Wikipedia talk:WikiProject Mathematics/Archive/2023/Feb

BIT predicate

Over on BIT predicate, we have an IP editor who seems intent on cramming as much off-topic notation-heavy WP:TECHNICAL detail as possible into the history section. More eyes on this would be helpful. —David Eppstein (talk) 21:50, 28 January 2023 (UTC)

@David Eppstein: The Ackermann coding is already discussed in the history section. It is clearly not off-topic. Where else would such content go?

That aside, your combative behavior over this constructive edit (calling it an "attack" and talking about "hurting my feelings") has been disturbing. One expects more maturity from a professor. See WP:AGF and WP:PA. 2601:547:501:8F90:6D91:586F:CC4B:73D2 (talk) 21:59, 28 January 2023 (UTC)

Your edit has been reverted by multiple people now. If you think there are good reasons for it, please open a discussion on the talk page of BIT predicate first so a consensus can be reached on whether this belongs in the history section, or in another section, or should not be in the article at all. PatrickR2 (talk) 16:13, 29 January 2023 (UTC)

@PatrickR2: What do you mean by "multiple people"? Also, see WP:OWNERSHIP. 2601:547:501:8F90:75EF:C82F:5D9:1C9 (talk) 23:20, 29 January 2023 (UTC)

Multiple, as in more than one: David Eppstein and Russ Woodroofe have both reverted you. 128.164.177.55 (talk) 16:12, 30 January 2023 (UTC)

WP:OWNERSHIP doesn't mean that editors who care about specific pages can't make arguments for their preferred versions or ask other editors to go to the talk page and establish some consensus before making significant changes. To quote that page, "Even though editors can never 'own' an article, it is important to respect the work and ideas of your fellow contributors. Therefore, be cautious when removing or rewriting large amounts of content, particularly if this content was written by one editor; it is more effective to try to work with the editor than against them—even if you think they are acting as if they "own" the article. [...] In many cases, a core group of editors will have worked to build the article up to its present state and will revert edits that they find detrimental in order, they believe, to preserve the quality of the encyclopedia. Such reversion does not indicate an "ownership" problem [...] Where disagreement persists after such a reversion, the editor proposing the change should first take the matter to the talk page, without personal comments or accusations of ownership. In this way, the specifics of any change can be discussed with the editors who are familiar with the article, who are likewise expected to discuss the content civilly." –jacobolus (t) 02:26, 1 February 2023 (UTC)

about Delta invariant

I suggest moving this article to the drafts space. I think the subject of this article meets WP:GNG, but I don't think this article meets the criteria for a stub. I thought about moving this article to the draft space, but WP:DRAFTIFY said articles older than 90 days should not be draftified without prior consensus at AfD, so it seems necessary to discuss it first. If someone extends this article, I will withdraw this suggestion. thanks ! SilverMatsu (talk) 11:22, 31 January 2023 (UTC)

No need to draftify. The content of this article is essentially reduced to an implicit link to the definition given in another article. So, I'll redirect this article to the anchor that I have already added in that article. D.Lazard (talk) 12:06, 31 January 2023 (UTC)

 Done D.Lazard (talk) 12:34, 31 January 2023 (UTC)

I agree. Thank you ! --SilverMatsu (talk) 13:30, 31 January 2023 (UTC)

Just popping in to say that there is another notion of delta invariant in K-stability of Fano varieties (see K-stability_of_Fano_varieties#Delta_invariant) which is probably mildly more esoteric than the notion for curves. I'm not suggesting anyone do anything with this information but if the article Delta invariant was to return it could even be a disambiguation page. Tazerenix (talk) 01:37, 1 February 2023 (UTC)

Thank you for letting me know. I added Template:Redirect to the top of the section. If someone adds an explanation about another notion of delta invariant to wikipedia, I think that they will create separate articles for each notion, or add explanations to existing separate articles for each notion, so create a Dab page at that time I agree that there is a need.--SilverMatsu (talk) 03:42, 1 February 2023 (UTC)

Root of unity modulo n

I am not sure that this article is not ready to have its own. It has lack context and many things. Most of the texts, as I glanced at, especially in this part, use many second-person pronouns; however, MOS:YOU mentions that one should avoid such words. Because of these problems, would it be possible to merge it into Roots of unity? Dedhert.Jr (talk) 15:14, 3 February 2023 (UTC)

I have cleaned the lead up to understand the real content of the article. IMO, Root of unity modulo n, Primitive root modulo n and Carmichael function must be merged in a single article, which could be called Root of unity modulo n. D.Lazard (talk) 17:10, 3 February 2023 (UTC)

would it be possible to merge it into Roots of unity? No. --JBL (talk) 22:29, 3 February 2023 (UTC)

Discussion at Help talk:Citation Style 1§ Proposal: Add parameter |eudml=

 You are invited to join the discussion at Help talk:Citation Style 1§ Proposal: Add parameter |eudml=. Need advice on whether the European Digital Mathematics Library (Parameter |eudml=) meets WP:GNG. thanks ! SilverMatsu (talk) 07:06, 4 February 2023 (UTC)

what is a cantellated great icosahedron?

