect number that is not the sum of successive odd cubes.

which at least is mathematical if a bit obscure. — Martin (MSGJ · talk) 09:20, 1 June 2009 (UTC)

Wikipedia:WikiProject Numbers lists some criteria. PrimeHunter (talk) 10:09, 1 June 2009 (UTC)

An editor assistance request

Hello, WikiProject Mathematics!

An editor has asked for help concerning a technical mathematical article here, and I wonder if someone who understands these things better than I could advise.—S Marshall ^Talk/_Cont 21:41, 3 June 2009 (UTC)

See also Wikipedia:Articles for deletion/Lukaszyk-Karmowski metric. —David Eppstein (talk) 05:05, 4 June 2009 (UTC)

Help Guys!

Resolved

Guys, i've been Reading this Project for many months, there are many Highly talented Folks here, i really want an answer for this, i Do believe Wikipedia is not a Forum but i really really want an answer for this, please guys don't Delete this here is the Problem:

solve for t-

60√t (sin(t/3))^2 = 150

only t is under root after 60

Please Help! 122.174.74.142 (talk) 17:01, 4 June 2009 (UTC)

You'd probably be better of posting this at Wikipedia:Reference_desk/Mathematics, but keep in mind that the reference desk will not do your homework for you decltype (talk) 17:11, 4 June 2009 (UTC)

Diagrams of Sheffer operators

User:Lipedia (formerly User:Boolean hexadecimal) added some odd diagrams to two articles; I've removed them. Diffs: Logical NOR and Sheffer stroke. This is not the first set of odd images added by this user; File:Hasse_diagram_of_all_logical_connectives.jpg was a previous one that, in the end, was not used in any articles. Thoughts? — Carl (CBM · talk) 21:13, 1 June 2009 (UTC)

It turns out there was another set at Henry M. Sheffer. — Carl (CBM · talk) 21:20, 1 June 2009 (UTC)

I thought we'd been through all this in Talk:Logical connective not so long ago. What has changed between then and now? I notice the German version of the article also removed his diagram recently. Dmcq (talk) 22:12, 1 June 2009 (UTC)

Surely there must be a limit to what we need to take seriously and discuss before rejecting. The symbols used are original research, and even apart from this his graphics only make sense with long explanations. From a discussion on his user talk page at de: [6]: "Ja, die Zeichen habe ich entworfen. Quellen außerhalb der Wikipedia bin ich erst dabei zu schaffen, was eine Aufgabe für die nächsten Jahre sein dürfte." I.e., it was he who designed the symbols; he is in the process of creating sources outside WP, which should be a task for the next few years.

A look at this user's contribution history shows that this is a single purpose account for pushing alternative conventions for numbers, logic and music. --Hans Adler (talk) 23:37, 1 June 2009 (UTC)

My thoughts are that if no reliable source is provided to indicate general usage, these diagrams should be removed without hesitation. Thanks for doing that. Johnuniq (talk) 02:25, 2 June 2009 (UTC)

Wow, File:Hasse diagram of all logical connectives.jpg is a 7016×9921-pixel, 5.13-MB JPEG. What an excellent candidate for an SVG (apart from its OR-ness). —Bkell (talk) 08:48, 2 June 2009 (UTC)

There seems to be more of it at commons:File:Hypercubeorder.svg. —Bkell (talk) 08:53, 2 June 2009 (UTC)

Quote: I thought we'd been through all this in Talk:Logical connective not so long ago. What has changed between then and now? I notice the German version of the article also removed his diagram recently. Dmcq
Please make sure, you've got the topic, before you add your opinion. Here we speak about the following two diagrams, and about nothing else. (They have never been used in any german articles.)

The same about Hans Adler: The symbols used are original research, and even apart from this his graphics only make sense with long explanations. Which symbols?! (Probably you remember these, but they do not appear in the diagrams we speak about. I've once used them as a means of explanation in the Wikipedia, to visualise the relations between logical connectives, and this was a mistake, indeed.)

Concerning Bkell: Ah ... ordering logical connectives in a Hasse diagram by implication is original research - very interesting. (Maybe you take a look at this homepage.)

Concerning CBM: Nice to meet the user, who removed the set theoretic definition of logical connectives (Added by Gregbard) with the most funny statement: It's quite unclear to me what these sets are supposed to represent. It was tagged as possible OR for some time. I mention this sentence, because here it seems to be the same.

Logical connectives expressed with NOR (file)

Logical connectives expressed with NAND (file)

The diagrams:

Prefix notations like

• NOR(A,B)
• NOR(NOR(A,A),NOR(B,B))
• NOR(NOR(NOR(A,A),NOR(B,B)),NOR(NOR(A,A),NOR(B,B)))
• NOR(NOR(NOR(A,A),B),NOR(A,NOR(B,B)))
  

are usual, but nearly unreadable for human beings. At the moment in the NAND article there is a section called Simplification, where the operation is not written, because it's always the same operation, NOR in this case:

• (A,B)
• ((A,A),(B,B))
• (((A,A),(B,B)),((A,A),(B,B)))
• (((A,A),B),(A,(B,B)))
  

That's easier, but still hard to read, because it's very difficult to see, which left and right brackets belong together. Combining them to circles is the easiest solution. And that's what you want to call original research? (To express operations by circles surrounding the arguments is nothing special, by the way: It's also done in existential graphs.)

At the moment these two diagrams are the easiest way to show, how every logical connective can be expressed by only one Sheffer operator. Greetings, Lipedia (talk) 16:34, 3 June 2009 (UTC)

Sorry for not noticing that your latest work doesn't feature your symbols. It's still similar enough in most respects. OK, it may not be original research in a strict sense, but it's still idiosyncratic notation on many levels. This includes an odd choice of what to present in great detail, an odd choice of variables, the odd choice of circles, a horrible colour scheme, accessibility problems and the complete lack of printable explanation. Some of these problems are easily fixed, but I recommend that you don't bother.

Your attack on CBM shows how detached from reality you are. CBM is a professional mathematical logician with wide-ranging interests throughout logic and an enormous amount of patience. He didn't understand your set notation, and neither do I (a model theorist), although I have a vague idea what it is supposed to be and don't doubt that I could in principle figure it out if I were willing to spend a few minutes on this nonsense.

Laying out the 16 binary logical connectives in a Hasse diagram is of course not original research. If we don't have a picture like the first one in your reference [7], then we probably should. The most important difference to your diagrams is that you stress your idiosyncratic stuff and hide the most important information in a link map. It's the difference between a straightforward illustration and a riddle like the Pioneer plaque. --Hans Adler (talk) 20:31, 3 June 2009 (UTC)

I do agree that, if a Lindenbaum algebra of the propositional language generated by two variables is included, it should be clearly labeled as such, rather than as a powerset algebra. But I don't see a good reason to include it.

Ultimately, I'm not convinced by unpublished the "Geometry of logic" reference. Certainly Lindenbaum algebras in general are well known, but Lindenbaum algebras are not really very often discussed in context with logical connectives. The relationship appears quite tenuous and unsupported by published work.

The final part of the reference, e.g. the part about Steve Vickers, is related to topological methods, not to automorphisms of the 16 element Boolean algebra.

The thing that seems to be emphasized in the diagrams is that both the powerset algebra of a four-element set, and the Lindenbaum algebra of a propositional language with two variables, are 16 element Boolean algebras. But this seems to be the sort of trivia that is not really of interest. I mean, we could also associate logical connectives with isomorphism classes of subgroups of Z₂₁₀ in the same way, but this would not motivate the "group theory of logical connectives"...

In fact, the reference admits the lack of a clear link, saying

"If, however, the 16 digital labels are interpreted as naming the 16 functions from a 4-set to a 2-set (of two truth values, of two colors, of two finite-field elements, and so forth), it is not obvious that the notion of partial order is relevant. For such a set of 16 functions, the relevant group of automorphisms may be the affine group of A mentioned above. One might argue that each Venn diagram in Figure 3 constitutes such a function-- specifically, a mapping of four nonoverlapping regions within a rectangle to a set of two colors-- and that the diagrams, considered simply as a set of two-color mappings, have an automorphism group of order larger than 24... in fact, of order 322,560. Whether such a group can be regarded as forming part of a "geometry of logic" is open to debate."

In these cases, I am willing to go along with published sources when they do indeed cover things that might appear trivial. But I haven't seen evidence of that here. — Carl (CBM · talk) 23:43, 3 June 2009 (UTC)

Just a short note: It's no problem including the connectives names in the diagrams. It's what I first did, but it became too crowded for my taste. The hint, that printable information is desirable is true indeed. Concerning the color scheme: I may choose darker colors, to make the appearance less gaudy. It's just important, that A and B have different colors. I will upload modified versions at the weekend. Greetings, Lipedia (talk) 07:33, 4 June 2009 (UTC)

You seem to have ignored my request for any published source that thinks these diagrams are interesting. — Carl (CBM · talk) 12:10, 4 June 2009 (UTC)

No, I didn't ignore it, but I doubt that it is justified.
Content must be verifiable, otherwise it's original research - and the content is undoubted in this case, and verifiable by any source you want. But like every encyclopedia, we should display this verified information in the way, that serves our readers best. An article is good, when the content is verifiable, and as many readers as possible (also non experts) can understand it as easy as possible. So your request aims in the wrong direction: The question is not "Does it appear somewhere in exactly this way?" but "Does it help anyone to understand Sheffer operators?".

This is disputable of couse. I think it does:

The article tells, that all sixteen logical connectives can be expressed in terms of NOR and NAND respectively, so I think we should show that - and not only mention some examples, presuming that the reader can easily deduct all others. This could be done in a sixteen row table of couse, but the most helpful way to display logical connectives is not the table (because the neighbour rows have nothing to do with each other) but the Hasse diagram showing all implications.
The formulas should be shown in a clear and easy way, so somewhat easier to read than (((A,A),(B,B)),((A,A),(B,B))), the notation used in the Simplification section in the present NAND article. Combining the parentheses to circles for better readability is really not a "idiosyncratic notation" (the Simplification section presumed) but a very simple step. The hint, that "the most important information" should be shown in the diagram itself was justified, so I changed it (and the color scheme as well).

This is how it could show at the end of the articles (= at the end of the Simplification section, which could be included also in the NOR article):

All logical connectives can be expressed in terms of NOR. In this diagram the parentheses of formulas like (((A,A),B),(A,(B,B))) have been combined to circles for better readability: The NOR operation is displayed by a circle including the two arguments. (file)

Greetings, Lipedia (talk) 12:26, 11 June 2009 (UTC)

I think the problem with such diagrams is that it is neither common knowledge nor easy to work out exactly how to read it. As a result, to justify including it into an article for the purpose of helping someone's understanding, it would need to accompanied by an explanation of the notation or a link to an explanation. If, however, such notation is not standard, then it is original research, and hence has no place in Wikipedia. Truth tables, however cumbersome you think they are, are an accepted method of presentation in most mathematical and logic books, and have been for decades.

Your comments that such truth tables are not the notation we should be using to represent them may be right; such discussion should be limited to academic books and journals, not on Wikipedia, which is a tertiary source. --Joth (talk) 12:53, 11 June 2009 (UTC)

"it would need to accompanied by an explanation of the notation or a link to an explanation"
Please note, that I proposed to include them in the Simplification section in the present NAND article (and its equivalent in the NOR article not yet created). Did you read it? In this section simplified notations like (((A,A),B),(A,(B,B))) meaning NAND(NAND(NAND(A,A),B),NAND(A,NAND(B,B))) are used. In the context of this section the short explanation below the diagram will do. (I wouldn't be so crazy, to include these files in the logical connectives article, and think it could help some reader there. Hope you didn't think that.)

"Truth tables, however cumbersome you think they are"
"Your comments that such truth tables are not the notation we should be using"
These lines tells me, that you missunderstood something I wrote, or something the others wrote about me. I did not even mention truth tables nor would I say anything against them (I actually love truth tables!). Here we speak about the linking of many equal operations in NOR logic and NAND logic, and what I don't like are unreadable formulas like NOR(NOR(NOR(A,A),B),NOR(A,NOR(B,B))) or even the simplification (((A,A),B),(A,(B,B))). I think these simplified formulas are better readable, when the outer parentheses are bigger and the inner parentheses are smaller.

(In this case the left and right parentheses touch in the middle, and become a circle. If anyone conciders my diagrams to be original research because of this, I can easily make a short break in the middle, so that every circle becomes a pair of semicircles, easily recognizable as a pair of parentheses - than it would be exactly the same like (((A,A),(B,B)),((A,A),(B,B))) and so on.) Greetings, Lipedia (talk) 15:41, 11 June 2009 (UTC)

I don't think I have any particular objection to something simple like the first or second diagram in [[8]] being added. I don't think it adds anything but it's not large and can be understood easily and filed away in the mind as a pretty picture. The funny diagrams are just not suitable though, they are large and peculiar and cluttered covering up any sense one might extract and they keep being put in as an alternative to the straightforward text. The straightforward text is what can be maintained easily and moving vital bits of the text to funny diagrams with non-standard tooltips and ways of showing things is just silly. Dmcq (talk) 23:10, 13 June 2009 (UTC)

If something is correct, it doesn't need to be "maintained". Possibly your focus is more on the editor than the reader - in my eyes a fundamental mistake, but it appears to me, that this is quite usual in the Wikipedia.
The blame against the first version was to be "a riddle like the Pioneer plaque" because I "hide the most important information in a link map". So I've got this information included, and now the blame is, that the diagrams are "cluttered". Isn't that a bit strange? Looks as if the rejection is more imporant than the reason.
I think it's sad, that all this debate is primarily harping on about principles, may they be real or imagined, and the question "Does it help someone?" does not play any role. Is "they keep being put in as an alternative to the straightforward text" really a senseful blame? For me it's too far away from "Does it help someone?" and thus secondary, borderline unimportant. For me an article is good if and only if it helps as many and as different people as possible. Greetings, Lipedia (talk) 15:56, 14 June 2009 (UTC)

Well, there's no way we can let the deciding criterion be "does it help someone". A lot of things might help someone. But throw them all in there and you've got an unreadable mess.

The images are, in their way, lovely. But they're too gaudy; they try to pack — not exactly too much information, because there's not really much there — but information in too many different ways, into a small space. In doing so they're more likely to confuse than inform.

Most importantly, they are not standard ways of presenting the information. They are idiosyncratic. This is not a bad thing in general, but it's a bad thing for an encyclopedia. --Trovatore (talk) 19:57, 14 June 2009 (UTC)

Of course I didn't mean someone when I said "someone", but rater a quantity of people worth mentioning. But sadly we have no means to check, what exactly is helpful to how many people. Concerning idiosyncracy I can only repeat what I said before: I can easily make a short break in the middle, so that every circle becomes a pair of semicircles, easily recognizable as a pair of parentheses - than it would be exactly the same like (((A,A),(B,B)),((A,A),(B,B))) and so on. But I'm not going to do that. We can agree that the diagrams don't match in Logical NOR, Sheffer stroke and Henry M. Sheffer and end the discussion. Lipedia (talk) 09:39, 16 June 2009 (UTC)

Hereditary set

Another funny diagram has been added to Hereditary set. At least it's smaller but I think it detracts from what little content there is in the article. A straightforward listing of a few sets would be better and could include some infinite ones. I think the article needs a bit of expansion. For instance a set containing itself and all subsets wouldn't have an ordinal number as far as I can work out. Dmcq (talk) 11:17, 14 June 2009 (UTC)

The set P^4({}) = P( P( P(P({})))) respectively it's infinite completition (the union of sets P^n({}) for all n) should be mentioned somewhere in the context of pure sets - but possibly this diagram could match better in Pure countable set.

The elements of P^n({}) do not only follow each other (in the way natural numbers do), but they also include each other (in the way Boolean functions imply each other). I don't think the second information is unimportant. Greetings, Lipedia (talk) 14:58, 14 June 2009 (UTC)

Would this project be interested in some collaboration with Wiktionary?

Basically, a significant number of math terms are virtually impossible to define for the layman, usually because the relevant Wikipedia articles are simply unhelpful, even useless (cf. hypoelliptic-wikt:) to people without knowledge of fairly advanced maths (and yes I fully acknowledge the difficulty of avoiding jargon in many math articles). Another problem often comes in that some terms may be ridiculously hard to give good quotations (i.e. from books or scientific publication), such as sphenic number-wikt:, even though they are clearly in use (in this case, the problem comes with the small amount of truly useful material in google books and google scholar).

Would WPMATH members be interested in answering the occasional requests for help in such cases? Circeus (talk) 02:44, 3 June 2009 (UTC)

Sure. Jakob.scholbach (talk) 06:11, 3 June 2009 (UTC)

Me too. I guess you could post the requests here—can anyone think of a better place? Ozob (talk) 15:19, 3 June 2009 (UTC)

Okay, so your first mission, if you accept it (sorry, couldn't help it :p), is to help define wikt:hypoelliptic in comprehensible term, and verify whether or not that definition directly relates to the current mathematics definition we have for wikt:elliptic. Personally, I'd appreciate some backgroung for dating the term. I find a fair amount of material that discusses or mentions Lars Hörmander's solution (?) ot the things (apparently at some point in the 50s or 60s), but none about when the term started being used (of course it might not have been formally used before Hörmander). A typical example is here. Circeus (talk) 17:32, 3 June 2009 (UTC)

The Mathematics Reference desk would also be happy to help. --Tango (talk) 17:52, 3 June 2009 (UTC)

I am not quite understanding what is required, but I try to say something. First, "elliptic" in (elementary) geometry is not the same (but related to) "elliptic" in PDE ("partial differential equations"). Second, "hypoelliptic" is a term of PDE (no counterpart in elementary geometry). Third, "hypoelliptic" admits some degeneration ("elliptic" does not), but not too much degeneration. Less technical it is impossible to explain, I am afraid. Boris Tsirelson (talk) 18:07, 3 June 2009 (UTC)

And, by the way, wiktionary for now interprets "elliptic" only geometrically (not PDE). Boris Tsirelson (talk) 18:09, 3 June 2009 (UTC)

And by the way the definition of an elliptic given at wikt:elliptic: "2. (mathematics) Of a function in which the sum of the squares of two variables is constant", is wrong! Paul August ☎ 18:31, 3 June 2009 (UTC)

• re:"elliptic" Okay, clearly, we need at least two definitions for wikt:elliptic in maths, the current one should be marked as (geometry) and is obviously linked to the general equation cited in ellipse: "Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters. Moreover, any canonical ellipse can be obtained by scaling the unit circle of $\mathbb {R} ^{2}$, defined by the equation $X^{2}+Y^{2}=1$". There are various other aspects of maths involving the adjective (e.g. elliptic function), and likely the Wiktionary article needs improvement to account them.
• re:hypoelliptic You have completely lost me already. It is clear to me the relevant sense of elliptic is the one involved in Elliptic operator, but that's as far as I got with it. Circeus (talk) 19:33, 3 June 2009 (UTC)

So, which help could I provide about "hypoelliptic"? You understand that it is relevant to elliptic operator, but weaker. Do you want to understand what does it really mean? To which extent? Do you need explanation about "degenerate"? Hypoelliptic operator is allowed to be degenerate at some points, and even at every point, but the direction of degeneracy must change from one point to another in such a way that some properties of elliptic operators still hold in a weakened form. If you want to be more specific here, then you really have to read the article in Wikipedia. Boris Tsirelson (talk) 20:41, 3 June 2009 (UTC)

Let me add that "hypoelliptic" is weaker than "elliptic" but stronger than semi-elliptic.Boris Tsirelson (talk) 20:47, 3 June 2009 (UTC)

Basically, the only thing I really think I understand (If I had actual understanding of calculus, I wouldn't need to ask!) is that a hypoellictic function (drawing from elliptic function) is a function in the complex plane. Would it be accurate to reverse the relation (in the same way sphenic must be dfined in relation to sphenic numbers, not the other way around) and define hypoelliptic as an adjective related to either wikt:hypoelliptic operator or wikt:hypoelliptic function? Circeus (talk) 21:08, 3 June 2009 (UTC)

Oops, I forgot about elliptic function! No, this is not related at all. This is a third meaning of "elliptic". No, there is no "hypoelliptic function" (as far as I know); only a differential operator or a differential equation may be hypoelliptic. Boris Tsirelson (talk) 04:56, 4 June 2009 (UTC)

Wow, there is also Elliptic curve, Elliptic complex etc. Boris Tsirelson (talk) 05:39, 4 June 2009 (UTC)

So, to get back to the question of a dictionary definition of hypoelliptic:

1. "Hypoelliptic" is a combination of hypo- (less than or weaker than) and elliptic, and is used to mean something that is like an elliptic thing, but weaker; the only usage of this we've found so far is in hypoelliptic operator.
2. A "hypoelliptic operator" is a differential operator that preserves smoothness. As the name implies, this condition is weaker than the conditions defining an elliptic operator.

Right? —David Eppstein (talk) 06:17, 4 June 2009 (UTC)

Right, with three reservations. First, there is also "hypoelliptic differential equation" (just a differential equation whose differential operator is hypoelliptic). Second, "preserves smoothness" is not very clear; but maybe this is the best one can expect from a dictionary. (Rather, the inverse operator preserves smoothness). Third, one could also mention "semi-elliptic". Boris Tsirelson (talk) 07:24, 4 June 2009 (UTC)

One extra question, not necessary, just out of my own curiosity: is it accurate that an elliptic operator will be hypoelliptic, but not the reverse (i.e. elliptics are a class of hypoelliptics), or is it that elliptic operators may be hypoelliptic (they merely intersect)? Circeus (talk) 15:41, 4 June 2009 (UTC)

Yes, every elliptic operator is hypoelliptic, but not the reverse. Boris Tsirelson (talk) 18:16, 4 June 2009 (UTC)

And it is in fact written, see Elliptic operator#Regularity properties: "thus, every elliptic operator is hypoelliptic". Though, misunderstandings are possible because of different levels of generality: usually one has in mind second-order differential operators, but sometimes higher order differential operators are also treated, and sometimes only second-order differential operators with constant coefficients are treated. Boris Tsirelson (talk) 18:26, 4 June 2009 (UTC)

To be accurate: every elliptic operator with infinitely differentiable coefficients is hypoelliptic. In particular, every elliptic operator with constant coefficients is hypoelliptic. Boris Tsirelson (talk) 19:31, 4 June 2009 (UTC)

Judging by this discussion, some preliminaries on dismbiguation by email might help. You can run things past me offline to get a general sense. Charles Matthews (talk) 10:55, 14 June 2009 (UTC)

Did you know

...that a mitimorphism is a morphism from the power set of a fibre bundle into another fibre bundle?

I was hoping someone here could clarify whether this newly created article is a hoax, a neologism, or just very obscure. Thanks, decltype (talk) 08:08, 4 June 2009 (UTC)

Hmm. 0 Google, Google Scholar and Google Books hits. Interesting editing history of article creator. --Hans Adler (talk) 11:59, 4 June 2009 (UTC)

I am under the impression that DYK requires at least one reference for the sentence they put on the main page. — Carl (CBM · talk) 12:06, 4 June 2009 (UTC)

I think DYK was just a humorous way of phrasing the question whether this is a hoax. The article would also fail for insufficient length. It looks to me like a definition made up by a mathematics student who is also a good dictionary game player. But then I have seen a serious definition of a "morphism" from one type of object to another once; not that I would approve of that kind of thing. --Hans Adler (talk) 12:22, 4 June 2009 (UTC)

Yes, it was indeed an attempt at humour. Article is now proposed for deletion. Thanks for your input. decltype (talk) 15:57, 4 June 2009 (UTC)

An anonymous user from the University of Waterloo, 129.97.58.107 (talk · contribs), removed the prod template, saying: "seen it; not sure about the etymology part". Ozob (talk) 19:52, 11 June 2009 (UTC)

Since Prod was rebuffed, I've put it forth for a real AfD at Wikipedia:Articles for deletion/Mitimorphism. — Charles Stewart (talk) 20:22, 11 June 2009 (UTC)

Visualization for integration by parts

Could someone look at the geometric argument for the integration by parts? I am thinking to add a section to the article about that and have a couple questions. I used xfig to create the picture, is there a better tool to create pictures like that? I could not find this particular trick in the literature, does it constitute OR if I add this argument to the article? (Igny (talk) 02:20, 5 June 2009 (UTC))

It's not OR. Leibniz used this exact argument, but I'm sure there have been countless references to this picture since then. --C S (talk) 02:39, 5 June 2009 (UTC)

I've seen this explanation of integration by parts in several books. The only source I can lay my hands on at the moment is Nelson's Proofs Without Words, see page 42. --Uncia (talk) 03:14, 5 June 2009 (UTC)

Nice book, thanks for the reference. (Igny (talk) 17:25, 5 June 2009 (UTC))

I think for art like this it would be preferable to use .svg (a vector format) for the graphics instead of .jpg (a bitmap format), if possible. I use Adobe Illustrator for that but it's kind of expensive; the most popular free alternative seems to be Inkscape. —David Eppstein (talk) 02:25, 5 June 2009 (UTC)

I will work on creating an SVG pic of good quality. (Igny (talk) 17:25, 5 June 2009 (UTC))

Category:Linear operators?

Category:Linear operators seems a rather strange category. It says that it is for linear operators defined on functions, but this seems rather overly restrictive. What should be done with it? Sławomir Biały (talk) 15:18, 7 June 2009 (UTC)

I have posted a more detailed discussion at Category talk:Linear operators. Please direct your input there. Sławomir Biały (talk) 15:46, 8 June 2009 (UTC)

Statistics portal at Featured portal candidates

Portal:Statistics is being considered for featured quality status, at the Featured portal candidates process. Comments would be appreciated at Wikipedia:Featured portal candidates/Portal:Statistics. —G716 <^T·_C> 01:26, 9 June 2009 (UTC)

Editor trying to remove talk page requirement from technical tag

See Template_talk:Technical_(expert)#This_template_is_for_article_namespace. User: Debresser has repeatedly tried to remove the talk page requirement, contrary to the explicit instructions in the technical guideline. I pointed out to him that since this tag is scarcely used, Coren's mistaken reformatting of the tag (which changed the template to an ambox, which is for articles) was not reverted, unlike the situation for the regular technical tag, which was reverted. Debresser insists that since Coren's reformatting of the tag as an ambox was unreverted, I must be completely mistaken about the consensus regarding the placement of the technical tag on talk pages. He has not explained why there is this distinction (one technical tag on the article, the other on talk pages) and has refused to read the guideline or its talk page to understand the consensus. Indeed, according to him, since this mistake was unreverted for 2 years or so, his position is the consensus! --C S (talk) 14:32, 11 June 2009 (UTC)

This seems to have been resolved amicably through better communication almost immediately after this post, but I guess help with moving the misplaced templates from articles to talk pages would be appreciated. --Hans Adler (talk) 15:37, 11 June 2009 (UTC)

No, absolutely not! Certainly all the misplaced templates are due to people who inappropriately tagged the articles and so they shouldn't be moved, rather they should be deleted to save editors wasted time.

Also, Debresser has rather foolishly taken the "informal RFC" initiated on the talk page of template:technical (which was never closed!) as a sign of consensus against placing the template on talk pages ("Please notice that the discussion on Template_talk:Technical#Informal_RfC:_Should_Template:Technical_be_added_on_the_article_or_talk_page.3F points to article namespace with 6 against 4"). So he has initiated his own proposal to reverse this. See Wikipedia_talk:Make_technical_articles_accessible#Templates_for_articles_or_talkpages.3F. --C S (talk) 20:19, 11 June 2009 (UTC)

Oh! Sorry for the mistake. --Hans Adler (talk) 22:36, 11 June 2009 (UTC)

"List of arithmetic topics"?

Lo and behold: List of arithmetic topics is a red link. Should we do something about that? Michael Hardy (talk) 03:50, 13 June 2009 (UTC)

Notice that List of basic arithmetic topics is a redirect to Outline of arithmetic. JRSpriggs (talk) 08:44, 13 June 2009 (UTC)

...which has a link to an alleged "main" article called List of arithmetic topics, which should be more detailed and extensive, including all Wikipedia articles that fit (just as with the other subjects). Michael Hardy (talk) 20:08, 13 June 2009 (UTC)

License update and PlanetMath

Under the terms of the licensing update being adopted across all Wikimedia sites, WMF projects will no longer be able to add GFDL-only text published elsewhere. Any GFDL text added to Wikipedia after Nov. 1, 2008 will have to be removed as a copyvio. PlanetMath uses the GFDL and hence this could shut down a potentially valuable source of content interaction. In order to avoid that, PlanetMath would need to also relicense to CC-BY-SA as explicitly allowed under GFDL 1.3.

If you have contacts at PlanetMath, or participate there yourself, I would encourage you to discuss this issue with them. See also: m:Licensing update/Outreach. Dragons flight (talk) 01:14, 14 June 2009 (UTC)

Abbreviations in algebra-related articles

I have a somewhat minor complaint with regards to some of the algebra-related articles. In particular, I find that too many technical terms are abbreviated. For example, although it is reasonable to abbreviate terms like "unique factorization domain" to UFD, or "principal ideal domain" to PID, abbreviations such as BFD, BD, HFD, AD etc... are ambiguous to some extent (try to guess what some of them refer to; I find that this is not at all trivial, even for algebraists). As an encyclopedia, we should aim to be as clear as possible, and abbreviations should only be done if absolutely necessary. Even in this case, the word which is abbreviated should be made clear, along with its abbreviation. I tend to find abbreviations such as ACCP to mean "ascending chain condition on principal ideals" somewhat pointless because along with abbreviations like UFD or PID, it is somewhat difficult to interpret (one may guess ACCP to be some sort of "domain" if he was not familiar with it). Furthermore, such abbreviations can lead to errors. For instance, one may write "UFD domain" instead of "UFD" thus being redundant to some extent. Therefore, although abbreviations of basic terms are OK, we should start defining/linking abbreviations when using them; especially if the term to which they correspond is somewhat unknown. --PST 04:44, 14 June 2009 (UTC)

I definitely agree. I haven't spotted any of these in algebra articles so far, but when I do, I'll get busy removing them. I think many of the mathematics articles need to have their jargon reduced and accessibility increased; removing pointless axioms is a great way to start this. --Joth (talk) 07:01, 14 June 2009 (UTC)

I just had a look at some articles with ACCP in them, and some have the abbreviation, but immediately after writing the term in full (for example in Unique factorization domain. I think it's OK to use such abbreviations in that context. --Joth (talk) 07:04, 14 June 2009 (UTC)

Often, abbreviated terms are used in articles which do not describe those terms specifically and exist for another purpose. For instance, a term such as ACCP might be used in an article on Bézout domains (not that it necessarily is) but may not be thoroughly explained there. However, in most cases, articles specific to a term, will pay great emphasis to clarifying ambiguities with respect to its abbreviation (such as UFD in the article on "unique factorization domain").

On the other hand, although an abbreviation may be explained in a particular area of an article, readers who do not read this area will not know of the abbeviation (if I read an article, it is usually the lead that I read last, so if the term whose abbreviation is ACCP were defined there, and I had never heard of it, I will most certainly be disadvantaged should I come across ACCP before reading the lead). I agree, of course, that if one uses an abbreviation and one writes the abbreviation in full, there is no problem. However, this must be done every time one uses an abbreviation for otherwise, especially if the article is long, a reader may not notice the one single time where the abbreviation is explained. --PST 13:51, 14 June 2009 (UTC)

Citing a footnote more than once

In WP:REFNAME, starting from 14 April 2008, I read: "In subsequent uses of the named tag the use of <ref name="name" /> is encouraged rather than copying the whole footnote again, as whole footnotes tend to reduce the readability of the article's text in edit mode, which makes finding specific parts of the text when editing tedious."

On the other hand, the short version is more prone to accidents under further edits; if the editor is not careful enough, his/her local edit may have unwanted global effect. See also Wikipedia_talk:Footnotes#Mark-up_would_be_better_than_encouraging_people_to_remove_reference_information.

For this reason I have used the long version in unbounded operator. (Initially I did not know about that style recommendation.) I wonder, do we mathematicians agree that the short version is preferable also in our texts? Boris Tsirelson (talk) 12:03, 15 June 2009 (UTC)

Basically there are three options:

• Refer to the previously named footnote
• Repeat exactly the same unnamed complete footnote
• Repeat exactly the same named complete footnote

I think we should use the same convention as everybody else, and I actually think that 1 is the best. 2 is inferior because it clutters the article; also if only one of two previously identical footnotes gets a correction it looks very unprofessional. 3 is really bad: If you have two footnotes with the same name and change only the first, nothing happens. You may not even notice, or you may get very confused. If you change only the second, you get a surprising regression when the first instance is removed or the two passages are swapped. With 1, when a reference is removed we get bold red text telling us what went wrong so it can be fixed immediately.

