Wikipedia talk:WikiProject Mathematics/Archive/2024

Jan 2024

Undue weight (Lambert function)

Looking at a recent edit in it.wiki, I noticed that the Lambert function page (as well as some related one) is full of references to the work of T.C. Scott and his collaborators always added by the same user (TonyMath), which I presume is Scott himself. The same applies to en.wikipedia (although here it is less obvious because the relevant pages are longer) and in many other languages. I cannot immediately judge all his additions, but my guess is that his work is being given undue weight, given all the scientific literature that is being published nowadays. For sure, the very recent work related to the Riemann hypothesis that he just linked seems not nearly notable enough to be referenced on Wikipedia. There are many many criterions for the Riemann hypothesis, only a few of which are notable, and the fact that an obscure one can be expressed by using also a generalization of the Lambert function (which is a very natural/simple function to come up in all sort of problems) is not very relevant at all. It would be helpful if someone could give a look to his edits to see if his works should be referenced or not. --Sandrobt (talk) 10:03, 2 January 2024 (UTC)

Yes, that paper from less than a month ago is not due mention in that context. XOR'easter (talk) 15:30, 2 January 2024 (UTC)

For clarification, I was given the green light to include the section on the Generalized Lambert W function by a Wikipedia editor. This Generalized Lambert W function has a number of successful applications in Physics and Applied Mathematics. The talk section for the Lambert W function will confirm that. I was told to be bold and make the changes myself. Since then I have taken it upon myself to make the updates in good faith. There is a considerable and noteworthy body of work associated with the Generalized W function. FYI, that work by Ross McPhedran on the Keiper-Li Criterion for the Riemann Hypothesis is notable. It might not be maybe ready to be cited on the Wiki page for the Riemann Hypothesis but IMHO, it is worthy of the Wiki page for the Lambert W function itself (which is always looking for applications). Having said all this, I will adhere to this change of policy. TonyMath (talk) 03:13, 3 January 2024 (UTC)

There's been no change in policy; WP:SECONDARY, WP:DUE and WP:COI have been the "law of the land" (as it were) for a long time. XOR'easter (talk) 04:24, 3 January 2024 (UTC)

Rest assured, I am not asking you to overturn your decisions. I am aware of these policies which is why I pleaded my case on the talk page for the Lambert W function. Robinh read my papers, deemed them worthy and gave me the green light and told me be bold and make the changes myself. TonyMath (talk) 04:45, 3 January 2024 (UTC)

Li's criterion is indeed notable as it attracted quite some interest at the time (I didn't realize you were referring to it since you used the non-standard name Keiper-Li). However your work on the criterion is clearly not sufficiently relevant to be mentioned in Wikipedia. And as far as I'm concerned a clean up should not be limited to that paper. Of all the generlizations of Lambert's function only yours are relevant? It's a function that has appear countless many times. I doubt the literature on its generalization reduces to your works only.--Sandrobt (talk) 20:48, 4 January 2024 (UTC)

The reason why the Wiki section cites my work is because this generalization of the Lambert W function is largely my invention albeit worked out with collaborators in different fields. It has indeed many applications in fundamental Physics including relativity and quantum mechanics. As I mentioned before, I was given the green light as I mentioned earlier. There is also the work of Mező István which is similar but his generalization is a special case of my own. He is also cited in Wikipedia. Apart from that, I am not aware of any other generalizations of the Lambert W function that are useful and have so many applications with all due respect. However, if you are aware of any of them, you are welcome to add to the Wiki site. FYI, my generalization is the only one mentioned at NIST (National Institute of Standards and Technology). See [1]. TonyMath (talk) 00:13, 5 January 2024 (UTC)

I have no particular insight about this topic, but note that "given the green light" is not really how Wikipedia works. Anyone (including you) is welcome to "boldly" create/edit articles here, but then other editors are likewise welcome to dispute or modify those edits, and the final content/form of articles is decided by consensus. Nobody here is accusing you of doing anything inappropriate, but the decision about how the article should finally look doesn't really depend on any permission granted beforehand. –jacobolus (t) 01:23, 5 January 2024 (UTC)

I fully appreciate what you are saying and I have tried to address this issue of consensus within the talk pages as best I could over the years. I should explain my motivations behind all this. The Lambert W function was one of those relativity obscure functions, invented by Lambert in the 18th century and "reinvented" every decade or so, ever since. Mathematicians and Physicists would stumble upon it without realizing it was Lambert's function. It wasn't until the 1990s, that the team of Mathematicians and Mathematical Physicists (including myself) involved with the Maple system that the ubiquitous nature of this function was realized. Applications grew in number and when the standard function was insufficient, generalizations were made to accommodate an even greater range of applications. Unlike other special functions, the Lambert W function was not developed in a holistic way. Rather we stumbled unto it by necessity. This is where the use of systems like Maple and Mathematica and awareness by e.g. Wikipedia and other online sites are very helpful. This helps avoid re-inventing the wheel. By now, there is definitely a body of work out there where some consensus has been achieved by users and researchers (although apparently, that consensus might not have been achieved w.r.t. Wikipedia). Please consider this before any further changes to the Wiki site. If I may (and at the risk of offending you), I cannot help but sense that part of the problem is that the Physics aspect might not be fully appreciated here. Let me point out that Lambert made contributions to Mathematics and Physics/Engineering. This work has always been inter-disciplinary. TonyMath (talk) 02:33, 5 January 2024 (UTC)

Like many Wikipedia articles about mathematical functions (including some I have contributed to), this article is unfortunately currently substantially a compendium of loosely organized data, heavy on numbers and formulas (and in this case also gratuitous distracting proofs about indefinite integrals) and light on explanation, with poor narrative flow. What prose it does have assumes an extreme level of background and is all but illegible to most readers, densely full of undefined jargon. If anyone wants to best improve the article, in my opinion the most valuable contribution would be to add to/clarify the prose, and possibly get a bit choosier about the more obscure formulas. I don't know enough about this topic to help with that though. –jacobolus (t) 04:13, 5 January 2024 (UTC)