Ya got yer

• great icosahedron (regular)
• truncated great icosahedron
• great icosidodecahedron (rectified)
• truncated great stellated dodecahedron (degenerate)
• great stellated dodecahedron (regular)

But where are the cantellate (great rhombicosidodecahedron is something else) and the omnitruncate? Are they also degenerate? It would be good to note that somewhere. —Tamfang (talk) 05:39, 5 February 2023 (UTC)

This type of thread is better reserved for Wikipedia:Reference desk/Mathematics. Partofthemachine (talk) 05:42, 5 February 2023 (UTC)

I put it here because on Refdesk (with which I am better acquainted than with Projects) my last sentence is likely to provoke "that belongs on the relevant Talk page(s)." Because you ask nicely I'll try it there, omitting that sentence. —Tamfang (talk) 06:28, 5 February 2023 (UTC)

Project-independent quality assessments

See Wikipedia:Village pump (proposals)#Project-independent quality assessments. This proposes support for quality assessment at the article level, recorded in {{WikiProject banner shell}}, and inherited by the wikiproject banners. However, wikiprojects that prefer to use custom approaches to quality assessment can continue to do so. Aymatth2 (talk) 20:23, 6 February 2023 (UTC)

RfD requiring input

Input is requested at the RfD concerning the target of the redirect page Free term. 66.44.62.177 (talk) 01:13, 8 February 2023 (UTC)

Lead Sentence to Integral

I randomly came across this village pump that points at the lead sentence is... not hitting the mark. Its too complex for a novice, not useful to an expert, and generally not helpful. I would generally agree. Now I know I should be be bold and change it, but I am not sure how things have changed in the decade since I lasted edited math articles regularly. Here are my thoughts about the sentence, I thought I would see if there was any agreement before I tried changing anything. For reference the sentence currently is:

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data

Here are my issues

• Assigning numbers to functions is both trying to be too technical and failing to be technically accurate. Its tip-toeing around integral as an operator, and what do you say to someone who said "Wait, you said a number and infinity is not a number, my calc prof said so but integrals can be infinite." or "You talk about displacement, isn't displacement a vector and not a number."
• in a way that describes I legitimately do know this means. Is way a reference way to linearity?
• displacement, area, volume, and other concepts feels like we are cramming too many applications in for a first sentence, we will get to all of these in a bit.
• combining if we are jumping to the hole infinitesimal thing, is there a reason not to at least say its a sum?
• infinitesimal is a term one typically only encounters in calculus or mathematical contexts that assume calculus. So most readers who understood this term would already know what an integral was.
• data the word is so generic its distracting, it makes me thing 'Am I working with functions and numbers or more general data?'

Does anyone else on the math project feel it needs a rewrite, or are we generally fine with it as it is? I bring this up here instead of the talk page of the article, because I came across it in the village pump, so I see it as a good community discussion.Thenub314 (talk) 21:55, 9 February 2023 (UTC)

What a terrible first sentence. Surely it is not hard to come up with something much better. Just as an example:

"In mathematics, an integral is a way of computing the area under a function, or more generally the volume under the graphs of functions of more than one variable. The region under the graph of a function may have an irregular shape (so that the familiar formula of area = base x height for regular shapes does not apply), and so integration uses the techniques of calculus and infinitesimals to compute areas and volumes."

Now that you have alerted WP:MATH to this, the discussion can be moved to the talk page. Tazerenix (talk) 21:56, 9 February 2023 (UTC)

This is not constructive, but: I notice that Integral was introduced as an example in that discussion as follows: For example, look at Mensural notation, a very technical and complex subject in music. ... Now look at Integral, which is a very basic concept in maths. I can't imagine trying to discuss this subject with someone who suffers from this degree of misunderstanding about technicality, complexity, and simplicity.

Separately, "the area under a function" is a no-go for many reasons. --JBL (talk) 23:37, 9 February 2023 (UTC)

I think that thinking "the area under a function" is a no-go is exactly what leads to an unreadable lead sentence. It captures 90% of the use case of integrals, and what they were originally invented for, and can easily be expanded upon in the next sentence or two. Tazerenix (talk) 00:51, 10 February 2023 (UTC)

"the area under a function" is a meaningless phrase. But also it is false that this is what they were originally invented for -- no one is or ever has been interested in computing areas under graphs of functions, that's a totally artificial framework that happens (miraculously!) to extend to allow one to compute interesting things. --JBL (talk) 18:09, 10 February 2023 (UTC)

An integral should be described off the bat as a continuous analog of a sum. –jacobolus (t) 02:36, 10 February 2023 (UTC)

"In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and other ways of measuring shapes." XOR'easter (talk) 12:37, 10 February 2023 (UTC)

It looks much better after your changes. Thanks for dealing with infinitesimal properly. I'd make the first sentence more general, e.g., In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta and other physical quantities. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:08, 10 February 2023 (UTC)

This addition is much too physics-specific for my taste. It makes it look like integrals are only used for physical quantities. Many integrals are unphysical. Areas and volumes can be but are not always physical. —David Eppstein (talk) 17:44, 10 February 2023 (UTC)

For a concrete example, a cumulative distribution function in probability is not about summing a physical quantity over a geometrical shape. It might be better to say that an integral is used to sum up the continuous values of a function in some part of its domain. We could still offer physical examples such as position displacement as the integral of velocity for some duration or total mass as the integral of mass density in some region. –jacobolus (t) 19:15, 10 February 2023 (UTC)

I'm going to continue to not be constructive (sorry to all): "continuous" and "domain" are both jargon, and "sum up he continuous values of a function" does not sound to me like it could be deciphered by someone who didn't already know what it meant. An integral of velocity is a displacement (also jargon, sadly), not a position. --JBL (talk) 20:30, 10 February 2023 (UTC)

I agree with you that in articles with topics as fundamental as integral it is best to err in the direction of too chatty and novice-friendly than the other way. Ideally a non-technical reader should be able to read the first 2–3 sections and have at least a vague idea what concept is being defined and what its context is.

I think it's potentially fine to wiki-link terms like velocity, displacement (geometry), domain of a function (though that article's lead is too technical) or 'continuous' which many readers will have heard of before (though Wikipedia in general needs a much better basic explanation of what 'continuous' / 'continuum' means than provided at continuous function, linear continuum, list of continuity-related mathematical topics which redirects from Continuity (mathematics), etc.).

What kind of definition of integral would you propose that can be understood by a layperson such as a middle school student or a politician without being too imprecise for someone like a math undergraduate?