These arguments are a bit weaker in the case of Harvard referencing as in unbounded operator, but even then I think it's better not to use 3 to avoid puzzling others who are not used to it. --Hans Adler (talk) 12:44, 15 June 2009 (UTC)

And if the prominent red bold text is not enough, there's a bot running around fixing these. — Emil J. 13:07, 15 June 2009 (UTC)

Does it fix the references by getting them from the page history? That would be great, but I have never observed this. --Hans Adler (talk) 13:25, 15 June 2009 (UTC)

Yes, it extracts the references from the page history. See Special:Contributions/AnomieBOT for examples. — Emil J. 14:02, 15 June 2009 (UTC)

There are three other options, none of which involve note ids. The first is to avoid the use of notes altogether, in favour of paranthetical references to a proper reference list. Second, one can use MLA-style notes, where the first version of the reference is given in full, and after that the note is given as a short reference, either the "AUTHOR_LIST, DATE" or "AUTHOR_LIST, SHORT_TITLE", possibly followed by the page ref. Or last, one can use parenthetical references in notes, rather as if they were short references in notes, which is what the Chicago Manual calls notes plus references style. — Charles Stewart (talk) 14:12, 15 June 2009 (UTC)

I see, thank you all; indeed, "1" is the best for my case. Special thanks to User:Algebraist for his help with "unbounded operator". Boris Tsirelson (talk) 14:43, 15 June 2009 (UTC)

Named footnotes have one disadvantage: they discourage grouping together several references cited in the same sentence. Thus, the degree to whch they shorten footnotes is debateable. Septentrionalis PMAnderson 18:42, 16 June 2009 (UTC)

That's true. But of course one may make a conscious choice to group those together that are not reused. --Hans Adler (talk) 19:16, 16 June 2009 (UTC)

But unbounded operator has one point where it references three notes, numbered 3, 15, and 5 IIRC; for situations like that, one must do one or the other. I prefer to have one note, which cites all three; the Harvard templates can then link the footnote to the bibliography, if necessary.

This is, of course, a matter of taste; but we should bear in mind tastes differ. Septentrionalis PMAnderson 23:02, 16 June 2009 (UTC)

First-order logic

I have been working, with help from other editors, to improve the article on first-order logic. If anyone has the time to review the relatively long article and give an outside perspective, it would be greatly appreciated. — Carl (CBM · talk) 18:01, 15 June 2009 (UTC)

Please look at Dirac delta function page

Can someone take a look at the Dirac delta function page? The editor User:Sławomir Biały may know what he is talking about, but it is beyond my area of expertise. Assuming that he is competent, I wonder if the article is being made unaccessible to anyone below his level of knowledge? PAR (talk) 03:50, 16 June 2009 (UTC)

His edits look right. He has also removed some text that seems to think that the Dirac delta function is just "notation", which is a good thing. What he has added can be found in any number of standard texts in functional analysis. It is possible this has made the article less accessible to many (e.g. physicists), however his edits have definitely made the article more accurate. Any attempt to make the article more accessible should start off from where the article is now incorporating the new changes. There were certainly several common misconceptions present in the article before User:Sławomir Biały's changes. Hope this helps. RobHar (talk) 18:13, 16 June 2009 (UTC)

cc-by-sa and citizendium

Some of you may or may know, but Wikipedia has switched its license to cc-by-sa. One consequence is that we are now permitted to import text from citizendium (an encyclopedia project started by a cofounder of Wikipedia). I have just imported a large chunk of text from CZ to Gamma function, which greatly improved the article (in a matter of minutes :) Anyway, I thought you might consider doing something like that. -- Taku (talk) 11:05, 16 June 2009 (UTC)

Does anyone know what sort of attribution is required in these situations? with the GFDL we had a well established practice of using a template at the bottom of the article to say we had imported text. What do we do with the new license? — Carl (CBM · talk) 12:09, 16 June 2009 (UTC)

For the time being I have created the {{Citizendium}} template parallel to the {{Planetmath}} template. I added it to Gamma function in the references section. — Carl (CBM · talk) 12:17, 16 June 2009 (UTC)

My recent edit to this section seems to have perversely disappeared.

Taku seems to assume we know what "cc-by-sa" is, and doesn't link to it. Here's the link: cc-by-sa. Michael Hardy (talk) 20:32, 16 June 2009 (UTC)

Oh: I never actually hit the "save" button on that one. Readers are hereby ordered to ignore my first comment above and read only my second comment. Michael Hardy (talk) 20:36, 16 June 2009 (UTC)

More concretely, see Wikipedia:Text of Creative Commons Attribution-ShareAlike 3.0 Unported License. JRSpriggs (talk) 07:46, 17 June 2009 (UTC)

Just a side note — Taku said that WP has switched to cc-by-sa. According to the notice I'm looking at below this text box, that does not appear to be exactly true. Apparently new content is multi-licensed under cc-by-sa and GFDL. I'm not a lawyer but it seems to me that this could get complicated for reusers. Ordinarily, when you make a derivative work from multi-free-licensed content, you can choose the license under which to release the derivative work, at least as I understand it.

But in the case of WP, the content from before the change is not available to be re-licensed under cc-by-sa, unless the authors all consent to this, which as a practical matter seems impossible. For content that WP has copied from Citizendium, this content cannot be relicensed under GFDL without the copyright holders' consent. So apparently the author of a derivative work, to be safe, must also release the work under both licenses, and so on for all derivatives of that work, and this seems contrary to the natural reading of each license separately. Have the lawyers really thought this through? --Trovatore (talk) 09:12, 17 June 2009 (UTC)

It's important to note that we haven't relicensed under CC-BY-SA – we've just adopted a dual-licensing scheme with CC-BY-SA and GFDL. —Anonymous Dissident^Talk 09:21, 17 June 2009 (UTC)

Yes, that I understood. That doesn't seem to answer the points I raise above. --Trovatore (talk) 09:28, 17 June 2009 (UTC)

I didn't mean to reply to you directly. I was just putting it out there. —Anonymous Dissident^Talk 09:37, 17 June 2009 (UTC)

I thought that one revision of GFDL had been modified to allow people to import text licensed under it to the CC-BY-SA license, and we were only going to use CC-BY-SA hereafter. Right? JRSpriggs (talk) 09:32, 17 June 2009 (UTC)

Not quite. All old GFDL wikipedia content has been relicensed as CC (which is permitted under GFDL 1.3, and hence requires no further consent from authors). New text submitted to Wikipedia by the copyright holder must be licensed as both GFDL and CC. New text imported from elsewhere must be CC and may (but need not) be GFDL-licensed also. Thus all text will be avaliable under CC-BY-SA-3.0 and may be available under GFDL 1.3, but a full history trawl is required to work out if a given page is GFDL-compatible. Details at Wikipedia:Licensing update. Algebraist 10:49, 17 June 2009 (UTC)

Since the principal motivation behind the license switch is to allow the importation of contents licensed under cc-by-sa, if you couldn't data-dump contents from citizendium, say, I don't see the point of the switch. This page [9] hopefully answers some questions raised above. But to summarize key points:

• (i) Any "old" contents are now licensed under cc-by-sa. (They are still available under GFDL, the old license, since anything licensed under GFDL stay under GFDL; you can't strip away GFDL.)
• (ii) But more important, after this update, only dual-licensed content or CC-BY-SA-compatible content can be added to the projects, and GFDL-only submissions will no longer be accepted..

Because of (ii), we can now data-dump contents licensed under cc-by-sa. But the other unintended? consequence is that we are no longer able to data-dump contents from PlanetMath. Since we've been relying less and less on PlanetMath lately, hopefully this doesn't cause much pain. -- Taku (talk) 10:52, 17 June 2009 (UTC)

In fact, any datadumps imported from PlanetMath since last November must now be removed. Algebraist 11:13, 17 June 2009 (UTC)

More on pi....

A user inserted this into the article on the square root of 2:

The square root of two can also be used to approximate π:

$2^{m}{\sqrt {2-{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2}}}}}}}}\to \pi {\text{ as }}m\to \infty \,$

for m square roots and only one minus sign.

I did some simple number-crunching that seems to bear out the assertion. The user has not responded to my inquiry about where to find a proof; I think this user hasn't been around lately. Can anyone tell us anything?

Probably this result should be mention in one or more of the articles related to π. Michael Hardy (talk) 19:57, 16 June 2009 (UTC)

[10] (Igny (talk) 20:22, 16 June 2009 (UTC))

This is one of the methods of numerically approximating π attributed to Archimedes — it follows easily from considering inscribed 2^m-gons and applying half-angle formulas. Arcfrk (talk) 21:00, 16 June 2009 (UTC)

(Edit conflict) Seems closely related to the duplication formula for cosine, in fact. Obviously the gadget with all plus signs under the square root tends monotonically up to 2, and this is related to "how fast". The "how fast" is related to twice cos of some angle you keep halving, according to my algebra. There is something more to prove here, which is why the number is pi. I suspect Euler knew, though. Charles Matthews (talk) 21:05, 16 June 2009 (UTC)

OK, here's a sketch. First, note that π = 2^m(π/2^m) and that π/2^m equals sin(π/2^m) with a third degree error term. Then we hit the sine with the half-angle formula:

${\begin{aligned}2^{m}\sin {\frac {\pi }{2^{m}}}&=2^{m}{\sqrt {\frac {1-\cos {\frac {\pi }{2^{m-1}}}}{2}}}\\&=2^{m-1}{\sqrt {2-2\cos {\frac {\pi }{2^{m-1}}}}}.\end{aligned}}$

The half-angle formula for cosine tells us:

$2\cos {\alpha /2}={\sqrt {2+2\cos \alpha }},$

which we now apply to the previous equation:

${\begin{aligned}2^{m-1}{\sqrt {2-2\cos {\frac {\pi }{2^{m-1}}}}}&=2^{m-1}{\sqrt {2-{\sqrt {2+2\cos {\frac {\pi }{2^{m-2}}}}}}}\\&=2^{m-1}{\sqrt {2-{\sqrt {2+{\sqrt {2+\cos {\frac {\pi }{2^{m-3}}}}}}}}}\\&=\cdots \\&=2^{m-1}{\sqrt {2-{\sqrt {2+{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2+2\cos \pi }}}}}}}}}},\end{aligned}}$

where there are m square root signs. Of course, cos π is −1, so the last term is zero. This leaves us with:

$2^{m-1}{\sqrt {2-{\sqrt {2+{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2}}}}}}}}}},$

where there are m − 1 square root signs. Shifting the index by one gives the desired formula.

I should be cleaning out the fridge. She's going to kill me. Ozob (talk) 23:57, 16 June 2009 (UTC)

Albert Einstein

...is at peer review. Help get it back to FA. Casliber (talk · contribs) 11:33, 17 June 2009 (UTC)

• Why should anybody care about FA?
• The demotion was pedantic and semi-literate; the recent FAC is a joke which complains that it does not cite printed sources, when it cites many. (This diff is immediately before the nomination; it hasn't changed much.)
• Any support for deleting Featured Articles altogether? It does real, if minor, services for Wikipedia; but as an article evaluation system, it could be profitably replaced by a random number generator. Septentrionalis PMAnderson 16:15, 17 June 2009 (UTC)

I suppose that you do not care about ever seeing a mathematics article on the Main page again? JRSpriggs (talk) 04:30, 18 June 2009 (UTC)

• I propose to take a longer road. Replace FA, or fix it, and the mathematical features will follow. I would prefer to see nothing on the front page than a good many FAs; it's one of Wikipedia's public embarrassments.Septentrionalis PMAnderson 17:34, 18 June 2009 (UTC)

I for one certainly don't care about that. But even though I have no desire to participate in the FA and GA processes, I have no objections if other people do. — Carl (CBM · talk) 04:46, 18 June 2009 (UTC)

Articles that are meant to serve a broad audience benefit from the kind of feedback you get from the GA and FA process. Articles of more specialist interest probably don't. I certainly want to get the Logic article to reach the GA/FA criteria. I can't think of any other articles that (i) I care about and (ii) I think are worth the effort. Maybe, someday, Mathematical logic and Arthur Prior, but they are harder sells. Einstein looks like a better bet, but I don't care enough to get involved. — Charles Stewart (talk) 08:38, 18 June 2009 (UTC)

Logic seems to be coming along very well. I spent some time on Mathematical logic last year, and it is not in bad shape. I know of several lingering defects in that article, and I am sure there are more that I don't know. But I think it would require someone with quite a bit of background to give a truly thorough review of the article. — Carl (CBM · talk) 13:55, 18 June 2009 (UTC)

Thanks. There's much, much more to be done, though. several lingering defects — I know that feeling very well. — Charles Stewart (talk) 14:05, 18 June 2009 (UTC)

I think Charles' comment about the intended audience and the value of encyclopedia wide reviews like FA and GA is insightful. Would there be any value in the mathematics project having it's own review process? Paul August ☎ 15:16, 18 June 2009 (UTC)

We have Wikipedia:WikiProject Mathematics/A-class rating. Algebraist 15:20, 18 June 2009 (UTC)

We do/did have the A-class review process, but it is defunct now.

After reflecting on that process, and my general experience with WP, my thought is that the sort of process we developed for A-class review has systemic problems that prevent it from working. To give a thorough review to an article such as First-order logic would require a comparable amount of effort to peer-reviewing a journal paper. The PDF version of that article is 22 pages long.

Few editors have the time and energy to do that type of intensive review for a never-ending list of articles. I certainly do not have the energy. Also, discussion page format for reviews is more suited for drive-by comments than to slow, thorough reading. The limiting resource here is reviewer time per article. — Carl (CBM · talk) 15:23, 18 June 2009 (UTC)

The discussion of FAC for this article may be moot; it's certainly premature. As noted at the peer review, the present coverage of Einstein's scientific work is not close to A- or FA-class; an NPOV assessment would probably put it at a high C-class. Until some editors with scientific knowledge devote themselves to improving that coverage, it probably shouldn't be listed as a Good or A-class article. Proteins (talk) 18:15, 18 June 2009 (UTC)

Euclidean algorithm on the Main Page

Hi, just an friendly heads-up that a mathematical article, Euclidean algorithm, will be featured on the Main Page in a few hours. Since Main-Page articles are usually a magnet for vandalism, it would be great if you could add it to your watchlists for the day and fix things as you happen to notice them. Others will undoubtedly be watching as well. My own schedule is very busy, however, so I'll have only a limited time to help out. Thanks! Proteins (talk) 20:29, 17 June 2009 (UTC)

Collaboration en.wp et fr.wp in mathematics

I've just posted a comment on the French WikiProject here and the German one. Are there currently any "institutionalized" means of collaborating with the guys there? For example, the French site is also using a grading scheme similar to the one used here, but nonetheless the actual article quality is not automatically comparable. I'd like to spot articles in French or German whose English equivalent is worse (or the other way round, but that's more relevant to fr.wp and de.wp). Any ideas about that? (Obviously, the same holds true for other languages, but I think it is a start to deal with these two.) Jakob.scholbach (talk) 19:51, 13 June 2009 (UTC)

Generally en is most complete and that the quality here is also generally better, I believe. (Otherwise I would be working at de or fr.) Translations from en to the other languages are going on throughout Wikipedia, all the time – this doesn't seem to require coordination, or at least not a new initiative. Some other points to consider:

• Since it's relatively rare for the French or German version to be better, we normally don't look there. The only times I have found myself on fr or de looking for maths articles were when something had gone seriously wrong (e.g. wrong title for years, such as prametric) and I wanted to see how they dealt with it. They are bound to know when their version is better. If they would notify us after significant improvements, that would be a great help for us.
• They might also have developed ways of presenting sets of articles that we could import and then keep synchronised.
• What can we give back?

--Hans Adler (talk) 20:41, 13 June 2009 (UTC)

Actually, I find that some of the articles in these languages are of a decent quality. For instance, manifold in the French language is a feature article and appears to be reasonably well-written. On the other hand, I have also noticed languages in which the articles are featured, although of poor quality. Lumbaart seems to be notorious for this. Perhaps the reason why many people edit the articles in English is that more people collaborate here. There is also the obvious reason that the articles are of a better quality. --PST 04:53, 14 June 2009 (UTC)

There are some French articles you should read if you can : fr:périmètre, fr:théorème du minimax de von Neumann, fr:théorème de d'Alembert-Gauss, fr:théorème du point fixe de Brouwer, fr:énigme des trois maisons for example. Maybe some of them deserve translation into English. --El Caro (talk) 08:44, 14 June 2009 (UTC)

Definitely. --Hans Adler (talk) 09:07, 14 June 2009 (UTC)

The French featured good [I was confused about the French system Hans Adler 07:05, 21 June 2009 (UTC)] article on the Brouwer fixed point theorem is interesting. Plenty of ideas, history, pictures. No mention of Sperner's lemma, though, which I would say was a failure of NPOV, since it gives a whole lot of space to the later work of Nash, thus favouring a famous American mathematician over an obscure German one. The German article on Brouwer is much superior to ours. Charles Matthews (talk) 10:48, 14 June 2009 (UTC)

If anyone has trouble following Charles about the differences between Brouwer fixed point theorem and the French version, it's because the translation is in progress. --Hans Adler (talk) 14:08, 14 June 2009 (UTC)

I have no opinion on NPOV and Sperner's lemma, but as a general comment: It's hard to get NPOV right when you are basically the only author and the featured good article discussion looks like this: fr:Discussion:Théorème du point fixe de Brouwer/Bon article. --Hans Adler (talk) 22:24, 14 June 2009 (UTC)

Jakob's idea seems very good, but what can we do concretely? --El Caro (talk) 19:25, 17 June 2009 (UTC)

I am not sure what we can do by way of organised co-operation, but it seems a good way to start is to do more cross- and trans-wiki work. So far I have translated two small maths articles into German, and I am currently translating a French featured article into English. (It's probably going to be a GA here.) If topic X has a strong affinity to language L ≠ English, e.g. Nicolas Bourbaki to French, then it's probably worth keeping the articles on X in English and in L synchronised to ensure that all improvements in one version make it into the other version. The other Wikipedias can then simply translate the English or L version. What I like about this approach is that we, the large English Wikipedia with its many native speakers of other languages, help some of the other Wikipedias to grow and get something back in return. --Hans Adler (talk) 11:40, 18 June 2009 (UTC)

I think that is a googd idea, but I think that you could add en.v and fr.v for collaboration fr:v:Projet:Mathématiques and v:School:Mathematics Regards, Otourly (talk) 10:25, 20 June 2009 (UTC)

GA Reassessment of Special relativity

I have done a GA Reassessment of the Special relativity article as part of the GA Sweeps project. I have found the article to need quite a bit of referencing. I have placed the article on hold for a week pending work. I am notifying all interested projects of this review which can be found here. If there are any questions please contact me on my talk page. H1nkles (talk) 17:59, 19 June 2009 (UTC)

Higher-dimensional algebra in need of attention

I gave it a preliminary cleanup, but the article seems unfocused and unsure of what to cover. Lots of redlinks (which could be redirects or piped, but I lack knowledge here). Also seems to draws heavily from one author (R. Brown).Headbomb {^ταλκ_{κοντριβς} – WP Physics} 14:24, 20 June 2009 (UTC)

Higher-dimensional algebra certainly lacks motivation (I don't really count wanting to be general) and orthodix organisation. Charles Matthews (talk) 15:30, 20 June 2009 (UTC)

What a depressing article. I had never heard of the term "higher-dimensional algebra", but Baez and Brown seem to be using it. Judging from the description, a "supercategory" might just be an n-category for some n. But then why are only 2-categories mentioned? Since there are technical problems with the definition of n-categories I suspect it's one of the competing variants. There are no links between this article and the apparently closely related article n-category. The applications in mathematical biology sound like a hoax based on an accidental use of the word "supercategory" in that field. I am not saying it is a hoax, but without any explanation it's hard to tell. Esquisse d'un Programme could serve as a motivation for studying n-groupoids (Grothendieck says they capture all of "tame" geometry, or something like that) but only appears under "see also". Hans Adler 16:28, 20 June 2009 (UTC)

Seifert–van Kampen theorem has some problems. One might go through the math articles citing Brown and see if there is a systematic coi/bias problem. JackSchmidt (talk) 16:33, 20 June 2009 (UTC)

This external link to Higher Dimensional Group Theory may or may not shed light on things. Charvest (talk) 02:41, 21 June 2009 (UTC)

Oh, I see the article already links to that page. Never mind. Charvest (talk) 02:45, 21 June 2009 (UTC)

François Viète

Hello, a lot of good faith information has been added to the page by someone who is French I believe, and it is therefore in dire need of cleanup. More importantly for this WP, it lacks inline citations, although it does have references. I wouldn't know if did find references for some statements, so if someone with more knowledge could look into it... it also makes some fairly heavy claims, that a) aren't sourced and b) sound fairly disputable. I know little of the history of algebra, but 'He was the first mathematician to have represented the parameters of an equation by letters' sounds like a big claim. Since the contributor has added a lot of information, it could be a really good page, so I suggest anyone who can should get involved. On another point, New algebra didn't exist until the contributor created it, which seems quite odd. Considering the title may be a direct translation, or not use English terminology, could someone who fully understands the subject, and knows what pages exist check that the page doesn't already exist. Factual correctness would be great, but as I said, the edits are in good faith. - Jarry1250 ^{(t, c, rfa)} 15:55, 21 June 2009 (UTC)

He was the first mathematician to have represented the parameters of an equation by letters is perfectly true (indeed, it hedges too much; Diophantus was doing something quite different). Septentrionalis PMAnderson 17:47, 21 June 2009 (UTC)

I wasn't suggesting it was an incorrect claim, I was just checking, and it should probably have a reference. - Jarry1250 ^{(t, c, rfa)} 18:30, 21 June 2009 (UTC)

http://sci.tech-archive.net/pdf/Archive/sci.math/2009-01/msg03978.pdf : "Viète introduced arbitrary parameters into an equation and distinguished these from the variables of the equation. But his notation was only *partly* symbolic and was still ultimately based on Euclidean geometry. But for the first time, one could speak of a general quadratic equation, not just certain particular equations with particular numerical values." --El Caro (talk) 18:54, 21 June 2009 (UTC)

Intrinsic curvature

Hi, that link redirects to Curvature. Which in turn directs you to Curvature of Riemannian manifolds. This article appears to be missing its first sentence dealing with expression but without, or skipping, definition? It has been unchanged for years (I know nothing about it myself) ~ R.T.G 16:24, 21 June 2009 (UTC)

The main problem is the lack of an introductory article on intrinsic curvature. Once you know what curvature is and what Riemannian manifolds are (we have that article), then you don't really need too much of a definition of the phrase "curvature of Riemannian manifolds", you can just get on with discussing the technical aspects. --Tango (talk) 18:28, 21 June 2009 (UTC)

If the question is where does one go to find out the meaning of intrinsic curvature, then at the moment (given the absence of the introductory article that Tango refers to above) as far as I can tell, the best place for that is "Curvature" not "Curvature of Riemannian manifolds". I think part of the problem is that "Curvature" links the first use of the term "Intrinsic curvature" to the article "Curvature of Riemannian manifolds", leading the reader to believe the reverse. Paul August ☎ 18:59, 21 June 2009 (UTC)

Well, the onus is on we editors to use a lead to describe every article as can be broadly understood. As a suggestion to anyone who knows different curvatures, what is the difference between circular curvature, elliptical curvature and Riemannian curvature? Could you say (if that is what it is) "A Riemannian curvature is, similar to a wave, an increasingly inclining curvature, one that smooths out, linear on the circle or the ellipse, a 3d swirling curvature or a difficult to describe combination of curves like that?" It is probably a straight line for all I know but if I read it in a book I would probably take a look at Wikipedia. ~ R.T.G 20:35, 21 June 2009 (UTC)

Riemannian curvature is simply the concept of curvature for Riemannian manifolds, so I think the definition is in the name. We have a problem with maths articles because it is often not practical for articles about advanced mathematics to be understandable to the layman, especially as a stand-alone article. Anyone trying to read curvature of Riemannian manifolds without having read Riemannian manifold is not going to get very far, and there isn't much we can do about that. --Tango (talk) 21:00, 21 June 2009 (UTC)

Okay but there is a way to describe it (of course if I come up with that I will write it all down!!) ~ R.T.G 13:20, 22 June 2009 (UTC)

All "propositions" are proven????

I noticed that Proposition and Proposition (mathematics) both say "... proposition is used for a proven statement ...". As a universal proposition, this is false according to my understanding and as "proposition" is used in propositional calculus, propositional formula, proposition (philosophy), and implicational propositional calculus. JRSpriggs (talk) 18:11, 21 June 2009 (UTC)

It is one meaning of Proposition: the statements in a textbook are often called Theorem 2.5, Proposition 2.6, Lemma 2.7.... The claim that Lemmas are harder proofs than Propositions is not my experience; indeed, it seems to me backward; but the entire discussion might be better at Wiktionary, since it is about the word, not the concept. Septentrionalis PMAnderson 18:17, 21 June 2009 (UTC)

I make no claim that my usage is standard, but in the one instance I can recall in which my co-authors introduced "propositions" as well as lemmas and theorems into one of my papers, they were intermediate between lemmas and theorems: proved statements that summed up a series of technical lemmas into a more general and simpler form, but that we did not want to claim as the main results of our paper. —David Eppstein (talk) 18:20, 21 June 2009 (UTC)

My understanding of the usual usage of the terms is that a Lemma is a result used to prove something else and a Proposition is an interesting result in its own right, but a fairly minor one when compared to a Theorem. These terms are all very subjective and depend on context, of course. What's a Lemma to one person may be a major result to another. --Tango (talk) 18:24, 21 June 2009 (UTC)

Like the trivial corollary of the modularity theorem for semistable elliptic curves. Dragons flight (talk) 06:53, 22 June 2009 (UTC)

I've prodded the article, on the grounds it belongs at Wiktionary; the principal sense of "proposition": a statement which can be true or false, (or the meaning of such a statement) is at proposition (philosophy) and the chief effect of this article has been to attract links which should go there. Septentrionalis PMAnderson 18:34, 21 June 2009 (UTC)

I've unprodded it, I think the article should either be kept or merged into somewhere, not deleted. It contains useful content. --Tango (talk) 18:52, 21 June 2009 (UTC)

I don't think that the contents of Wiktionary are useless, and that's where it should go - unless you can find a better place here. Septentrionalis PMAnderson 19:05, 21 June 2009 (UTC)

I have to agree with Sept here. I doubt there's anything encyclopedic to be said about the distinction between propositions (in the sense of mini-theorems) and lemmata. Really proposition in this sense is hardly ever used stand-alone — it's just part of a labelling scheme, allowing you to write things like we now finish the proof of Theorem 3.3 by a straightforward application of the method used to prove Proposition 3.1.

On the other hand, the default meaning of proposition in mathematics is "statement that is either true or false". So proposition (mathematics) absolutely should redirect to proposition (philosophy), because it's the same usage.

I'm not in principle opposed to merging content from the existing article, but I didn't actually see anything worth merging. I'm willing to be persuaded otherwise, if I've missed something. --Trovatore (talk) 20:33, 21 June 2009 (UTC)

We currently have a section, Theorem#Terminology, which makes an attempt at explaining the differences. I think there could be a full article on this topic, explaining the history of this way of structuring papers, explaining any differences in how it is done in other countries, etc. An article specifically on propositions doesn't make much sense, but it would be good as part of a larger article on the subject. --Tango (talk) 21:06, 21 June 2009 (UTC)

Well, could be, but I still don't see anything worth saving from the current article. --Trovatore (talk) 21:29, 21 June 2009 (UTC)

In any case the article proposition (philosophy), at least in its current state, has nothing to do with "Proposition 3.1", and in fact I have difficulty seeing much of a connection with mathematics. I think the "Proposition 3.1" sense is dominant in mathematics in general compared to the propositional formula or propositional variable sense, and that in turn is certainly more common than the proposition (philosophy) sense. Trovatore has redirected to proposition (philosophy), and I think that's totally unacceptable. I think that was way too bold and the previous situation, while not at all good, is at least not totally confusing. Therefore I have reverted. Hans Adler 00:31, 22 June 2009 (UTC)

So first of all, the "Proposition 3.1" sense may well be the one with the highest total count of occurrences. But this is a very poor target for anything called proposition (foo), because it doesn't mean anything. It's just a label, the way some streets are called "lane" and come are called "place", but there's no time you'd want to say that such and such a street "is a lane" or "is a place". This sense has encyclopedic value approximately zero; I don't think it ought to enter into this discussion at all.

As for propositional variables and so on, again I don't think you would ordinarily call these propositions. They're propositional variables or propositional what-have-yous, but not propositions. So again I don't think this sense enters into the discussion.

On the other hand, how are you going to describe, say, the continuum hypothesis? You can't call it a "theorem" in the contemporary sense (Hilbert did, apparently intending theorem in the sense of "part of a theory" or some such, but that sense of the word is hardly understood nowadays). It's not really a hypothesis or a conjecture, because most people don't think it's true. You could call it a "sentence", I suppose, but that seems overly syntactic; it won't work if I'm talking about the meaning of the sentence.

But you can very well call it a proposition. And in fact you can argue about whether it really is a proposition or not. This, I would say, is truly and by far "the dominant sense" of the word proposition in mathematics, when the word is being taken seriously as opposed to simply used to organize a paper. --Trovatore (talk) 03:36, 22 June 2009 (UTC)

By the way, in Russian "proposition" as in "Proposition 3.1" is "предложение", while "proposition" as in "a proposition is either true or false" is "высказывание". I wonder, what happens in other languages? Boris Tsirelson (talk) 06:33, 22 June 2009 (UTC)

In German, the meanings related to logic are called Aussage, while the numbered things are a bit rarer than in English and called Proposition. Hans Adler 09:27, 22 June 2009 (UTC)

I think when the CH is referred to as a "proposition" it is not usually appropriate to link this to proposition (philosophy). Perhaps in a philosophy of mathematics context – but otherwise it's no more than a synonym for "statement". A dedicated article for "Proposition [3.1]" is inappropriate, but an article on mathematical terminology, and in particular theorem/lemma/proposition/remark/corollary is certainly encyclopedic, although it's obviously a bit hard to find the appropriate sources that no doubt exist somewhere.

Without such an article we have the philosophical meaning and the technical meaning in mathematical logic. With it we have 3 mathematical meanings. Keep in mind that proposition (mathematics) is already partially disambiguated. We can't start proposition (philosophy) with a hatnote saying:

Proposition (mathematics) redirects here. For other meanings in mathematics see Propositional formula and Mathematical terminology#Theorem, lemma etc.

Therefore as it's ambiguous it must be either a disambiguation page or an article that can contain a hatnote pointing to the other meanings in mathematics. If proposition (mathematics) were a redirect to proposition (philosophy), then there would be no reason to link to proposition (mathematics). If there are no appropriate incoming links anyway, I don't see why it can't be a disambiguation page. I think there should be a general principle that if "X (A)" is still ambiguous, it should not be a redirect to a completely disambiguated article "X (B)". I can't find anything relevant in WP:Disambiguation or the archives of its discussion page, though. Hans Adler 09:27, 22 June 2009 (UTC)

(left) We have a dab page; it's at proposition. When there is a common meaning of a word about which we have no article (verbs, for example), dab pages will often mention it, but not link to it, or else offer a cross-wiki link to Wiktionary. That's what we should do here; we can update proposition as soon as this discussion is over.

Almost all the links to proposition (mathematics) (I don't see any exceptions, but I may have missed some) mean proposition (philosophy); that is the sense with mathematical content. This includes Lemma (mathematics), which defines a lemma as a "proven proposition"; if the textbook sense were meant, a lemma would not be a proposition, and "proven proposition" would be redundant.