I agree! The development of the Lambert W function over the years according to the historical dynamic I described has indeed lead to a somewhat chaotic and chunky site. IMHO, the Wiki page for the Lambert W function needs to be streamlined. A possibility would be to compartmentalize the Wiki site into at least two sites: one page for the main overall description and thrust of the function and the other with various identities and details i.e. a much needed overhaul. TonyMath (talk) 04:53, 5 January 2024 (UTC)

Concerning the work on the Keiper-Li criteria, this is largely the work of Ross McPhedran. You insist that the paper is unworthy of mention. McPhedran is a mathematical Physicist of considerable renown. You can look him up in Google scholar. Have you even read the paper? IMHO, it's a considerable achievement and worthy of mention albeit not on the site of the Riemann hypothesis itself. TonyMath (talk) 00:34, 5 January 2024 (UTC)

McPhedran appears to have published four works on the Li criterion (arXiv:1801.07415, 2003.14241, 2311.06294, and ACM CCA), with a grand total of two citations on Google Scholar. There is no evidence that these works have had any impact whatsoever. He is indeed a notable physicist, but not notable for this. —David Eppstein (talk) 00:46, 5 January 2024 (UTC)

Fine. Concerning McPhedran's work, clearly this has to be given time. At any rate, I am not asking to overturn the actions made so far. I was only answering the messages by @Sandrobt. TonyMath (talk) 01:08, 5 January 2024 (UTC)

For further clarification on the issue of why there aren't more generalizations reported in Wikipedia, when it comes to developing the Lambert W function, there are really only two main groups. There is the group of Robert Corless, David Jeffrey and co-workers including the canonical publication with the famous Computer Scientist Donald Knuth and my group with its collaborators including the great British physicist Alexander Dalgarno. There are a few other players, most of which I know or the group Corless et al. know. I wish there were more groups. On this issue of "consensus', from time to time, there have been individuals that have tried to contribute to the Wiki page only to be rejected. On the whole, I'd say Wikipedia editors have done their necessary filtering and supervision over the years. TonyMath (talk) 03:51, 5 January 2024 (UTC)

Bernoulli polynomials and Euler polynomials

The article Bernoulli polynomials is almost as much about the Euler polynomials as it is about the Bernoulli polynomials. Would it be a good idea to rename the article to "Bernoulli polynomials and Euler polynomials"?  --Lambiam 19:08, 21 December 2023 (UTC)

See also Talk:Bernoulli polynomials § Requested move 24 December 2023.  --Lambiam 09:34, 5 January 2024 (UTC)

Derivative#Total derivative, total differential and Jacobian matrix

The Derivative article looks pretty fair overall until towards the end, particularly § Total derivative, total differential and Jacobian matrix. It could use attention. I'm not convinced that it's adequately cited or that the {{citation needed}} tags are in the right places; the text seems overly detailed in places. XOR'easter (talk) 15:44, 2 January 2024 (UTC)

The article is about a special case, so I've uptated the {{about}} to reflect that and to provide more links. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:04, 2 January 2024 (UTC)

That's an awful lot of links. Would anyone really expect to find pushforward (differential) when they click on a link for Derivative? XOR'easter (talk) 17:07, 2 January 2024 (UTC)

My guess is that this article should be focused on the derivative concept, with some types and generalizations; that section is overly detailed IMO, and it could probably be removed and written on its own article, Total derivative. Hopefully, someone can give an alternative opinion. Dedhert.Jr (talk) 06:16, 6 January 2024 (UTC)

I was just thinking that the material that really gets into the weeds could be moved over to total derivative. I'm reluctant to abandon it entirely, because it at least tried to explain motivations, but it needed work and probably did not belong in the same article that covers how to differentiate $x^{2}$. XOR'easter (talk) 14:43, 6 January 2024 (UTC)

I already hide them for temporarily. It is almost complete, just only referencing problems in some sections. One citation needed tag appears in the definition by using the limit. The history of continuity and differentiable still needs more sources, especially for the claim that most of the functions are differentiable at all or almost every point. The directional derivative is a similar problem with the overly detailed total derivative; I guess this redundant point could be removed, but keep the last paragraphs and find some sources. The rest is the verifiability of the sources in some sections that I have to check and then find more sources again. Dedhert.Jr (talk) 14:51, 6 January 2024 (UTC)

Sums of three cubes, and sums of four cubes

We have a page on the sum of four cubes problem, as well as the sums of three cubes problem. The two problems have significant overlap. The four cubes problem is definitively known for numbers not congruent to 4 or 5 mod 9 and is suspected true for numbers satisfying that congruence, while the three cubes problem is only suspected true for numbers not congruent to 4 or 5 mod 9 and definitively false for numbers satisfying that congruence. Also, naturally, if one were to prove the three cubes problem, then adding 1 or -1 would solve the four cubes problem too. Given the similarity, and the relative lack of content on the four cubes problem, is it worth keeping the two pages separate? GalacticShoe (talk) 22:00, 5 January 2024 (UTC)

I think they are both distinct from each other in flavor, and long enough that a merger is not called for and would be unhelpful to readers seeking information on either one. —David Eppstein (talk) 23:42, 5 January 2024 (UTC)

Fair enough. Would it be useful for each article to include at least a short section on the other problem? As it stands, I feel like the two problems are connected enough to merit more than an inconspicuous listing in their See alsos. GalacticShoe (talk) 17:26, 6 January 2024 (UTC)

E (mathematical constant)#Alternative characterizations

I'm vaguely dissatisfied with e § Alternative characterizations. When I came across it, it was an uncited grab-bag of unmotivated properties without motivations or relations. I've tried to flesh it out, but I'm still not convinced this is the right way to present the material. XOR'easter (talk) 21:03, 1 January 2024 (UTC)

I don't like the numbered list. I'd prefer just paragraphs of prose. –jacobolus (t) 17:03, 2 January 2024 (UTC)

I've prosified that passage now and rearranged things somewhat. XOR'easter (talk) 17:37, 2 January 2024 (UTC)