It’s also sometimes possible to take a couple of swings at definitions within the same article lead, aimed at different audiences. –jacobolus (t) 21:47, 10 February 2023 (UTC)

Silvanus Thompson says:

The great secret has already been revealed that this mysterious symbol ${\textstyle \int }$, which is after all only a long S, merely means “the sum of,” or “the sum of all such quantities as.” It therefore resembles that other symbol ${\textstyle \sum }$ (the Greek Sigma), which is also a sign of summation. There is this difference, however, in the practice of mathematical men as to the use of these signs, that while ${\textstyle \sum }$ is generally used to indicate the sum of a number of finite quantities, the integral sign ${\textstyle \int }$ is generally used to indicate the summing up of a vast number of small quantities of indefinitely minute magnitude, mere elements in fact, that go to make up the total required. Thus ${\textstyle \int dy=y}$, and ${\textstyle \int dx=x}$.

Any one can understand how the whole of anything can be conceived of as made up of a lot of little bits; and the smaller the bits the more of them there will be. Thus, a line one inch long may be conceived as made up of $10$ pieces, each ${\textstyle {\tfrac {1}{10}}}$ of an inch long; or of $100$ parts, each part being ${\textstyle {\tfrac {1}{100}}}$ of an inch long; or of ${\textstyle 1{,}000{,}000}$ parts, each of which is ${\textstyle {\tfrac {1}{1{,}000{,}000}}}$ of an inch long; or, pushing the thought to the limits of conceivability, it may be regarded as made up of an infinite number of elements each of which is infinitesimally small.

Yes, you will say, but what is the use of thinking of anything that way? Why not think of it straight off, as a whole? The simple reason is that there are a vast number of cases in which one cannot calculate the bigness of the thing as a whole without reckoning up the sum of a lot of small parts. The process of “integrating” is to enable us to calculate totals that otherwise we should be unable to estimate directly.

[...]

–jacobolus (t) 21:59, 10 February 2023 (UTC)

What kind of definition of integral would you propose that can be understood by a layperson such as a middle school student or a politician without being too imprecise for someone like a math undergraduate? I think this is an extremely difficult question; hence the labeling of my comments as non-constructive, the small font, and the apologies. --JBL (talk) 22:52, 11 February 2023 (UTC)

Clearly the answer is that the integral computes the area under the graph of a function? Tazerenix (talk) 23:17, 11 February 2023 (UTC)

What part of a circle is under its perimeter? XOR'easter (talk) 14:39, 12 February 2023 (UTC)

The whole disk is under the graph of the function f(x,y)=1 restricted to the disk.

Anyway, I didn't say the integral *only* computes the area under graphs of functions. But if our standard is what would a layperson or politican understand, you are all assuming way too much mathematical knowledge to think they can parse the sentence "The integral is the continuous analog of the sum" or "The integral sums up an infinite number of infinitesimal quantities" Tazerenix (talk) 20:33, 12 February 2023 (UTC)

If that meaning of "under the graph of the function" already makes sense, you're not learning what an integral is from Wikipedia. XOR'easter (talk) 14:36, 13 February 2023 (UTC)

That is a special case and wont cast much light on, e.g., ${\textstyle \iiint _{D}\mathbf {r} \times \mathbf {p} \,dx\,dy\,dz.}$ The first sentence should be general. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 22:02, 12 February 2023 (UTC)

Touché -- the difficult question is not a definition, but a first sentence of an encyclopedia article with the requested properties. --JBL (talk) 19:40, 13 February 2023 (UTC)

I suggests the following for the firat paragraph:

In mathematics, an integral is, roughly speaking, the sum of infinitely many quantities that are each infinitely small. For example, a surface in a plane can be divided into narrow strips whose areas are approximated by the product of their widths by their lengths; when the widths of the strips tend to zero, their areas tend each to zero, and their number tend to the infinity; the infinite sum of these infinitesimal areas form an integral equal to the area of the surface. Also, the distance traveled by a vehicle, is the product of the speed by the time of the travel; when the speed varies, one divides the time in smaller and smaller intervals. At the limit, the traveled distance is an integral that is the sum of the products of infinitively small time intervals by the instantaneous speed during each interval.

Integration is the process of computing an integral. It is, with differentiation, a fundamental operation of calculus, and is widely used in all mathematics, as well as in physics, and most sciences and technologies that use mathematics.

I have removed the notes and citations, which should be kept is this is accepted. Also, some more linkd should be added; however this must be done with care, as an informal explantion must not be overlinked.

Feel free to improve this draft.

IMO, such informal examples is the best way for explaining what is integration and why it is used almos everywhere. Clearly, if this is accepted, some more work is needed for the remainder of the lead and of the article. D.Lazard (talk) 16:02, 12 February 2023 (UTC)

I have painful memories of trying as a teenager to make sense of such language in "Calculus for the Practical Man", and I only started to understand Calculus when I read a copy of Thomas's Calculus and Analytic Geometry, loaned by a Jr. High teacher for me to read in class, which used Epsilontics. What about In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta, other physical quantities, and more abstract physical or mathematical entities. It can be thought of non-rigorously the sum of infinitely many quantities that are each infinitely small. ...?? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 22:02, 12 February 2023 (UTC)

Collapsed proofs: WP:ACCESSIBILITY concerns

Hello, a common method of organising mathematical proofs seems to be to place them inside {{collapse top}} and {{collapse bottom}}. This is specified in Wikipedia:WikiProject Mathematics/Proofs. However, this conflicts with two broader guidances Wikipedia:Manual of Style#Scrolling lists and collapsible content and Wikipedia:Accessibility. If there is some reason why the local consensus should override the sitewide consensus, I'd like to know. Otherwise, if this is an oversight, then does anyone have any alternatives that would be suitable? Pinging users who participated in the proceeding discussion on my talkpage: @DMacks and D.Lazard: Mako001 (C)  (T)  🇺🇦 04:54, 9 February 2023 (UTC)

I want to say: I don't like collapsed proofs either. For example, I noticed some people prefer to print out Wikipedia articles and then the print-out wouldn't contain collapsed materials. If it is desirable to hide proofs, for a better flow, for example, then a better solution is to put the proofs in the footnotes. -- Taku (talk) 07:49, 9 February 2023 (UTC)

It should be technically possible to implement this in such a way that a print stylesheet expands them automatically, though many readers may prefer to have proofs collapsed even when printing.