Retaining the article means moving all of them, and policing the page to keep editors from making the natural link. Much easier to get rid of this page, which has no sources, and no encyclopedic content. I have restored Trovatore's link, in the hopes of getting readers to the right place in the meantime; the text is here. Septentrionalis PMAnderson 13:59, 22 June 2009 (UTC)

Inappropriate moving of article

JamesBWatson (talk · contribs) has unilaterally moved Newton's method to Newton–Raphson method. This is contrary to our policy of using the most common name in English. JRSpriggs (talk) 10:45, 23 June 2009 (UTC)

Raise this at WT:WPM. Both names are widely used from what I know. Oleg Alexandrov (talk) 10:46, 23 June 2009 (UTC)

<<above copied from Oleg's talk page>>

I know what Newton's method is, but I don't think I have ever heard the name Raphson before. Hoever, this is far from my area and the relevant part of my mathematical education wasn't in English. Hans Adler 11:12, 23 June 2009 (UTC)

I don't feel strongly either way, but note that "Newton-Raphson" is the name used by the various GCE exam boards in the UK - see, for example, Q7(b) on this AQA paper, Q4(c) on this Edexcel paper and Q4 on this OCR paper. Is this perhaps a UK/US difference in terminology ? Gandalf61 (talk) 11:35, 23 June 2009 (UTC)

The Google popularity test says there's not much in it: combining the search with "numerical analysis" gives 21,500 for "newton-raphson" and 37,100 for "newton's method". Enough to move back, though, I guess. — Charles Stewart (talk) 12:34, 23 June 2009 (UTC)

I have tended to take the term Newton's method to refer to the one-dimensional case and Newton–Raphson method to mean the case of a function of several variables (but still a one-dimensional range space. But I don't know how prevalent that usage is. Michael Hardy (talk) 19:22, 23 June 2009 (UTC) ...and now I see that there's nothing at all about higher-dimensional domains in the article. Michael Hardy (talk) 19:47, 23 June 2009 (UTC)

The Calculus texts I learned from and taught from (circa 1960s -1970s) all used "Newton's method", with no mention of "Raphson", I believe. I think it should probably be moved back. Paul August ☎ 19:50, 23 June 2009 (UTC)

I think that Newton's method is more commonly used in textbooks and in the literature. Although I have heard of the Newton-Raphson method, the occurence of this term was in a negligible source. In particular, I think that this term is used mostly in school curricula. Therefore, the article should be moved back, but only followed by mention that another term exists (to ensure no future moves). --PST 01:33, 24 June 2009 (UTC)

Newton calculated with specific polynomials of degree 3 and didn't write down a general iteration formula. He expanded the polynomial at the current iteration point and neglected then the higher order terms. What Raphson was doing was to write down the "Newton"-iteration for polynomials of degree 3 with variables as coefficients. It was only Simpson that generalized the method to differentiable functions (note that a function at that time was something that could be calculated, i.e., piecewise analytic). The multidimensional method is sometimes called "Newton-Kantorovich method", but I would be surprised if it wasn't already used before 1940.--LutzL (talk) 05:42, 24 June 2009 (UTC)

Well, the history is interesting, but I don't think it is relevant to the article's title. Many concepts are named after people who had little or nothing to do with their development - see Stigler's law of eponymy. The central question with regard to the best title for the article is what is the most commonly used name for this method in English. Gandalf61 (talk) 09:18, 24 June 2009 (UTC)

Sure. So if this is to remain Newton-Raphson, which is specific for the real one-dimensional case, one would then need a new Newton's method overview article pointing also to Gauss-Newton and quasi-Newton methods, and a specialized Newton-Kantorovich method article specialized on multidimensional pure Newton.--LutzL (talk) 10:34, 24 June 2009 (UTC)

I have now moved the article back, since I seem inadvertently to have annoyed various editors by the move, for which I apologise. However, in my defence I should say (1) I did not "unilaterally" move the article: as can be seen from the talk page, two others had suggested the move, and it seemed that nobody had objected to the suggestion, so I thought the move was unopposed. I have now realised that there was, in fact, further discussion of the matter, but for some reason somebody started a new section on the talk page, instead of continuing the discussion where it had been started, so I did not realise it was there, and (2) As for the move being "contrary to our policy of using the most common name in English", I am not sure which name is more common: I first learnt the method as "Newton's method" back in the 1960s, but in recent years the majority of references I have seen to it refer to it as "Newton-Raphson". Anyway, it seems that the majority opinion expressed on the matter favours "Newton's method", so I am happy to accept it: I certainly had no intention of going against consensus. JamesBWatson (talk) 21:08, 24 June 2009 (UTC)

Multilinear stuff / neologisms?

MSGJ requests (at my talk page) a comment about

• Wikipedia talk:Articles for creation/k-array
• Wikipedia talk:Articles for creation/Multilinear transformation

I personally have never heard of k-array. Is this a neologism? Also, what about the second? Jakob.scholbach (talk) 17:45, 23 June 2009 (UTC)

"Multilinear transformation" seems to miss the point that what tensors do for you is to remove the need for this concept. Not much here, I think. Charles Matthews (talk) 18:38, 23 June 2009 (UTC)

Both proposed articles are poorly written and have vague, non-specific sources. "k-array" looks like a neologism. For multilinear transformations we already have multilinear map. I think both article requests should be declined. Gandalf61 (talk) 19:48, 23 June 2009 (UTC)

Multilinear transformation shouldn't be a redlink though. It should redirect to multilinear map, and now does. Algebraist 12:00, 24 June 2009 (UTC)

Consensus Please

Excessive cross-posting. Spammed to 11 WikiProjects. [11] Hans Adler 14:30, 24 June 2009 (UTC)
The following discussion has been closed. Please do not modify it.
In the article Physics of the Impossible a single editor removed material that I believe, very much enhanced this article. The other editor’s view is that the removed material was off topic. My view is that it is very much on topic. The current article is here: (current) The version which I restored is at my sub page here: (restored) Everything that was removed is related to the book. This is because, as the author writes: “The material in this book ranges over many fields and disciplines, as well as the work of many outstanding scientists.” There is a two and one half page list of the individuals, “who have graciously given their time for lengthy interviews, consultations, and interesting, stimulating conversations.” Most on this list happen to be scientists. I listed only the first 22 individuals and these are scientists. In addition, I linked their names to their biography on Wikipedia. I also listed each scientist’s fields of specialties. Many on the list in the article have more than one field of specialty (view here), and hence this reflects the breadth of knowledge contained in this book. If you look at this section in the restored article you will see what I mean. In addition, before this material was removed by the one editor, the article was much more interactive. It was also more in line with the intent of Wikipedia that that the readers (as well as the editors) have a satisfying experience with Wikipedia. One aspect of this more satisfying experience is being able to access the knowledge that is available at Wikipedia on the sciences, and, perhaps, the mathematics. So, I linked not only the names on the list, but also many of their scientific disciplines to the respective Wikipedia article. Accessing this knowledge supports the following WikiProjects and their respective portals: (there are more I am sure) WikiProject Astronomy WikiProject Books WikiProject Physics WikiProject Space WikiProject History of Science WikiProject Science WikiProject Mathematics WikiProject Technology WikiProject Computing WikiProject Computer Science WikiProject Engineering Also, there were graphics that were removed which support the article and the concepts in the book. I believe these should be restored as well. These are on the restored article page, at my sub page. The captions of the graphics show that the book is grounded in real science. If you scroll through the restored article you will see the variety of graphics. I believe these enhance the article aesthetically, as well as help to give a clearer picture of the concepts contained in the book and the article. Lastly, there were external links that were removed which reflect the concepts in the book. These external links were removed as though they were not relevant. For example, I will list some of the external links, and then the page number in the book, to which each link is related: Solar sails: pp. 152, 158 - 159, 166, 172… Space elevators: pp. 165 – 169 Black holes: 156, 232, 235 – 236… Travel at the speed of light: 159 – 161, 163 – 165, 169 – 170… Unfortunately the external links that were removed are going to have to be restored one at a time, because they cannot be cut and pasted back from the revision history without some distortion. I think these external links should also, be restored to the article. I think the bottom line is, let common sense decide. Even Wikipedia guidelines say that they are just guidelines, not letter of the law. I would appreciate a consensus on whether or not to keep the removed material. Please place your comments here: Consensus please. This is on the talk page of Physics of the Impossible. Thanks for your time Ti-30X (talk) 13:29, 24 June 2009 (UTC)

Template:Define

I am glad to see that we actually have ${\stackrel {def}{=}}$ as a template; it's currently up for deletion, but I hope that will blow over. If others find this as intuitive (for non-mathematicians) as I do, let's use it more widely. Septentrionalis PMAnderson 00:58, 25 June 2009 (UTC)

First, the template doesn't seem to be in a wide use. Second, how does one use it? In practice you usually have some formulae or more likely identities that contain def equal somehow in middle. There is no many opportunities to use this template. The deletion therefore seems to be a natural choice. -- Taku (talk) 10:38, 25 June 2009 (UTC)

If you want to put such definitions in-line, it's a natural choice; I think that this is one of the templates that is rare because nobody knows about it. Septentrionalis PMAnderson 19:42, 25 June 2009 (UTC)

But TeX shouldn't be used inline, and it looks dreadful: x${\stackrel {def}{=}}$15. Algebraist 19:47, 25 June 2009 (UTC)

XKCD / "In popular culture"

It seems that inevitably some people like to add an "In popular culture" section to an article whenever the webcomic xkcd happens to make even a passing reference to it. Thus Paul Erdős (Talk), Erdős number (Talk), even Proof that the sum of the reciprocals of the primes diverges, etc. Since this is likely to keep coming up at mathematics articles, I was wondering if we could have a policy page or some centralised discussion to point people at?
For what it's worth, my opinion is that mere incidental mentions are not worth recording, but nontrivial uses in popular culture (even on xkcd) might be. (XKCD comic.) No doubt there are others who think that all "in popular culture" mentions are cruft. Shreevatsa (talk) 17:46, 26 June 2009 (UTC)

We already do have a guideline on this: WP:TRIVIA. This also provides a good retort whenever this sort of thing comes up. —David Eppstein (talk) 20:03, 26 June 2009 (UTC)

It's a big stretch to call an xkcd mention as being a somehow significant "popular culture" mention. Obviously a number of people that like to edit Wikipedia have a somewhat distorted view of what constitutes "popular culture" (I've noted for a while that the article on Crucifixion seems to devote more space and importance to mentions of crucifixions in anime as compared to those in classic artwork and literature). xkcd, as great as it is, is basically a niche webcomic that is only now starting to emerge more into the mainstream. The most defensible insertion would be into Erdos or Bacon number articles...topics which are inherently about popular culture (although the former is more limited to the geek crowd). --C S (talk) 21:20, 26 June 2009 (UTC)

It's likely to be the only mention in nontechnical work of the reciprocals of the primes; but an external link may be a better solution. Septentrionalis PMAnderson 23:17, 26 June 2009 (UTC)

Jul 2009

Self-referential function

Is anyone interested in trying to salvage something from the fairly new article self-referential function ? At present, the first sentence of the article "Cantor's diagonalisation produces a function that makes reference to itself" is simply wrong; the definition "A self-referential function is a function that applies to itself" is hopelessly vague; and the references are not actually related to the contents of the article. See Talk:Self-referential function for further discussion.

We already have fine articles on self-reference, recursion and functional equation. There may be a useful article to be written on self-referential functions, but the current article is not close to it, in my opinion. Gandalf61 (talk) 09:24, 25 June 2009 (UTC)

I removed the text about the Cantor function, which is unrelated to the references and is also wrong; there is no self-reference there.

It looks like this title should simply redirect to the article on recursively-defined functions. The second reference given (of two) uses the term in this way. The first is in theoretical physics, which is concerning. — Carl (CBM · talk) 12:18, 25 June 2009 (UTC)

It's also concerning that the link is both broken and to the statistics department of the government of Malaysia. Algebraist 12:48, 25 June 2009 (UTC)

After removal of irrelevant content the article was left as a stub with a disputed and probably incorrect definition - so I have been bold and replaced it with a redirect to self-reference. Gandalf61 (talk) 07:54, 29 June 2009 (UTC)

Calculating residues

Hi. I made an edit to the section of Residue (complex analysis) on calculating residues, and I'm posting here requesting a few more pairs of eyes look at it and make sure I didn't introduce any errors or anything. -GTBacchus^(talk) 18:24, 30 June 2009 (UTC)

Minimal subtraction scheme

I would be grateful for some expert opinions on the example I propose to add to Minimal subtraction scheme. Comments at the article talk page would be welcome. A.K.Nole (talk) 20:08, 30 June 2009 (UTC)

Pentation etc.

Family of successors to Tetration are being created....

• Pentation
  • Proposed merge into Hyperoperation, substantive material which might be merged is disputed
• Hexation
  • on AfD; I don't see any substantive material
• Heptation
  • redirected to Hexation, when I remember. There hasn't yet been substantive material.
• Octation
  • on AfC, but as a redirect (!)

Any assistance in keeping this in order would be appreciated. — Arthur Rubin (talk) 02:29, 30 June 2009 (UTC)

• There's also an AfC for heptation: Wikipedia talk:Articles for creation/Heptation. — Charles Stewart (talk) 12:34, 30 June 2009 (UTC)
• I've closed the hept* and oct* AfCs as neologisms. — Charles Stewart (talk) 11:32, 1 July 2009 (UTC)

Help

Resolved

Hi, I'm posting this on the Maths Wikiproject talk as we need editors who are knowledgeable about Mathematics to evaluate the following discussion and check out the editors and articles affected. Please follow the link below and comment if you can help.

Wikipedia:Administrators'_noticeboard/Incidents#Block_review_-_uninvolved_admin_request.

Thankyou. Exxolon (talk) 18:30, 1 July 2009 (UTC)

Aise Johan de Jong

We don't have an article about Aise Johan de Jong (notable for resolution of singularities in characteristic p; a Cole prize winner). I'm not so much into biography articles, but if somebody is, he's certainly deserving an article. Jakob.scholbach (talk) 12:59, 27 June 2009 (UTC)

de Jong didn't resolve singularities in positive characteristic; that's still open, though there's been recent progress. What he did was find a way around it using a type of morphism he called an alteration. Ozob (talk) 02:29, 2 July 2009 (UTC)

In the meantime, prior to creating an article, any biographical details can be added to:

Wikipedia:WikiProject Mathematics/missing mathematicians. Charvest (talk) 13:59, 27 June 2009 (UTC)

I didn't know that page; doesn't it duplicate the list of mathematicians at Wikipedia:Requested articles/Mathematics? (I mean, it does doesn't it?) -- Taku (talk) 18:10, 27 June 2009 (UTC)

Hmm. A merge seems to be in order. Should all the requested mathematicians be put into the missing page or should the missing page be put into the requested page. And are all the requested names notable ? Charvest (talk) 18:18, 27 June 2009 (UTC)

The Requested articles list is longer, but has attracted less information; it would be better to merge into Missing mathematicians, which has a format which encourages notes. I don't know whether they're all notable, but I'm shocked to se Vinogradov on both - how did we miss him? Septentrionalis PMAnderson 23:03, 27 June 2009 (UTC)

We do need an article for A. I. Vinogradov. N.B.: don't confuse him (as I have done) with Ivan Matveyevich Vinogradov. CRGreathouse (t | c) 21:36, 28 June 2009 (UTC)

Short of a full merge (since some names may not be notable), I plan to remove names from the requested list that are also in the missing list and put a notice at the top of the requested list asking names to be moved to the missing list whenever there are some biographical details available. Charvest (talk) 20:29, 5 July 2009 (UTC)

Bow and arrow curve

Bow and arrow curve has been proposed for deletion. Opinions? Michael Hardy (talk) 03:57, 2 July 2009 (UTC)

Could someone have a look at Diffequa contribs ? They seem to be odd. --El Caro (talk) 12:57, 2 July 2009 (UTC)

One possibility is that there is some textbook that gives these as examples. — Carl (CBM · talk) 13:10, 2 July 2009 (UTC)

At first I assumed it was just innocent exploration, but the claim that the bow and arrow was named by Euler pushes into hoax territory. If Euler had really named this thing, Google would know about it. Melchoir (talk) 18:26, 2 July 2009 (UTC)

What are the appropriate terms in Latin and German? I'd search for those in Google Books, with "Euler" as the author's name.

In German:

"Bogen" = bow

"Pfeil" = arrow

"Bogenschiessen" = archery

"Bow and arrow" has some plausibility, since the line y = x is part of the graph, and a curve crossing that line is as well. It's not implausible that Euler wrote about these curves and someone later called them by that name. Michael Hardy (talk) 19:22, 2 July 2009 (UTC)

Hmm, no dice there either. Melchoir (talk) 22:28, 2 July 2009 (UTC)

It's now an AfD rather than a proposed deletion: Wikipedia:Articles for deletion/Bow and arrow curve. As Michael Hardy often writes, please contribute with a reason for your decision rather than a simple keep or delete vote. —David Eppstein (talk) 23:02, 6 July 2009 (UTC)

Help at Kepler Conjecture

A persistent anon keeps editing Kepler conjecture to add a supposed counterexample attributed to Archimedes Plutonium. I have reverted twice today already, but anon has just inserted their nonsense for a third time. Please can someone keep an eye on the article and revert and/or semi-protect as you see fit. Gandalf61 (talk) 16:41, 3 July 2009 (UTC)

• That's the IP address range that M. Plutonium has edited from many times before. Uncle G (talk) 00:32, 7 July 2009 (UTC)

Gate-keeping on Wavelength

I have been trying for some time to add some material to Wavelength quoted below:

Spatial and temporal relationships

The mathematical form for the wave involves the argument of the cosine, say θ, given by:

$\theta ={\frac {2\pi }{\lambda }}\left(x-vt\right)\ .$

Using θ, the amplitude of the wave is:

$y=A\cos(\theta )\ ,$

which shows a particular value of y corresponds to a particular value of θ. As time advances, the term (−vt) in θ continuously reduces θ, so the position x corresponding to a chosen value of θ must increase according to:

$x=vt+\theta \ {\frac {2\pi }{\lambda }}\ ,$

in order that the value of θ stay the same. In other words, the position x where the amplitude y has the value Acos(θ) moves in time with the wave speed v. Thus, the particular mathematical form x − vt expresses the traveling nature of the wave.

In the case of the cosine, the periodicity of the cosine function in θ shows that a snapshot of the wave at a given time finds the wave undulating in space, while an observation of the wave at a fixed location finds the wave undulating in time. For example, a repetition in time occurs when θ increases by 2π; that is, when time increases by an amount T such that:

$\theta (t+T)=\theta (t)+2\pi \ ,$  or  $vT=\lambda \ .$

Likewise, a repetition in space occurs when x increases an amount Δx enough to cause an increase in θ by 2π:

$\theta (x+\Delta x)=\theta (x)+2\pi \ ,$  or  $\Delta x=\lambda \ .$

Thus, the temporal variation in y with period T at a fixed location is related via the wave speed v to the corresponding spatial variation with wavelength λ at a fixed time.

Using the same reasoning, it may be noted that any function f(x − vt) propagates as a wave of fixed shape moving through space with velocity v. However, to obtain a wavelength and a period, the function f must be a periodic function of its argument. As noted, the cosine is a periodic function and that is why a wave based upon the cosine has a wavelength and a period.

The sinusoidal wave solution describes a wave of a particular wavelength. This might seem to make it a specific solution, not applicable to more complicated propagating waves. In particular, the sinusoid is defined for all times and distances, whereas in physical situations we deal with waves that exist for a limited span in space and duration in time. Fortunately, an arbitrary wave shape f(x − vt) can be decomposed into a set of sinusoidal waves using Fourier analysis. As a result, solutions describing the simple case of a single sinusoidal wave can be applied to more general cases.

This well-sourced material has been reverted by Srleffler on grounds found at Talk:Wavelength#Spatial_and_temporal_relationships, along with my response.

I would not take too much notice of this event were it not simply one more instance of reversion of my efforts based upon rather weak premises.

Can someone take a look at this example, and possibly look over the talk page itself to see what might be done here? Brews ohare (talk) 12:12, 6 July 2009 (UTC)

I tend to agree with those who do not think it belongs in the article on wavelength. Perhaps a general article on waves? — Arthur Rubin (talk) 12:59, 6 July 2009 (UTC)

Rannow's Theorem

Some quick observations on the new article titled Rannow's Theorem:

• Wikipedia:Manual of Style (mathematics) is conspicuously ignored. So are some frequently needed provisions of Wikipedia:Manual of Style.
• The use of an asterisk for ordinary multiplication in TeX is uncouth.
• No google hits. (And no references.)
• I've never heard of it. That's rather odd, for a "key theorem of calculus". And it's not just that I don't know it by this particular name (that happens).

As to actual content:

• The statement looks as if it would need to rely on some continuity assumptions, but none are stated.

So I am somewhat suspicious.

I'll say more after I've read it more closely. Michael Hardy (talk) 22:16, 6 July 2009 (UTC)

... OK, now I've looked at it closely enough to see what it says. I've nominated it for deletion. See the discussion at this link: Wikipedia:Articles for deletion/Rannow's Theorem. Don't just say Keep or Delete; give your arguments. Michael Hardy (talk) 22:49, 6 July 2009 (UTC)

Citation formatting, discussion in Talk:Matroid

There's a discussion in Talk:Matroid re citation formatting that probably applies more broadly to mathematics articles on Wikipedia in general. —David Eppstein (talk) 06:22, 4 July 2009 (UTC)

It does; but I disagree very strongly with what David has been saying there. Insofar as the {{citation}} templates are formatting tools, they are nearly useless; even if the format they enforce were optimal (which I dispute), they take me longer and more trouble than formatting by hand. The Harvard style links are useful, but unimportant for most mathematical articles. Septentrionalis PMAnderson 22:53, 7 July 2009 (UTC)

I suggest using a creation of our own Jakob.Scholbach to help you format {{citation}} templates: [12]. I don't format them by hand anymore, ever. Ozob (talk) 18:06, 8 July 2009 (UTC)

Thanks. Still easier to cut and paste an already formatted one. Easier to read and maintain, too. Septentrionalis PMAnderson 22:58, 8 July 2009 (UTC)

Algebra articles on WP

Recently, I have attempted to improve some algebra-related articles to a reasonable standard. I feel that there are far too many stubs in this field, as well as many articles which deserve more content. Mainly, I think that we need to improve the somewhat less well-known articles on algebra so that people who read algebra articles, other than laymen, may benefit. I understand, however, that User:Jakob.scholbach has done significant work on the well-known concepts and hence my motivation.

In particular, if you happen to come across an algebra article which I have edited, and notice something incorrect by Wikipedia standards, please comment/criticize if possible for I am not particularly experienced in WP when it comes to expanding articles. Thus far, I have improved Jacobson radical and created Quasiregular element. I am mainly focusing on related concepts at the moment, such as Nakayama's lemma, Nilradical and Simple module. Any comments would be most appreciated.

With respect to citations, I am mainly citing the book by Isaacs. Although I am aware that there are other excellent books in algebra, I think that other books can easily be cited if necessary. I have chosen Isaacs because in my view, this is one of the better books in the field. You might notice, however, that Jacobson radical and Quasiregular element have more citations than necessary. --PST 06:36, 7 July 2009 (UTC)

I may be showing my age, but it would be nice to see citations of Jacobson's own Algebra. For numbers of citations, see WP:SCG. Septentrionalis PMAnderson 21:54, 7 July 2009 (UTC)

Nah. I always preferred van der Waerden's book. What does that make me? Sławomir Biały (talk) 22:18, 8 July 2009 (UTC)

I should point out that there are books out there other than the one by Isaacs. I don't have this book, but it seems to make rather a wreck of Nakayama's lemma. It is better to stick with more standard sources, like Matsumura, Atiyah-MacDonald, Zariski-Samuel, or Eisenbud. Sławomir Biały (talk) 04:46, 9 July 2009 (UTC)

I certainly do not challenge the assertion that there are better books than Isaacs. Furthermore, I have not used his book in any way, in the recent improvements of Nakayama's lemma. Rather, I have cited facts in the article using his book. Your edit summary, "what is going on with Nakayama's lemma, drop the Isaacs book for a minute please" is rather rude in my view. Although I do not claim the new version to be better than the old, note that (essentially) no-one has added significant material to the article for sometime (for one year, precisely), and at least my additions constitute some advance in writing the article. Could you please state what you dislike about the current version? I am more than happy to discuss this, but I do not appreciate rude remarks. --PST 05:24, 9 July 2009 (UTC)

Certainly. The article now has an entirely one-sided view on Nakayama's lemma that is not at all helpful in understanding the typical applications of the lemma and is more or less at odds with the general usage in the mathematical community. It is first and foremost a result in commutative algebra, not chiefly a result of ring theory more generally (as your current version suggests). Most references to Nakayama's lemma in the literature are to the commutative version. Secondly, the lemma itself is rather difficult to appreciate as such. The current structure of the article emphasizes maximal generality over understandability, whereas I think the article should focus exclusively on the commutative case (which is fairly typical in dealing with the result), and give a variety of examples how it can be used for "geometrical" problems. This can then be followed by a short section on how it generalizes to non-commutative rings. As for whether "there are better books than Isaacs", as I've already said I cannot really evaluate the Isaacs book. But it does seem a rather poor source on commutative algebra, given the article it produced. Sławomir Biały (talk) 05:44, 9 July 2009 (UTC)

Blahtex and mathml support in Mediawiki (and Wikipedia)

Is anyone still working on Blahtex and mediawiki's support for blahtex? The blahtex's site doesn't work (well, actually works only main page), so doesn't blatex wiki. There is project called blatexml (the only source I know where it is now possible to download blahtex). In preferences there is option to show MathML if possible (experimental), but doesn't work anywhere. So does anyone know what with progress of the project? Or is it dead? Anyone could post any informations about it? Maybe someone informed could create article blatex on Wikipedia?

Also, if blahtex isn't "mature" enough to handle Wikipedia's math formulas, maybe should Wikipedia consider other tools like itex2mml (used, for example, with instiki)? ;) Silmethule (talk) 20:08, 8 July 2009 (UTC)

Third set of eyes requested

Could someone please have a look at Talk:Dirac delta function#too many directions? Sławomir Biały (talk) 20:42, 4 July 2009 (UTC)

The article might need a more careful consideration of the "concentric" style of presentation, which returns to topics in a more sophisticated way later, rather than introducing entirely new ideas. Charles Matthews (talk) 21:28, 6 July 2009 (UTC)

Uh, what is "concentric style"? (I know concentric circles in mathematics.) -- Taku (talk) 11:24, 7 July 2009 (UTC)

The "concentric style" is just defined, a line above, isn't it? Boris Tsirelson (talk) 12:18, 7 July 2009 (UTC)

I think the article already is fairly concentric in your sense. Each of the initial sections is either written in a non-sophisticated way, or begins with a paragraph explaining things in an intuitive sense for non-mathematicians. Is this what you mean? Sławomir Biały (talk) 13:58, 7 July 2009 (UTC)

No, I was thinking more about getting to section 7.2 and "suddenly" we are talking about probability theory. This is an organisational problem, mainly. I don't have so much sympathy with the criticism in general, but here I think "too many directions" might be a valid point. There is some point here about what I think of as the Lighthill-style approach to distributions (it doesn't matter so much whether you make a Gaussian narrower and taller, or some other shape); but if probability theory is really central, one should be warned earlier. (So I think it isn't central to telling people what the idea is). Charles Matthews (talk) 21:38, 8 July 2009 (UTC)

Yes. That's a valid point about bringing in probability distributions. It was my own clearly less than ideal attempt to consolidate some facts that had been carelessly dumped into an earlier incarnation of the article. But there is still no suitable home for this errant paragraph. Sławomir Biały (talk) 03:53, 10 July 2009 (UTC)

Links to exampleproblems.com

The site exampleproblems.com is linked to from several articles[13]. As the site is a wiki and not as such a reliable reference per our usual standards I was going to delete these per WP:EL. However, on closer inspection I noticed that these links have been added by established user Tbsmith (talk · contribs) who doesn't seem to be active here on a regular basis. I asked on the reliable sources noticeboard and was (wisely) told to ask for input from this project before removing them[14]. I'd like to know if these links are normally considered acceptable by this project or not. If not, I'll remove them from mainspace. I know this may sound like I'm being overly cautious but I'm trying to avoid a conflict by not ignoring some consensus I may not be aware of. Thanks, Vyvyan Basterd (talk) 15:30, 7 July 2009 (UTC)

Look at User:Tbsmith: "Todd Smith, a mathematician and creator of ExampleProblems.com". --El Caro (talk) 19:18, 7 July 2009 (UTC)

Exactly, I noticed that too. I was going to assume good faith though and ask if the project want these links kept or not. I don't think he added them in bad faith, I question if they meet the usual standard required here. Vyvyan Basterd (talk) 19:37, 7 July 2009 (UTC)

I do see some merit to relevant links to the site: deep links to a particular article hosted by ExampleProblems.com. However, many of these are links to the main ExampleProblems.com page. To me this crosses the line from providing a useful resource to outright promotion of the site. I would suggest replacing these main page links with more targeted links if possible. Perhaps deletion should be entertained as a last resort. Sławomir Biały (talk) 15:28, 8 July 2009 (UTC)

I think that links to the main page should be deleted if not replaced. I don't mind good-faith external links, even to a wiki, if appropriate -- but the general page won't really be helpful anywhere. CRGreathouse (t | c) 02:18, 10 July 2009 (UTC)

Pageview stats

After a recent request, I added WikiProject Mathematics to the list of projects to compile monthly pageview stats for. The data is the same used by http://stats.grok.se/en/ but the program is different, and includes the aggregate views from all redirects to each page. The stats are at Wikipedia:WikiProject Mathematics/Popular pages.

The page will be updated monthly with new data. The edits aren't marked as bot edits, so they will show up in watchlists. If you have any comments or suggestions, please let me know. Thanks! Mr.Z-man 20:31, 9 July 2009 (UTC)

Changes to popular pages lists

There are a few important changes to the popular pages system. A quick summary:

• The "importance" ranking (for projects that use it) will be included in the lists along with assessment.
• The default list size has been lowered to 500 entries (from 1000)
• I've set up a project on the Toolserver for the popular pages - tools:~alexz/pop/.
  • This includes a page to view the results for projects, including the in-progress results from the current month. Currently this can only show the results from a single project in one month. Features to see multiple projects or multiple months may be added later.
  • This includes a new interface for making requests to add a new project to the list.
  • There is also a form to request a change to the configuration for a project. Currently the configurable options are the size of the on-wiki list and the project subpage used for the list.
• The on-wiki list should be generated and posted in a more timely and consistent manner than before.
• The data is now retained indefinitely.
• The script used to generate the pages has changed. The output should be the same. Please report any apparent inconsistencies (see below).
• Bugs and feature requests should be reported using the Toolserver's bug tracker for "alexz's tools" - [15]

-- Mr.Z-man 00:10, 12 July 2009 (UTC)

Function

In spring 2007, after long discussions and painstaking consensus forming, the article Function (mathematics) reached a decent state. After a long period of relative calm, a new editor restarted a discussion about the rigorous mathematical definition of the function. This opened some of the old splits between "formalists" (those who pay most attention to the definition and syntax) and "encyclopaedists" (those who try to convey the meaning and illustrate uses). As a result, Rick Norwood wrote a new lead to the article. Several people objected to his changes, and I tried to reach a compromise by restoring part of the old lead and improving upon it. Sadly, this was followed up by a wholesale revert and chest-pumping at the talk page. I request that members of the project try to help form a consensus. This is one of the most important and frequently viewed mathematics articles here, and we cannot be too careful in making it as broadly appealing as possible. Thanks, Arcfrk (talk) 14:19, 12 July 2009 (UTC)

Category:Relations

I emptied it, rather than leaving it set for a merge back to Category:Mathematical relations, because the creator of the category mangled other categories some of the articles were in, such as Category:Closure operators. I had hoped that the cfm I created would have been sufficient, but then I noticed removal of other appropriate categories. If this was improper, please let me know. — Arthur Rubin (talk) 10:17, 27 June 2009 (UTC)

Not to endorse that; but I notice that Category:Set theory requires a fair amount of work placing articles into appropriate subcategories. Charles Matthews (talk) 13:51, 29 June 2009 (UTC)

I can see that. Can someone provide a current category tree for categories which should be subcategories of Category:Set theory? I don't want to kick articles down one level, requiring further sorting.... — Arthur Rubin (talk) 02:16, 30 June 2009 (UTC)

As a followup question: Should Category:Relational algebra be in Category:Mathematical relations? Seems to me to be a different concept entirely. In fact, Category:Relational algebra does seem to be exactly part of mathematics at all.... — Arthur Rubin (talk) 06:32, 6 July 2009 (UTC)

I don't follow your reasoning. This is database theory, but the theory used is mathematical - what else would it be? Charles Matthews (talk) 21:42, 12 July 2009 (UTC)

I'd say yes Category:Relational algebra should be in Category:Mathematical relations given the first sentence of the article Relational algebra: "Relational algebra, ..., deals with a set of finitary relations". Also although Relational algebra is probably mostly studied by computer scientists, I'd say theoretical computer science is part of mathematics, and the book Universal algebra, algebraic logic, and databases is definitely mathematical. I mean it even has a chapter on Galois theory of databases. How cool is that? Charvest (talk) 08:31, 13 July 2009 (UTC)

Matrix calculus: Definition of the matrix derivative

We could use some help to resolve a controversy about the correct formulae for the matrix differential and the matrix derivative at the article Matrix calculus. See the talk page, especially the section Disputed information: Matrix derivative.  Cs32en  22:52, 11 July 2009 (UTC)

I concur we need assistance, primarily as to the notation(s) actually used in serious mathematical works. — Arthur Rubin (talk) 15:49, 13 July 2009 (UTC)

See Talk:Matrix calculus#Scope of questions for my view as to the matters in dispute, and my take on them. My desired outcome is not necessarily represented in all cases. — Arthur Rubin (talk) 21:19, 13 July 2009 (UTC)

Certain hyphens

How many size-3 subsets does a size-8 set have?

The set of dimension-2 subspaces of a dimension-4 space is an example of a Grasmannian.

He was wearing size-10 shoes.