After looking at this again, the whole section seems pretty redundant (there's also a "Representations" further down). It could possibly be just eliminated. –jacobolus (t) 18:29, 2 January 2024 (UTC)

That's a good point; however, I tend to feel that there's a difference between what is presented as a definition of e and a formula that eventually works out to e. People define e by saying that it's the sum of an infinite series or that it's the number which satisfies some nice calculus property, not that it is the result of a Wallis-like infinite product. I've edited the beginning of "Representations" to make it less redundant. XOR'easter (talk) 19:00, 2 January 2024 (UTC)

While we're here, what major things about $e$ is the article missing? XOR'easter (talk) 00:39, 7 January 2024 (UTC)

Requested move at Talk:Information processing (psychology)#Requested move 7 January 2024

There is a requested move discussion at Talk:Information processing (psychology)#Requested move 7 January 2024 that may be of interest to members of this WikiProject. Vanderwaalforces (talk) 19:13, 7 January 2024 (UTC)

Diagonal and co-diagonal

Since there was no source for the diagonal morphism, I added references to the article and then I realized that some of those references also explain the co-diagonal morphisim. So, I thought I'd add the definition of co-diagonal morphism to the Diagonal morphism. Is this notion in the correct place? If it is a correct, I'm thinking of renaming the article to the "Diagonal and co-diagonal" and create a redirect co-diagonal morphism. Also, which is better, codiagonal or co-diagonal? --SilverMatsu (talk) 00:00, 1 January 2024 (UTC)

I added a figure. But, rather than adding a thumbnail to the top of the article, it may be better to split the figure into two and insert it into the body of the article. --SilverMatsu (talk) 00:17, 8 January 2024 (UTC)

Proposed new project topic: Mathematics Didactics

Wikipedia is an educational platform in itself and this project, in particular, focuses on mathematics. Therefore, I believe it is essential to present the topic of ‘Research in Mathematics Didactics’. This field of study is crucial for improving the teaching and learning of mathematics, and I hope that by making it known, we can contribute to its development. Lucas Varela Correa (talk) 16:30, 7 January 2024 (UTC)

See existing article at Mathematics education and especially its extensive subsection Mathematics education § Research. —David Eppstein (talk) 17:38, 7 January 2024 (UTC)

I don't understand what you are proposing specifically. Please feel free to contribute to Wikipedia articles about math education per se and also include material about math education where it is relevant to other articles.

Many of the Wikipedia articles about basic mathematical topics (at the primary/secondary school level) are incomplete or mediocre, and can definitely use help. If you give some idea of your expertise / interests, maybe someone can recommend a place to start. –jacobolus (t) 19:18, 7 January 2024 (UTC)

I think the topic is research in mathematics education, rather than the practice of mathematics education or the subjects typically taught in the practice of mathematics education. My impression is that when people call it "didactics" they tend to mean a greater focus on the philosophy of the topic and less focus on how to actually go about doing it, but that may be an inaccurate opinion based on unfamiliarity. Regardless, see the link for our existing coverage of this topic. —David Eppstein (talk) 19:54, 7 January 2024 (UTC)

The section Mathematics education § Research is IMO not very good. It's a grab bag of miscellaneous topics at different levels of abstraction, missing many fundamental related topics, with weak sourcing and several with inaccurate summaries of current scholarly consensus / pushing the POV of particular researchers. It would be great to have some experts work on improving this article and ideally expanding some of the pieces as separate articles. –jacobolus (t) 20:04, 7 January 2024 (UTC)

Because randomized trials provide clear, objective evidence on “what works” — good news, everyone! We don't need no stinking meta-analyses! XOR'easter (talk) 01:33, 8 January 2024 (UTC)

Agreed that this section is not good. I've made a small edit to read "Because of an opinion that randomized trials..." which I think is an improvement, although I don't have any expertise in these topics. Gumshoe2 (talk) 03:26, 8 January 2024 (UTC)

When I say Mathematics Didactics I make reference to the investigation of how to improve the way why teach maths. I know one journal specialized in this topic is call PNA https://revistaseug.ugr.es/index.php/pna/ the language of the papers can be three English/Spanish/Portuguese Lucas Varela Correa (talk) 20:53, 7 January 2024 (UTC)

why no we sorry Lucas Varela Correa (talk) 21:03, 7 January 2024 (UTC)

Also see Category:Mathematics education journals. —David Eppstein (talk) 23:01, 7 January 2024 (UTC)

Original proof of Gödel's completeness theorem

There is a dispute at Original proof of Gödel's completeness theorem. Dirsaka claims to have found a fundamental flaw in Gödel's original proof. (Dirsaka does not claim that the actual result is wrong, just that particular proof.) I do not have time at the moment to follow through all the arguments, but the chance that an error so basic, in such a prominent piece of mathematical history, would have escaped notice till now, strikes me as ... unlikely. If anyone wants to dive in and figure it out, that would be a service. --Trovatore (talk) 19:02, 5 January 2024 (UTC)

Well the latest addition obviously violated WP:OR and basic principles of how to write an encyclopedia article, and Dirsaka had never responded to the previous round of objections to their additions (several months ago), so I have reverted their addition. This did not require having an opinion on the underlying validity of either the proof or the objection. --JBL (talk) 19:16, 5 January 2024 (UTC)

Yeah, that's fine procedurally. It would still be nice to understand the objection on the merits, even if not strictly required for purposes of maintaining the article. --Trovatore (talk) 19:23, 5 January 2024 (UTC)

Here is my article explaining the error in Gӧdel's claimed proof of his incompleteness theorem better than my now deleted Wikipedia article comment does.--Dirsaka (talk) 04:56, 8 January 2024 (UTC)

I just had a glance at your article. I didn't understand all details, but here is why your article doesn't convince me:

You quote from some version of Gödel's proof "let F be a functional variable" which I read as "let F be a symbol for a (binary) relation (on natural numbers)". Lateron, your main point of criticism appears to be that Gödel doesn't show that "F is of degree 0". However, degree is a property of formulas in prenex normal form, essentially counting the number of $\forall$/$\exists$ changes. So F, or, more precisely, F(r,n), as it occurs in the formulas B and C, with r, n being two bound variables over natural numbers, is an atomic formula, without any quantifiers; therefore it of course has degree 0. - Jochen Burghardt (talk) 10:00, 8 January 2024 (UTC)

More on 0

There are a few remaining {{citation needed}} tags in the article 0. Almost half of them are in the "Computer science" section and can probably be sourced to technical manuals explaining the fundamentals of various languages. I have no will to push it through the GA or FA process, but it's highly visible as far as math articles go, and it'd be nice to have it free from flagged problems. XOR'easter (talk) 22:01, 13 January 2024 (UTC)

"differentiable symmetry"?