Putting long proofs in footnotes is not a good solution in practice. They are then detached from the content and hard to read. –jacobolus (t) 02:25, 10 February 2023 (UTC)

But putting them in {{collapse top}} and {{collapse bottom}} makes them impossible to read for many (if not most) readers (i.e. anyone using a mobile device). Setting all proofs to auto expand would "solve" the accessibility problem, but would make (for want of a better term) "a bit of a mess". Mako001 (C)  (T)  🇺🇦 11:34, 10 February 2023 (UTC)

I don't ever read Wikipedia on a mobile device, but I just navigated to Homomorphism#Epimorphism on my phone and the proof at the bottom of that section (intended to be collapsable and collapsed by default) shows up inline in the content not possible to collapse.

This seems like a problem; that content should be collapsed and only show when a reader tries to expand, and I would assume it would be the same on either desktop or mobile. Why can't the CSS/javascript be set up so that mobile devices can properly expand/collapse these sections? –jacobolus (t) 18:54, 10 February 2023 (UTC)

@Jacobolus: Hmm, I'm seeing the same thing. You would have to ask the WMF why the Minerva skin (mobile view) doesn't work with collapsible content properly. In any case, we need to focus on what we are able to do something about. Mako001 (C)  (T)  🇺🇦 01:50, 11 February 2023 (UTC)

Well, collapsing the proof usually makes the article more readable (unless the article itself is about the proof of something), especially if there are multiple proofs and each one is long. PatrickR2 (talk) 21:57, 9 February 2023 (UTC)

Proofs are in many cases irrelevant and distracting to most readers while still being helpful (or even indispensible) for readers who care about the details for one reason or another. Figuring out how to elide tedious or distracting details is a persistent problem that all mathematical writing must deal with. There are no perfect answers. Some possibilities, none of which will satisfy all authors or all readers: (1) skip proofs altogether but link to a source which includes them, (2) put proof sketches but leave out the details, (3) put proofs in a collapsing section, (4) put proofs in a footnote, (5) put proofs in a floating box to the margin of the main content, (6) put full proofs inline in the text. I think local per-page consensus is probably better to aim for than a blanket site-wide policy. One more thing to notice: Wikipedia mobile rendering by default collapses article sections, and readers must tap to expand them; so collapsing elements are clearly not entirely anathema to Wikipedia. –jacobolus (t) 02:30, 10 February 2023 (UTC)

Sure, there is no perfect solution. In fact, solutions probably would depend on articles. I would however say: if the proofs are irrelevant, those proofs should not be in the article in the first place. Unlike research papers or monographs, in Wikipedia, we don’t need to justify the results with proofs; references to the reliable sources would do. If the proofs are relevant, they don’t need to be hidden. It’s actually the matter of why we put proofs in the first place. The reason is that proofs are integral parts of mathematics. It’s sometimes important to know how some facts are true not just if they are true. —- Taku (talk) 05:53, 10 February 2023 (UTC)

There is no absolute standard by which we can decide what is "irrelevant". Wikipedia needs to serve a very wide range of audiences, ranging from members of the general public who have a curiosity about some topic's basic definition and context, through students who are trying to learn about something for the first time and don't yet understand the details, through practitioners in related fields who want a quick reference of concrete results they can use, through historians who want to know the evolution of an idea with numerous citations and experts who want to read generalizations and relations to more advanced topics.

The problem with proofs (though other kinds of technical content have similar issues, such as large tables of statistical data, detailed timelines, code samples for complicated algorithms, details of chemistry experiments, or full phylogenetic trees) is that they are both necessary to make convincing mathematical arguments, while also being difficult to skim (especially for non experts) and taking significant effort to fully comprehend. If non-specialists hit a wall of formulas or a detailed proof they are likely to be intimidated, discouraged, or bored, and at worst bounce away even if they might be interested in other parts of the page; by contrast, if specialists can’t see a proof they will be unable to fully validate the claims made, and if students can’t see proofs they may develop a false conception about whether/why something is true and what is needed to demonstrate that.

The point of collapsing the proofs is that it is effectively the same as removing them for that part of the audience who wants to skim past or ignore them, except they can still be seen for that part of the audience who is interested.

Not every mathematical claim needs to be proven in an encyclopedia article (probably most don’t), but personally I think there are many pages that would benefit from including a few more (collapsed) proofs of statements that are currently just stated. YMMV. –jacobolus (t) 06:27, 10 February 2023 (UTC)

So, suggestion: When using {{refn}}, you can give a footnote a name, like "Proof", which displays in the article like this . This would make it clear where the proof is, leave it acessible to all readers, but still move it out of the way. Would this work? Mako001 (C)  (T)  🇺🇦 11:27, 10 February 2023 (UTC)

There are different reasons for including or not a proof in Wikipedia. Proofs deserve to be included when they provide insights on a result and the involved concept; in this case, they must be given is plain text and not collapsed. On the other hand, a long techncal proof may have no encyclopedic value if a reference for it is provided.

I see several reasons for providing proofs that are not included in the flow of the text, which are related to WP:Verifiability and WP:LEAST. In many articles, properties or formulas are presented as bulleted lists (for example, List of integrals#Integrals of simple functions and Heronian triangle#Properties of side lengths). In this case, per WP:Verifiability, as source is normally provided for each item. This is rarely done, and when it is done, it is boring for the reader to get access to many sources. So, providing a proof allows readers to verify the assertions without searching in the literature. Also, in some cases, some of the listed properties may appear as "magic", and some readers may want to understand why they are true without accessing the provided source. In both cases, putting the proof in an explanatory footnote seems the best solution. An example of this is Heronian triangle#Properties of side lengths, where I have added such footnotes because I was too lazy for searching the sources.