${\begin{aligned}{\text{size-3 subsets of a size-8 set}}\\8-3=5\end{aligned}}$

In the second case above, I'd prefer "2-dimensional subspaces". But it would never have occurred to me that those could be mistaken for minus signs. But user:r.e.b. wrote on my talk page:

Putting hyphens - that look rather like minus signs in front of numbers seems a bad idea, whatever the MOS says. r.e.b. (talk) 19:39, 12 July 2009 (UTC)

This discussion is complicated by the fact that the traditional use of hyphens is a slightly endangered species, still used by book publishers, magazines, and newspapers, often no longer used in package labeling and advertising. It is a splendidly efficient disambiguating or clarifying tool in some cases. "The correlation between maternal alcohol use and small for birth weight" is a phrase I had to look at several times to parse it. Why was someone concerned with correlations between "small", on the one hand, and on the other hand, maternal alcohol use, and why just for birth weight? "The correlation between maternal alcohol use and small-for-birth-weight" would not have caused any mental hesitation. "The German occupied town of Caen" and "the German-occupied town of Caen" is an example of very efficient disambiguation. "A man-eating shark" scares people away from beaches, whereas "a man eating shark" is a customer in a seafood restaurant.

Opinions? Michael Hardy (talk) 20:33, 12 July 2009 (UTC)

A referee recently chided me for writing "depth first search" when I should have used depth-first search, so I think hyphenation as a part of English grammar is alive and well. But I agree that "size-10" could easily be misread as "size −10", so rephrasing to avoid digits after hyphens seems like a good idea. —David Eppstein (talk) 20:46, 12 July 2009 (UTC)

I agree with you! I would in fact find the absence of hyphens—"size 3 subsets", or "size 10 shoes"—confusing or at least somewhat odd, and to my eyes the hyphen in "size-10 shoes" is at no risk of being confused for a minus sign. I do agree that it is possible that they are confused, so rewriting might be a good idea, but I think simply dropping the hyphen isn't. Shreevatsa (talk) 21:42, 12 July 2009 (UTC)

Just to complicate the issue, American and British English differences#Punctuation suggests that omitting the hyphen is more acceptable in British than American English. —Blotwell 13:23, 14 July 2009 (UTC)

This also (implicitly?) has something on the use of hyphens in mathematics:

A key ingredient of the proof is a Borsuk-type theorem on the existence of a pair of antipodal 2-faces of a 5-polytope whose boundaries are linked in a given embedding of the 1-skeleton in 3-space.

(But maybe not bearing directly on the present question.) Michael Hardy (talk) 23:11, 12 July 2009 (UTC)

"Valentina Harizanov" nominated for deletion

See Wikipedia:Articles for deletion/Valentina Harizanov. Don't just vote Keep or Delete; give your arguments. Michael Hardy (talk) 05:30, 15 July 2009 (UTC)

Equation solving

I have just added the Wikiproject Mathematics template to the talk page of Equation solving. The article seems to have been pretty much ignored until now and it needs a lot of work. I have filled in the bits on ratings etc.. If someone wants to do a more official assessment then please do. Yaris678 (talk) 18:03, 15 July 2009 (UTC)

Pseudo-edge

Pseudo-edge needs attention. In particular, there is no definition. Michael Hardy (talk) 05:43, 16 July 2009 (UTC)

A quick googling suggests that the word "pseudo-edge" has been used in different context in a fairly ad-hoc manner, just like someone might define and use terminology such as "blue edges" to refer to something that does not have a generally accepted name. Delete? — Miym (talk) 06:52, 16 July 2009 (UTC)

Judging from the creator's comment on the talk page and some other anonymous edits from the same IP range, this is just some guys from Hampshire College fooling around. After a removed speedy and a removed prod, AfD seems to be the only option. The English Wikipedia is quite good at wasting hours of productive editors' time with each minor incident of vandalism of this type. Hans Adler 07:46, 16 July 2009 (UTC)

Actually, the problem with it is that this is an (implicit) definition: a pseudo-edge is a requirement, in a graph coloring problem, that two non-adjacent vertices differ in color, and nothing else. Wiktionary exists for statements like that. Septentrionalis PMAnderson 15:26, 17 July 2009 (UTC)

Well-behaved functions

Well-behaved is currently all about mathematics. However, in my opinion, it is very poorly written. I am not a mathematician, and a lot of mathematical content pages link to it - but the page does not tell me what all those pages actually mean when they write that a function needs to be 'well-behaved', and instead claims the meaning of the word is up to "fashion", and gives a bunch of examples of which functions are "better behaved" than others, according to "someone" (there are no citations, and the talk page seems to indicate people disagree on these matters). I've left a comment on the article's talk page to this effect, then checked the history and noticed it seems not to really ever have gotten a lot of attention. I was wondering if there were people here who would be able to fix this. I would do it myself, but don't know enough about the subject to write anything that would actually be usable (that's why I wanted to read up on it!). Thank you! :-) Gijs Kruitbosch (talk) 20:01, 17 July 2009 (UTC)

Well-behaved (or, more often, "sufficiently well-behaved") is a piece of hand-waving = "under some narrow set of conditions which (probably) will be specified later." I see this in the article, but it may not be visible to the lay reader. Septentrionalis PMAnderson 20:38, 17 July 2009 (UTC)

The term is not very well-defined ;-) That doesn't prevent us from writing an article about it, however, as long as the term is notable. Whether a function is well-behaved or not depends on the context - this at least is the way I have seen the term being used. The article doesn't make that sufficiently clear. I'm a bit too lazy to look for reliable sources on this at the moment, so I hope someone else will fix this problem (and, potentially, other problems) of the article.  Cs32en  21:38, 17 July 2009 (UTC)

GA Review of Obstacle problem

I am conducting a Good Article review of this article. Have just scraped a pass at Maths A Level over forty years ago, I am unable to comment on matters pertaining to the accuracy of the article. I have concerns over whether the article is accessible to the general reader, whether it uses too much un-explained jargon, some unreferenced statements and I cannot determine whther the article is broad in scope, focussed and contains no original research. Please comment at Talk:Obstacle problem/GA1. Thanks. Jezhotwells (talk) 09:34, 12 July 2009 (UTC)

I really could do with some input into the discussion at [[Talk:Obstacle problem/GA1], otherwise I will have to fail the nomination. Thanks. Jezhotwells (talk) 00:22, 20 July 2009 (UTC)

• Second Could somebody with some analysis or PDEs background please have a look at this article? Thanks, Ray^Talk 00:25, 20 July 2009 (UTC)

List of mathematical examples

The ancient article titled List of mathematical examples is still in a somewhat neglected and stagnant condition. (I just added another item to it.) Does it deserve our attention? Michael Hardy (talk) 00:04, 18 July 2009 (UTC)

Awesome article, but does anyone read it? Anyways, should we link to the section that contains the example, instead of the article? - Peregrine Fisher (talk) (contribs) 07:59, 20 July 2009 (UTC)

Adding Near set to the "See Also" section on the page Set (mathematics)

Hello all,

I would like to add the page on Near Sets to the "See Also" section on the page Set (mathematics) and I was told this is the place to start a discussion on the matter.

To borrow from the Wikipedia set page:

By a "set" we mean any collection M into a whole of definite, distinct objects m (which are called the "elements" of M) of our perception [Anschauung] or of our thought.

In near set theory, the elements of a near set are distinct objects that are elements of our perception. A set $X$ is considered a near set relative to a set $Y$ in the case where the feature values of one or more of the objects in the set $X$ are almost the same (within some epsilon) as the feature values of one or more of objects in a set $Y$. In effect, any traditional Cantor set $X$ is called a near set whenever the nearness requirement is satisfied. I would be more than happy to send a copy (or post a link) of an article giving the underlying theory on near sets.

Thanks,

Christopher Henry NearSetAccount (talk) 19:07, 20 July 2009 (UTC)

I think perhaps an addition to Set might be appropriate, rather than to Set (mathematics). It appears not to be a mathematical object.

That is, provided that any of the sources in the article show the concept is used at all. — Arthur Rubin (talk) 19:33, 20 July 2009 (UTC)

Agree with that. I'd have put it into the see also links of some pages about automatically classifying and grouping data rather than mathematical sets. Also near set doesn't have any see also section - surely that would be a good guide to related articles? Dmcq (talk) 20:06, 20 July 2009 (UTC)

(edit conflict) First of all, the context of this doesn't seem to be mathematics at all, but the kind of computer science that deals with topics that are so trivial that one has to complicate everything by inventing application-dependent non-standard terminology for all basic terms.

According to your definition, whenever two sets X and Y have non-empty intersection, X is considered a near set relative to Y. Is that what you want? Unfortunately your definition is undistinguishable from pseudo-mathematics because

• in the first sentence "near set" refers to a type of mathematical object more general than a normal set,
• in the second sentence "near set" is a relation between two ordinary sets (and it doesn't look like a particularly useful one, I would say), while
• in the third sentence, being a near set is a property that an ordinary set may or may not have.

I would not have used this strong language if upon looking it up in the article near set I hadn't encountered the following:

• A lead that doesn't define anything but only gives a very vague idea that even leaves it open whether "near sets" are objects or being "near sets" is a relation.
• A section "Definition" that fills several screens with what looks like The Emperor's New Clothes mathematics. It's also extremely badly written. For example Definition 2:

A perceptual system $\langle O,\mathbb {F} \rangle$ is a real valued total deterministic information system where $O$ is a non-empty set of perceptual objects and $\mathbb {F}$ is a countable set of probe functions.

The most straightforward reading is that a perceptual system is a real valued total deterministic information system with additional properties. But what is a real valued total deterministic information system? You don't tell us. (You don't even tell us in which branch of science or the humanities we should look for a definition.) Is it an information system with additional properties? Is it an information system? Probably not. You are linking to rough set, an article that defines information system as attribute-value system, which turns out to be an obfuscated way to refer to a matrix with named rows and columns. I will just call it a "matrix" for simplicity. At this point I came to the conclusion that the words "total" and "deterministic" are probably completely redundant and simply express that the matrix doesn't have holes, i.e. undefined entries (which according to the definition it can't have anyway), and that it's really just a single matrix, not a set of similar matrices with us not being sure which one it is (also implicit in the definition). So we are one step further (I am also using the fact that by "probe function" you mean a real-valued function defined on some set of "physical objects", although that's not actually what your Definition 1 says):

A perceptual system $\langle O,\mathbb {F} \rangle$ is a real-valued matrix where $O$ is a non-empty set of perceptual objects and $\mathbb {F}$ is a countable set of real-valued functions.

This doesn't make any sense, but assuming "perceptual objects" = "physical objects" we can now guess what you mean:

A perceptual system $\langle O,\mathbb {F} \rangle$ consists of a non-empty set $O$ (called perceptual objects) together with a set $\mathbb {F}$ of real-valued functions $f:O\to \mathbb {R}$.

Then, under the heading "Perceptual relations", you pretend to define without further assumptions what the "description" of an object $x\in O$ is. Of course that's not what you do. What you really do is, you fix a finite sequence $\phi =(\phi _{1},\phi _{2},\ldots ,\phi _{i},\ldots ,\phi _{l}),$ of real-valued functions defined on $O$ and then call $\phi (x)$ the description [vector] of $x$. Since $\mathbb {F}$ seems to have been lost in the process, we are supposed to guess that when you called $\mathbb {F}$ a set you actually meant a finite sequence, and $\phi =\mathbb {F}$. (In particular, I would guess that the same function is allowed to occur twice, so if you want to think of it as a set, it's a "linearly ordered multiset".)

Now you get into a long-winded tangent about the Euclidean norm, announcing your intent to apply it to the difference of two descriptions.

We are still far from the section "Perceptual tolerance relation" (which in turn is very far from the end of this tour de force of senseless obfuscation of what is presumably a totally simple definition), but my tolerance is already completely exhausted. Hans Adler 21:08, 20 July 2009 (UTC)

I question whether Near set should be in the Category:Systems of set theory where it has been placed. JRSpriggs (talk) 10:34, 21 July 2009 (UTC)

It certainly should not. Algebraist 15:14, 21 July 2009 (UTC)

I'd like to thank Hans Adler for his explanation of the article, without which I would have been lost. It's clearer now that it does not belong in set theory (the article or category). CRGreathouse (t | c) 17:05, 21 July 2009 (UTC)

I think I should be offended by Hans equating computer science with bad mathematics, but otherwise it's a very helpful summary. —David Eppstein (talk) 17:36, 21 July 2009 (UTC)

Sorry for almost offending you. That's not what I meant. I know that there is some brilliant mathematics going on in computer science, although even some of that suffers from very poor terminology. I said "the kind of computer science that...". I don't think the bad mathematics in computer science can be defined in terms of subfields . I first encountered this bad kind of computer science when a friend of mine who was doing a PhD in artificial intelligence gave a talk about geometric reasoning in the plane. He spent at least 20 minutes motivating, defining and explaining an apparently novel concept (not of his invention) named by an acronym assembled from terms such as "disjoint" and "covering". It turned out to be a synonym for "partition". Hans Adler 17:53, 21 July 2009 (UTC)

There's plenty of reinvention of the wheel within computer science, but isn't that just an instance of Sturgeon's law? I don't think it's a defining property of the field. —David Eppstein (talk) 17:57, 21 July 2009 (UTC)

That and Not Invented Here syndrome. Exactly because it's not a defining property I don't accept the excuse: "It's only computer science." Hans Adler 18:12, 21 July 2009 (UTC)

Wow! This has generated a lot of comments. Great, I always enjoy a healthy discussion. I think some of the confusion about what is written in the current version of the Near set Wikipedia page is good indicator of the need to clarify and simplify the page content.

$>$ That is, provided that any of the sources in the article show the concept is used at all.

Yes, it has been shown that near sets provide, for example, an effective way to solve the image correspondence problem, i.e., retrieving images from a database that are similar to a given query image. See, e.g.,

Peters, J.F. Tolerance near sets and image correspondence. Int. J. of Bio-Inspired Computation 4 (1) 2009, 239-245.

Hassanien, A., Abraham, A., Peters, J.F., Schaefer, G., Henry, C. Rough sets and near sets in medical imaging: A review, IEEE Trans. Info. Tech. in Biomedicine, vol. 13, 2009, In press.

$>$ Also near set doesn't have any see also section - surely that would be a good guide to related articles?

An oversight on my part. I will a See also section in the revised page.

$>$ First of all, the context of this doesn't seem to be mathematics at all, but the kind of computer science that deals with topics that are so trivial that one has to complicate everything by inventing application-dependent non-standard terminology for all basic terms.

Interesting comment. Sure, initially, the concepts are simple. However, formal concepts from mathematics are needed to establish a framework for near sets. Admittedly, it is a straightforward task to write a computer program that implements the near set approach to measure the correspondence between perceptual objects such as digital images. We are interested in a formal method of describing the process being used to solve the problem so that we can write theorems, proofs, propositions, etc. The goal is to establish a formal system that makes it possible to prove that our algorithms are correct rather than relying on empirical evidence from the output of our simulations. Furthermore, the theory presented in the Wikipedia page on Near Sets is well-published and grew out of Rough Set theory which is a well-established (over 25 years) and also a well-published research area.

$>$ According to your definition, whenever two sets $X$ and $Y$ have non-empty intersection, $X$ is considered a near set relative to $Y$. Is that what you want?

No, that is not what is intended. Sets $X$ and $Y$ are disjoint. For example, sets $X$ and $Y$ could represent different digital images obtained from an image archive. It is then possible to extract a description of each subimage and compare the descriptions of $x,y$. Furthermore, descriptions are formulated using probe functions (a term introduced by M. Pavel in 1993 as part of a study of image classification [M. Pavel, Fundamentals of Pattern Recognition, 2nd Ed. NY, Marcel Dekker, Inc., 1993.], and it is possible to measure the degree of similarity of $X$ and $Y$ based on a comparison of the image descriptions. If the degree of similarity of $X$ and $Y$ is non-zero, $X$ and $Y$ are considered near sets.

$>$ In the first sentence "near set" refers to a type of mathematical object more general than a normal set.

Incorrect. The first sentence states: "In mathematics, sets containing objects with similar descriptions are called near sets." This does not imply that a near set is a generalization of a traditional set, but rather a near set is a special case of a Cantor set. In fact, near sets are defined with respect to two or more Cantor sets, i.e., sets of perceptual objects with descriptions that are, in some degree, similar. The idea is to look for similarities among sets of perceptual objects which can be described by probe functions.

$>$ in the second sentence "near set" is a relation between two ordinary sets (and it doesn't look like a particularly useful one, I would say),

Yes, it is a relation between two "ordinary sets" as long as the objects in the sets can be described by some probe functions.

$>$ in the third sentence, being a near set is a property that an ordinary set may or may not have.

Generally, one considers two or more sets when using near set theory. Yes, a set can be "near" itself, but this is a trivial case. Sets can be near each other in some degree depending on the objects in the sets and the method used to describe them.

$>$ A lead that doesn't define anything but only gives a very vague idea that even leaves it open whether "near sets" are objects or being "near sets" is a relation.

Thank you for pointing that out. I will change the lead sentence. We are dealing with a relation between two sets.

$>$ A section "Definition" that fills several screens with what looks like The Emperor's New Clothes mathematics. It's also extremely badly written. For example Definition 2: A perceptual system $\langle O,\mathbb {F} \rangle$ is a real valued total deterministic information system where $O$ is a non-empty set of perceptual objects and $\mathbb {F}$ is a countable set of probe functions.

Again, thank you for pointing that out. Some terms in a given research area are so well known that one does not need to define them. However, for the sake of clarity, I will insert a link (or directly explain) for each of the technical terms in the definition of a perceptual system. The information system considered here is the same as in Rough Set theory, i.e., a perceptual system can also be called an attribute-value system in the case where it defined relative to information tables.

$>$ You are linking to rough set, an article that defines information system as attribute-value system, which turns out to be an obfuscated way to refer to a matrix with named rows and columns. I will just call it a "matrix" for simplicity. At this point I came to the conclusion that the words "total" and "deterministic" are probably completely redundant and simply express that the matrix doesn't have holes, i.e. undefined entries (which according to the definition it can't have anyway), and that it's really just a single matrix, not a set of similar matrices with us not being sure which one it is (also implicit in the definition).

I can see where you are coming from. The only problem is that I did not create this definition. As you correctly guessed, it is used in both Near set theory and Rough set theory. I chose to leave the definition as it stands in two well-established research areas. I also know that there is a group of researchers currently working a revision of the Rough set Wikipedia page.

$>$ This doesn't make any sense, but assuming "perceptual objects" = "physical objects" we can now guess what you mean:

Thanks again. I can clarify this point. Yes, a "perceptual object" is an object that has it origins in the physical world. The idea is that Near Set theory is only concerned with physical objects that can be described in some manner. I see now that it would help to define this concept beforehand.

$>$ Then, under the heading "Perceptual relations", you pretend to define without further assumptions what the "description" of an object $x\in O$ is. Of course that's not what you do. What you really do is, you fix a finite sequence $\phi =(\phi _{1},\phi _{2},\ldots ,\phi _{i},\ldots ,\phi _{l})$ of real-valued functions defined on $O$ and then call $\phi (x)$ the description [vector] of $x$. Since $\mathbb {F}$ seems to have been lost in the process, we are supposed to guess that when you called $\mathbb {F}$ a set you actually meant a finite sequence, and $\phi =\mathbb {F}$.

Thanks again. $\mathbb {F}$ is the set of all probe functions that can describe the objects in $O$. For instance, when comparing two sets, $\mathbb {F}$ will contain all possible ways of describing the objects, yet the comparison is only made on a small subset of $\mathbb {F}$.

$>$ Now you get into a long-winded tangent about the Euclidean norm, announcing your intent to apply it to the difference of two descriptions.

Thanks again. I agree with you. Instead of what is written about the Euclidean norm, I will replace what is written with a link to Norm (mathematics).

In sum, I have addressed the specific comments in response to my post. I now plan to revise the Near set Wikipedia page, taking into account the comments that have been made. The goal will be to simplify and reduce what has been written and, hopefully, reach a point where there is agreement. Thank you to all who have posted. Christopher Henry(NearSetAccount (talk) 18:44, 21 July 2009 (UTC))

Thanks for taking my comments in this way. I am afraid the way I said it didn't make it easy! I will comment as I am reading your response. I saw one misunderstanding: By the "first sentence" I wasn't referring to the article yet. I meant "In near set theory, the elements of a near set are distinct objects that are elements of our perception." Which repeats a vague definition of "set" except that it drops "definite". So it's more general. Hans Adler 18:54, 21 July 2009 (UTC)

OK, just one more thing: I guess that instead of perceptual/physical objects this theory can start with whatever you want. You just have to fix some set of probe functions. If that is the case, based on normal mathematical conventions it is misleading to "define" them before you define the perceptual systems. The normal mathematical approach would be the following:

A perceptual system $\langle O,\mathbb {F} \rangle$ consists of a non-empty set $O$ together with a set $\mathbb {F}$ of real-valued functions $f:O\to \mathbb {R}$. The elements of $O$ are called perceptual objects or physical objects. The elements of $\mathbb {F}$ are called probe functions.

Just like we don't say "A vector is a physical quantity. A vector space is a set of vectors together with...". Instead we define the vector space first, and then the vectors are simply its elements. If this is no longer the normal way to express this kind of thing in theoretical computer science, then the schism is already worse than I thought. Hans Adler 19:16, 21 July 2009 (UTC)

Thank you Hans. I see exactly what you mean. Do not worry, the schism is not as bad as you think. Us non-mathematicians need guidance every once in a while.(NearSetAccount (talk) 18:20, 22 July 2009 (UTC))

To go back to the original question, it seems clear that this belongs to the same niche as fuzzy sets, rough sets, and dynamically varying sets, all of which seems closer in spirit to concept analysis than what logicians mean by set theory. Is there any way that we could have an article on this, that we could link to in place of such specific articles in see also sections? I can't think how best one would give such an article coherence, but ther is some sort of common thread. — Charles Stewart (talk) 22:44, 21 July 2009 (UTC)

Perhaps we could have a section at the bottom of the Set (mathematics) article, called "Generalizations". Charvest (talk) 23:15, 21 July 2009 (UTC)

It doesn't sound like a generalization to me. It is just a different subject with very little connection except the word 'set' as far as I can see. Dmcq (talk) 23:57, 21 July 2009 (UTC)

Dmcq, Could you clarify your comment? To borrow from the Wikipedia page "Sets can be used as a foundation from which nearly all of mathematics can be derived." Such is the case with Near Sets. The whole theory is based on observing/measuring the degree of similarity between sets of objects based on the description of the objects contained in the sets.(NearSetAccount (talk) 18:20, 22 July 2009 (UTC))

Sets are a foundational subject. Near sets are not a foundational subject. They are not a basis for deriving much in mathematics from, they are a leaf subject and look like a heuristic for classification like lots of other ways of grouping objects. They are possibly of great practical application but I see very little likelihood of them being used in number theory or topology for instance. As far as I can see you might as well try saying they are part of category theory because they put things in categories. Dmcq (talk) 22:23, 22 July 2009 (UTC)

They're all trying to be formal theories of collections, which we might classify as three kinds:

1. Set theory, type theory, domain theory — complete accounts of notion of collections, trying to encompass all mathematical objects, perhaps relative to a restricted notion of mathematics;
2. Combinatorial species, study of collections in abstract datatypes — algebraic theories of representation of theories, typically interested in studying the properties of various collection composition operators;
3. These things — interested in studying relations that hold between the elements of a homogenous collection of objects.

How about calling these last group as "Qualitative set theories", if we can't find an established term? It's a neologism, but I think we should have some name for the ensemble of these things. — Charles Stewart (talk) 05:57, 23 July 2009 (UTC)

I like the name but it would be WP:OR to use it I think. There is an article alternative set theory which contains a mish-mash including fuzzy sets and alternative axioms unfortunately. Whatever fuzzy sets falls into would I guess be suitable. I think of fuzzy sets as being quite distinct from sets. The closest I can think of where real numbers and norms comes into the subject and yet is close to foundational in treatment and possible development that I can think of is Quantum logic, and even there I'd probably try abstracting out as much as possible that doesn't depend on cranking numbers for the logic side. My idea of an alternative set theory is one where one has something like the Axiom of determinacy instead, but you can't mix that up in the same paragraph as fuzzy sets in a meaningful way. Personally I'm sorry the title Alternative set theory has been hijacked the way it has and I wish the article just died but I guess it's not wikipedia's place to go saying how the world should be. Dmcq (talk) 06:55, 23 July 2009 (UTC)

I can see the problem looking at the see also section of Set (mathematics). It contains a whole bunch of stuff that are only very loosely related and I'd have put into the Set page for disambiguation instead. I don't think even a dense set belongs there. Probably the top of the article shoudl sy it is principally to do with maths foundations and direct to Set for everything else. Dmcq (talk) 00:16, 22 July 2009 (UTC)

James Stirling (mathematician)

Hello,
Is James Stirling's date of birth right on James Stirling (mathematician) ? Many sources give "may" instead of 22 april. Is it a Old Style and New Style dates problem ? --El Caro (talk) 06:56, 22 July 2009 (UTC)

 Done by Lilyu. --El Caro (talk) 12:09, 22 July 2009 (UTC)

Branches of combinatorics?

The section of outline of combinatorics titled Branches of combinatorics lists only the following two items:

• Combinatorial chemistry
• Graph theory

Does combinatorial chemistry really constitute a "branch" of combinatorics? And the section omits virtually everything. Would someone with competence in that area clean this up? Michael Hardy (talk) 01:43, 14 July 2009 (UTC)

Combinatorial chemistry isn't a branch, it's application. --EsfirK (talk) 19:02, 23 July 2009 (UTC)

Diophantus II.VIII

Hi

Would like to invite comment on the above article ie Diophantus_II.VIII. Readership stats do not appear to justify a stand-alone item and I am wondering if it should not rather be moved to be a subsection of another article - eg Arithmetica or Diophantus. An alternative might be to put links in from these pages and any others to which it is relevant.

Neil Parker (talk) 05:48, 24 July 2009 (UTC)

As far as I can see this looks to be about constructing Pythagorean triples. Perhaps that would make a more specific merge target. —David Eppstein (talk) 05:51, 24 July 2009 (UTC)

Erdős–Bacon number

Erdős–Bacon number was shrunk a fair bit: Before After (diff). As I'm not too attached to the article, I don't have an opinion, but perhaps someone else, with different ideas of what's OR and what's obvious, may be interested. :-) Shreevatsa (talk) 18:15, 25 July 2009 (UTC)

I am not convinced this belongs into Wikipedia at all. It seems to have happened mostly in blogs, with some very restricted coverage in the news (Daily Telegraph and BBC) by a single journalist. Of course it's OK to mention the Erdős number in six degrees of Kevin Bacon, and to discuss the Bacon number in Erdős number. And in this context it makes sense to mention the Erdős–Bacon number in a sentence or two. But more than that doesn't seem to be reasonable, especially not a separate article. Hans Adler 18:57, 25 July 2009 (UTC)

Extensive discussion at WP:OR/N#Erdős–Bacon number. Hans Adler 13:28, 26 July 2009 (UTC)

I admire your forceful, complete, pertinent, and entirely correct summation of the matter. —Dominus (talk) 03:17, 27 July 2009 (UTC)

Squaring the circle

This diff and this one identify a circle-squarer posting "original research" among us. Michael Hardy (talk) 19:00, 25 July 2009 (UTC)

I put the page on my watchlist. Magidin left an explanatory note on the user's talkpage already. — Carl (CBM · talk) 19:15, 25 July 2009 (UTC)

Their web site looks like an attempt to score high on John Baez's "crackpot index" by conforming to stereotypes of a certain flavor of crackpot. Michael Hardy (talk) 19:22, 25 July 2009 (UTC)

Jensen's formula

Can someone address the issues I raised at talk:Jensen's formula? Michael Hardy (talk) 16:08, 26 July 2009 (UTC)

Routh's theorem

MathWorld's page about this states two separate results. The first of them might be called a generalization of Ceva's theorem, and the second is an equivalent generalization of Menelaus' theorem. But all the other web sources I've looked at, and the WP page, only give the first equation. Does the second equation have a name? Is it due to Routh? Should we have it, either on the Routh's theorem page or elsewhere? —Blotwell 19:45, 24 July 2009 (UTC)

The current diagram is inconsistent with the current text. JRSpriggs (talk) 14:05, 25 July 2009 (UTC)

Good catch, I've fixed the text. (Hopefully the problem I fixed was the same as the one you noticed.) —Blotwell 16:20, 27 July 2009 (UTC)

That is it. Thank you. JRSpriggs (talk) 02:01, 28 July 2009 (UTC)

Sieve of Atkin

The addendum that was added last year (!) seems questionable to me. Can anyone verify this?

Also, the article could use some work, if anyone's wiling to lend a hand.

CRGreathouse (t | c) 02:27, 27 July 2009 (UTC)

(A normal link for those who do not log in using the secure server: [16].) It seems quite dubious to me as well. It's certainly not more efficient to work with rationals instead of integers, and the algorithm to trace the quadratics suggested in the paper and implemented by D. J. Bernstein works with integers. A description of that would be nice to have in the article, actually. — Emil J. 13:40, 27 July 2009 (UTC)

Contiguity space

Contiguity space is opaquely written. There's enough there that I think I can probably figure out just what it's about, but I shouldn't have to decipher the first paragraph the way I need to. Michael Hardy (talk) 13:22, 27 July 2009 (UTC)

Married to a pseudonym

Here's one of the weirder sentences I've found in Wikipedia (as you can see, I've fixed it). (It's not a pseudonym, unless "Tom Xmith" is a pseudonym for "Thomas Xmith".)

It seems the article on Chandler Davis was initially written by people who know him as a science-fiction writer; they didn't even mention in the first sentence that he's a mathematician. I've re-written it so that it mentions that first.

One of his theorems is mentioned in eigengap. That's an orphaned article—can someone help with that?

Davis–Kahan theorem is now a redirect to eigengap. Maybe someone here can make it into an article. (If that is done, then Davis-Kahan theorem (with a hyphen instead of an endash) should then get redirected to Davis–Kahan theorem. Michael Hardy (talk) 23:12, 27 July 2009 (UTC)

Matrix calculus: Definition of the matrix derivative

Content from the archive. The issue is still unresolved.  Cs32en  18:18, 28 July 2009 (UTC)

We could use some help to resolve a controversy about the correct formulae for the matrix differential and the matrix derivative at the article Matrix calculus. See the talk page, especially the section Disputed information: Matrix derivative.  Cs32en  22:52, 11 July 2009 (UTC)

I concur we need assistance, primarily as to the notation(s) actually used in serious mathematical works. — Arthur Rubin (talk) 15:49, 13 July 2009 (UTC)

See Talk:Matrix calculus#Scope of questions for my view as to the matters in dispute, and my take on them. My desired outcome is not necessarily represented in all cases. — Arthur Rubin (talk) 21:19, 13 July 2009 (UTC)

Three year old WW Rouse Ball Copy Vio

Turns out the vast majority of the content of W. W. Rouse Ball has been a copyright violation since Aug. 10, 2006 (see this diff). It was ripped straight out of the Mac-Tutor bio. I reverted back to the pre-Aug 10, 2006 version. If anyone has time, it would be good to rewrite the article, and readd anything newer than three years ago. RobHar (talk) 03:21, 29 July 2009 (UTC)

Hoax article Base 69

Jamie.D.Mac (talk · contribs) has created an article Base 69 which purports to be a description of base-69 arithmetic but in fact is a corrupted version of the article Octal, with all the 8s replaced with 69s, and some extra garbling. Mercurywoodrose (talk · contribs) PRODed it, but this was declined without comment by the author. I have proposed it for speedy deletion under CSD G3. --Uncia (talk) 03:50, 29 July 2009 (UTC)

I have deleted it. PrimeHunter (talk) 04:44, 29 July 2009 (UTC)

Strangest edit war I've ever seen

In the article Proofs involving the totient function, the single-purpose account Prmishra1 (talk · contribs) and several IP addresses (59.180.44.246 (talk · contribs · WHOIS), 59.180.127.247 (talk · contribs · WHOIS), 59.180.127.247 (talk · contribs · WHOIS), 59.180.7.238 (talk · contribs · WHOIS)) have been engaged in the past few days in an attempt to replace one proof of $\sum _{k=1}^{n}{\frac {\varphi (k)}{k}}=\sum _{k=1}^{n}{\frac {\mu (k)}{k}}\left\lfloor {\frac {n}{k}}\right\rfloor$ for another one. I was asked for a 3rd opinion via WP:3O and sided with what had been in the article, but Prmishra1 is persisting, without any dialog. Two things:

• Is it common to have heated disputes over unsourced proofs in math articles, with one side not discussing the matter on the talk page? I don't hang out in math articles so I don't know the usual routine.
• If anybody has expertise in that area, can they please check the proofs in question, as sort of a 4th opinion? I am not a mathematician and am certainly no expert in proof style and elegance. Here is a sample diff.