Hi Math folks. Noether's theorem starts out with this sentence:

• Noether's theorem or Noether's first theorem states that every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law.

The two words "differentiable symmetry" are both linked and the blue links make it appear to be one thing, a "differentiable symmetry", but the two links are to different articles. The pairing also appears in the section "Informal statement of the theorem" but no where else. It does not appear in Symmetry (physics) for example. Is it a thing?

If I search on Google for "differentiable symmetry" this exact sentence comes up again and again, making me wonder if the wikipedia version has become the source. I did not see "differentiable symmetry" anywhere in Noether's paper.

Things I read about symmetry use "continuous symmetry". For a physicist, we'd simply assume that a continuous symmetry was differentiable and vice versa until corrected by some math person. But is it true? I'm looking for a reference I can use for the combination. Johnjbarton (talk) 18:40, 8 January 2024 (UTC)

Here is an arxiv article and a published sequel on non-smooth extensions of Noether's theorem. --{{u|Mark viking}} {Talk} 18:53, 8 January 2024 (UTC)

I gather that your reply is equivalent to "differentiable symmetry is not required for Noether's theorem as evident by ..."? Johnjbarton (talk) 19:08, 8 January 2024 (UTC)

Right, continuity isn't sufficient, but it doesn't strictly need to be smooth, either. But in the common nomenclature, people say continuous symmetry without thinking too hard about differentiability requirements. I'd agree with linking to continuous symmetry. If editors felt a need, they could report on differentiability requirements farther down int he article. --{{u|Mark viking}} {Talk} 19:30, 8 January 2024 (UTC)

It should probably just be a link to Continuous symmetry. (That article could be considerably expanded with more analysis of concrete examples.) –jacobolus (t) 18:53, 8 January 2024 (UTC)

Yes, that's my reaction. Johnjbarton (talk) 19:13, 8 January 2024 (UTC)

Thanks, I edited the article. (but not all of the internet that quotes it!) Johnjbarton (talk) 19:33, 8 January 2024 (UTC)

Don't worry too much about quotations of old versions of Wikipedia floating around. There's nothing you can easily do about them, and they tend to have a relatively short half-life. –jacobolus (t) 20:17, 8 January 2024 (UTC)

I would expect the phrase "differential symmetry" to mean something like a diffeomorphism, which is a single symmetry defined by a smooth function. But instead, here it refers to a smooth family of symmetries. Maybe that could be clarified. (Also, "smooth" is usually usable in place of differentiable and is much less technical. It is somewhat vague as to how smooth is smooth, but I think at the start of the article that's an ok price to pay for reduced technicality.) —David Eppstein (talk) 21:27, 8 January 2024 (UTC)

I wouldn't assume everyone reads "smooth" as vague. I think it's reasonably common to use "smooth" to mean specifically $C^{\infty }$. --Trovatore (talk) 21:53, 8 January 2024 (UTC)

Unless explicitly specified in a source, this seems an abuse of terminology, and people should definitely not make that implicit assumption. "Smooth" is probably most commonly used to mean "continuously differentiable", but is generally a pretty vague term. –jacobolus (t) 22:59, 11 January 2024 (UTC)

Well, in any case it's what's used in Differential Topology by Guillemin and Pollack, which was the text for my introduction to the subject as a first-year grad student. I don't know how widely used it is. --Trovatore (talk) 22:21, 13 January 2024 (UTC)

I assume this book makes an explicit definition though. For instance, Lee's Smooth Manifolds has the disclaimer: "You should be aware that some authors define the word smooth differently—for example, to mean continuously differentiable or merely differentiable. On the other hand, some use the word differentiable to mean what we call smooth. Throughout this book, smooth is synonymous with C^∞." –jacobolus (t) 23:12, 13 January 2024 (UTC)

Vietoris-Rips filtration

I have been trying to fix a link to a disambiguation page on Vietoris-Rips filtration. Unfortunately, I have to admit that the article is way over my head. Can someone here solve this link and point is to the right article? Thanks in advance. The Banner talk 19:46, 11 January 2024 (UTC)

@The Banner: It might help if you said what the relevant disambig page was. --JBL (talk) 20:10, 11 January 2024 (UTC)

Never mind, I figured it out (and disambiguated). --JBL (talk) 20:12, 11 January 2024 (UTC)

Thank you very much! The Banner talk 20:13, 11 January 2024 (UTC)

I have just corrected the article's title so that it is called Vietoris–Rips filtration (with an en-dash, as required by WP:MOS) rather than Vietoris-Rips filtration (with a hyphen rather than an en-dash). I also corrected numerous occurrences of the phrase in the article, and fixed the links to the version with they hyphen.

I further corrected the omission of the links to the articles about the two eponyms, Leopold Vietoris and Eliyahu Rips.