In my opinion, the cases where collapsed proof are the best solution are rare. The main case is for a rather long proof that is too technical for the article that contain it, and for which a single and not too technical source is hardly to find. I have encountered this in Homomorphism#Monomorphism and Homomorphism#Epimorphism. In particular, in the latter section, the sentence the two definitions of epimorphism are equivalent for sets, vector spaces, abelian groups, modules (see below for a proof), and groups requires verifiability, and I do not know any source that does not requires a good knowledge of category theory. This the reason for which I have added a proof in a collapsed box (at the end of the section, for not breaking the flow).

In summary, for a guideline, I recommend something like For a proof that, otherwise, would break the flow of reading, use a footnote, and reserves collapsed boxes at the end of the section for exceptional cases. — Preceding unsigned comment added by D.Lazard (talk • contribs)

It is my understanding that collapsible proofs do not actually break accessibility. The relevant guideline is MOS:PRECOLLAPSE, and it is simply that in the absence of JavaScript and/or CSS, the content is not hidden. The templates collapse top/bottom have been implemented in accordance with this guideline and fallback gracefully to show the content in the absence of JS. I saw some other comments too that screenreaders work fine with collapsed sections (didn't save the link though). So there no accessibility problem with collapsing proofs. It is only MOS:COLLAPSE which states "Collapsible templates should not conceal article content by default upon page loading." which explicitly contradicts the usage of collapsed proofs. And arguably, if the proofs were expanded by default on page load, it would be following the guideline.

Now as far as actual style, the Wikipedia:WikiProject_Mathematics/Proofs sort of hints that long proofs are not suitable for WP. For example, considering the Homomorphism page, I think it would be better to cite the proofs that require a good knowledge of category theory, than to do WP:OR and construct an elementary proof out of whole cloth. The elementary proofs can be added to other sites such as Wikibooks, ProofWiki, etc. Mathnerd314159 (talk) 18:07, 10 February 2023 (UTC)

D.Lazard has already said what I wanted to say but better. But to add his and to respond to jacobolus: I think it's essentially the matter of what proofs we should include and what we shouldn't. To echo D.Lazard, we shouldn't include proofs that merely serve to justify some facts; references to reliable sources are preferrable ways, like any other facts in Wikipedia. However, some proofs do serve to help understand the concepts or the facts discussed in the article. Here is an example: the article Bounded operator includes a (short) proof of the fact that an operator is bounded if and only if it is continuous. This fact can be easily referenced by reliable sources but giving the proof is helpful, since a reader can see how the continuity is used and can also see how the proof actually proves stronger continuity (Lipschitz continuity). Hiding it is not only unnecessary, but would make the article less helpful. There does arise an occasion where we feel a need to give a proof or some short justification to defend ourselves against experts who find the statement suspicious (e.g., some algebraic fact is stated without the Noetherian assumption.) In such a case, the use of footnote is a better solution, since most readers wouldn't care about such technical issues. -- Taku (talk) 09:12, 11 February 2023 (UTC)

Very well said. I agree with this. PatrickR2 (talk) 21:26, 13 February 2023 (UTC)

There is actually one more case: de Rham theorem currently redirects to de Rham cohomology; the theorem is discussed there but without a full proof. We could add a collapsed full proof but a better solution is to stop the redirecting and then put a non-hidden full proof to the de Rham theorem article. (By the way, which I think we should do.) —- Taku (talk) 09:29, 13 February 2023 (UTC)

I've seen texts with proofs in an appendix. How about putting proof for foo in foo/proofs and linking to them? — Preceding unsigned comment added by Chatul (talk • contribs) 06:08, 13 February 2023 (UTC)

That has been determined to go against WP:SP which states that "using subpages for permanent content that is meant to be part of the encyclopedia" is disallowed. Mathnerd314159 (talk) 00:48, 14 February 2023 (UTC)

If the proof itself is notable, a self-contained topic, and would overload the main page on the theorem, then WP:SPLITting it into a separate page is widely endorsed. What's forbidden is the slash to indicate a subpage, and the general idea of each article needing to be its own topic. We already do that: for Fermat's Last Theorem, we have splitoff articles Proof of Fermat's Last Theorem for specific exponents and Wiles's proof of Fermat's Last Theorem. This approach also helps provide a criterion for whether to include the proof: whether external sources actually comment on it beyond merely stating the proof itself. DMacks (talk) 04:50, 14 February 2023 (UTC)

References

should we have an article for a 'geometric figure'?

Geometry is often defined or described as the study of the properties/relationships of "geometric figures", but we don't really have a good basic definition/explanation for what that means. The existing article shape seems focused on description of a "single" object of some sort (e.g. a polygon, closed curve, or whatever), and especially with classifying shapes up to similarity (i.e. separating "shape" from "size"), whereas the article configuration (geometry) seems primarily concerned with incidence relations between finitely many / discrete collections of points and lines, rather than e.g. metrical relationships like distance or angle, pencils of lines, arbitrary curves, etc. Should we try to add a new such article, and what would be a good accessible definition? Geometric figure currently redirects to Shape § In geometry which doesn’t seem like it really covers the topic.