Thanks. Eubulides (talk) 17:27, 28 July 2009 (UTC)

I say, scrap both. The "alternate proof" at the bottom of the section is much more clear then either version of the inductive proof. — Emil J. 17:49, 28 July 2009 (UTC)

It does not have to be phrased as a counting proof, if someone sees that as a problem. It is basically just changing the order of summation:

${\sum _{k=1}^{n}\sum _{d|k}{\frac {\mu (d)}{d}}=\sum _{1\leq k,d\leq n \atop d\mid k}{\frac {\mu (d)}{d}}=\sum _{d=1}^{n}\sum _{1\leq k\leq n \atop d\mid k}{\frac {\mu (d)}{d}}=\sum _{d=1}^{n}{\frac {\mu (d)}{d}}\sum _{1\leq k\leq n \atop d\mid k}1=\sum _{d=1}^{n}{\frac {\mu (d)}{d}}\left\lfloor {\frac {n}{d}}\right\rfloor .}$

— Emil J. 18:14, 28 July 2009 (UTC)

Dear Emil J., I think the trick where you use the fact that

$\left\lfloor {\frac {n+1}{k}}\right\rfloor -\left\lfloor {\frac {n}{k}}\right\rfloor \;=\;{\begin{cases}1,&{\mbox{if }}k|(n+1)\\0,&{\mbox{otherwise, }}\end{cases}}$

is worth preserving, especially since it generalizes, as is evident in the next section, where

$\left\lfloor {\frac {n+1}{k}}\right\rfloor ^{2}-\left\lfloor {\frac {n}{k}}\right\rfloor ^{2}\;=\;{\begin{cases}2{\frac {n+1}{k}}-1,&{\mbox{if }}k|(n+1)\\0,&{\mbox{otherwise.}}\end{cases}}$

is used. Anyhow in the meantime our unusual friend has reverted the page again to their version. -Zahlentheorie (talk) 18:38, 28 July 2009 (UTC)

These proofs are not particularly remarkable, it has to be said. If there is anything distinctive here, it could be merged into totient function. There is nothing really encyclopedic in manipulation of Sigma-notation. Charles Matthews (talk) 20:42, 28 July 2009 (UTC)

They may not be difficult but I believe the subject of proofs using the totient function is notable and deserve its place in wikipedia. Dmcq (talk) 20:53, 28 July 2009 (UTC)

That is the point at issue. "Proofs using the totient function" is not a conventional mathematical topic, to my knowledge of number theory. It seems to me less notable than proofs using the Moebius function, for example. If there is some aspect of sieve theory (for instance) where there are discernible techniques or methods worth discussing, then it might serve to establish greater notability. Simple manipulations in the style of (say) Hardy & Wright don't count, I would say. Charles Matthews (talk) 10:09, 29 July 2009 (UTC)

Actually the leader for the article says it is for proofs involving either the totient or Möbius function which is fair enough I think, I suppose sticking both in the title would make it rather too long. Perhaps there is a more all encompassing name? Dmcq (talk) 11:01, 29 July 2009 (UTC)

Hi all, I see three possibilities to resolve this: first, revert it to the version that made the slashdot listing, second, give up on it and leave it as is, third, scrap the inductive proof. And after that, LOCK the page to keep it from constantly being reverted. It seems to me that Charles Matthews would be a good mediator. What do you think? Best regards, -Zahlentheorie (talk) 16:21, 29 July 2009 (UTC)

Well, I think this page should be merged immediately into average order of an arithmetic function. These examples show techniques where the average order is accessible by elementary methods. Arguing about exactly which is not so interesting: aliter. Charles Matthews (talk) 16:30, 29 July 2009 (UTC)

Interesting suggestion. What do you propose to do with the section on inequalities? I wonder if you are aware of the fact that the average order computations listed on average order of an arithmetic function can all be done by Mellin inversion. I can do one of these for you if you like. BTW, our mysterious friend has again reverted the page to their version. -Zahlentheorie (talk) 20:14, 29 July 2009 (UTC)

I have opened up a sockpuppet investigation request at Wikipedia:Sockpuppet investigations/Prmishra1. For now I reverted the change again. Eubulides (talk) 20:29, 29 July 2009 (UTC)

Hi there, I blundered, I don't think all can be done by Mellin inversion, but some certainly can. Let me think about this some more first. -Zahlentheorie (talk) 20:44, 29 July 2009 (UTC)

What I'm referring to here is the Mellin-Perron formula:

$\sum _{k=1}^{n}\lambda _{k}={\frac {1}{2}}\lambda _{n}+\int _{c-i\infty }^{c+i\infty }\left(\sum _{k\geq 1}{\frac {\lambda _{k}}{k^{s}}}\right)n^{s}{\frac {ds}{s}}$

where the integral is evaluated by a shift to the left, picking up residues for for an asymptotic expansion at infinity. E.g. since

$\sum _{k\geq 1}{\frac {\varphi (k)}{k^{s}}}={\frac {\zeta (s-1)}{\zeta (s)}}$

the first pole that contributes is the one at $s=2$ with residue ${\frac {1}{2}}n^{2}{\frac {6}{\pi ^{2}}}$. Similarly, since

$\sum _{k\geq 1}{\frac {d(k)}{k^{s}}}=\zeta (s)^{2}$

the first pole that contributes is the one at $s=1$ with residue $n\log n+n(2\gamma -1)$. Same for $\sigma (k)$. -Zahlentheorie (talk) 22:07, 29 July 2009 (UTC)

My preference, in general, for mathematical proofs on Wikipedia, is:

1. An article about a proof should be about a notable proof, it should not be itself a proof. Likely Erdős' elementary proof of the prime number theorem and Wiles' proof of Fermat's Last Theorem deserve their own article, because in both cases what's notable is not just the fact that was proved but the proof itself. However, I think most other proofs would not qualify in this respect. And in those two cases, at least, it would be a very bad idea to try to reproduce the whole proof within the article.
2. By the same token, if content consisting of a proof of a mathematical fact belongs in Wikipedia at all, it generally belongs in the article about that fact rather than in a separate proof article. If the proof isn't notable in its own right, it shouldn't be the subject of an article.
3. Only include the details of a proof in an article when they are important for helping the reader understand the subject. If the only thing the reader gets out of a proof is "this fact is true and can be proved by induction", don't give the proof, just say that it can be proved by induction and provide a proper citation.
4. Per WP:NPOV, don't include proofs when they would severely unbalance the article.

So in this particular case, I agree with Charles Matthews that the content belongs in average order of an arithmetic function, if anywhere. I am not yet convinced that the proof details would be helpful or important to include there, though. —David Eppstein (talk) 21:27, 29 July 2009 (UTC)

Having had another look at the article I must admit it has no statement about notability nor much by way of citation. In fact it has very little straightforward text at all which is just wrong. Dmcq (talk) 23:24, 29 July 2009 (UTC)

Livermore loops article

Could someone please take a look at the Livermore loops article. There's a lot of red links there that either need articles to be created for them, or need redirecting to appropriate articles, if they exist. There may also be more terms that could use linking. Raul654 (talk) 16:15, 30 July 2009 (UTC)

One of the blue links was to Monte Carlo, a place in southern Europe on the coast of the Mediterranean Sea. Obviously that's not what was intended. People should use common sense in linking. Michael Hardy (talk) 21:04, 30 July 2009 (UTC)

Method_of_analytic_tableaux

Resolved

Do the SVG images at Method_of_analytic_tableaux look OK to anyone? To me the fonts are placed too low and too right, overlapping the lines. — Carl (CBM · talk) 22:44, 29 July 2009 (UTC)

Does not look OK to me, I also see some overlap. Ulner (talk) 22:56, 29 July 2009 (UTC)

I think I've seen this problem before. You should be able to solve it by going into inkscape and and for each text component choosing "Convert text to path". I'd do it, but my inkscape appears to be unhappy right now. I can try again later. RobHar (talk) 23:23, 29 July 2009 (UTC)

I've fixed one of the files (File:Prop-tableau-2.svg) as described above. I also had to change the font from Times new roman to arial for some presumably unrelated problem. Hopefully no one will object. I'll go about changing the other files now. RobHar (talk) 00:34, 30 July 2009 (UTC)

That's wonderful, and it fixes the display problem completely on my browser. Thanks, — Carl (CBM · talk) 01:04, 30 July 2009 (UTC)

My web browser and operating system are set up to display web pages as white text on a black background, and all the images at Method_of_analytic_tableaux appear blank, just like many of the images on Wikipedia. I'm guessing these images use a transparent layer thereby mixing the content of the image with the colour settings of the browser. HTML web pages are not in control of how they are displayed on a user's browser and Wikipedia should not assume that they are. Images should be just that - images. Not overlays. Having said that I'm now going off to tilt at some windmills. Charvest (talk) 05:47, 30 July 2009 (UTC)

I can fix that tomorrow. The background white were misaligned in the originals so I just deleted them. It didn't occur to me that a transparent background would be a problem for anyone. Sorry. RobHar (talk) 06:39, 30 July 2009 (UTC)

Oh, thanks. I really wasn't expecting anything. I just felt like raising the issue again. I mean there are many many articles in wikipedia using transparent images. I posted a comment at the village pump a while ago and the replies were along the lines of: it probably isn't practical to change them all, and there would be opposition from those who favour transparent backgrounds. Charvest (talk) 06:59, 30 July 2009 (UTC)

No problem. I too favour transparent backgrounds, but not if it's a problem for other people. However, I think the better permanent solution would just be to have wikipedia display in-article images with a white background. In the meantime, you might be able to tweak your css file to do so. RobHar (talk) 07:11, 30 July 2009 (UTC)

Ah, but that's just the point. The browser is set-up to use black and white regardless of any web site's colour and style settings and Windows desktop theme is High-Contrast Black and white. What's really needed is to rewrite Firefox (and IE) so that transparent images are rendered not as transparent but with a background that matches whatever the background would have been if the browser was following the page's suggested colours. Charvest (talk) 08:16, 30 July 2009 (UTC)

Hmm, that's weird. Anyway, I've put backgrounds on the images. Have you tried GreaseMonkey (for firefox at least)? RobHar (talk) 23:11, 30 July 2009 (UTC)

Thanks for the suggestion. I'll investigate it. Charvest (talk) 06:03, 1 August 2009 (UTC)

The text-curve alignment in the images looks ok to me, but I'm seeing a different problem: the mathematical formulas in some of the image captions are wider than the images themselves are displayed, and are cut off by the box around the caption rather than being fully visible. —David Eppstein (talk) 05:53, 30 July 2009 (UTC)

I also saw that bug. I will see if it is in bugzilla, and file a bug if it isn't. — Carl (CBM · talk) 13:18, 30 July 2009 (UTC)

After investigating, I found the issue isn't unique to math, it happens with plain text as well. I asked about it at Wikipedia:Village_pump_(technical)#Image_captions_can_be_too_wide. — Carl (CBM · talk) 13:38, 30 July 2009 (UTC)

Cusp article

I've done a bit of work on the Cusp (singularity) article. Could someone take a look at it and make any suggestions as to improvement. The classification of cusps comes down to Arnold's A_k-series (which wan't mentioned in the original article). I've tried to give examples and explanations. Is there anything that I haven't explained properly? ~~ Dr Dec (Talk) ~~ 11:49, 30 July 2009 (UTC)

Suggest an ordering of the material that is a bit less top-down. For example, mention the ramphoid cusp much earlier. Use this to explain that the issue of why it is not 'the same' as the simple cubic cusp leads to the diffeo issue. Use that to bring in the general machinery. Charles Matthews (talk) 16:58, 31 July 2009 (UTC)

A-class discussion

As these discussions have tended to suffer from a lack of participation, I respectfully request advice and constructive criticism on Wikipedia:WikiProject Mathematics/A-class rating/Maximum spacing estimation. Thank you. -- Avi (talk) 15:40, 31 July 2009 (UTC)

Reclaiming your Project's name

Hi there, here's an FYI. If you delete all content from {{WikiProject Mathematics}}, and place the following code in it's stead...

#REDIRECT [[Template:Maths rating]]

...you will successfully redirect any use of {{WikiProject Mathematics}} to your correct template. See for example {{WPLISTS}}. The old pageforces use of the correct template. One could use either {{WPLISTS}} or {{WikiProject Lists}} on talk pages and get the correct template. If you knew all this, nevermind. But if not, give it a try if you feel it is helpful at all. Prapsnot (talk) 06:56, 1 August 2009 (UTC)

Aug 2009

Hopkin's theorem

There does not appear to be an article on the important "Hopkin's theorem" due to Charles Hopkins. Although I am aware that this theorem is referred to by other names (such as in the Wikipedia article Artinian ring), none of these names seem to yield an article. Does anyone know if there is an article on the fact that a right (or left) artinian ring is right (or left) Noetherian? Thanks, --PST 09:26, 1 August 2009 (UTC)

If there's nothing more to say about the theorem than what you've said, then I'd just create a redirect to Artinian ring, and maybe mention the name Hopkins' theorem or Hopkins's theorem there. Not Hopkin's theorem of course -- I assume that was a momentary lapse on your part. --Trovatore (talk) 20:24, 1 August 2009 (UTC)

a little help with style at Schauder estimates

Hi - I thought what I had up was more or less in line with WP:SCICITE -- after all, the material is basically formulae pulled out of a textbook, and inline referencing would have been fairly redundant. I'm a little hesitant to remove the tags the newpage patroller put up, and I would like some feedback -- are there any glaring deficiencies in the article? Thanks, Ray^Talk 06:51, 2 August 2009 (UTC)

The article is probably OK, and I've taken down one of the templates. Charles Matthews (talk) 08:31, 2 August 2009 (UTC)

Formatting of equations etc.

I know this is not the right place to ask this but I really would like to find the guidelines/policy for how to format math equations and the like on wiki. cheers. 114.30.110.26 (talk) 10:55, 3 August 2009 (UTC)

Try MOS:MATH#Typesetting of mathematical formulas. Charles Matthews (talk) 11:16, 3 August 2009 (UTC)

The Manual of Style tells you what to do. To see how to do it, see Help:Displaying a formula. JRSpriggs (talk) 12:35, 4 August 2009 (UTC)

just a heads up

I tagged Mathematical Association of America with your project. Cheers. APK that's not my name 21:43, 4 August 2009 (UTC)

Mathematics GA status

I know for the most part we've decided to ignore GA and I support that, but I don't think the unilateral action by User:Gary King is tolerable. Please take a look. --Trovatore (talk) 04:24, 3 August 2009 (UTC)

That would be at Talk:Mathematics/GA1; I've commented there. This sort of unilateral "review" is how Gratuitous Aggravation does things; it gives a feeling of power to those who know nothing about a subject and do not understand our actual guidelines, so it will probably continue. Our recourses are three:

1. Take this to WP:GAR, where the GA for Special relativity now is.
2. Take over, or abolish, GA, which would be best if practical - but is it?
3. Ignore it. This is the easiest, so we'll probably do it.
4. One active variant of #3 would be to withdraw all mathematical and scientific articles from GA and FA, making a note on the respective pages that this has been done. Septentrionalis PMAnderson 18:24, 3 August 2009 (UTC)

If you take the nuclear option (#4), please realize that this means creating a rift between mathematical articles and the rest of the project. While it is true that WP:MATH may be better served that way, most visitors would not know this, and may incorrectly judge the articles. Second, the internal A-class discussions need to be thoroughly revived. -- Avi (talk) 18:39, 3 August 2009 (UTC)

(renumbering to distinguish between letting sleeping dogs lie and taking our articles and going home) I would consider #2 the nuclear option, since it would involve tagging or revising WP:GA itself, but that's a quibble. If we go with #4, we should contact other Wikiprojects (we might do so anyway); I doubt contempt for illiterate and ignorant reviewers is limited to us. Septentrionalis PMAnderson 18:48, 3 August 2009 (UTC)

GA is a project-wide status, not a maths status. We have "Bplus", which recognizes articles of better quality than "B", but did not have to jump through the GA hoops. Similarly, perhaps we can have our internal "A" be the content equivalent of an FA without that process. Personally, I'd rather work with the rest of the project, and perhaps start making more obvious to non-regulars that our Bplus is the equivalent quality to a GA, even if we don't have all the citations in-line, etc. -- Avi (talk) 18:42, 3 August 2009 (UTC)

GA is a project-wide failure, which was intended to supplant FA's project-wide failure. The actual equivalent to GA is C-Class, under conditions: that the article have lots of useless footnotes, several pretty pictures, and comply with rules of English grammar made up in school one day. Septentrionalis PMAnderson 18:52, 3 August 2009 (UTC)

Be that as it may, I think that we should focus on our internal Stub-->Start-->C-->B-->Bplus-->A system, and if an editor wants to jump through GA/FA hoops too, so be it, but the internal "maths rating" value should be paramount. -- Avi (talk) 19:55, 3 August 2009 (UTC)

Suggestions? Septentrionalis PMAnderson 19:34, 3 August 2009 (UTC)

I have a question and a "suggestion". To what extent has the Math project's concerns with GA been brought to the attention of the "GA people"? Without having to really answer this, my suggestion would be the same as Avi's above: use an internal evaluation procedure (A-class for example) as our main goal for articles. Then, if someone outside the project (or someone inside the project) wants to take any specific article to GA or FA they can, but we need not consider that a goal for any math article. After a discussion within this project, it could be determined that the official position of the project would be that the ultimate goal of improving a math article would be to attain the, say, A-class appellation; FA and GA would become the wikipedia project at large's business. In my opinion, this would be the practical thing to do. It would involve beginning a discussion under a new header, since this has gone a far ways from the GA issues of the article on mathematics. Thoughts? RobHar (talk) 19:53, 3 August 2009 (UTC)

GMTA :) -- Avi (talk) 19:56, 3 August 2009 (UTC)

Yes, quite seriously. What we need is a {{GMA}} template, which will replace our B-plus class and GA for math articles. Then we tweak User:VeblenBot/MainTable to include it and we're done. Septentrionalis PMAnderson 00:42, 4 August 2009 (UTC)

If "GA people" want more citations and "math people" find excessive citations visually distracting, wouldn't an ideal solution be a less distracting variant of citations? For example, perhaps we could simply have "irrelevant" citations in comments so that those who really want to know where each piece of information comes from could find the information by reading the source code? — Miym (talk) 20:03, 3 August 2009 (UTC)

In a similar vein, I wonder if it would be possible to have a "hide/show extra citations" for some of the citations. I certainly like having citations for statements, but I also find excessive citations to be visually jarring. RobHar (talk) 20:45, 3 August 2009 (UTC)

I would say that if we ignore GA, this is more a problem for GA than for us. The tension around the citation issue is certainly to do mostly with a stylistic preference, but the preference is for writing surveys of mathematical topics in a style that is not neurotic about details. That is what is needed: that is what (in fact) the mathematical literature is short of. The narrower the topic, the greater density of required citation (certain facts, at the limit, are only written down in one place). This actually fits the GA/FA worldview of trying to optimise an article, which frankly for a topic like topology is just ridiculous (no way can one write that article in such a way as to get close to a comprehensive treatment). Anyway, the schism is going to be made worse if inappropriate reviews of broad mathematics articles are carried out by applying myopic templates to the situation, not better. Charles Matthews (talk) 21:18, 3 August 2009 (UTC)

The problem for broad articles is surely mitigated by guidelines at Wikipedia:Scientific citation guidelines#Summary style and Wikipedia:Summary style#References, citations and external links. Leaving aside the human implementation (or not) of such guidelines at GA or FA, would you say they are adequate to resolve the issue in principle? Melchoir (talk) 00:39, 4 August 2009 (UTC)

It would be sufficient, if GA people read them, or indeed read WP:V on the purpose of citation. But they don't; they count footnotes. If this were an isolated case, I would simply renominate; but the same nonsense happened at Talk:Special relativity/GA1, and is now being discussed at GAR in great confusion, here. Septentrionalis PMAnderson 00:49, 4 August 2009 (UTC)

Yes, when the human implementation of the review function is isomorphic to a bot run, as in this case, there is certainly a problem, and the problem relates to the reputation of GAR. Charles Matthews (talk) 08:45, 4 August 2009 (UTC)

• Taken to Review, here: I've cited this section, but comments are welcome. If anybody supports King's notions, do say so; and do defend them from guideline and policy if possible. Septentrionalis PMAnderson 01:39, 4 August 2009 (UTC)

It seemed polite to let the GA project know about this discussion, so I have placed a note at Wikipedia talk:WikiProject Good articles. Gandalf61 (talk) 09:32, 4 August 2009 (UTC)

It's okay - the GAR will have done that. Geometry guy 09:50, 4 August 2009 (UTC)

Oh my, what a lot of fuss over one crap review. Two line reassessments are totally against the spirit and practice of the GA process, but bad stuff happens. Instead of dealing with it like adults we have a furore that pits the "math people" against the "GA people" and demands a take over or withdrawal of maths from GA. The argument is soooo 2007. Such tribalism fails to take into account that Wikipedia is a bunch of individuals. Some mathematical editors find GA very helpful, others do not: each to their own. The GA process has good reviewers and reviews and ones which are not so good. It deals with the lack of uniformity by making it relatively easy to list or delist, and providing a reassessment process in the event of disagreement. It is akin to simulated annealing, and right now the temperature is a touch too high.

Community reassessment is needed to reach a consensus and hopefully improve the article in the process. I encourage editors to engage with the article and with Wikipedia:Good article reassessment/Mathematics/1. In particular, something needs to be done with Mathematics#Common misconceptions: cutting it entirely is one option; leaving unsourced opinion isn't. Geometry guy 09:50, 4 August 2009 (UTC)

I don't think this discussion is just about one single review or the status of one article (although that was the trigger). I think it is about the applicability of GA status and the GA process to Wikipedia mathematics articles as a whole. Looking at the lists at Wikipedia:Good articles, I notice that there are just 24 GAs for mathematics and mathematicians - whereas there are 141 GAs for warships, 159 GAs for Atlantic tropical cyclones, 222 GAs for video games and 220 GAs for "animated television episodes" ! So there are at least two wider questions here: (a) why are there so few mathematics GAs and (b) is this important ? Gandalf61 (talk) 11:06, 4 August 2009 (UTC)

Stating the obvious: there are few GAs and FAs because few people who edit mathematics articles are interested in the GA and FA processes. There are a few who are interested in getting articles they care about into the GA and FA lists, and more power to them. I don't think it's particularly important if there are not many; GA and FA are optional processes, not requirements, and certainly not the unique "goal" that all editors have to work towards. I could go on at length about why I personally avoid these processes, but the summary is that I don't feel their benefit justifies the effort involved. — Carl (CBM · talk) 12:04, 4 August 2009 (UTC)

GeometryGuy, I, for at least one, am simply suggesting it might be useful for the math project to devise a set of criteria that it considers any "good" math article should satisfy. Instead of dismissing this whole thread as a big fuss and furor (of which, I believe, only one particularly annoyed editor has engaged in), I think it would be more important to address what has come to light. I too don't believe this is about one "crap review". It appears as though one editor's mention of unhappiness with a review has lead several other editors to express their general dissatisfaction with the GA process. As you mention "Some mathematical editors find GA very helpful, others do not"; I believe this discussion may be about the ones who don't find it helpful trying to determine if there's something they can do about it, possibly without having to take on the current GA process (though one editor started off with that possibility, maybe out of fury). Do you think that, were the math wikiproject to devise its own set of criteria, or rather revive a currently existing instituation (Wikipedia:WPM/ACR), this would negatively affect the general wikipedia project? As someone who participates in both the math wikiproject and the GA project, your opinion on such subjects would be valuable. Cheers. RobHar (talk) 15:18, 4 August 2009 (UTC)

Certainly I mean only to dismiss furore, not useful comments that are triggered by it. In that respect, it would certainly be very valuable to revive mathematics A-Class review, and there is a suggestion for a lightweight process on Carl's talk page which looks good to me. GA is not intended to handle completeness of coverage, and it simply can't do it in specialist areas. However, anyone interested in nominating a math article for GA is welcome to ping one of the more scientifically literate GA reviewers to review or contribute to the review. Geometry guy 19:58, 4 August 2009 (UTC)

I would make less fuss if the last three GA reviews (I include one at Talk:Sophocles/GA1, from outside this project) I'd run into hadn't all been crap - and the same sort of crap. I would appreciate examples of conscientious reviews. Septentrionalis PMAnderson 17:59, 4 August 2009 (UTC)

Talk:Guitar Hero World Tour/GA1, Talk:Reptile (Mortal Kombat)/GA1, Talk:Nemesis (Resident Evil)/GA1, Talk:High-level radioactive waste management/GA1, Talk:Minority Report (film)/GA1, Talk:Call of Duty: World at War/GA2, Talk:Mac OS X/GA2, Talk:Therion (band)/GA1, Talk:The Hardest Part (Coldplay song)/GA1, Talk:Burundi/GA2, Talk:Otto Julius Zobel/GA1 Gary King (talk) 19:28, 4 August 2009 (UTC)

I cannot agree that all of the points of grammar are well taken; MoS is not a reliable source. But I am glad to see that Gary King can provide more respectable reviews on articles on subjects he knows something about, like Call of Duty. Septentrionalis PMAnderson 19:40, 4 August 2009 (UTC)

So basically you're going to continue to be like this for a while? Gary King (talk) 19:47, 4 August 2009 (UTC)

No, I am glad to see it; it means, for example, that I will not request, if this continues, that Gary King be barred from doing reviews, since he can do useful ones when he tries. When Mathematics is relisted, and we have assurances that there will be no recurrences of mechanical, two-sentence, reviews (negatively; Ohana is right that "looks like a GA to me" is sometimes all that can be said), then I will stop. Septentrionalis PMAnderson 19:55, 4 August 2009 (UTC)

I don't mind seeing one line of review if it's a pass, but the situation is that it was on hold with 2 sentences provided. If the reviewer doesn't have the time to identify the specific for improvement, then don't do it. It is causing more drama than it is worth. User:Gary King should not be playing a game and passes the ball off to community GAR when he couldn't find more words to defend his poor review. What I propose is to amend the GA criteria by adding WP:SCG to 1(b). It will not affect projects outside of Mathematics, Physics, Molecular and cellular biology and Chemistry while adequately addresses any present and potential concerns raised in future WP:GAN and WP:GAR where the articles fall within the scope those projects mentioned. OhanaUnited^{Talk page} 18:50, 4 August 2009 (UTC)

I don't see how that can hurt, and it may solve the problem. Please do so; I see there is a related proposal at WT:WIAGA which would clarify what policy says: that citations are only required in limited circumstances. Septentrionalis PMAnderson 19:20, 4 August 2009 (UTC)

 Done. Proposed a quick fix on 1(b) at Wikipedia talk:Good article criteria#More proposed changes, which would solve this and future problems with references and related policies/guidelines. OhanaUnited^{Talk page} 20:25, 4 August 2009 (UTC)

See also the related discussion at WT:GAR. Geometry guy 19:58, 4 August 2009 (UTC)

Speaking as a possibly ignorant scientist, my impression is that most of the Good Articles in mathematics and mathematical physics are indeed pretty good, which suggests that the process is working. The level of referencing doesn't bother me and (I conjecture) most readers. Far more than reference density, the biggest problem I see for GA- and A-level mathematical articles is that they are poorly written for lay-people. If reaching such readers is part of the assessment, then articles such as golden ratio and Pythagorean theorem would probably be better ranked as C-class.

It is interesting that so few mathematical articles have reached GA-, A-, or FA-level. If we discount biographies, there seem to be roughly 8 mathematical FAs after 8 years of work, several of them on very restricted topics. As one poster noted above, that's probably because most contributors don't judge the rewards to be worth the effort. But perhaps we could organize things to change that? Either lower the effort or increase the rewards? For example, could we organize teams of contributors with complementary skills or interests? Could we reach out to organizations interested in math education and developing future mathematicians? Could we identify the rate-determining steps of an FA and make those more efficient, perhaps with scripts?

Incidentally, although some have surely noted this already, a TFA for the Riemann hypothesis on its 150th anniversary might draw welcome attention to the math itself and to the article's gifted contributors... Proteins (talk) 20:09, 4 August 2009 (UTC)

I just wanted to point out that back in May, I requested that members of this project help with reviewing the mathematics articles. Editors here are more knowledgeable on topics about the guidelines and material related to the article's content. Reviewing can be difficult for reviewers who are not familiar with the topic (the reviewer may not know what is common place, what is lacking, what is incorrect, etc.). Although it can be beneficial to get outsider's reviews since they notice things that editors familiar with the topic don't (even more importantly, what readers might see), members of the project would probably be best for ensuring the article's quality meets the project's guidelines and GA criteria. --Happy editing! Nehrams2020 (talk • contrib) 20:24, 4 August 2009 (UTC)

That's a fair point. And reviewers need nominations to work on. There was only one open GA nomination in the mathematics section (Aces and eights (blackjack)), so I have just added a few more:

• Complete icosahedron
• Jeep problem
• Mathematics and art
• Penrose tiling
• Proof without words

I have picked articles that I think are a good match to GA criteria - articles that are well written and accessible, use in-line citations, are stable, untagged, and have illustrations. I don't think any of these articles have been nominated for GA before. Reviewers - over to you ! Gandalf61 (talk) 12:47, 5 August 2009 (UTC)

While we're on the topic, Maximum spacing estimation has been brought to GA, and is currently undergoing an A-class discussion, possibly in preparation for a FAC. -- Avi (talk) 14:31, 5 August 2009 (UTC)

Questions

How do I join this WikiProject? 116.14.72.74 (talk) 12:49, 5 August 2009 (UTC)

You should start by registering a username [17]. Then simply begin editing math articles. You can put your username at Wikipedia:WikiProject Mathematics/Participants if you like, but that is purely optional. Read Wikipedia:WikiProject Mathematics for more information about the mathematics wikiproject. — Carl (CBM · talk) 12:57, 5 August 2009 (UTC)

Internal categories

Besides the fact that we don't have an article on a topic that is included in MacLane's book and in Borceaux's 1st volume, does anyone here happen to know who gave the modern definition of internal categories? There's been some discussion/confusion at cat theory timeline page.

There's a high-level description of the Ehresmann-Schein-Nambooripad theorem in the inverse semigroup article, but a prerequisite for writing that in more detail is defining an inductive groupoid, which is an ordered groupoid, which is an ordered category, which in turn is an internal category. I'm guessing the first three of these concepts aren't used often enough outside semigroup theory to justify separate articles, although according to Ehresmann's wife ordered categories appeared in some 700 papers (see link in the discussion above). Pcap ping 18:07, 5 August 2009 (UTC)

Here's a link to the correct (singular) Wikipedia article title: internal category. Michael Hardy (talk) 18:38, 5 August 2009 (UTC)

Thanks, that's better than no help at all... Pcap ping 18:52, 5 August 2009 (UTC)

Residuated mapping and Galois connection

Since the (more "modern") notion of a monotone Galois connection and (unary) residuated mapping essentially coincide, I was wondering what's the best way to deal with these two topics. I was the one that started residuated mapping a year or so ago; the latter notion suffers from much fewer vagaries in terminology and notation.

A possible approach would be to delete most of the "properties" stuff from Galois connection, which appear written in a rather rambling manner (and using non-standard notations), but keep the rest, essentially the examples, some of which naturally appear as antitone Galois connections, and also keep how the Galois connections relate with other notions from math, while the "low level" stuff could be expanded in residuated mapping, where it also benefits from a more standard notation.

One could also redirect residuated mapping to Galois connection, but then one would need to explain yet another set of synonyms for lower/upper adjoint. More troubling though, a binary operator is defined to be residuated in a manner that gives rise to left and right division, but that's not the same as the mapping (considered as a unary map being residuated). This and other notions of residuation, e.g. quasi-residuals in a semigroup, feel off-topic for someone wanting to read just what a Galois connection is.

Some suggestions how to organize/divide this material would be appreciated. Pcap ping 01:58, 6 August 2009 (UTC)

It looks like {{mergefrom}} residuated mapping, {{mergeto}} Galois connection to me. Maybe the scope of Galois connection does not completely include that of residuated mapping, but I suspect these concepts should be studied and written up together. Charles Matthews (talk) 07:26, 6 August 2009 (UTC)

Thanks for your suggestion. The core material of these two articles does indeed need to be explained in only one place; and there are indeed presentations that go that way without becoming confusing, e.g. [18] On the other hand, the generalizations diverge due to their focus. When one focuses on the notion of residuation as property of a function, the component-wise residuation leads to residuated algebraic structures. When the focus is on the connection between posets, the two generalizations that I'm aware of (see link above) are H. Crapo's connections, in which the two posets are connected by order preserving functions that are only quasi-inverses of each other (Crappy connections?!), and Lagois connections (yeah, they really call them that), where both idempotents can be closure operators. Of course some properties get lost in both of these approaches. But there doesn't seem to be that much diverging material, so it can be explained in a single section of the merged article. I'm going to tag the articles as you suggested, and I will merge them too unless someone objects on some other grounds. Pcap ping 12:21, 6 August 2009 (UTC)

Monus, an ordered-monoid operation

The article Monus is unsourced and gives what I think is an incorrect description of a subject in ordered monoids. I know almost nothing about this subject, so I would appreciate a look from expert eyes. In summary the article defines the monus of elements a, b as max(a−b, 0), which seems problematic because we don't know there is a subtraction operation in the monoid. I only found one discussion of monus online (here); the definition there is more plausible, namely as the smallest c such that a ≤ b + c. Thanks for any attention to this article. --Uncia (talk) 13:02, 6 August 2009 (UTC)

It looks like a clear case of someone having misunderstood the definition. (The fact that the article assumed that in a partial order always a ≤ b or b ≤ a clearly supports this.) I have fixed it and added a trivial example. Hans Adler 14:15, 6 August 2009 (UTC)

The confusion comes from the less general monous over N encountered in computability and comp. sci.; the def with "max" is correct over N (the - and "max" are obviously over Z in that case). Perhaps it should be given as example? Never mind, I see it is given. Pcap ping 14:48, 6 August 2009 (UTC)

Mathworld neologism at Heegner number?