One task that should be looked at by those familiar with the topic is to ascertain which other Wikipedia articles ought to link to this one and in particular whether the articles about the two eponyms should link to it. @The Banner: Michael Hardy (talk) 20:44, 16 January 2024 (UTC)

Mathematical theory

Mathematical theory and its history could use more attention. —David Eppstein (talk) 17:53, 16 January 2024 (UTC)

I think you should merge that article into Theory (mathematical logic). Johnjbarton (talk) 18:31, 16 January 2024 (UTC)

I agree that the current content is better addressed at the link you give, but is that the right target for the title? Theory (disambiguation) says that the topic is "an area of mathematical research that is relatively self-contained", but recent edits have taken over the title and moved it in a different direction. —David Eppstein (talk) 18:35, 16 January 2024 (UTC)

I think, to the extent that there's something for an article called (or redirected from) "mathematical theory" to be about, it has to be a theory in the sense of logic. It's certainly true that you can combine the words "mathematical" and "theory" in natural language to refer to other stuff, but we don't (or at least shouldn't) write articles to document how people can (or even do) put particular English words together according to the ordinary rules of English. There needs to be some encyclopedic "aboutness". Usually multi-word titles should be terms of art. --Trovatore (talk) 19:51, 16 January 2024 (UTC)

It seems worth trying to somewhere explain what the word theory in set theory, number theory, graph theory, group theory, etc. etc. is supposed to mean. This is not the same as Theory (mathematical logic). It's closer to scientific theory, but not quite the same. –jacobolus (t) 20:02, 16 January 2024 (UTC)

I suspect that's going to be kind of OR-y. No doubt someone somewhere has written on the subject, but I don't think there's a general accepted answer. In general I'm skeptical of attempts to abstract some commonality out of language and write about it in Wikipedia. --Trovatore (talk) 20:13, 16 January 2024 (UTC)

It's only worthwhile to the extent that suitable secondary references exist. I see zero in the current article. Johnjbarton (talk) 20:27, 16 January 2024 (UTC)

Honestly I would still find it concerning even if a ref or two could be dug up. I doubt there's any generally accepted account of what makes ring theory and fine-structure theory both "theories". I'm sure someone somewhere has made such a proposal, but just having written about it shouldn't entitle you to hijack general mathematical usage and make it sound as though everyone accepts your (ahem) theory on the subject.

If we do want to cover such an account, we should do it in a way that attributes it to the specific workers proposing it. --Trovatore (talk) 20:43, 16 January 2024 (UTC)

Well in that case perhaps Mathematical theory should just be a redirect to List of mathematical theories, maybe with a quick 1- or 2-sentence definition/explanation at the top. –jacobolus (t) 20:48, 16 January 2024 (UTC)

That sounds like a decent solution. --Trovatore (talk) 20:49, 16 January 2024 (UTC)

(Added after Jacobolus suggested a quick explanation at the top.) I think we need to be careful in any such explanation not to reify a particular abstraction of the notion of "mathematical theory". --Trovatore (talk) 20:52, 16 January 2024 (UTC)

I like Jacobolus's suggestion and have boldly gone ahead and done that. I also added Theory (mathematical logic) to the hatnote at the redirect target. —David Eppstein (talk) 20:57, 16 January 2024 (UTC)

LGTM --Trovatore (talk) 21:02, 16 January 2024 (UTC)

I don't think I agree with erasing the discussion of what a mathematical theory is. For example in the Gauge theory (mathematics) I made a clear distinction between the physical use of the term "theory" as in mathematical model of a particular physical phenomenon and the mathematical term "body of knowledge". I reject the implication that every use of the term "theory" in mathematics is "a set of sentences in a formal language" and given the level of confusion the layperson tends to have over the word "theory" in maths and science it seems particularly bold to erase that discussion altogether. Tazerenix (talk) 21:19, 16 January 2024 (UTC)

There is a bit of (unsourced) discussion remaining at Theory#Mathematical. –jacobolus (t) 21:22, 16 January 2024 (UTC)

Do you have a reference that the mathematical term is "body of knowledge"? That is the problem with the article, it is basically hearsay. Johnjbarton (talk) 22:51, 16 January 2024 (UTC)

Here's one example, doi:10.1007/978-3-319-90035-3_8. There's also some relevant discussion at JSTOR 2695275, JSTOR 2026666, JSTOR 2214851, doi:10.1016/S0039-3681(01)00007-3, doi:10.1007/978-94-015-9558-2_24, https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf, https://www.blackwellpublishing.co.uk/content/BPL_Images/Content_store/Sample_chapter/9780631218692/Jacquette.pdf. –jacobolus (t) 01:30, 17 January 2024 (UTC)

Per WP:LEAST, I have changed the target of Mathematical theory into Theory#Mathematical. Indeed, a reader searching for "Mathematical theory" will probably want a definition of the concept rather than an indiscriminate list of mathematical theories. I have also edited the new target.

About the above discussion: it is sure that, in mathematics, "theory" and "mathematical theory" are terms of jargon that are widely used and rarely defined. The number of our articles that have "theory" in their names is a testimony of this. So, this has to be explained in Wikipedia. However, I do not believe that there is much more to say about this than that it is already in Theory#Mathematical. So, for the moment, there is no need of a separate article, and it suffices to improve Theory#Mathematical. D.Lazard (talk) 16:34, 18 January 2024 (UTC)

FAR for Emmy Noether

I have nominated Emmy Noether for a featured article review here. Please join the discussion on whether this article meets the featured article criteria. Articles are typically reviewed for two weeks. If substantial concerns are not addressed during the review period, the article will be moved to the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Delist" in regards to the article's featured status. The instructions for the review process are here. Z1720 (talk) 20:30, 15 January 2024 (UTC)

I've long since lost any sense of what makes an article "featured", but what this article needs more than anything else is an algebraist who has a decent sense of which textbooks are the least incomprehensible to leave a few footnotes here and there. XOR'easter (talk) 00:19, 20 January 2024 (UTC)

History of Hindu–Arabic numerals images are almost certainly copyright violation

I just added the following comment at Wikimedia Commons Village Pump:

The image File:Evolution of Hindu-Arabic numerals.jpg is a very lightly modified version of a diagram from Karl Menninger's book Number Words and Number Symbols (1969), page 418, originally published in German (1934) as Zahlwort und Ziffer. This is a very clear copyright violation, though the author user:Hu741f4 claimed this as their own cc-by-sa licensed work.