Related, geometric object currently redirects to Geometry § Objects which has no basic definition, just a (short, nowhere near exhaustive) list of specific types: {Lines, Planes, Angles, Curves, Surfaces, Manifolds}. Nowhere in that page are such basic concepts (related to geometric objects) defined/discussed as 'locus', 'envelope', 'pencil', 'join', 'meet', 'intersection', etc. Perhaps we could also make a page about that one. Anyone have a suggestion of a good definition, or an idea which sources to look to for one? (And while we're here, mathematical object could use a lot of help.) –jacobolus (t) 01:08, 14 February 2023 (UTC)

I don't understand the distinction you are trying to make between single objects and multiple objects. It seems to be a distinction of grammar and convention rather than anything intrinsic. A finite set of points is both a single set and multiple points. A polygon, which you describe as a single object, could be a finite set of vertices and edges, an infinite set of boundary points, or a different infinite set of boundary and interior points. Even a point, which you might think of as unavoidably singular, could be considered as equivalent to a line in the projective dual plane, and therefore equivalent to an infinite set of points on that dual line. —David Eppstein (talk) 01:20, 14 February 2023 (UTC)

You are missing my point; I assume I wasn't clear enough. I am not trying to make any claim about what what the limits of a "geometric object" could be, which types of objects should be considered primitives (in one or another context), whether an object should be defined in terms of set theory, or any other such thing. (Though those are all worthy questions which should probably be discussed somewhere on Wikipedia.)

My claim is that the article shape as it currently exists does not describe any arbitrary collections of geometric primitives, but only certain ones which it considers to be "shapes", which is a small subset of what I would consider to be the universe of "geometric figures". We don't really anywhere a good basic explanation or definition about these topics.

If I want to wiki-link from any arbitrary article to "geometric object" or "geometric figure" (or whatever similar term you might prefer, perhaps "configuration" or "arrangement" or ...?) there is currently no good endpoint for that wiki-link to point. –jacobolus (t) 01:48, 14 February 2023 (UTC)

So this discussion is a bit more concrete, here are definitions from Kisilev (Geometry):

1. Geometric figures. [...] A set of points, lines, surfaces, or solids positioned in a certain way in space is generally called a geometric figure. Geometric figures can move through space without change. Two geometric figures are called congruent, if by moving one of the figures it is possible to superimpose it onto the other so that the two figures befome identified with each other in all their parts.

2. Geometry. A theory studying properties of geometric figures is called geometry, which translates from Greek as "land-measuring". This name was given to the theory because the main purpose of geometry in antiquity was to measure distances and areas on the Earth's surface.

First concepts of geometry as well as their basic properties, are introduced as idealizations of the corresponding common notions and everyday experiences. [...]

And Hadamard (Lessons in Geometry):

1. A region of space which is bounded in all directions is called a volume. [...]

Any collection of points, lines, surfaces, and volumes is called a figure. [...]

2. Geometry is the study of the properties of figures and of the relations between them. [...]

–jacobolus (t) 03:35, 14 February 2023 (UTC)

As an example of the kind of wiki-link I am thinking of, in angle we have:

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

This definition of angle originated with Sidorov (Encyclopedia of Mathematics) which more explicitly uses the term geometric figure. But the word figure in the angle article is not defined or wiki-linked, and it may not be immediately obvious to all readers what it means. Similarly, in congruence (geometry) we have:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

In this case there is neither definition nor link for what 'figure' means, though the term is used throughout the article. Then we have geometry itself:

Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures.

Again, no explanation anywhere of what figure means. In polygon we have:

In geometry, a polygon (/ˈpɒlɪɡɒn/) is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

But in this case figure is wiki-linked to shape, which defines:

A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.

From there, graphical representation links to graphics, which defines:

Graphics (from Ancient Greek γραφικός (graphikós) 'pertaining to drawing, painting, writing, etc.') are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain.

This does not seem like a correct/adequate definition for this purpose. In my understanding the word figure in geometry refers to the collection of geometric objects and their specified (or derived) relationships, rather than a physical picture drawn on a piece of paper. I think it would be useful to have a better definition of geometric figure somewhere, because in my opinion no current Wikipedia article adequately handles this. –jacobolus (t) 04:24, 14 February 2023 (UTC)

If I understand right, it does seem weird to speak of a figure consisting of one circle and one triangle as a single shape, linguistically speaking. Maybe the shape article should be renamed as a figure? A figure seems a bit more general. —- Taku (talk) 18:35, 14 February 2023 (UTC)

Basic Question

OK, I have a super basic question because I am rusty. How does the archiving of talk pages work? I thought it was done by bots, but visiting some pages I edited a decade ago, they have these enormous talk pages going back a decade. Is this done manually? Thenub314 (talk) 15:58, 15 February 2023 (UTC)

@Thenub314 It's only automatic if the page has been set up for auto archiving. If you think there are talk pages that need archiving manually please see Help:Archiving a talk page for suggested methods. Nthep (talk) 16:35, 15 February 2023 (UTC)

great books about calculus

Hello, I want to expand and update the contents such as integral, differential, Fourier series, limits of continuity of functions by using two very rich and important books in the book of calculus.

references:

aetemad.iut.ac.ir https://aetemad.iut.ac.ir › filesPDF Essential calculus with applications / by Richard A. Silverman.

stewartcalculus.com https://www.stewartcalculus.com Stewart Calculus Textbooks and Online Course Materials

Mohammad.Hosein.J.Shia (talk) 09:33, 15 February 2023 (UTC)

It's been more than half a century since I looked at them, but I was impressed at the time by

• Apostol, Tom M. (1960). Mathematical Analysis: A Modern Approach to Advanced Calculus. Addison-Wesley Publishing Company.
• Thomas, George Brinton Jr. Calculus and Analytic Geometry (6th ed.). Addison-Wesley Publishing Company. ISBN 978-0201162905.