Dear all, it appears that the term Heegner number was most likely made up by mathworld. I've started a section on the talk page to discuss whether or not this is so. If it is, I believe the correct course of action is to delete and merge content into other articles. Opinions welcome. RobHar (talk) 00:36, 5 August 2009 (UTC)

IMO, determining that a name is nonnotable is not in itself a reason to refactor the article. What content belongs together in a single article should be determined by the content we have: choosing a name for the article should be a secondary concern. (If you had determined that most of the current content of Heegner number was nonnotable and should be deleted, that would be a different issue.) —Blotwell 18:43, 5 August 2009 (UTC)

I felt that the content of the article would be better merged into other articles anyway. As it stands this article contains a definition and two marvelous, surprising, disjoint results in number theory, one of which had its own article (that User:PMAnderson has now merged into Heegner number, despite the term Ramanujan's constant being more prevalent than Heegner number) and the other was described in an article on similar results. There is also a List of number fields with class number one. Anyway, I would've settled for a renaming of the article. RobHar (talk) 15:13, 7 August 2009 (UTC)

Lambda calculus

(Cross-posting from Comp. Sci. wikiproject since activity is rather low there) Can someone with (at least) a graduate-level understanding of the topic take a look at the article, in particular the confusion with various typed lambda calculi; see the article's talk page for details. Pcap ping 17:33, 5 August 2009 (UTC)

Oops, the lead is written in an opaque and highly questionable fashion. The issue of consistency is possibly relevant to the foundational ambitions Church had; but it is not so relevant to introducing lambda calculus. This all looks wrong-end-of-the-microscope to me, as if the paradigm was Russell's theory of types, rather than functional programming. (That, historically, would make sense, but the weight of current attention would surely be in FP.) Since untyped lambda calculus is basically the situation with one type X that coincides with X → X, it is feasible to treat it in the foundational article as the case one should look at, so that the labelling with types is treated as at best a distraction. Anyway the historical introduction and air of paradox should be moved out of the lead, and the idea that "lambda calculus" is at minimum a notation for keeping track of higher-order functions should be given fair play. Charles Matthews (talk) 18:20, 7 August 2009 (UTC)

Manual of style disagreement

On Talk:Exponential_function#Overview and motivation an editor has replied to my objections citing the maths manual of style with 'I wipe my arse with the Mathematics manual of style!!'. I don't mind arguing about whether some ground rules should or should not apply or what they mean or whether they should be disregarded in particular instances, but this doesn't sound like a basis for constructive discussion. Dmcq (talk) 16:19, 5 August 2009 (UTC)

My sense (which may well be wrong) is that the remark was intended semi-humorously. The other editor does seem genuinely concerned about the state of the article. I suggest that you assume good faith, point out how easy it is to misinterpret such remarks in online discussions, and suggest that further discussion be carried out in a more restrained mode. —Dominus (talk) 17:12, 5 August 2009 (UTC)

The editor has stated, "The single best way of introducing the exponential function is by its Taylor series." In any case, this kind of singular view (POV) is not appropriate for writing on Wikipedia in general, and math articles too should try and comply with WP:NPOV as reasonably as possible. --C S (talk) 23:25, 5 August 2009 (UTC)

Words genuinely fail me. Having an opinion on the best way to write an article now constitutes a point of view, in contravention of some Wiki-law or other? Is this the way mathematics articles are going to be written around here? Will every entity from a triangle to tensor have to be introduced with a historical overview and given multiple equivalent definitions for completeness?

In my own opinion, which is now a point of view, people do not come to mathematics articles on Wikipedia for chit-chat. They come here to find out what mathematical objects are. In short they come here for definitions and properties. My views is you tell them, in order 1) What it is, 2) What it does, 3) What it's used for. If you try and mix up this order you will be helping no one; only confusing them.

With regard to the exponential function and Taylor series, it would appear my point of view is not an isolated one(Encyclopedia Britannica presumably qualifying as a prominent adherent), so perhaps we should all form a WP:Cabal of some description to better discuss this alternative world view of e^x and how it can be given due weight and properly included so as best to preserve the neutrality, impartiality and unbiased nature of the Exponential Function article. ObsessiveMathsFreak (talk) 15:20, 6 August 2009 (UTC)

There are two different cases of your opinion being dealt with apparently. The first concerns your opinion on how to organize the content in the article. This is certainly something that should be discussed and debated. A consensus will be reached and that will be how the article is written. There are several math articles that are structured as you'd like them to be, however each article is dealt with individually. If you'd like to make sure that consensus is against you on this article, you could attempt to attract more editors to the discussion. In the end, you do have to accept the consensus opinion (and, as a note, consensus is not simply a democratic majority).

Secondly, your opinion on how to define the exponential function is an issue. You seem to chide "completeness" in an encyclopedia article, but completeness is exactly the point. To strongly state that there is just one good way to do it means that you are pushing a point of view. Now obviously there are more common ways of defining things, and these should generally be given more weight in the article. As I recall certainly many basic analysis books define the exponential function as a power series. Demonstrating this is a good way to support your point of view. People don't want you pushing your point of view. Stating that there is only one good way to define exp is a point of view. I for one prefer defining it as the solution to a first-order differential equation with initial condition. This is simple and embodies the meaning of exponential growth, and the power series then comes immediately out of Picard iteration. But I'm an algebraist and this is my point of view on how definitions should be given: simple and meaningful. RobHar (talk) 16:21, 6 August 2009 (UTC)

So, Wikipedia is not a textbook, yet we must include enough definitions for a Treatise. This article must be complete to the point of confusing the reader, yet Trivia sections and Pokemon articles must be excised at all costs. Nigh every other mathematics article has a formal definition for its first section, yet I must obtain a consensus for the Exponential Function article, which I note is unsurprisingly one of the top 500 viewed mathematics articles, is of top priority and currently has a less than stellar B rating(who ever gives out those).

I'll repeat my assertion that people do not come to the mathematics articles for chit chat, historical perspectives, unexpected interconnections, or strict rigour; at least not initially. The cast majority come here for basic information, so that is what should come first on the page, albeit after a brief introduction. Unfortunately, since such opinions, now being "Points of view", put myself and anyone holding them in the same category as creationists, moon landing conspiracy theorists, and Holocaust deniers, I very much doubt they will be taken seriously by any of the gatekeepers around here.ObsessiveMathsFreak (talk) 17:44, 7 August 2009 (UTC)

{<<<<< Indenting back}. It is another point of view that people do not come here for chit chat or historical perspective, it may be true but the essential point is that wikipedia is a hyperlinked encyclopaedia so you can always jump to the mathematical definition if you want to go in at the deep end. If you want it easy you just read straight on. If you feel you would move the consensus then the Manual of style page is the one to work on. If you don't then you don't have a consensus and you are just engaged in a fight to push your own point of view. It is perfectly okay to go against the manual of style but you'll need to justify yourself. And you haven't made a good case that I can see. As to starting exponential function with either a series or a differential equation, if you know anything about those you probably already know quite a bit about the exponential function. It is putting the cart before the horse to require them right at the start. And the series definition is particularly unilluminating to someone without much maths, it is just a random sequence of terms. The exponential function is a very basic function that people with very little mathematics come across. That is why it is one of the most popular mathematics articles. Dmcq (talk) 19:11, 7 August 2009 (UTC)

It seems no matter what I do or suggest I'll end up breaking sacred neutrality. All while others (neutrally!) go about happily making and undoing edits left and right. Is the act of making an edit in itself a biased act? Do we not exclude alternative opinions and pass skewed judgements when we reformat paragraphs, correct spelling mistakes and excise material?

Apparently, suggesting people come here for basic information is a point of view. Naturally, suggesting otherwise is of course not. Hence, editing articles to place emphasis on basic definitions and properties is obviously culturally, socially or morally biased in some way; whereas providing inquisitive readers with a panoramic vista of connections, applications and history of a function they know little or nothing about, complete with hyper-links to more topics they didn't come to read about is accordingly the more inclusive option. The former merely provides information plainly and concisely. The latter allows the reader to experience the wonders and potential of web 2.0 enabled, worldwide community sourced knowledge through digital collaboration. Oh, and unicorns.

Now, since the Null hypothesis (by consensus!) is clearly that people come to Wikipedia for a magical wonder-trip of learning, my alternate opinion... sorry point of view, that people are simply looking for basic information is something that must be proven.. sorry, which a consensus must be reached on. Obviously the way to do that... sorry to make a good case, would be to conduct surveys, questionnaires or various other analysis. Luckily however, no-one around here bothers with anything like that, and so we can turn to existing consensus for the final answer; which is that I'm a terribly biased, uncooperative old grouch, too mired in my outdated opinions on mathematical exposition to see WP:SENSE.

Take for example the specific case of the exponential function. I've been stuck so long in my equations that I can't see the intrinsic superiority in presenting a mathematically lay person with the definition

$\,\exp(x)=\lim _{n\to \infty }\left(1+{\frac {x}{n}}\right)^{n}.$

which despite Bernoulli's great difficulties can clearly be seen to converge for any x by anyone first presented with it. Any proofs which might be needed are of course trivial. Moreover it speaks to their intimate understanding of the principles of compound interest, which even starving street urchins know as well as they would their own mother's lullabies. Just look at the confidence with which people in our modern world borrow credit!

Instead I would subject the unhappy reader to an infinite sequence of essentially random symbols, namely

$e^{x}=1+x+{x^{2} \over 2!}+{x^{3} \over 3!}+{x^{4} \over 4!}+\cdots =\sum _{n=0}^{\infty }{x^{n} \over n!}$

which they could have no hope of ever understanding, seeing as how such esoteric mysteries as infinite series and the ratio test are reserved only for a select elite; namely 14 year old schoolboys(girls/persons/aspiring learners). Moreover, my subsequent appeal to the ease with which the function is shown to be its own derivative would only compound the folly, as defining the function as an eigen-function of differentiation makes this step confusingly redundant and is after all the more illuminating introduction the the whole topic.

So what is it that makes me persist in my disgraceful bias, my shameful lack of neutrality? What is it that drives me to try and improve articles with elitist notions of coherent mathematical exposition? Malice, perhaps? Or hate? Bile? No doubt my nightly sojourns with neo-Nazi's and crackpot Pseudoscientists have driven all the consensus out of me and left me a wretched point-of-view filled troglodyte.

So, it is good that one of the most popular mathematics articles on this site, nay on the web, is do diligently defended from the vile vandalisms which I might unleash upon it. A solid defence of rules, regulations, guidelines, customs and procedures, each more unbiased in intent than the last, stand squarely in the path of unhelpful interlopers like myself who know little and less of how an online repository of human knowladge should be properly run. Why, leave the page to my tender mercies, and people might log on, get the information they came from, and then leave! We can't have that! ObsessiveMathsFreak (talk) 22:58, 7 August 2009 (UTC)

You are not making allies. Ozob (talk) 00:38, 8 August 2009 (UTC)

I said illiterate peasants rather than street urchins and there was a couple of other small changes but yes I agreee with most of the stuff the sarcasm is about. I even read your reference We can't have that! and have come to exactly the opposite conclusion about what the problem was. The article that person looked up contained terms he did not understand before he came to a decent definition of what he was looking up. It may have been that it wasn't really possible to satisfy his requirement, I don't know as I don't know what the original query was, but for the exponential function I really do fail to see how a series which is essentially arbitrary as far as someone not in the know is concerned is better than compound interest. That it is easier for a mathematician to work with is not very relevant that I can see. A quick mathematical definition is given in the leader and the mathematical definition part gives things which are easier for a mathematician. The other articles which are more of the straight into the maths style are probably not ones that people with only very elementary maths will come across. 10:55, 8 August 2009 (UTC) —Preceding unsigned comment added by Dmcq (talk • contribs)

Everyone here supports the idea of coherent mathematical exposition. But inherent in the idea of "exposition" is that the reader will read the article, not merely skim it looking for a bulleted definitions.

Also, concerning the exponential function, there are numerous definitions, and we need to present them all. But unlike a textbook, there is no reason why our introductory articles need to pick one particular definition as the definition, above the others. There are at least three independent definitions of the exponential function, and each has its own role. — Carl (CBM · talk) 12:16, 8 August 2009 (UTC)

"reader will read the article, not merely skim it looking for a bulleted definitions"

Generally speaking, I don't think that is a valid assumption. Nor is it reasonable — as possibly mentioned in a previous discussion about infoboxes, there is no reason why articles should intentionally be made harder to use for readers just looking for something specific (that is why we divide articles into sections after all) and require everyone to read the whole article no matter what their level of understanding. Shreevatsa (talk) 15:21, 8 August 2009 (UTC)

Deleting Pie method

I've put a prod on Pie method which is a putative method of fair division because I believe it is simply wrong. I actually found a place on the internet though where somebody quoted it though not as the 'pie method' and it probably didn't come from wikipedia! I sort of wonder if it is notably wrong and I should keep it and say it is rubbish? Perhaps I should put it under Proportional (fair division) as an attempt which is wrong and explain - but then the explanation could be counted as WP:OR. Dmcq (talk) 23:34, 7 August 2009 (UTC)

It's just Divide and choose, isn't it (with a completely wrong extension to >2 people)? Algebraist 14:49, 8 August 2009 (UTC)

It's a shame that divide and choose does not give any discussion to the problem of fair division between more than two parties. I gather that this has been the subject of considerable research over the years. —Dominus (talk) 15:01, 8 August 2009 (UTC)

Why should it discuss that? Divide and choose is about the divide-and-choose algorithm, which applies only to two-party division. The general problem of fair division is covered at fair division, as it should be. Algebraist 15:05, 8 August 2009 (UTC)

I see, thanks. —Dominus (talk) 05:52, 9 August 2009 (UTC)

I believe the last divider method in Proportional (fair division) is probably what the person who wrote the article meant butnthey left out an important part. Dmcq (talk) 16:50, 8 August 2009 (UTC)

MAJOR CHANGES: 4 hours ago

By a very simple verified equation we wiped out Prime numbers and Riemanns Hypothesis articles that are rendered obsolete and Wikipedia is the first place we went because you treated us with freedom and respect. The simple equation that is verifiable at face value was posted at the Math forums etc 4 hrs ago"IS 180-PRIME NUMBER(below180)= 180+PRIME NUMBER(any over 180) Till infinity ,So there is no need to be digging for these prime numbers now any more. See also the site Inverse19mathematics.com, or google inverse19 mathematics. THIS IS SIMPLE VERIFIABLE AS IT IS(ipso facto ). GO WIKPEDIA BE THE FIRST. Vinoo Cameron M.D , Theo Denotter.--Vinoo Cameron (talk) 05:38, 8 August 2009 (UTC)--Vinoo Cameron (talk) 05:38, 8 August 2009 (UTC)

This needs peer-review and publication by a reliable source before it is acceptable here as we cannot accept original research. Please propose this again when this has happened. Rodhullandemu 13:27, 8 August 2009 (UTC)

I do not think I quite understood that which was asserted, but if my interpretation is correct it seems either trivial or incorrect. Furthermore, I do not think that such a trivial equation can resolve the theory of prime numbers or the Riemann hypothesis completely (or to even a small extent). --PST 09:28, 9 August 2009 (UTC)

Shouldn't the title be MAJOR CHANGES: 2 days and 5 hours ago? Dmcq (talk) 08:19, 10 August 2009 (UTC)

GA Review of Proof without words

Edge3 has started a GA review of Proof without words. Their main concern so far is that the article does not give sufficient coverage of its topic. Review status is "On hold: this article is awaiting improvements before it is passed or failed". If anyone has the time and inclination to expand the article, please do so. Gandalf61 (talk) 10:57, 11 August 2009 (UTC)

Composition of functions

This is perhaps a trivial topic but I feel that some discussion is necessary. In calculus, functions are often composed from right to left and this is therefore the convention with which most people are familiar. However, group theorists prefer to compose from left to right, and in general, many influential algebraists have selected this convention. Consequences of this convention include the consideration of only right modules (rather than left modules) and specific cases of this (for instance, right ideals rather than left ideals). However, in Wikipedia, for the most part, only left ideals, left modules and related concepts associated to "left" rather than "right" are considered. In my opinion, this is an inconsistency, and at can at times lead to incorrect assertions (in the context of rings, only, since a ring need not be isomorphic to its opposite ring). Should something be done about this? --PST 14:58, 11 August 2009 (UTC)

I believe that the "opposite" composition descends from Philip Hall; it is true that it is used by group theorists, mainly in that tradition. I think if you broaden to "influential algebraists", it is very much a minority point of view, which is why it isn't much represented here. Obviously we do have bimodule as an example against your thesis that the point is neglected. In computer science there is a convention of writing f;g for gof as the "opposite" notation for composition. I don't see much virtue in carrying around extra verbiage about composition across mathematics generally; Wikipedia does what almost all mathematicians do in this area. Category-style R^op notation can say enough where necessary, I think, where close attention is required. Please flag up any actually incorrect statements so we can deal with those. Charles Matthews (talk) 15:57, 11 August 2009 (UTC)

Isn't this discussed under Composition of functions#Alternative notation? In computer science, the (fg)(x) = g(f(x)) is preferred to the point that they made an ISO standard for it (the Z notation), which introduced the "fatsemi" symbol as the dual of the circle. Pcap ping 17:18, 11 August 2009 (UTC)

P.S. As you can see below the LaTeX \fatsemi does not work on Wikipedia because it doesn't include the right package. If you read the Composition of functions article on Linux, or on anything else with decent Unicode fonts (Mac?), the Unicode fatsemi appears correctly; but not on Windows XP. Pcap ping 17:21, 11 August 2009 (UTC)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \fatsemi}

P.P.S: I see that I had added some of these details to the article on Composition of relations last year, but completely forgot about it... Pcap ping 17:31, 11 August 2009 (UTC)

Also looking at something I added to that article, you could use $\circ _{l}$ and $\circ _{r}$, as done in Kilp et al., if you really need both notions, and need to distinguish between them in an article. Pcap ping 17:39, 11 August 2009 (UTC)

Equality (mathematics)

Can someone review that article and remove, or at least frame properly, the ramblings that permeate it? I've done a little work on it, but I have the rewriting fish to fry, for which there are way fewer knowledgeable Wikipedians around (as far as I can tell given how bad the article was). Pcap ping 17:07, 11 August 2009 (UTC)

P closures

I've added a section to the article on Closure (mathematics) article describing a related notion. The name used by Baader and Nipkow is somewhat non-descriptive. Has anyone encountered it under some other name? Also, is that article the best place to discuss it? Pcap ping 18:52, 11 August 2009 (UTC)

Also, can these be somehow defined as closure operators? Pcap ping 19:17, 11 August 2009 (UTC)

According to your definition, the P-closure of a binary relation R on S is a subset A of S. An obvious "P-closure operator" maps R to A×A.

But I think the definition makes no sense because it only depends on P union all first or second elements in pairs from R. Shouldn't it be "the least set with property P that is closed under R"? Then the P-closure operator would map R to the smallest symmetric and transitive relation that extends both R and P². Hans Adler 20:29, 11 August 2009 (UTC)

No, the P-closure (say Q) of R is a subset of S×S, just like R. The P here is a predicate; e.g. for the symmetric closure the predicate P_sym is "forall x,y in S: (x,y) in Q implies (y,x) in Q". I guess you could see the P-closure as an operator on S×S parametrized by some predicate P. Pcap ping 20:42, 11 August 2009 (UTC)

Oh, I see. P is actually a property of subsets of S×S? I didn't read this literally. Seems quite a technical notion to me then. Hans Adler 20:57, 11 August 2009 (UTC)

Well, Nipkow's specialty is higher-order logic (one of his celebrated results is extending Knuth-Bendix to higher order logic, and he's the guy behind Isabelle/HOL). But the "Term Rewriting and All That" book is written for undergrads, so I guess he didn't want to complicate "P closures" with a formal definition, which appears to require higher-order logic because the predicate P appears as an argument. Pcap ping 21:07, 11 August 2009 (UTC)

I am sure these can be defined as closure operators provided the property in question is nice, for example monotone. But the property P(Q) = "Q is empty" is not going to appear as any sort of closure operation. This all seems to be a special case of the fixed-point theorems (e.g. Kleene fixpoint theorem). — Carl (CBM · talk) 01:50, 12 August 2009 (UTC)

I think "nice" (as you put it) is "closed under arbitrary intersections" (as Baader and Nipkow put it). Pcap ping 09:29, 12 August 2009 (UTC)

You're right that it is also enough for P to be satisfied by the full relation on S × S, and for P to be closed under intersections. But the intersection of any number of empty relations is empty, so some variation of the first condition would also be required. I said nice because there are several fixed-point theorems with slightly different hypotheses. For example, one can assume the map is expansive instead of monotone, and neither of these properties is implied by the other. Also, to use the fixed point theorems one has to convert P into a map, which is easy to do in the examples given (symmetric relations, transitive relations, etc) but nonobvious in general. — Carl (CBM · talk) 11:43, 12 August 2009 (UTC)

By the way

Did anyone see how terrible our article on predicate (mathematical logic) is? Pcap ping 20:49, 11 August 2009 (UTC)

Oh dear. Hans Adler 20:57, 11 August 2009 (UTC)

The real issue with the title of that page is that predicates are trivial from the point of view of mathematical logic, because all the interesting questions have been collapsed by the use of set theory. There is a lot to say about predicates from the point of view of philosophy, but that isn't mathematical logic. We can discuss what to do with that article on its talk page in any case. — Carl (CBM · talk) 01:39, 12 August 2009 (UTC)

Aren't there non-trivial things one can say about predicates in contexts where set theory is not assumed as a foundation? E.g., in categorical logic, each topos has an internal language in which one ought to be able to formulate predicates. Also, isn't there some notion (again in categorical logic) called a "theory"? (Or maybe I'm thinking of a "sketch"?) Which, if I have the right intuition, would have a notion of a predicate. I remember skimming Borceaux's Handbook and seeing these sorts of things. (Much more so than I saw geometric things! Unfortunately, as far as I know, the only decent book about the geometric aspects of topoi is still SGA4.) Ozob (talk) 13:35, 12 August 2009 (UTC)

Equational logic?

Am I just blind, or we don't have an article on this? Equational theory redirects to Universal algebra, which sort of touches on the idea of a model theory, but I don't see the fundamental result that equational logic is sound and complete mentioned there. I was trying to find something to link to from rewriting in order to explain what the motivation is, but no luck... Compare with [19]. Pcap ping 02:45, 13 August 2009 (UTC)

You've probably found a gap in the coverage. http://eom.springer.de/E/e120140.htm may be more useful than the MathWorld page (EoM is a reliable source in just about all areas, I think). Charles Matthews (talk) 16:18, 13 August 2009 (UTC)

Help needed

Could anyone give some feedback on the discussion under Talk:Bijection#Terminology? It might not be a very deep discussion, but I think it's important nontheless. Some extra views would be more than welcome. Thanks! 145.88.209.33 (talk) 08:27, 13 August 2009 (UTC)

Reorganize the Computability articles

We have these "general" articles:

• Computability, which incorrectly implies that computability in CS and Math are somehow disjoint. This should not be a dab or a stub!
• Computability theory (computer science), a poor quality article that focuses narrowly on automata and Turing machines (despite the name). Barely mentions lambda calculus in the history section and makes no mention of recursion theory or random access machine!!
• Model of computation, a sort of WP:DICTDEF

We also have much better articles on the important topics, recursion theory, lambda calculus, Turing machine, and random access machine; we also have a decent overview article on register machines in general.

The way I see it computability should be is a high-level intro to the often encountered equivalent models of computation: recursion theory, lambda calculus, Turing machine, and random access machine. This is along the along the outline of S. Barry Cooper's Computability Theory (see pp. 7-8), which despite being written by mathematician was quite satisfying for me as a computer scientist (despite the many misprints, and his insistence on calling RAMs URMs, but that's another matter).

(I will cross-post to the CS wikiproject to attract participants from there too, but that project is nearly dead.)

Thoughts? Pcap ping 11:22, 13 August 2009 (UTC)

I don't know why there was originally a split between computability theory (computer science) and recursion theory. However, I know why I have never tried to merge them, which is that it seemed too difficult to write a single article on "computability" that gave the proper focus to both areas.

At some point I worked on getting the recursion theory article up to shape. This article does not describe a model of computation; "recursion theory" is a field of mathematical logic concerning computability and definability. The model of computation is described at μ-recursive function. The article recursion theory gives a pretty reasonable overview of that field of logic.

It would be possible to merge computability theory (computer science) into the article recursion theory, but I have never been convinced that many computer scientists would be happy with the result. I could work on that next week if there is a desire for it among the computer scientists.

We should discuss that at Talk:Recursion theory. — Carl (CBM · talk) 11:43, 13 August 2009 (UTC)

Okay, discussion continues there. Pcap ping 12:45, 13 August 2009 (UTC)

Compact -> Compact Hausdorff

I would like to propose a change for the convention. Can we assume that a compact space is Hausdorff (and use quasi-compact for a space where an open cover has a finite subcover)? I think today this is fairly standard and helps to reduce clutters.

One problem with this change is what we do with other related notions like locally compact, or compact generated space (i.e., k-space): should we assume them also to be Hausdorff or not. I don't have a concrete idea for this problem. -- Taku (talk) 12:40, 10 August 2009 (UTC)

Is this fairly standard? I've only ever seen this mentioned as something Bourbaki does; I've never encountered anyone who actually used this convention themselves. Algebraist 13:52, 10 August 2009 (UTC)

I am looking at the textbook "Topology" by James R. Munkres (second edition, 2000); there, a compact space need not be Hausdorff. The same holds for "Introduction to topological manifolds" by John M. Lee (2000). Boris Tsirelson (talk) 14:35, 10 August 2009 (UTC)

So far as I know, the definition that includes Hausdorff is relatively standard in France and very widespread in Germany, but not at all standard internationally. I think it's best to use only the terms compact Hausdorff and quasicompact in topology contexts, except where the two notions are equivalent. This is analogous to how we are already dealing with $\subseteq /\subsetneq /\subset$. It minimises the potential for misunderstandings. And we can still say "Let X be a regular space. If X is compact...". Hans Adler 14:51, 10 August 2009 (UTC)

I think it may be a matter of the branch of mathematics in question. Certainly within algebraic geometry and number theory the Bourbaki convention is pretty strictly followed. Schemes are almost never Hausdorff, but often quasi-compact, so one often deals with quasi-compact spaces, which, frankly, are not nearly as nice as (Hausdorff) compact spaces. In a branch like topology, one can afford to allow "compact" to apply to non-Hausdorff things since one quickly restricts oneself to studying topological manifolds, which are generally taken to be Hausdorff (as they are in John M Lee's book). I am strongly in favour of the Bourbaki definition. RobHar (talk) 15:09, 10 August 2009 (UTC)

The "usual" definition of compact does not include Hausdorff. This is supported by the "standard" texts, Willard, General Toplogy (1970), Steen & Seebacch, Counterexamples in Topology (1970), Armstrong, Basic Topology (1997), Bredon, Topology and Geometry (1997), Munkres Topology (1999), etc., as well as references like Schecthter, Handbook of Analysis and Its Foundations (1997) and Hazewinkel, Encyclopaedia of Mathematics (2002). In my experience as a practicing topologist Bourbaki is definitely in the minority. Whatever our personal definitional preferences our, we should follow the standard sources. Paul August ☎ 16:01, 10 August 2009 (UTC)

The "usual" definition in topology does not include Hausdorff, but what I'm saying is that the "usual" definition in algebraic geometry does. Now, one can say that compactness is a topological notion, and that's fine, but despite this, I believe the bourbaki definition to be better. Questions: as a practicing topologist, how often do you study non-Hausdorff spaces? How many of the texts you list only refer to non-Hausdorff compact spaces to discuss their pathology? RobHar (talk) 16:14, 10 August 2009 (UTC)

Rob, I'm not sure what you are getting at. My only position here is that, based upon current usage, Wikipedia in its article compact space ought to continue to define a compact space as it currently does (every open cover has a finite subcover). Do you disagree with this? Paul August ☎ 16:32, 10 August 2009 (UTC)

Yes, I do. I'm not simply arguing for the sake of arguing. My position is that, also based on current usage, Wikipedia should change its definition. My argument is that though topologists often define compact without Hausdorff, they rarely actually use it (beyond basic pathological examples in textbooks), whereas algebraic geometers, who actually use non-Hausdorff compact spaces require the Hausdorff condition, and otherwise use the term quasi-compact. I may be wrong in the statement that topologists rarely use non-Hausdorff topological spaces, and this is why I asked you the above questions. You've shown that the standard definition in (basic) topology texts does not require Hausdorff, but that does not mean that the standard definition in mathematics is so. As an example that a major branch of mathematics does not use the same definition as topology, I point out algebraic geometry. I realize my opinion may (or may not) be a minority one, but I saw fit to express it. RobHar (talk) 16:50, 10 August 2009 (UTC)

My area of research was in categorical topology, so I'm less familiar with the current usage of the term in algebraic geometry, though I would guess that many texts will not in fact give a definition of something so basic. Note however Smith, An invitation to algebraic geometry, p. 9:

A compact space is a topological space for which every open cover has a finite subcover. Some authors call those spaces quasicompact reserving the term "compact" for Hausdorff spaces with this property.

Notice the word "some". Also that most modern research may be conducted in contexts where all spaces are Hausdorff is really neither here nor there.

Paul August ☎ 17:28, 10 August 2009 (UTC)

I happen to know that Karen Smith says "quasi-compact" just like all of us algebraic geometers do. And when she describes a variety as "compact" she, again like all of us algebraic geometers, means "complete" (i.e., the map to the one-point space is a proper morphism). This is simply a convention. The convention of using "quasi-compact" in algebraic geometry comes from two things, I think:

1. There is a strong French influence coming from Serre and especially Grothendieck.
2. There is more than one natural topology on an algebraic variety. If X is a complex variety, then you can either view it as a scheme (with generic points and the Zariski topology), or you can view it more classically as its set of complex points and their Euclidean topology. Whether or not a variety is compact changes depending upon your viewpoint: All varieties are quasi-compact in the Zariski topology by definition (and in fact, non-quasi-compact schemes are usually so pathological that they are not even considered); but to be compact in the Euclidean topology is to be compact in the traditional sense, and this is a strong assumption, just like compactness of a manifold is a strong assumption.

So what should Wikipedia do? I think we all agree that "compact" for "every open cover has a finite subcover" is the most common usage in English, and I, together with the other algebraic geometers here, can attest that "quasi-compact" is an active, but minority, usage. My own opinion is that we should stick with the most common usage of "compact" and mention "quasi-compact" as a notable minority usage. Ozob (talk) 17:45, 10 August 2009 (UTC)

Agree. And this is in fact what our article currently does. However more ought to be added about the "minority" usage, in particular reflecting what Ozob has written above. Paul August ☎ 18:06, 10 August 2009 (UTC)

I also agree. I work in both differential and algebraic geometry, but am also aware and interested in work in computer science, logic and category theory that uses topological spaces which need not be Hausdorff. Combining the two concepts in one definition is conceptually bad, in that Hausdorff-ness is a local property, whereas compactness is not. However, it is not Wikipedia's mission to change the world (even the mathematical world), only to reflect what we find in reliable sources. Geometry guy 20:13, 10 August 2009 (UTC)

(undent) Hausdorff is not a local property. If it were, non-Hausdorff manifolds would not exist. Plclark (talk) 21:54, 11 August 2009 (UTC)

I am somewhat inclined to the view that:

• Some spaces are Hausdorff spaces, but no space is Hausdorff, because Hausdorff was a person. In other words, "Hausdorff space" is a compound word, not a phrase in which "Hausdorff" is an adjective.
• Some compact spaces are not Hausdorff spaces. There's this nice little undergraduate exercise that says:

Suppose T is a topology on X and (X, T) is a compact Hausdorff space. Suppose S is some other topology on X. If S is finer than T, then (X, S) is not compact; if S is coarser than T then (X, S) is not a Hausdorff space. This makes me wonder if maybe there's some way of looking at it (e.g. something in category theory, maybe) from which "compact" and "Hausdorff" are some sort of duals of each other.

I'd rather keep the terminology as is.