A couple other images are almost certainly also copyright violation: File:Numeration-brahmi fr.png is translated into French, and according to the image description got the numeral images from Datta and Singh (1935) History of Hindu Mathematics which according to History of Hindu Mathematics and IA is in the public domain (I am not sure if that is accurate; the copyright page of these scans says "all rights reserved", but perhaps the copyright has expired in India). I can't immediately tell if this is true and the uploader user:Piero remade the image, or if this was also just scanned from Menninger then overwritten with translated labels, but either way this diagram is too closely based on Menninger's diagram to not be a clear-cut derivative work, and it's especially shady that there's no attribution to Menninger. This was then translated back into English as File:The_Brahmi_numeral_system_and_its_descendants.png by user:Tobus. Again Menninger is not credited, and this one has a description page which no longer makes any claims about where the glyph images come from.

It would be nice if someone would redraw an image that is not such a blatant ripoff. The wide use of these images across Wikimedia projects testifies to their importance. –jacobolus (t) 00:28, 22 January 2024 (UTC)

Andrew Wiles

Just reminder. The article Andrew Wiles is preparing for the possibly the next FA. However, the content of this article may need attention from an expert. It is already more than two months since PR. Dedhert.Jr (talk) 03:41, 22 January 2024 (UTC)

Fuzzy set

I noticed that Category:Iranian inventions and Category:Azerbaijani inventions have been added to Fuzzy set. I've never seen a category related to nationality added to an article about mathematics, so I find it a little strange. SilverMatsu (talk) 02:46, 23 January 2024 (UTC)

It was added in this edit back in March 2020. I agree that it seems odd to add nationality to mathematical 'inventions'. GalacticShoe (talk) 02:57, 23 January 2024 (UTC)

Thank you for your comment. I removed two categories related to nationality from the Fuzzy set. --SilverMatsu (talk) 15:31, 23 January 2024 (UTC)

Good article reassessment for Vector space

Vector space 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. ~~ AirshipJungleman29 (talk) 03:01, 25 January 2024 (UTC)

I'll be honest. Three articles have been nominated to reassess the quality by GA criteria. One of them is Derivative, which is already under control; two of them are still ongoing (E (mathematical constant) and Vector space). I do think there are some old GA Mathematics that could be potentially delisted. Dedhert.Jr (talk) 11:03, 25 January 2024 (UTC)

Sumudu transform

This discussion ought to be here on this page rather than at the Reference Desk. Michael Hardy (talk) 18:55, 21 January 2024 (UTC)

As well as Sumudu transform (re-created after a prod as a trivial variation of the Laplace transform) we now also have new articles Elzaki transform and Aboodh transform. These all have many citations in Google Scholar in what in many cases appear to be low-quality journals. Is this mainstream? Is it something we need to treat similarly to WP:FRINGE, something that can only meet our standards for neutrality if we have mainstream sources assessing it by mainstream standards? — Preceding unsigned comment added by David Eppstein (talk • contribs) 20:39, 21 January 2024 (UTC)

Both Elzaki transform and Aboodh transform are named after their inventors by their inventor themselves, in articles published in the same predatory journal. So the citations of these articles are probably authored by members of their teams. So, I'll PROD these two articles, and if the Prod tag is removed, I recommend to nominate the three articles to AfD. D.Lazard (talk) 09:52, 22 January 2024 (UTC)

There are many self-citations but there are many not. I think it would be more accurate to say that the citations are authored by members of the same subcommunity of researchers. But if the whole subcommunity largely publishes in predatory journals, then we should not take their citation counts as meaningful. —David Eppstein (talk) 23:46, 22 January 2024 (UTC)

@D.Lazard: Update: Aboodh transform has been unprodded. —David Eppstein (talk) 20:15, 28 January 2024 (UTC)

Feb 2024

Which publisher mathematics books that are reliable?

While improving some mathematics articles, I'm skeptical about adding references because some of them are reliable, whereas the rest are self-publishers. As far as I'm concerned, the only reliable publishers are Dover Publications, Cambridge University Press, Oxford University Press, Springer, AMS, and many more. However, what about publishers such as Bod (Book of Demand) and Read Books Ltd.? Are these remains reliable? Dedhert.Jr (talk) 02:11, 30 January 2024 (UTC)

Do you have a specific example book you are curious about? Sometimes if a reputable scholar self publishes a book it can be a reliable source, but some self-published books are about as credible as pseudonymous blog posts or forum comments. A book published by a university press (or similar) is clearly preferable if you can find it. –jacobolus (t) 02:41, 30 January 2024 (UTC)

@Jacobolus I do. One example while I was trying to improve the article Wedge (geometry) is this one [2]. Dedhert.Jr (talk) 02:46, 30 January 2024 (UTC)

That was published by Ginn & Company in 1893. They were a reliable publisher of textbooks. Old, but I suppose usable. The modern 'publisher' is just reprinting a public domain book since it has aged out of copyright. MrOllie (talk) 02:57, 30 January 2024 (UTC)

Ah. I see. Thank you. I am somewhat confused with some sources that are self-publisher. However, it seems that the sources do not have the specific pages, as I am more skeptical in the Google Books settings that exhibit the page, but not accurate. Dedhert.Jr (talk) 02:59, 30 January 2024 (UTC)

This is a book from 1893 published by Ginn of Boston. (Edit: beaten to the punch.) –jacobolus (t) 03:03, 30 January 2024 (UTC)

Really appreciate your work. Dedhert.Jr (talk) 03:04, 30 January 2024 (UTC)

For math books (or any other specialist book), if they get reviewed (and not mocked) by other mathematicians or pedagogues in a reliable publication, they're probably fine. The nice thing about using super-popular oft-reprinted math textbooks is they're easily verifiable and unlikely to have typos. The nice thing about that hidden gem book you might like to cite is that it may have some wonderfully illustrative example problems suitable for adapting to our WP articles (unlike, say, several notoriously difficult but ubiquitous textbooks; or perhaps Dover which is generously assigned because it's cheap, but may not always be the cleanest.) SamuelRiv (talk) 03:07, 30 January 2024 (UTC)