Both of these are available in more recent editions. Also,Apostol has written a two volume Calculus book that I would certainly want to check if I were teaching a course. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:25, 15 February 2023 (UTC) -- Revised 15:52, 15 February 2023 (UTC)

You make a good point. By using these four books and other old and new books, we can expand the topics of mathematics. Mohammad.Hosein.J.Shia (talk) 13:36, 15 February 2023 (UTC)

Don't forget Spivak Thenub314 (talk) 16:00, 15 February 2023 (UTC)

ok

Mohammad.Hosein.J.Shia (talk) 16:31, 15 February 2023 (UTC)

Try Goursat (1904) https://archive.org/details/courseinmathemat01gouruoft/

Courant (1937) https://archive.org/details/ost-math-courant-differentialintegralcalculusvoli/

Apostol (1967) https://archive.org/details/calculus0000apos/

Piskunov (1969) https://archive.org/details/n.-piskunov-differential-and-integral-calculus-mir-1969/

–jacobolus (t) 15:12, 15 February 2023 (UTC)

According to the sources mentioned by Mr. Jacobolus, the best sources are ebooks. Mohammad.Hosein.J.Shia (talk) 16:31, 15 February 2023 (UTC)

These are all scans of physical books. –jacobolus (t) 17:06, 15 February 2023 (UTC)

We can search in this,book address[1]Mohammad.Hosein.J.Shia (talk) 07:40, 16 February 2023 (UTC)

Good article reassessment for Albert Einstein

Albert Einstein has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. Onegreatjoke (talk) 18:06, 17 February 2023 (UTC)

Move discussions about Prime and e (mathematical constant)

In Talk:Prime (disambiguation), it is discussed whether Prime should remain a redirect to Prime number or should be moved to Prime (disambiguation).

In Talk:e (mathematical constant)#Requested move 14 February 2023, it is discussed whether e (mathematical constant) should moved to e (number). D.Lazard (talk) 12:24, 18 February 2023 (UTC)

Proposal: move Gregory's series to arctangent series

I’m not sure if a discussion here is sufficient or if I should try a more formal process, but it seems like it might be an improvement to move Gregory's series to arctangent series, since this was discovered independently by Kerala school mathematicians in the 14th–15th century, Gregory in 1671, Leibniz in 1673, and perhaps various others. That article can then be expanded to fill in some of the historical/mathematical details of the separate derivations, as well as subsequent developments, connections to other areas of mathematics, etc.

We already have an article Madhava series which covers various other series as well as this one, but calling this Gregory's series seems to be somewhat pushing a POV, as all of the names "Gregory series", "Leibniz series", "Madhava series", "Nilakantha series", "Gregory–Leibniz series", "Madhava–Gregory series", "Madhava–Leibniz series", "Gregory–Nilakantha series", "Leibniz–Gregory–Nilakantha series", "Madhava–Nilakantha series", etc. can be found in the literature, with no clear preference. The name "arctangent series" also gets regularly used in practice (along with similar names like "arctan series", "inverse tangent series", "Taylor series for arctan", etc.), and it seems to me that a neutral descriptive title would best match Wikipedia:Article titles. Thoughts? –jacobolus (t) 06:55, 17 February 2023 (UTC)

I can agree with what he said Mohammad.Hosein.J.Shia (talk) 09:45, 17 February 2023 (UTC)

I did a Google search of "arctangent series" and "Gregory's series" and Gregory's series got six times as many hits. People can find arctangent anyway so I don't see how this proposal helps readers. It is not our duty to right great wrongs. As to the various other names there already is a Madhava series article. NadVolum (talk) 11:44, 17 February 2023 (UTC)

If I do a Google scholar search of papers since 1980, of the form: ("Gregory's series" OR "Gregory series") -"Madhava-Gregory" -"Leibniz-Gregory" -"Nilakantha-gregory" and likewise for other names, I get:

• Leibniz: 401 results (some sources mean specifically the series for arctan(1))
• Gregory: 349
• Madhava: 43 (many for the sine series)
• Nilakantha: 12
• Gregory–Leibniz: 159 (also counting Leibniz–Gregory)
• Madhava–Leibniz: 49
• Madhava–Gregory: 40
• Nilakantha–Leibniz: 2
• Nilakantha-Gregory: 4
• Madhava–Nilakantha: 6
• Madhava–Gregory–Leibniz: 19 (including other orders)
• Nilakantha–Gregory–Leibniz: 3

Then we also have (combining e.g. "arctan series", "series for arctant", and "series for the arctan"):

• arctangent: 205
• arctan: 224
• inverse tangent: 135
• inverse tan: 4

(The numbers for all of the above names are not entirely reliable, as these terms are also sometimes used for something else.)

But my basic point is that there’s not currently any strong consensus in the literature about what the name should be. –jacobolus (t) 18:18, 17 February 2023 (UTC)

While we are at it, "Gregory series" seems somewhat more popular than "Gregory's series". –jacobolus (t) 19:11, 17 February 2023 (UTC)

What is the point in doing a Google scholar search for this? It is secondary or high school mathematics. NadVolum (talk) 23:51, 17 February 2023 (UTC)

The point is to figure out what name is used in recent literature. A google scholar search is generally a much better way to count than a web search, as fewer of the results are complete garbage (e.g. SEO spam, blog posts, plagiarized copies of Wikipedia, etc.). Plenty of high school / undergraduate level topics are discussed in journals, books, etc. included in citation indices such as Google scholar. –jacobolus (t) 01:05, 18 February 2023 (UTC)

I suppose with ChatGPT it won't be long before mathematicians are scammed uysing messages mentioning Gregory series ;-) NadVolum (talk) 20:33, 19 February 2023 (UTC)

This discussion shows a redirect from Arctangent series to Gregory's series is needed.  Done. D.Lazard (talk) 12:42, 18 February 2023 (UTC)

Sounds like nobody else thinks there is any issue, so I’ll leave the title at Gregory's series. Hopefully we can still expand this over time, add some more figures, etc. Can anyone find a clear source where one of Madhava of Sangamagrama's followers directly credited him for the Maclaurin series for arctangent? The sources I saw seem to suggest that current scholarly consensus leans more toward this being worked out by one of Madhava's followers in the 15th century, instead of Madhava himself. Madhava series § Madhava's arctangent series quotes "Madhava's own words" but from what I can tell these are not Madhava's words, but those of a later follower. –jacobolus (t) 23:48, 19 February 2023 (UTC)

Khayyam-Newton expansion in math Ittihad

Hello, according to a discussion, I have read a method in books called Khayyam-Newton expansion in the unification of mathematics. I want to include this article in the Etihad (mathematics) article so that they can get acquainted with the common method of two scientists, one of whom is Iranian and the other is European.