Michael Hardy (talk) 21:25, 10 August 2009 (UTC)

Wow, I didn't expect this much response :) I agree that the convention depends on fields. But I would point out that you rarely see "compact Hausdorff" because what happens most of the time is that the underlying space is often assumed to be compact to begin with: manifolds, topological vector space/group, etc. So, compact groups or compact manifolds are Hausdorff. (Yes, I noticed I use Hausdorff as an adjective, despite Michael Hardy's objection, but I don't think it is only a minority who commits this misusage. It's similar to "Cauchy"; you say "Since the sequence x_n is Cauchy, it is bounded and ....) The argument for compactness subsuming Hausdorff-ness is therefore simple and natural in that it only tries to reflect the reality. By the way, there is a nice explanation for the duality that Michael Hardy wondered about: in a Hausdorff space an ultrafilter converges to at most one point: in a compact (not necessarily Hausdorff) space an ultrafilter converges to at least one point. Thus, a compact Hausdorff space is where an ultrafilter converges to exactly one point. Conceptually speaking, in other words, it makes no sense that there is no term for compactness plus Hausdorff-ness, as if we have terms "injective" and "surjective" but not "bijective". Since a non-Hausdorff compact space is pathological (without doubt?), "quasi-" is also a very appropriate prefix to use.

Of course, if the standard doesn't seem to have adopted this Bourbaki convention, we can't adopt it in Wikipedia either. But really? Yes, some textbooks on topology don't follow Bourbaki, but isn't that simply because they are old? I thought Bourbaki texts are "definitive accounts" on many things, including topology. In fact, many texts refer to Bourbaki for results on topology. -- Taku (talk) 22:23, 10 August 2009 (UTC)

The sources I cited above are not old, here are few more modern texts: Shick, Topology: Point-Set and Geometric (2007); Reid, Geometry and Topology (2005); Crossley, Essential Topology (2009), I'm sure there are many more. Can you provide any topology texts which follow Bourbaki? Paul August ☎ 01:09, 11 August 2009 (UTC)

I don't know of any topology textbooks that follow bourbaki, but then again I've never read a topology book. I also make no claim that topologists follow Bourbaki, though it's possible some do. From Hans Adler's comments, it seems like a good place to look would be French or German books. I know that EGA, SGA, Hartshorne and Mumford's red book all follow Bourbaki. RobHar (talk) 01:33, 11 August 2009 (UTC)

For some reason, I can't edit Wikipedia with my user account. (What did I wrong??) J.P. May's A concise course in Algebraic Topology follows Bourbaki. It is the only topology book I have ever read (or more precisely trying to read :). Maybe that's why I got a wrong impression. -- Taku —Preceding unsigned comment added by 67.186.28.195 (talk) 02:21, 11 August 2009 (UTC)

A Google books search returns a few more examples, such as: Topology by Horst Schubert, General topology by Ryszard Engelking, Handbook of the history of general topology by Charles E. Aull and Robert Lowen, Lectures on algebraic topology by Albrecht Dold. In Klaus Jänich's book "Topology", he doesn't assume the Hausdorff condition, but he says "Many authors call such spaces 'quasicompact'", whatever "many" means. RobHar (talk) 04:20, 11 August 2009 (UTC)

To add to the categorical point of view of "duality" between compactness: for schemes, the analogue of Hausdorff is "separated" and the analogue of compact is "proper". The so-called valuative criteria of separatedness and properness offer the same kind of relation that Taku describes above for ultrafilters. There's a nice discussion of the analogy between properness and compactness in 1.9 of Mumford's Red Book (where he's talking about complete varieties) and in Bourbaki's topology book. RobHar (talk) 22:48, 10 August 2009 (UTC)

In model theory, we have an invariant of complete first order theories that is called the Lascar group. Its inventor defined that a theory is called G-compact if its Lascar group is a compact Hausdorff group. Since the group is always quasicompact, this amounts to saying that it's Hausdorff. This may make sense in French, but based on observations on several occasions I would say it confuses most model theorists outside France, because they expect compact=quasicompact.

I still maintain that the best thing we can do is to use quasicompact or compact Hausdorff whenever there is a difference, and compact when there is none. Since we are writing for an international audience of people from different subfields of mathematics, this is the only way to make sure that our readers needn't guess what we mean. Even if we could agree on one of the two main conventions for the entire project, there would always be some articles that wouldn't follow the convention, e.g. because they are recent additions by a new author who doesn't know about the convention. And it still leaves the flexibility of defining compact as one of the two variants at the beginning of an article, if it's necessary to prevent awkward language. Hans Adler 23:26, 10 August 2009 (UTC)

Let's look at some other Wikipedias:

• FR: A topological space E is called quasicompact if it satisfies the Borel-Lebesgue axiom: of every open covering one can extract a finite subcovering. The space is called compact if it is also separated [i.e. Hausdorff].
• DE: Some authors such as for example Boto von Querenburg [an influential German Bourbaki-style topology text] use the term quasicompact for the property defined here and reserve the term "compact" for compact Hausdorff spaces; due to French influence this is customary especially in algebraic geometry.
• IT:Some authors require that a compact space be Hausdorff; in this case, a space that satisfies the present condition but is not Hausdorff is called quasicompact.
• ES:[Defines compact without Hausdorff. The French terminology is not even mentioned.]

Hans Adler 06:52, 11 August 2009 (UTC)

Very interesting. So, this is really a French convention. Let me add:

• JA: A topological space X is said to be compact if every open cover of any subset of X has a finite subcover. Bourbaki refers to a compact Hausdorff space by a compact space and use "quasi-compact" for a compact but possibly non-Hausdorff space.

(By the way, isn't this definition incorrect?)

-- Taku (talk) 12:21, 11 August 2009 (UTC)

(It is. According to this definition, any compact Hausdorff space is discrete, and therefore finite.) — Emil J. 13:08, 11 August 2009 (UTC)

This is the definition of a Noetherian space (aka Heriditarily compact). Since the spectrum of a Noetherian ring is a Noetherian space, what Emil J has pointed is out is why most schemes aren't Hausdorff. RobHar (talk) 13:29, 11 August 2009 (UTC)

I'm so sorry. I got the translation wrong :) For the record, this is the correct one

• JA: A subset of a topological space is said to be compact if its open cover has a finite subcover.

So, this is slightly more general but is actually equivalent to the usual one (and definitely correct). -- Taku (talk) 21:01, 11 August 2009 (UTC)

Not to pile onto Paul August's list, but Davis (2005, p. 87) also does not include Hausdorff. Unfortunately I can't seem to find my algebraic geometry text at the moment. CRGreathouse (t | c) 07:01, 11 August 2009 (UTC)

I very much favour Hans's position above - "use only the terms compact Hausdorff and quasicompact in topology contexts, except where the two notions are equivalent. This is analogous to how we are already dealing with $\subseteq /\subsetneq /\subset$." Where authors are inconsistent, the best way to avoid confusion is to rely solely on unambiguous terms, even if that usage isn't consistent with any particular author. Dcoetzee 07:37, 11 August 2009 (UTC)

Could anyone remind me how we're dealing with $\subseteq /\subsetneq /\subset$? My understanding is that we're dealing with it by not dealing with it. -- Taku (talk) 12:30, 11 August 2009 (UTC)

It's described at Wikipedia:WikiProject Mathematics/Conventions#Notational conventions:

Subset is denoted by $\subseteq$, proper subset by $\subsetneq$. The symbol $\subset$ may be used if the meaning is clear from context, or if it is not important whether it is interpreted as subset or as proper subset (for example, $A\subset B$ might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that $A=B$). All other uses of the $\subset$ symbol should be explicitly explained in the text.

By the way, the most creative approach to these symbols that I have seen so far was when a single formula $a_{i}\subset a_{j}$ that occurred in a definition absolutely had to be interpreted as $\subseteq$ for certain values of i,j and had to be interpreted as $\subsetneq$ for certain others. Hans Adler 12:43, 11 August 2009 (UTC)

Ah, so here it is. Am I the only one to think that these guidelines would be much easier to find if they were integrated in MOS:MATH? — Emil J. 13:02, 11 August 2009 (UTC)

No. Good idea. Hans Adler 14:54, 11 August 2009 (UTC)

In Encyclopaedia of Mathematics, "Compact space" [20] has this comment:

In the West "compact" is used for both compact and T_2-compact, and the former is sometimes called quasi-compact. In topology the majority of Western authors equate compact and compact Hausdorff (T_2-compact), because the latter spaces are much better behaved; on the other hand in, e.g., algebraic geometry the term compact does not as a rule include T_2.

(The emphases are mime.)

I'm somehow unsure about the accuracy of this. I thought "quasicompact" typically appears in algebraic geometry. -- Taku (talk) 12:29, 11 August 2009 (UTC)

Having read this thread, I feel that some strong statements were made by User:RobHar, but that is simply my opinion. Firstly, "topology" is not exclusively reserved for manifolds; there are people who research point-set topology, set-theoretic topology and other related branches. Furthermore, non-Hausdorff spaces are not simply "pathological examples" in textbooks. There is an interesting theory behind non-Hausdorff spaces; one example is the result that the bug-eyed line does not have the homotopy type of any Hausdorff space (although it is a topological manifold). This, although fairly well-known, serves to illustrate how even "nice" Hausdorff spaces have a complex structure. I do not disagree that major areas of mathematics such as algebraic and differential geometry (and topology) assume all topological spaces to be Hausdorff, but in those branches, topology is a "tool" and not an object of study. By incorporating a Wikipedia convention that "compact" is to mean "compact Hausdorff" suggests not only the non-existence of many "pure topologists", but also the seemingly popular view that non-Hausdorff is pathological (and this is certainly incorrect). It may be that I am biased, by I vehemently oppose to the suggested convention. --PST 14:31, 11 August 2009 (UTC)

Here's an example of a non-Hausdorff topological space which arises naturally but which I think nobody has mentioned: L^p with the strong topology. As we all know, a measurable function R → R is in L^p if and only if its p-norm is finite; and in particular, all functions that are almost everywhere zero have zero p-norm for every p (even in the goofy cases when 0 < p < 1). Now, a lot of books take the quotient by the subspace of a.e. zero functions, but not all do; e.g., David Williams's Probability with Martingales doesn't, and even makes the claim that taking this quotient is never done when working with continuous-time objects in probability theory (I don't know enough probability to verify the truth of this claim, though).

More generally, of course, any seminorm which is not a norm will define a non-Hausdorff topology on a vector space. Ozob (talk) 15:18, 11 August 2009 (UTC)

My statements were made with the explicitly stated caveat that they may be wrong and were accompanied with questions. I realize that topology is not only algebraic and differential topology (subjects in which topology is the object of study), however I am pretty sure that point-set topology, set-theoretic topology, etc form a very small minority of the subject. In other words, in terms of usage of the term, compact most often means compact Hausdorff since the space is assumed Hausdorff to begin with. I also don't see how the "bug-eyed line" is not pathological. I believe that it is true that non-Hausdorff is pathological in most areas of study.

Anyway, I find Hans Adler's suggestion to use "quasicompact" and "compact Hausdorff" (mimicking the convention on subsets) to be quite sensible. Especially since in most cases it would be sufficient to simply say "compact" as the object in question will likely already be assumed Hausdorff. This is probably my first choice of convention.

However, it is true that different subjects have different conventions, and a possible compromise would be to say that in articles in topology (and someone mentioned some computer science) the term "compact" need not refer to a Hausdorff space, whereas otherwise (or something) it refers to compact Hausdorff. As most subjects other than topology (and algebraic geometry/number theory that use the term quasicompact) only deal with Hausdorff spaces only "compact" will be required. This would thus not represent a significant change to the wording in almost all articles. Thoughts? RobHar (talk) 15:14, 11 August 2009 (UTC)

So, are you asserting that point-set topology and set-theoretic topology are less important than differential geometry and topology? --PST 09:44, 12 August 2009 (UTC)

So much discussion. We have basic conventions to avoid getting sucked into such time-consuming stuff. "Quasi-compact" as used in scheme theory is a standard definition and means what you'd guess, but it is not a definition most mathematicians have to worry about. I think Bourbaki had a rather limited point in making that definition back in the day, and we lose little by ignoring the point in our conventions. Charles Matthews (talk) 16:07, 11 August 2009 (UTC)

Let me weigh in, as someone who has spent some time re/writing the articles on general topology. I have various comments:

1) Both conventions have a great deal of support. The use of quasi-compact is more widespread in French than it is in English (indeed, the above references seem to show that compact virtually always implies Hausdorff in French), but it is certainly widespread in English as well. As a rough rule of thumb, "quasicompact" is preferred by the algebraists (including algebraic geometers, algebraic number theorists, model theorists, etc.) whereas "compact" is preferred by the analysts and geometric topologists. There is enough use of each convention that it seems absolutely mandatory to mention both alternatives as being in common use.

2) In terms of authoritative texts on General Topology, in my opinion (as someone who has spent some time perusing them) the following are the most authoritative, in historical order:

1955 Kelley's General Topology 1958 Bourbaki's Topologie Generale 1970 Willard's General Topology 1975/1977 Engelking's General Topology

I find it strange that nowadays people seem to name Munkres' book as the definitive reference on the subject. It is a very nicely written book (it was used for my first course on topology, and I had an entirely positive experience with it), but it does not have the scope of a reference. From the author's preface: "This book is intended as a text for a one- or two-semester introduction to topology, at the senior or first-year graduate level."

In terms of the authority of the above books, I would rank them in descending order as: Bourbaki, Engelking, Willard, Kelley. Note that the first two of these use the term "quasi-compact".

3) Except for the fact that it is probably not in majority use among English-speaking mathematicians, I have never heard a reasonable argument against Bourbaki's convention. There are many arguments for it, most of all the fact that it clues the student in to the fact that many of the nice properties of compactness in metric spaces hold only when the Hausdorff axiom is assumed. Moreover, the alternate terminology gets awkward when one is seriously interested in non-Hausdorff spaces. For instance the term "compactification" is used in every text I have ever seen to mean "Hausdorff compactification", but the fact that this is not built into the terminology can cause confusion.

4) I would myself prefer that wikipedia adopt the quasi-compact convention. This would be a progressive move: choosing terminology that we feel is best even if it is not in the majority use. I appreciate though that this is a big step for wikipedia to take. I think that Hans Adler's advice is ultimately best: mention both conventions in the foundational articles, and then in the applications try to phrase things so as to make sense independent of which convention has been chosen. Plclark (talk) 21:54, 11 August 2009 (UTC)

What a plethora of opinion. Plclark, I gave a perfectly good argument against the Bourbaki convention above, but you didn't read it: Hausdorffness is a local notion, whereas compactness isn't. Conflating the two is logically confusing and unacceptable in most fields. Bourbaki and others were simply seduced by the happy combination that compact and Hausdorff spaces provide (uniqueness of the compact Hausdorff topology etc. etc.) You can pick and choose your references according to your prejudices, but you can't argue against the principle that there is no such thing as a locally Hausdorff space, whereas locally compact spaces are prevalent in mathematics. Geometry guy 23:23, 11 August 2009 (UTC)

Actually he did read your argument, and he commented on it above. He said Hausdorffness is not a local notion. RobHar (talk) 23:42, 11 August 2009 (UTC)

My apologies: we evidently have different conceptions of what "local" means. It is precisely the nonexistence of locally non-Hausdorff spaces which differentiates Hausdorff-ness from compactness. Geometry guy 23:49, 11 August 2009 (UTC)

Geometry guy, I'm afraid I have no idea what you're talking about. Are you familiar with local property and locally Hausdorff space? I can't tell from what you write. Certainly there are spaces which are not locally Hausdorff (or even locally non-Hausdorff), for instance the trivial topology on a set with more than one element. Plclark (talk) 07:08, 12 August 2009 (UTC)

My apologies again. I'm only used to dealing with topological spaces in specific arenas (albeit several unrelated ones that include Hausdorff and non-Hausdorff spaces). The notion of local you describe is entirely the right one, and I use it regularly myself. So I should not have caused confusion by using the word "local" in this context. What I meant was that a witness to non-Hausdorffness only involves two points and arbitrarily small neighbourhoods of these points. In contrast compactness is a feature of the whole space. One can delete a point from a non-Hausdorff space to make it Hausdorff, while one can also delete a point from a compact space to make it noncompact. This seems very different to me, but perhaps you can clarify. Geometry guy 20:58, 14 August 2009 (UTC)

To respond to Plclark's 3), I'm no expert but I believe that the strongest argument against the inclusion of Hausdorff-ness would be that the category of Hausdorff spaces is not well behaved (I never quite understood what topologists mean by "not-well-behaved"). Hence, it is important to work with -- in algebraic topology in particular -- the category of spaces with some weaker separation axioms such as weak Hausdorff space. (See also [21]) This is not surprising since Bourbaki introduced their convention before the category theory became mainstream. -- Taku (talk) 11:59, 12 August 2009 (UTC)

It is usual at some point to "appeal to common sense". As far as I can see, typing "compact Hausdorff" is not really so bad if you know you have to do it; and the advantage seems to be that with the two terms "compact" and "compact Hausdorff" in use, the worst that happens is that someone may read a proposition like "if X is a compact space then blah" in too restrictive a sense. Which cannot be said if Hausdorffness is tacitly assumed. Charles Matthews (talk) 14:11, 12 August 2009 (UTC)

The consensus seems clear by now, but let me indulge a bit more, because I don't understand Charles Matthews' comment at all. Yes, it is true that there is no serious problem that could be solved by adopting a new convention: there is nothing wrong with "compact Hausdorff", especially because like 99% of times spaces are Hausdorff and so this is usually simply non-issue. (Likely, I was bored before a new semester, which started the whole thing :) But, but, why reject the idea of having a discussion on conventions at all? It is important to adopt a correct convention; not just because that helps the reader but because that's the whole point of this project. Isn't it? We strive for the accurate description of (contemporary) mathematics, and the choices of conventions are therefore extremely important because they're reflection of philosophy. It is possible that, as PST pointed out, adopting the Bourbaki convention gives a wrong impression that certain materials in topology are unimportant (because they are?) I don't see why we, as the authors of this encyclopedia, can't have a long discussion then choose conventions that best reflect views that we think correct? Because we can't agree ever or why try? (Excuse me for ranting.) -- Taku (talk) 01:34, 13 August 2009 (UTC)

Well, the discussion seems to show that your initial comment I think today this is fairly standard is simply not correct. Of course conventions can be discussed - there is a talk page for the conventions page. I thought you were misunderstanding a little "quasi-compact" as it used in scheme theory, and its significance. The Bourbaki style is (was, I think) to be very aggressive in discussions on terminology and conventions. That is not very suitable for us, and we have to compromise a little between reflecting the terminology used by mathematicians, and being self-consistent. Sometimes this means accepting "least bad" solutions to convention issues. Charles Matthews (talk) 16:26, 13 August 2009 (UTC)

New behavioral guideline: Wikipedia:Editing scientific articles

See discussion here Count Iblis (talk) 15:01, 13 August 2009 (UTC)

Why do you say it's a guideline when it's an essay? Charles Matthews (talk) 16:15, 13 August 2009 (UTC)

Because of a misconceptions about the way we create new guidelines. [22] Hans Adler 16:38, 13 August 2009 (UTC)

Yeah, we gotta be careful with every comma in a science article on this wiki or the world might explode! Seesh... Pcap ping 17:22, 13 August 2009 (UTC)

It is necessary, because the usual wiki rules are not enough to prevent nonsense from being edited in articles. The reason why it isn't usually a problem has a lot to do with the fact that most editors intuitively stick to my propsed guidelines and in cases where editors do not and thatleads to conflicts, Admins intervene in a reasonable way. But, strictly speaking, you can find yourself on the wrong side of wiki rules when some editor tries to edit in nonsense in articles that seems to be supported by sources if you can't simply quote from a source a direct refutaton of these edits.

This is a recent case. You can see that the existing wiki rules and guidelines leave too much room for quack editors to argue and put the editors who want to keep nonsense out of articles too much on the defensive. All I want to do is have a few guidelines that that points out some pitfalls when arguing like: "My book says X, the wiki article says Y, so I'm right and you're wrong".

Besides conflicts between editors, there have been cases of seriously flawed wiki articles. In most cases the articles would have been ok if editors had stuck to the simple rules in my guidline. Count Iblis (talk) 18:34, 13 August 2009 (UTC)

We don't need a new guideline just because a clueless editor tried to defend the valuable resource that Wikipedia has in the person of Randy in Boise against exasperated experts. If we augment our guidelines each time an editor makes a serious error of judgement, they will become even more contradictory than they already are and they will only be useful as something the parties of a dispute can point to, but not helpful to anyone who wants to be guided. Hans Adler 18:58, 13 August 2009 (UTC)

(ec) "There have been cases of seriously flawed wiki articles." O RLY? What else is new? Did you look at the recent history of lambda calculus? Reliable sources occasionally get some stuff wrong too, or they may express something in a misleading fashion even when it's not downright wrong. An example from about a year ago is here. But you can't really enforce clue with a guideline; you will always have editors making use of appeal to authority, because that's a basic pillar of the wiki. Thankfully, we're not writing math articles that way here, despite what the rules say. (Yes, Wikipedia has an inconsistent axiomatic system.) So, next time when someone is a clueless WP:DICK, remember there's a policy against that, making your guideline superfluous. :) Pcap ping 19:00, 13 August 2009 (UTC)

Sorry for being off-topic... I just want to thank Count Iblis for his contribution to the article Helmholtz free energy and its talk page; these are very helpful to me. Probably, editors in physics have more problems with quack editors than we mathematicians.Boris Tsirelson (talk) 06:43, 14 August 2009 (UTC)

Agree with Pcap. There's no point in having further policies like this. A manual of rules needs to be as short as possible whilst including everything that's really necessary. This policy would be like telling grandmother how to suck eggs as far as anyone with a clue is concerned and would be ignored by the idiots with a mission. Besides it's unworkable - how would an administrator decide it was broken except by asking the parties to discuss the matter which is what happens for edit wars anyway? Making the rules any longer diminishes the ones already there. This could be put into a tutorial text but that's about it I think. Dmcq (talk) 09:33, 14 August 2009 (UTC)

Boris, thanks! To the critics here, an Admin who intervenes in a dispute would have the option of pointing one or both editors to these guidlines. The word "edit war", could be avoided in some cases where now Admins would have to use that word. That could prevent tensions being raisd. Some newcomer who thinks that he his right and that his opponent is removing his "sourced edits" will have difficulties accepting the judgement that he is "edit warring", given that the wiki rules seem to support his condiuct and not the conduct of his opponent.

An expert at Wikipdia would also have something concrete to point to when someone complains that he is removing sourced edits, and that he is violating wiki rules. Many experts have left wikipedia after a few days out of frustration. Count Iblis (talk) 16:08, 14 August 2009 (UTC)

Not every expert is able to "cooperate" with Randy, although some are quite good at it. But some simply want to write a complete new article from scratch and upload it. I think it would be better overall if those experts who are really stressed by the Wikipedia editing environment simply went to Citizendium and worked on writing and approving articles there. As far as I know approved Citizendium articles can be used as reliable sources for Wikipedia. And since we are now using basically the same licence, large passages can simply be copied. The Citizendium article can work as a known good state of the Wikipedia article, and consensus will autmatically crystallise around that in many cases. Conversely, improvements that happen here can be folded back into Citizendium and formally approved there after a while.

The complaints about removing sourced facts are a general problem of Wikipedia. They have nothing to do specifically with science articles and need to be addressed sooner or later. AFAIK it's not written policy or guideline but there was an old Arbcom decision saying persistently removing sourced statements is disruptive. I believe they were careless with their formulations at the time, so that now it can be quoted as justification to defend nonsense or irrelevancies that are properly backed with formally reliable sources.

Even if your text were policy it would have no effect whatsoever on edit warring. Your text might conceivably help to find out who is right in an edit war. But that's irrelevant because it's a purely behavioural concept. There are exceptions for vandalism, BLP and probably OTRS and copyvios, but your text won't add a new justification for edit warring. It might conceivably help admins to stop or prevent an edit war by deciding which side is right. But I think that would be very controversial. Hans Adler 16:50, 14 August 2009 (UTC)

GA review of "Mathematics and art" and "Jeep problem"

Protonk has started a GA Review of Mathematics and art (review page) and Jeep problem (review page). In both cases Protonk feels that the articles are some distance away from GA quality. Mathematics and art has "many challenges", which Protonk has listed in detail; Jeep problem "requires a substantial rewrite" and so Protonk has given it a more summarised review. Both reviews have a status of "On hold: this article is awaiting improvements before it is passed or failed". If anyone has the time and inclination to improve these articles, please do so. Gandalf61 (talk) 10:25, 14 August 2009 (UTC)

Protonk's review Talk:Mathematics and art/GA1 is thoughtful, detailed, and well written, addressing the content of the article rather than just stylistic issues. It is the type of review I would be happy to see more often. — Carl (CBM · talk) 11:51, 14 August 2009 (UTC)

I agree, and that is partly because the article is close enough to the GA standard that detailed suggestions for improvements might lead to a GA list. I encourage editors here to contribute to achieve such a result. Geometry guy 21:03, 14 August 2009 (UTC)

Theta function

I just wrote Theta function (disambiguation) as a possible expansion to the hatnote at Theta function. I think that the list of functions should be split into the true theta functions (Jacobi's, Ramanujan's, and the q-theta functions, at least) from the other functions that merely use (or are called) theta. Something like

A theta function is a special function in complex analysis. the Jacobi theta function $\vartheta (z;\tau )$ Jacobi theta functions (notational variations) $\vartheta _{ij}(z;\tau ),\vartheta _{j}(z),\theta _{i}(z;q)$ the q-theta function $\theta (z;q)$ Other theta functions include the Chebyshev function $\vartheta (x)$ the Riemann theta function $\mathbb {H} _{n}$

Other possibilities: leave all 10 functions in one large list; split by field (analysis/number theory/set theory).

Here's a list of possibly-related pages for comparison:

• Theta function
• Theta (disambiguation)
• Psi function
• Psi

Any thoughts? I wanted to at least let some other people look it over before I put an {{about}} tag on Theta function.

CRGreathouse (t | c) 18:11, 14 August 2009 (UTC)

Fine good, I never knew there was so many of them as that disambiguation page has grown to now! Dmcq (talk) 07:47, 15 August 2009 (UTC)

Morally the Riemann theta function probably encompasses the Jacobi functions. It's for several variables, and if you make it for one variable and tweak it a bit you presumably find all the one-variable special cases. In other words there is the family of theta functions associated with abelian varieties, and they are all related in a structural way. Charles Matthews (talk) 09:27, 15 August 2009 (UTC)

Links to Bonse's inequality

I've just created a new article titled Bonse's inequality. It's a stub. So:

• Expand and otherwise improve it if you can;
• Help figure out which other articles should link to it. I've created about three or four links (I can't count that high at the moment). (I'm surprised we have no list of prime number topics. If we did, it would belong there.)

Michael Hardy (talk) 00:16, 15 August 2009 (UTC)

Is it clear that this topic is notable enough for its own page? Searching MathReviews, I found that it intervenes in four reviews. If am not mistaken, can't one immediately deduce better estimates by applying Chebyshev's result that there exist explicit constants C_1 < 1, C_2 > 1 with $C_{1}<\pi (x)/(x/\ln x)<C_{2}$ for all (explicitly given) sufficiently large x? Chebysehev's result was proven at least 50 years before Bonse's, and has an elementary proof. (For that matter, I had some trouble finding this result on wikipedia: where is it?) I think it would be more efficient to have a page devoted to inequalities involving $\pi (x)$. Plclark (talk) 03:45, 15 August 2009 (UTC)

I'd have thought it followed even quicker from Bertrand's postulate which really is elementary. Once the factors get more than 8 you know that four times the second last prime and twice the last prime must both be bigger than the next prime. I wonder why it was thought interesting. Dmcq (talk) 07:31, 15 August 2009 (UTC)

Sorry I see that Chebysehev did actually use his results about bounds for the prime number theorem to prove Bertrand's postulate so it should really now be called the Bertrand-Chebyshev theorem or Chebyshev's theorem. Dmcq (talk) 07:40, 15 August 2009 (UTC)

It does look like it should be merged in somewhere discussing the initial segment of their primes and their distribution. Charles Matthews (talk) 09:30, 15 August 2009 (UTC)

Conventions

Following a suggestion of Emil J., I've created a new section of the math MOS: Wikipedia:Manual of Style (mathematics)#Conventions. This is mostly a link to the current page on conventions, Wikipedia:WikiProject Mathematics/Conventions. I feel like it would be a big improvement if the conventions page were merged into the MOS: The conventions page is short, is highly relevant to the MOS, and would be easier to find and maintain. Does anyone else have an opinion on this? Ozob (talk) 15:57, 11 August 2009 (UTC)

In the past sometimes people have objected to including things in MOS subpages that are not strictly speaking style issues. But I think that was often motivated by unrelated political concerns, and I hope there are no such politics involved here. I support the move. It's not entirely clear to me whether the logic conventions should be merged as well, since they are also used by philosophers, who might not otherwise be interested in MOSMATH. But that can be decided later (and in the logic project). Hans Adler 16:10, 11 August 2009 (UTC)

Probably inevitable. We do need to recognise the implications, and that the MoS generally has taken on a much more prescriptive role in recent years. Which is not always for the best. Charles Matthews (talk) 17:00, 11 August 2009 (UTC)

It is not clear to me how many of our articles follow the conventions page, and when they do it is possible they do so only because the conventions described are already somewhat common elsewhere. But I don't have any strong objection to the merge as long as some cautionary language about not applying them blindly is present. I added that to the MOS just now. — Carl (CBM · talk) 12:15, 12 August 2009 (UTC)

I'm sorry if this is the wrong place to write this (please delete if so), but there needs to be more consistency with respect to how formula are presented. For example, consider the difference between how relations are written in the definition of an asymmetric relation and an anti-symmetric relation (i.e. aRb vs. R (a, b)). Conventional consistency seems to always be preferable here. —Preceding unsigned comment added by 72.90.67.27 (talk) 18:27, 17 August 2009 (UTC)

This is a fine place to write it, but I don't agree with you. Yes, there is some advantage to keeping an eye on how things are presented in different articles, to avoid confusing readers who click on a link where "compact" implies "Hausdorff" and arrive at an article where it doesn't, especially if the difference is not mentioned. But trying to prescribe prefix versus infix notation for relations is a waste of effort in a project as sprawling as this one, and will just annoy contributors. Any reader who has a chance of understanding the material in the first place, will be able to handle notational diversity at this level. --Trovatore (talk) 18:50, 17 August 2009 (UTC)

Differential of a function

The definition of differential of a function that appears in that new article has appeared in calculus textbooks for more than 30 years now, and that's an unfortunate gap between mathematicians and authors of calculus textbooks. You'd hope that authors of calculus textbooks would be mathematicians, but it seems they're a different culture (I don't mean Spivak and Apostol, and I think there are a few others....). And they write books by zeroxing each other's books. It might not be politic to propose burning them at the stake as heretics, so I won't mention anything like that. But I've made some comments here.

Would other mathematicians here agree with me that this abomination is an abomination? Michael Hardy (talk) 02:36, 17 August 2009 (UTC)

Yes, I completely agree. In fact, what is presented in the article is rather worse than what I've found in most calculus textbooks I've looked at lately. In my experience, most 21st century calculus textbooks are written so as to never say something that is mathematically incorect, because mathematicians who teach calculus complain more vocally about actual mathematical errors than other deficiencies. Plclark (talk) 03:58, 17 August 2009 (UTC)

Thank you. Now if possible, can you add some comment to the linked-to talk page? I'm not at all sure the creator of that article is reading this present page. Michael Hardy (talk) 04:46, 17 August 2009 (UTC)

Yes, I'm reading. I'm following all the disscusion [23] [24] [25] [26]. You may read my last input in the discusion on the article's talk page. Usuwiki (talk) 02:27, 18 August 2009 (UTC)

I think there is a bit of a culture clash here. As far as I can make out, and I could very easily be wrong, this has come from an analysis/numerical viewpoint and may have started in Russia investigating linear differential operators including both Δx and dx and suchlike, and they'd want them in the same terms and comparable. I'd guess more people here see differentials as being more part of studying manifolds and start with a topological outlook and aren't so interested in finite differences. You got them both using linear maps and the same symbols so it grates. Dmcq (talk) 06:22, 17 August 2009 (UTC)

Sorry I see I should have gone to that page, okay will copy my comment there. Dmcq (talk) 06:26, 17 August 2009 (UTC)

I for one have tried to redirect the new article to a section of the existing article, plus I have made some other comments in the new article's page. As for calculus textbook, I can't say much: I am Italian, and textbooks when I was a student had, if anything, the opposite problem, being a bit too formal for, say, first-year students. But I see that presently there is a tendency towards "American" calculus, using new books translated from English and even renaming courses from "Analisi matematica" to "Calcolo". Goochelaar (talk) 07:34, 17 August 2009 (UTC)

A triviality: are tuple and word (mathematics) the same concept?