Dover reprints a wide variety of old out-of-print math books, some of which are solid and others of which are really excellent. It's cheap because they get the publishing rights cheaply from publishers uninterested in issuing their own new versions, so you're paying not that much more than the production cost for an average-quality paperback book. When citing material found in a Dover reprint, it's worth trying to figure out the original publisher and title (sometimes Dover changes it); usually, but not always, there's a decent scan at the Internet Archive. –jacobolus (t) 03:30, 30 January 2024 (UTC)

(ec) : I think "Books on Demand" is self-published, so not reliable. More reliable publishers: Addison-Wesley, Prentice Hall, and Wiley (publisher). And look to see if it is reviewed by the AMS! Bubba73 ^{You talkin' to me?} 03:12, 30 January 2024 (UTC)

But what about the case of sources that is taken from Wikipedia content? During the improvement of the same article again, I found this book with Springer as its reliable publisher, but the images are taken from the Wikipedia articles; or another example is in Reeve tetrahedra, where the journal source is taken the reference from the Wikipedia article Pick's theorem? Is it fine to pick them? Dedhert.Jr (talk) 03:21, 30 January 2024 (UTC)

Springer is a massive publisher owned for the past couple decades by a string of financial firms and therefore not especially caring about book quality anymore. Many of the monographs they publish are mediocre, and they also publish things like conference proceedings for niche conferences which can have mixed quality. Some Springer titles have excellent content, though unfortunately nowadays they almost all are printed on demand, with horribly bad printing/binding quality. You should look at the name/reputation of the author, try reading some of the book, look at reviews, etc. to decide if the book is the best source for a particular claim; just the name of the publisher is not a particularly strong indicator. –jacobolus (t) 03:37, 30 January 2024 (UTC)

I'm sorry to hear that about Springer - they were so good back in my day. I think their graduate-level books were called the "yellow peril". Bubba73 ^{You talkin' to me?} 04:14, 30 January 2024 (UTC)

I think their GTM series is still good, but other Springer series can require more care. I just recently ran into a case while adding sources to conical surface of a 2015 Springer book, Encyclopedia of Analytical Surfaces, that had clearly copied from us (at least one identical sentence with an earlier appearance in our article than the publication date of the book), making it unusable per WP:CIRCULAR. That's one reason I sometimes look for older books as sources: as well as being freely available online, they are not going to have that problem. And the mathematics may occasionally be stated in an out-of-date style, but in most cases it is unlikely to become incorrect. —David Eppstein (talk) 07:40, 30 January 2024 (UTC)

There's even worse available in Springer, see e.g. the last chapter of https://doi.org/10.1007/978-3-031-29046-6 which manages to combine modules of sheaves, Ricci flow, the positive mass theorem, and K-theory in the study of echocardiography. It reads like GPT-2. Gumshoe2 (talk) 13:32, 30 January 2024 (UTC)

Wow. Anyway, I think Cambridge University Press is reliably good, and Princeton University Press almost as good. Oxford University Press is likely good as well but I don't have so much experience with them. Springer and CRC are both rather more careless as these examples suggest. Unfortunately MAA Press can sometimes read as thrown-together web scrapings as well. The more researchy imprints of AMS are better. You might expect the Dover mathematics books to be dubious (because cheap paperbacks), but they are surprisingly good, because they are mostly well-chosen reprints of older books. (Disclaimer: I have published with both Cambridge and Springer.) —David Eppstein (talk) 18:26, 30 January 2024 (UTC)

@David Eppstein My question regarding about this problem is how do I know that a publisher is reliable? Dedhert.Jr (talk) 02:57, 2 February 2024 (UTC)

If you have serious doubts then you can ask on WP:RSN but they are going to say that all the publishers we are discussing are good enough. Beyond that I think it comes down to past experience and individual evaluation of how polished and accurate individual sources appear to be. —David Eppstein (talk) 03:09, 2 February 2024 (UTC)

You have to use your judgment. You can look at both internal signals such as how clearly written it is and whether the authors seem careful or sloppy about citing past work, or external signals such as what reviewers said about it, how highly cited the source (or other sources by the same author) is, what honors the author has received, and so on. Even without looking at external signals, some works will give you the sense that a deep expert wrote them with loving attention to detail and were then carefully copyedited, have nicely drawn figures, etc., and others just seem slapped together carelessly. YMMV. –jacobolus (t) 03:30, 2 February 2024 (UTC)

Noted. Thank you. Dedhert.Jr (talk) 04:53, 2 February 2024 (UTC)

Images wouldn't give me pause, especially when they are given proper attribution. Likewise material taken from wikipedia in an otherwise original work can be assumed to be have been vetted by that author, and thus becomes as reliable as the author. Headbomb {t · c · p · b} 03:38, 30 January 2024 (UTC)

WikiProject proposal related to Mathematics: Geometry

You can view the proposal here. Looking for interested Wikipedians. Writehydra (talk) 04:57, 2 February 2024 (UTC)

Wikipedia:WikiProject Polyhedra

Someone has just set up/revived this project. I am wondering whether it would be better placed inside the maths project because it seems a rather narrow field for a new project and will probably not become active as a result — Martin (MSGJ · talk) 19:21, 19 January 2024 (UTC)

As far as I can see the main use for this revival is quality assessment of articles: we can now find the Category:WikiProject Polyhedra articles, sorted by importance and by quality. This may be helpful after the banner shell Borg nuked the |field= parameter we used to use to find sorted collections of articles in mathematics subtopics. —David Eppstein (talk) 00:39, 20 January 2024 (UTC)

It wasn't the "banner shell borg" that nuked the 'field' parameter. This was changed in 2020 in special:diff/986062061 by @MSGJ. It could plausibly be un-changed somehow, but I don't know how worthwhile it would be (then the banner shell bots would need to be reconfigured to ignore the restored parameter, etc.). –jacobolus (t) 17:43, 20 January 2024 (UTC)