I proceed according to the example This method is obtained in the form of Khayyam's triangle and Newton's union. ${\textstyle (a+b)^{5}=a^{5}+5a^{4}b+10a^{3}b^{2}+10a^{2}b^{3}+5ab^{4}+b^{5}}$Mohammad.Hosein.J.Shia (talk) 09:57, 17 February 2023 (UTC)

In English, the formula for expanding powers of a sum of two terms is called the binomial theorem. When the power is not a positive integer, there are infinitely many terms in the expansion and it is called the binomial series. And of course there is lots of related content in the articles on binomial coefficients and Pascal's triangle. --JBL (talk) 17:38, 17 February 2023 (UTC)

I can write an article about this topic Just wants a references Mohammad.Hosein.J.Shia (talk) 18:55, 17 February 2023 (UTC)

Of course, Pascal's triangle is also a complement to Khayyam's triangle. I mean, according to the Persian, German, English, and Arabic books, this theorem of Khayyam and Pascal's triangle can be generalized for coefficients. Mohammad.Hosein.J.Shia (talk) 10:01, 19 February 2023 (UTC)

By its generalization, you mean maybe the article we already have at multinomial theorem? —David Eppstein (talk) 20:44, 19 February 2023 (UTC)

Yes Mohammad.Hosein.J.Shia (talk) 11:12, 20 February 2023 (UTC)

Merge discussions about algebraic manifold

 You are invited to join the discussion at Talk:Algebraic variety#Merger proposal. --SilverMatsu (talk) 23:00, 20 February 2023 (UTC)

References in the article Point (geometry)

I have updated some references in the article Point (geometry). However, I could not find sources for corresponding the footnotes Bracewell 1986 and Schwartz 1950. I have found three sources that correspond to the footnotes. Any assistance would be appreciated. Dedhert.Jr (talk) 12:44, 23 February 2023 (UTC)

Just guessing but it seems plausible that they are

• Bracewell, Ronald N. The Fourier transform and its applications. Third edition. McGraw-Hill Series in Electrical Engineering. Circuits and Systems. McGraw-Hill Book Co., New York, 1986. xx+474 pp. ISBN: 0-07-007015-6
• Schwartz, L. Théorie des distributions. Tome I. (French) Publ. Inst. Math. Univ. Strasbourg, 9. Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1091 Hermann & Cie, Paris, 1950. 148 pp.

--JBL (talk) 18:12, 23 February 2023 (UTC)

Thank you. I knew that the footnote Bracewell must be connected to The Fourier transforms..., but I cannot find the accurate one. I'll go add it later. Dedhert.Jr (talk) 02:24, 24 February 2023 (UTC)

Just one more thing before I'll add some references. This article has already used CS1 in the lead, but I didn't notice and accidentally add the sources with CS2 in the references section. Along with inline citations, should I change all of them to inline citations with {{sfnp}} in notes and convert them to CS2 in references, or change all of them with no inline citations? My apologies for asking this, because I honestly was perplexed with WP:CITEVAR, and seek consensus first before changing them. Any explanation would be appreciated. Dedhert.Jr (talk) 16:56, 24 February 2023 (UTC)

Before you started, the article was already using an inconsistent mix of (full ref in footnote, formatted in CS1) and (harvnb in footnote, manually and inconsistently formatted full ref later). I don't think there is any single consistent style that you can fall back to. So it should be ok to just pick a single consistent style and reformat everything to be in that style. —David Eppstein (talk) 17:33, 24 February 2023 (UTC)

If that's the case, I'll change it to CS1. For the time being, I will keep using short citations, but some changes to {{sfn}} or {{sfnp}} (or {{harvtxt}} for multiple short citations in one <ref>). Please revert it if I did a mistake there. Will discuss later if someone wants to change them. Dedhert.Jr (talk) 09:44, 25 February 2023 (UTC)

I'd just go for CS1 style as it seems more popular and more or less the same idea as CS2, and the names 'cite journal', 'cite book', etc. are helpful for understanding at a glance what type of source is being cited. But I honestly don't understand why there are two whole separate sets of templates. YMMV. –jacobolus (t) 21:53, 24 February 2023 (UTC)

My personal preference is for CS2 because. All. The periods. Annoy. Me. and because I'd rather just have one template than have to figure out which of 10 different cite templates is the best fit for each citation. But the differences are small. As for why: it grew up that way and now it's difficult to change. —David Eppstein (talk) 21:59, 24 February 2023 (UTC)

As an aside: One thing people might not know about (I didn't until recently) but can be very useful when these templates inevitably break in complicated cases is using {{wikicite|ref={{harvid|Name|Year}} |reference=...}}, which can be wrapped around plain-text citations (or other cite templates with ref=none set on them) and then highlight/pop up everything inside when used with {{harvp}}, {{sfn}}, and the like. This is handy when a paper has been reprinted several times in different books, or when a book was translated from another language edition, or when a paper was split into several parts and published serially across multiple issues of a journal, etc. Downside: it's harder for machines to figure out the citation metadata if you use plain text. Upside: Citation Bot won't come and try to add 50 different useless identifiers from random citation indices. –jacobolus (t) 22:32, 24 February 2023 (UTC)

"Improper point" listed at Redirects for discussion

The redirect Improper point has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 February 26 § Improper point until a consensus is reached. —Mx. Granger (talk · contribs) 21:54, 26 February 2023 (UTC)