Clearly the notion of an n-tuple is distinct from that of a word, but I but a quick search in google books failed to find a set theory definition for tuple; only n-tuple is defined. This is related to a debate on List (computing), but the article on tuple could use some clarification as well. Pcap ping 12:49, 17 August 2009 (UTC)

Word (mathematics) is not being explained in String (computer science) and shouldn't redirect there.  Cs32en  13:01, 17 August 2009 (UTC)

Whether it should redirect there or not, it is explained there. Pcap ping 13:02, 17 August 2009 (UTC)

I've just changed the redirect to point to that section. Pcap ping 13:05, 17 August 2009 (UTC)

Normally one does not use the term "word" unqualified, it is always a word over some given finite alphabet. But otherwise there is no real difference, both word and tuple mean a finite sequence. — Emil J. 13:07, 17 August 2009 (UTC)

I agree. It is mostly a matter of consuetude: probably one would not say that a vector space such as ${\mathbb {R} }^{n}$ consists of words. Similarly, the operations on tuples one would spontaneously think of are mostly termwise ones, while two words tend to be concatenated, or shuffled, and the like. So, in a sense, if you use one of the two terms rather than the other, you predispose the audience to a certain set of properties and operations. Goochelaar (talk) 13:13, 17 August 2009 (UTC)

No, because "words" in ${\mathbb {R} }^{n}$ are all n-tuples, i.e. the words have all the same length. Pcap ping 13:42, 17 August 2009 (UTC)

Indeed. One would not usually describe ${\mathbb {R} }^{n}$ as consisting of all words on $\mathbb {R}$ of length n either. Goochelaar (talk) 14:41, 17 August 2009 (UTC)

Actually, I think that the definition of tuple from that article is a Wikipedia original, and that it was caused by renaming the article some four years ago from n-tuple; according to MathWorld "tuple" means just n-tuple for some fixed n obvious from context; it does not mean word. See further discussion at Talk:Tuple#Problem_with_def_of_tuple. Pcap ping 13:42, 17 August 2009 (UTC)

Apparently the word "tuple" (without n) is mostly used by computer scientist, especially in Python programming language, where it is the actual name of a data structure. Goochelaar (talk) 14:44, 17 August 2009 (UTC)

Indeed. In Python a tuple is an immutable list. Gandalf61 (talk) 14:54, 17 August 2009 (UTC)

The term is also in wide currency among relational database theorists, who use it to refer to a row of a table. (Each table is a relation, in the mathematical sense, and rows in the table are elements of the relation, and so are tuples.) —Dominus (talk) 16:10, 17 August 2009 (UTC)

There is a distinction: perhaps it should be clarified by means of the concepts of internal operation and external operation. The "point" of words is that concatenation is an internal binary operation - we are living in the free monoid. Obviously you can concatenate tuples of any finite length, but this then appears as an external operation on two Cartesian powers ending up in a third. In other words (in other tuples?) as soon as you write * for concatenation with its type data you become conscious of an overloading of the notation. Charles Matthews (talk) 14:54, 17 August 2009 (UTC)

Matrix calculus: Definition of the matrix derivative

Content from the archive. The issue is still unresolved.  Cs32en  13:04, 17 August 2009 (UTC)

We could use some help to resolve a controversy about the correct formulae for the matrix differential and the matrix derivative at the article Matrix calculus. See the talk page, especially the section Disputed information: Matrix derivative.  Cs32en  22:52, 11 July 2009 (UTC)

I concur we need assistance, primarily as to the notation(s) actually used in serious mathematical works. — Arthur Rubin (talk) 15:49, 13 July 2009 (UTC)

See Talk:Matrix calculus#Scope of questions for my view as to the matters in dispute, and my take on them. My desired outcome is not necessarily represented in all cases. — Arthur Rubin (talk) 21:19, 13 July 2009 (UTC)

This really should be resolved by verifying that the formulae stand as stated in the references (and noting the conventions in operation, per reference). I edited the section on the nature of the so-called "matrix derivative" - and there doesn't seem to be controversy about that. So that leaves only the formulae collected from the literature. Charles Matthews (talk) 14:47, 17 August 2009 (UTC)

Leibniz function

With respect to article Leibniz function, can someone please verify its meaning in regards to its derivative ( f ( x ) f ' ( x ) = 1 ). Not familiar with the term in this context and the word "Leibniz" is not found anywhere inside the books listed as references.

My addition/contribution to the article is with respect to Lie groups/algebra, with cleanup under the good-faith assumption that such an identity exists and is named after Leibniz. Henry Delforn (talk) 16:56, 17 August 2009 (UTC)

I haven't seen that usage before, and I find it at least a little bit implausible that any such convention is widespread. Michael Hardy (talk) 22:41, 17 August 2009 (UTC)

Category:Type theory and Category:data types

Cat Data types lists Cat Type theory as sub-category, which causes a lot of data types articles, e.g. some, but not all in Category:Composite data types, to be added (manually) to type theory as well. This appears wrong to me as a way of organizing this stuff. Pcap ping 03:20, 18 August 2009 (UTC)

At a quick glance, I agree. Type theory is not about data types, at least not as data types are understood in computer science (although there are certainly analogies). Neither should be a subcat of the other. Possibly a few pages belong in both, but not very many, I think. --Trovatore (talk) 03:25, 18 August 2009 (UTC)

I think you're confusing data types with data structures. Pcap ping 05:33, 18 August 2009 (UTC)

I don't think so. Type theory and data types are quite different things. --Trovatore (talk) 06:38, 18 August 2009 (UTC)

Most articles on this wiki in this area are crappy and fail to explain the link, but see initial algebra, and [27] for more details. How categories and types are related, I probably don't have to explain to you, but given that we don't have an article on the syntactic topos (as Steve Awodey calls Lambek's topos generated by a type theory), and that neither topos or type theory mentions the notion (or the other article), you may want to read about it in Lambek's book Introduction to Higher Order Categorical Logic, or if you want an executive summary, see Steve Awody's paper. Pcap ping 07:05, 18 August 2009 (UTC)

P.S. Bart Jacobs in Categorical Logic and Type Theory (1999), appears to call the syntactic topos, effective topos, but that might be a more general notion; I haven't read close enough his book, and I don't have the time currently to do so. But Jacobs book also explains in more detail how these notions relate to date types in ML etc., including a chapter on parametric polymorphism etc. Pcap ping 08:49, 18 August 2009 (UTC)

On that point, "effective topos" is something based on realisability; "syntactic topos" as you define it sounds like a general construction from a language. Charles Matthews (talk) 14:19, 18 August 2009 (UTC)

You're right, there is a difference. I don't pretend to understand it well enough to write about it on Wikipedia though. Sketches of an Elephant, chapter D1, has more general construction of a syntactic category (wrong article on the wiki) for a first order language, of which first order logic is a particular case. Johnstone then introduces sketches as being "in some sense intermediate between a theory [of a first order language] and its syntactic category [...]; it has some of the advantages of each, but also some of the disadvantages of each.", p. 861, and goes on to explain those advantages and disadvantages. He then generalized these notions in chapter D4 over higher-order signatures, of which simply typed lambda calculus (with product types) is particular case (a lambda signature has no relation symbols). Then he gets to Lambek's well-known result of the correspondence between simply typed lambda calculus and CCCs. This correspondence is rather technical, there's no "classical completeness theorem" for lambda-theories; I won't try to describe it here. He then goes on to define tau signatures (tau stands for topos/type), which are more general than lambda-signatures in that they allow primitive relation symbols. As you guessed, the syntactic category of tau-theory is a topos, and rather surprisingly, there is a completeness theorem for tau calculus. He then introduces mu-lambda-calculus (Martin-Löf type theory), which corresponds to LCCCs. Quite an interesting expose. Pcap ping 18:57, 18 August 2009 (UTC)

Look, you can find all the connections you like. It isn't even remotely the point. Neither of those categories should be a subcat of the other, period. They are from different fields of endeavor. --Trovatore (talk) 10:03, 18 August 2009 (UTC)

How so? Is type polymorphism for instance not applicable to programming (thus data), or not covered by type theory as an endeavor? Category:data types is a bit of a misnomer by using the adjective "data", but is anyone willing to have something called just Category:types? Pcap ping 18:57, 18 August 2009 (UTC)

Types in general are not amenable to treatment by computer. For example they tend to be uncountable. Even when they're not, they're not things you find in a programming language — they're at least one level more abstract than that, the Platonic ideal objects underlying what you find in a programming language. On the other hand, data types as I understand them are something you would find in a programming language, something with language-specific syntax. --Trovatore (talk) 20:03, 18 August 2009 (UTC)

Simply not true. Pcap ping 20:09, 18 August 2009 (UTC)

Which part? --Trovatore (talk) 20:11, 18 August 2009 (UTC)

Data types and types are the same thing as explained at Type system#Fundamentals, not Platonically removed as you see it. Pcap ping 20:12, 18 August 2009 (UTC)

They aren't. Types are essentially the structure V_ω+ω, except that you can't mix ranks. --Trovatore (talk) 20:15, 18 August 2009 (UTC)

Yes they are. A type system is a countable collection of ideals of V. See Cardelli and Wegner, section 3, starting on page 14. Pcap ping 20:27, 18 August 2009 (UTC)

Who mentioned type systems? The category is called type theory. The obvious thing people are going to think of is Russell's type theory. The natural interpretation of that is the one I said. --Trovatore (talk) 20:29, 18 August 2009 (UTC)

← Which "people" are we talking about? See the pretty picture in theoretical computer science. Pcap ping 21:08, 18 August 2009 (UTC)

Even if you want to focus on the things there, they still aren't data types. Come on, I think you're just being argumentative here. Data types are things like int and bool and double, structs and classes, things that you find in a specific language or an IEEE spec. They're not part of theoretical computer science at all, which takes at least one extra step towards Platonic abstraction. This is how almost everyone is going to interpret them. If the data types category intends something else, then it's misnamed. --Trovatore (talk) 21:29, 18 August 2009 (UTC)

I did my best to explain it, but you just don't get it, or don't want to get it. Bye. Pcap ping 21:31, 18 August 2009 (UTC)

Don't let the door hit you on the way out. --Trovatore (talk) 21:34, 18 August 2009 (UTC)

Element (mathematics)

Someone just created symbol (formal) with a redirect from symbol (logic). In my opinion such mini-articles with no potential are a maintainability nightmare and should be merged. In a note to the editor I was about to write that symbol (formal) is redundant with formal language in the same way that element (mathematics) doesn't exist because it's redundant with set (mathematics). Fortunately I checked this first: It turns out that we do have this article.

Do we really need this? Hans Adler 10:26, 18 August 2009 (UTC)

Element (mathematics) is in Category: Basic concepts in set theory; set (mathematics) is in Category:Set theory. This indicates to me a difference in pedagogic level. So which "we" are we talking about? Charles Matthews (talk) 14:22, 18 August 2009 (UTC)

I think it is a useful article. Paul August ☎ 14:30, 18 August 2009 (UTC)

Henry Gordon Rice was...

At Henry Gordon Rice, we are informed that:

Henry Gordon Rice was a logician and mathematician best known as[.....]

No dates of birth and death. Only the word "was" implies he is deceased. But on the talk page it says the article must comply with Wikipedia's policy on biographies of living persons.

Which is it? Michael Hardy (talk) 04:20, 18 August 2009 (UTC)

That's probably undecidable based on what's available on google. :p Pcap ping 04:48, 18 August 2009 (UTC)

SSDI gives a Henry G. Rice (20 July 1920 - 14 April 2003) which was probably him.John Z (talk) 22:49, 19 August 2009 (UTC)

Stanford Encyclopedia of Philosophy

Shouldn't we cite this as a reference instead of external link in math logic articles? The two math articles I've looked at Type Theory, and Second-order and Higher-order Logic are written by published academics, and in the type theory case, by a well-known researcher in that area (despite the fact that he doesn't get a Wikipedia article), so the article is much better than what we have here, which describes type theory up to 1941 or so. Pcap ping 16:38, 19 August 2009 (UTC)

I agree. I think in the past I have changed several references in this way. We could consider a specific template for such references to encourage this and make the citations uniform. Like Template:PlanetMath or Template:ScienceWorld. Hans Adler 17:10, 19 August 2009 (UTC)

A template would be good. But the difference between a "reference" and an "external link" should be determined structurally (notionally, references are used in putting the article together), with the "External links" section having the same status as "Further reading". Charles Matthews (talk) 19:41, 19 August 2009 (UTC)

The other point is that encyclopedias in general are not usually thought of as high-quality references. Tertiary sources like Wikipedia are supposed to reference mainly secondary sources and possibly a few primary, but not other tertiary sources. It could be that the SEP is something more than an "encyclopedia" in that sense, and in that case it might be OK. But it's understandable that editors would be reluctant to use as a reference a work with Encyclopedia in its name. --Trovatore (talk) 19:46, 19 August 2009 (UTC)

Count me among the people who do not want to see us citing SEP. The problem is not the word "encyclopedia", although that is related. There are two sorts of refernces that we should cite predominately in our "content articles" (for lack of a better term).

1. Journal articles, for for establishing the dates of discoveries and attributing them to the correct mathematicians. Occasionally, esoteric facts are only going to be found in journals.
2. Monographs and other book-length treatments, including textbooks, Lecture Notes in Mathematics, and compilations such as the Handbook of Mathematical Logic. These can devote enough pages to cover a topic in much greater depth than we can, and will usually provide a rigorous and formal treatment. They provide enough context that the reader can really dig into the topic and come away with a depth of knowledge. These are the sorts of things I would be likely to cite in a journal paper if I needed a basic fact from graduate school.

We generally avoid the following for general content:

1. Newspaper and magazine articles: these are useful for popular culture and opinion but lack enough depth to be a useful reference for the mathematics itself
2. Short handouts people have used in classes (book-length lecture notes are a separate issue)
3. Expository articles that do not differ significantly from what our ideal article on the subject would say. These do not go any deeper than our article does, and so do not provide additional depth of understanding. Actually, WP:EL discourages even linking to these, but we have a general practice of linking to PlanetMath, Mathworld, Citizendium, the Stanford Encyclopedia, etc.

In essentially every case, the sorts of facts that we could source to these will also be covered in book-length treatments that provide much more value to the reader than these sorts of references provide. — Carl (CBM · talk) 21:02, 19 August 2009 (UTC)

"do not differ significantly from what our ideal article" - Many wikipedia articles are not ideal and may never be, so why not link to expository articles ? Also links to free online sources are useful in that it is easier to check something online than go to the library, especially if your library doesn't have the item you want. Charvest (talk) 21:30, 19 August 2009 (UTC)

I am saying we should include these as "external links", not as references, because there are better things to use as references. There is also the issue of lack of context and lack of depth in short expository articles, which do not provide enough information to allow readers to actually learn much about the topic. For example, if our article presents various theorems without proof, we want to provide "references" that include the proofs that we omit, not "references' that just list the same theorems without proof. — Carl (CBM · talk) 21:38, 19 August 2009 (UTC)

I have created an external link template for the Encyclopedia at {{SEP}}.  Skomorokh  22:42, 19 August 2009 (UTC)

Bhatia–Davis inequality

I've just written a short article titled Bhatia–Davis inequality. I could use work both on itself and on links to it from other articles. Michael Hardy (talk) 18:11, 18 August 2009 (UTC)

I didn't find the result hard to believe, once I'd understood the extremal case; but I was a little surprised it wasn't more classical. I found this PDF which has plenty of context, at one level: http://www.collectionscanada.gc.ca/obj/s4/f2/dsk1/tape10/PQDD_0027/MQ50799.pdf. (Not either of the things you were asking for, I know). Charles Matthews (talk) 14:35, 20 August 2009 (UTC)

Sweeping revisions to differential of a function

I have just radically revised the whole article.

I deleted the "Disputed" tag I added earlier.

You'll notice the definition of total differential and partial differential. One of the various great virtues of the Leibniz notation is that it makes ideas like this so simple. Is there any easier heuristic argument for the chain rule for partial derivatives than that?

(And at this time, chain rule for partial derivatives is a red link! Should we remedy that?)

Also, I've proposed a merger with differential (calculus).

We should consider adding to the article the more advanced and otherwise different viewpoints, including 1-forms. Michael Hardy (talk) 16:52, 20 August 2009 (UTC)

....and now I see that someone else has drastically revised it after my edits. Michael Hardy (talk) 16:58, 20 August 2009 (UTC)

The chain rule in more than one variable is already covered in the chain rule article; see here. Although it does need a lot of work to be done to it. ~~ Dr Dec (Talk) ~~ 17:02, 20 August 2009 (UTC)

With regard to your observation that someone else had drastically revised the article after your own, I think it is fairer to say that your (welcome) revision occurred sometime in the midst of my own incremental revisions. As a matter of fact, I was about to do something similar in spirit to your first paragraph, but I was unable to save my revision due to an edit conflict. I do hope that our collaborative effort has, at least, brought the article a significant step along the road to being a worthy encyclopedia article. Sławomir Biały (talk) 17:59, 20 August 2009 (UTC)

Maths Pedagogy

Every so often it seems schools come up with some yet sillier way to make maths inaccessible. Lots of different words to learn about distinctions between different triangles, funny rigmaroles when adding or subtracting, points will be taken off for misspellings and suchlike. I noticed in article Negative and non-negative numbers someone put in raised minus as in ⁻5 for instance. Seemingly they are now learning to put in ⁺5 and ⁻5 to show the numbers are positive or negative and should say subtract, negative or opposite of in the appropriate situations. I was wondering if an article on such ideas might be an idea or what it should be called? I probably would have too strong a POV for it :) I suppose it would be something referenced from Mathematics education as I can see it growing quite large so it wouldn't fit within that. Dmcq (talk) 18:25, 20 August 2009 (UTC)

Well, we can't go creating an article just to rant about things we think are silly in trends in math ed. We can't even synthesize criticisms made by others. However, if you find some self-conscious organization or movement, about which there are reliable sources, that makes these criticisms, then you can write about it. --Trovatore (talk) 22:11, 20 August 2009 (UTC)

Already done: Tom Lehrer got there first. Kan8eDie (talk) 23:38, 20 August 2009 (UTC) (Edit: I was thinking of New Math)

If you ever wrote a parser, you'd know it's not totally trivial to distinguish unary minus from binary minus. I guess they want to make it easier for the kids by simplifying their parsing function :P Pcap ping 00:35, 21 August 2009 (UTC)

Fast algorithms

I read this article a while ago, and thought that it is someone's attempt at creating a page on efficient algorithms. Perhaps I am mistaken, but what in the world is a "fast algorithm"? Is this a field of research in computational mathematics? How is this different from the usual algorithm design that computer scientists do? --Robin (talk) 21:34, 20 August 2009 (UTC)

Well, here is some web page with a definition of a "fast algorithm": [28]. It would take some research in the computational complexity literature to see if this is actually a well-established term. — Carl (CBM · talk) 21:47, 20 August 2009 (UTC)

Do we have any experts in numerical algorithms here? I avoided that topic in grad school. In complexity theory "at large", "fast algorithm" is just too vague to have a definition. Pcap ping 22:57, 20 August 2009 (UTC)

What they seem to do is to consider bit complexity instead of assuming a RAM where you can add intergers increment an integer (of any length!) in O(1). It's obviously written by fokes outside US which use their own terminology... Pcap ping 21:54, 20 August 2009 (UTC)

The algorithms and concepts listed on that page seem very well-studied in the field of algorithms: Karatsuba algorithm, Divide and conquer algorithm, Coppersmith–Winograd algorithm, fast Fourier transform. Perhaps the word "fast" is just a translation artifact from Russian to English, with the word "efficient" being used in English instead of "fast"? I haven't ever read the term "fast algorithms" in the complexity literature, but maybe I'm not reading the right stuff. --Robin (talk) 21:58, 20 August 2009 (UTC)

Me neither. The complexity difference between a RAM and a plain Turing machine, which is what the use, is a logN factor. Pcap ping 22:05, 20 August 2009 (UTC)

Is it fast, as in fast transforms: fast fourier transforms, fast wavelet transforms, fast hadamard transforms etc... Charvest (talk) 22:16, 20 August 2009 (UTC)

... fast multiscale transforms, fast gauss transforms, fast Johnson-Lindenstrauss transforms, ... Charvest (talk) 22:19, 20 August 2009 (UTC)

fast hough transform, fast hartley transform, Fast Walsh Transform, fast m-transform, fast Karhunen-Loeve transform, fast jacket transform ... Charvest (talk) 22:27, 20 August 2009 (UTC)

The article tinkles a little alarm bell for me, not very loud, but enough that I'd at least like to ask: Is it standard practice to combine these things under the rubric of fast algorithms? If not, then the article might be a neologism, or original synthesis.

Also the technical definition of fast is unreferenced. Again I would like to know whether this is standard, or something abstracted by the editor who wrote it. --Trovatore (talk) 22:30, 20 August 2009 (UTC)

Here's a page talking about automating the process of creating fast algorithms: Automatic Generation of Transform Algorithms "it is possible to automatically generate fast algorithms for discrete signal transforms". Charvest (talk) 22:38, 20 August 2009 (UTC)

That does not appear to be what our article is about though. How is matrix multiplication related to that? Pcap ping 22:42, 20 August 2009 (UTC)

From http://www.ccas.ru/personal/karatsuba/algen.htm, which what is article is based on, it appears he's concerned with Kolmogorov complexity of evaluating a function with a given precision(?!) I don't have the patience to read all the stuff on his web page. The bottom line as I see it is that the article is based solely on that guy's web page, including the overreaching terminology. It's a paper that appeared in some "internal" Steklov proceedings. I think we need a better source to have a shot at understanding what's he saying there... In the mean time, the article should be moved to the creator's user space. Pcap ping 22:55, 20 August 2009 (UTC)

I think that guy is a chick. My uninformed random guess is that this is just another east/west split, and that if the Russian sources were in English then we would see this as just another esoteric topic that we would not mind as an article topic. — Carl (CBM · talk) 23:05, 20 August 2009 (UTC)

I was confused because Karatsuba that developed the original algorithm wasn't a chick. The chick is probably related to him. Pcap ping 23:18, 20 August 2009 (UTC)

(ec) Let's recap:

• My first impression was correct: the issue is bit complexity in operations on large integers (or possibly arbitrary precision reals as well); see Karatsuba algorithm or Toom–Cook multiplication.
• This article is not about random algorithms that have "fast" in their name. Nor is it about automatically generating algorithms for some transformations. It also does not involve Kolmogorov complexity; it just happens that Kolmogorov was also interested in this.
• The generic terminology "fast algorithm" is non-standard. It appears to be an attempt to define a class of algorithms that are like Karatsuba etc. It's surely non-standard because it doesn't appear in any of our other articles linked from it. Pcap ping 23:08, 20 August 2009 (UTC)

Browsing the literature starting with the elder Karatsuba's web page, and Google scholar, suggests that the term "fast" must have some meaning to people in the area, or they wouldn't use it as often. It's a fallacy to assume that our coverage here is half complete. — Carl (CBM · talk) 23:31, 20 August 2009 (UTC)

Fast in this context is actually well-defined later in the article (I've commented on the article's talk page). But what is still unclear to me is the importance of this notion. Pcap ping 23:48, 20 August 2009 (UTC)

If I understand correctly from the article, an algorithm is said to be fast if it is only log factors slower than the best known lower bound. An interesting concept, but I've never seen it before. --Robin (talk) 23:56, 20 August 2009 (UTC)

You mean slower than multiplication by a polylogarithmic factor. But why is this definition important? The article fails convey that... Pcap ping

Oh, I see. It's slower than multiplication by log factors (log factors = polylog factor). Which means an algorithm is called fast, if it runs in time Õ(n). I have no idea why this definition is important though. --Robin (talk) 00:35, 21 August 2009 (UTC)

Õ(M(n)) time indeed. Pcap ping 01:05, 21 August 2009 (UTC)

Which is the same as Õ(n) since M(n) = Õ(n) --Robin (talk) 01:21, 21 August 2009 (UTC)

Anonymous recursion

Although this has marked as a computer science topic (by changing its category), it doesn't contain any programming or the like, and it tries, but fails to define a mathematical concept. The article has good number of issues. See it's talk page. Pcap ping 02:01, 21 August 2009 (UTC)

I think that this sort of thing can be discussed on the article's talk page. If every bad article were reported on this page, everyone would be overwhelmed. — Carl (CBM · talk) 02:04, 21 August 2009 (UTC)

Okay, in the same vein however, the dubious notion of an "anonymous function" (as opposed to ??? in lambda calculus) appears at Fixed point combinator as well; see the talk page there. Pcap ping 05:41, 21 August 2009 (UTC)

Algorithm up for GA reassessment

Algorithm has been nominated for a good article reassessment. Please leave your comments and help us to return the article to good article quality. If concerns are not addressed during the review period, the good article status will be removed from the article. Reviewers' concerns are here. Wizardman 22:15, 18 August 2009 (UTC)

I found that article pretty terrible for me as lecture, like other work of Wvbailey's I've looked at; Random access machine comes to mind. It focuses on minutiae, most of which is barely relevant, to the point that one cannot see the forest because of the trees. The writing style making very frequent direct references to the sources with page numbers and in-text are very distracting to me. The first thing that came to my mind after I finished reading it is how true is what User:Donhalcon said in his goodbye to Wikipedia: "this is a multi-subject fan site." I'm not going to spend my time pissing on Wvbailey's parade. Just not worth the return on investment like Don said.Pcap ping 18:37, 22 August 2009 (UTC)

Kostant partition function

This article has been proposed for deletion. Would merging it to Weight (representation theory) be a good alternative to deletion? If so, or if there's a better merge target, could someone do the merge? My maths doesn't extend to understanding this. Fences&Windows 01:35, 21 August 2009 (UTC)

It should be kept. Someone removed the deletion tag. That is as it should be. Michael Hardy (talk) 03:48, 22 August 2009 (UTC)

Now the article has been expanded (it was very short previosly) and as Hardy writes, the deletion tag has been removed. I also think the article should be kept. Ulner (talk) 18:51, 22 August 2009 (UTC)

Excellent. It is still Greek to me, but if it's independently notable in maths then all is well! Fences&Windows 22:41, 23 August 2009 (UTC)

Mathematics deletion sorting list

I've recently been doing quite a bit of deletion sorting, and while many topics have associated deletion sorting lists, mathematics is a notable exception. I find this surprising given that maths is a subject that can be completely impenetrable to someone like me who has no understanding of almost everything above GCSE level. This means that there is often a need for input from someone able to understand the importance (or otherwise) of the subject being nominated.

My question therefore is whether people here feel there would be a benefit in creating such a list? Thryduulf (talk) 20:20, 23 August 2009 (UTC)

Mathematical articles that are proposed for deletion or nominated on AfD are noted in Wikipedia:WikiProject Mathematics/Current activity, which is maintained by a bot. Category:AfD debates (Science and technology) is also useful. I don't see much point to yet another list, but if someone wants to maintain it, then why not. Gandalf61 (talk) 20:44, 23 August 2009 (UTC)

Evenness of zero is under peer review

Comments welcome at Wikipedia:Peer review/Evenness of zero/archive1. (I suppose this'll be picked up on current activity soon enough, but why wait?) Cheers, Melchoir (talk) 03:31, 24 August 2009 (UTC)

(Wikimedia) Intersection categories

After having a look at math article alerts, as well as Jitse's activity bot, I concluded that a lot of that stuff could be done by a simple feature in Wikimedia: "intersection categories". Basically to find out if a math article is nominated for whatever, or needs expert input (cleanup and what not) could be done almost trivially if Wikimedia natively supported intersection of categories. I see that there's actually a request for enhancement on bugzilla; somebody even wrote the code, it just needs to be tested and committed. Perhaps you could weigh in on that? Pcap ping 07:28, 23 August 2009 (UTC)

P.S. There's a more generic, but still 3rd party Cat scan. Pcap ping 07:31, 23 August 2009 (UTC)

P.P.S. The {{expert-subject}} template is yet another (special purpose) implementation of intersection categories. Pcap ping 07:40, 23 August 2009 (UTC)

I see that an official extension that supports this does exist. It's called DynamicPageList, but it's only installed on wikinews. Pcap ping 10:32, 23 August 2009 (UTC)

Alas I fear this is one of the many good ideas on wikipedia which have a small chance of ever making it into en-wikipeida. This has been around the block several times Wikipedia:Category intersection was the most recent proposal. There does not seem to be a sufficient number of highly committed people to push this through, and the developers are wary. There are some very real performance issues and some big unanswered questions as to precise method of implementation. For the most part, people seem to work around the problem with various bots creating special purpose categories and third party tools.--Salix (talk): 13:09, 24 August 2009 (UTC)

Thanking Wikipedia

Just for fun, a quote: "We thank the anonymous referees of the conference and journal versions of the paper for providing useful comments and references, and the anonymous writers of the article on the central limit theorem in Wikipedia for leading us on to the Berry-Esséen theorem." Page 510 of the journal Algorithmica (2009), vol. 55, the paper "Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem" by Jaikumar Radhakrishnan, Martin Rötteler and Pranab Sen. Boris Tsirelson (talk) 16:03, 24 August 2009 (UTC)

Great find! Thanks for posting it here. --Robin (talk) 16:25, 24 August 2009 (UTC)

Hilbert space gradually moving towards GA

I'm in the process of bringing the Hilbert space article up to scratch for GA. It was delisted by User:Geometry guy last year, but it has progressed substantially since that time. It's almost in a shape that I would consider nominating for relisting as GA, but I thought I should solicit input here somewhat unofficially before doing so. Thanks, Sławomir Biały (talk) 18:11, 27 August 2009 (UTC)

I'm afraid this is probably off-topic, but is $\langle ,\rangle$ a good choice for denoting an inner product? I know it's fairly standard but the problem is that it conflicts with the other standard notation $\langle x,f\rangle =f(x)$ where f is a linear functional. For this reason, I use $(\cdot \mid \cdot )$ for inner products, and I don't think I'm in minority. I'm not proposing anything, but just wondering.

Also, a note to myself and the others: we need Operators on Hilbert spaces. Arguably, this is more important than Hilbert spaces. -- Taku (talk) 23:19, 28 August 2009 (UTC)

I see nothing wrong with using $\langle ,\rangle$. The potential conflict with a (somewhat uncommon) notation for the pairing of a vector space with its dual is not likely to lead to any major confusion. I find notation resembling the bra-ket notation aesthetically abhorrent, although perhaps because I have too often seen it abused in quantum mechanics. Also, (-|-) is certainly a minority notation in mathematics: much more common is to use a comma as the delimiter: (-,-). However this runs the obvious risk of confusion with an ordered pair. Sławomir Biały (talk) 01:23, 29 August 2009 (UTC)

I don't think this should be a really big deal. The Riesz representation theorem says that the Hilbert space inner product determines an isomorphism of the Hilbert space V with its dual V^*, and under that isomorphism, the inner product pairing transforms into the natural pairing of V and V^*. The article explains all this at Hilbert space#Duality, so after that subsection I see no reason why we should have to squint at each use of a pairing and try to determine whether it's the inner product or the duality pairing: We can just use $\langle \,,\rangle$ for both. If it's really necessary to make that distinction (e.g., before Riesz's theorem has been explained), then we should probably do what I remember Halmos doing in his Finite-dimensional vector spaces. He uses brackets for one pairing and parentheses for another, and at some point he has a section named "Brackets versus parentheses" where he explains how the two are really the same; afterwards he doesn't distinguish the two.

On another note, I can't see the left and right angle brackets on this browser, Firefox 2.0.0.20; I get a ? instead of an angle bracket. Ozob (talk) 20:13, 30 August 2009 (UTC)

There's no problem, this is just the vector-covector interpretation given to evaluating a linear function (covector) on a vector. ~~ Dr Dec (Talk) ~~ 20:29, 30 August 2009 (UTC)

Category:Markov chains and Category:Markov models

There is a naming dispute considering the correct name for the category for the main article Markov chain and related articles, see WP:CFD. 76.66.192.144 (talk) 03:20, 28 August 2009 (UTC)

Point on plane closest to origin

The article titled Point on plane closest to origin is in pretty sorry shape. I thought of correcting its many obvious failures to follow usual and useful Wikipedia conventions, but it's not clear that the article is worth keeping.

Using Lagrange multipliers for this thing that can be done by simple geometric or algebraic methods is not so different from some things I've seen actual mathematicians do, even if it is swatting a fly with a pile driver. But it's certainly needless complication. I'd think of two things: (1) inner-product-space methods; and (2) secondary-school algebra and geometry. Those two points of view seem worth mentioning if there is to be such an article. But Lagrange multipliers don't seem worth more than a terse statement. Michael Hardy (talk) 23:04, 28 August 2009 (UTC)

I would consider adding an discussion of the distance from a point to a subspace in the article Euclidean distance, perhaps. For now, I don't think the content justifies a separate article. Sławomir Biały (talk) 12:59, 30 August 2009 (UTC)

I would suggest that the article be proposed for deletion, since Wikipedia is not an indiscriminate collection of information ~~ Dr Dec (Talk) ~~ 20:46, 30 August 2009 (UTC)

Sep 2009

Wikipedia talk:WikiProject Mathematics/Archive 53

Oct 2009

Wikipedia talk:WikiProject Mathematics/Archive 54

Nov 2009

Wikipedia talk:WikiProject Mathematics/Archive 55

Dec 2009

Wikipedia talk:WikiProject Mathematics/Archive 56