@David Eppstein, @Jacobolus, @MSGJ I'm planning for reviving this WikiProject. However, it seems that I forgot what was the reason. One thing that might pushed me to do so currently is to improve many articles on polyhedron in which tables only and facts are unsourced—sorry I totally forgot. Dedhert.Jr (talk) 13:54, 2 February 2024 (UTC)

Coxeter diagram

For the background, I and @Jacobolus are discussing the table explaining the bipyramids while improving the article Bipyramid. One problem if someone applied the table {{Bipyramids}} created by @Tomruen is the Coxeter diagram, which is somewhat technical to understand. Can someone explain what are these notations, and how to understand them? The article Coxeter diagram exists, but the content is already problematic. Dedhert.Jr (talk) 09:39, 27 January 2024 (UTC)

My understanding is that Coxeter diagrams describe Coxeter groups, which in this specific case can be described as groups generated by the reflections of a spherical triangle across its edges. The Coxeter diagram has a vertex for each mirror (three vertices for the three sides of the triangle) and an edge or non-edge indicating the angle at which two mirrors meet (no edge for π/4, an undecorated edge for π/6, and a number n for π/2n). So for a spherical bipyramid, the given diagrams describe the shapes of the faces and represent the symmetries generated by reflections across edges of the bipyramid. —David Eppstein (talk) 19:16, 27 January 2024 (UTC)

Coxeter diagrams for polyhedra represent Wythoff constructions of mirror planes, each node is a mirror. A ringed mirror is "active", with generated point off the mirror plane, generating an edge. This constructs unform polyhedrons. Uniform dual polyhedra are represented with a vertical line through the ringed node(s) of the dual polyhedron. They are indeed somewhat technical, and could be removed, but a useful system with basic understanding. Tom Ruen (talk) 23:29, 27 January 2024 (UTC)

@Tomruen The question is what are the basics to understand this notation? How do I write the notation for every polyhedron, including the bipyramid as mentioned by @David Eppstein? Let's see if I looked up at the table again, where there are some Coxeter diagrams representing the bipyramids.

Regular right symmetric n-gonal bipyramids:

Bipyramid name	Digonal bipyramid	Triangular bipyramid	Square bipyramid	Pentagonal bipyramid	Hexagonal bipyramid	...	Apeirogonal bipyramid
Polyhedron image						...
Spherical tiling image						Plane tiling image
Face config.	V2.4.4	V3.4.4	V4.4.4	V5.4.4	V6.4.4	...	V∞.4.4
Coxeter diagram						...

I've seen more examples of Coxeter diagrams describing four Platonic solids.[3], but it is somewhat different than our articles. Dedhert.Jr (talk) 04:05, 28 January 2024 (UTC)

@Dedhert.Jr The reason I think the discussion of symmetry should be kept (and indeed extended) is that crystallography is the primary application of bipyramids and related shapes. It would be helpful if someone who was an expert crystallographer could take a look though. In my opinion scalenohedron should be split into its own article with a short summary at bipyramid. The current text we have about this and the other related polyhedra is somewhat incoherent and overly technical, and seems to be a bit idiosyncratic / perhaps with some original research thrown in. –jacobolus (t) 07:32, 28 January 2024 (UTC)

@Jacobolus The only thing I could not create this new article is because of lack of sources. I could only found the definition of scalenohedra, but not the symmetry and many other related topics. If it does, I'm aware that it will be redirected again under WP:BLAR; this was already happened with our articles such as the family of duoprisms. Dedhert.Jr (talk) 09:56, 28 January 2024 (UTC)

A search for "scalenohedron" has >1000 sources in Google scholar. It's unquestionably a notable topic about which much can be said that is verifiable. I'm not an expert so couldn't by any means write that article off the top of my head, but if someone wants to put in the work to do a literature review it also shouldn't be inordinately difficult. –jacobolus (t) 10:01, 28 January 2024 (UTC)

Really? I never knew that numerous sources mentions about it. Unfortunately, I don't think I can make it because of the restricted access. Maybe I leave it to someone else. Dedhert.Jr (talk) 10:13, 28 January 2024 (UTC)

Aside: should Icosahedral bipyramid, Tetrahedral bipyramid, Cubical bipyramid, Dodecahedral bipyramid really be articles here? It seems like original research. The only source given is a personal web page, and I can't find any reliable sources about this (I can find this example of "dodecahedral bipyramid" being used to mean something clearly different). –jacobolus (t) 08:02, 28 January 2024 (UTC)

I have no idea how to deal with the original researches. Maybe AfD is the only option if there are no sources mentions about them? Dedhert.Jr (talk) 10:01, 28 January 2024 (UTC)

I also can't find any reliable sources using the name "Blind polytope". The cited sources are user:Tamfang's website https://bendwavy.org and the "Polytope Wiki". user:Tomruen do you have any reliable sources for these topics, or is this a neologism you and/or Tamfang coined? –jacobolus (t) 15:37, 28 January 2024 (UTC)

I'm don't know who first offered the categorical name. It could be moved to Convex polytopes with regular facets. Johnson solids were referenced in 1969 as "Convex polyhedra with regular faces", while the actual lists neglects regular and semiregular forms. I can't say who gave Johnson the honorific name, might also just be websites like MathWorld]. It could be Klitzing's reference is an original source [4]. Tom Ruen (talk) 04:47, 29 January 2024 (UTC)

The earliest example of "Johnson solids" Google scholar finds is Rankin, John R. (1988). "Classes of polyhedra defined by jet graphics". Computers & Graphics. 12 (2): 239–254. doi:10.1016/0097-8493(88)90036-2. But it's certainly plausible that Klitzing and/or MathWorld popularized the name. –jacobolus (t) 10:49, 29 January 2024 (UTC)

To clarify, I host Richard Klitzing's polytope pages at bendwavy.org, but have no hand in writing them. —Tamfang (talk) 05:10, 3 February 2024 (UTC)

Proposed deletion of Mina Ossiander

The article Mina Ossiander has been proposed for deletion because of the following concern:

Adjunct prof with h-index of 7

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Abductive (reasoning) 05:07, 3 February 2024 (UTC)

As the page is presently written there’s no evidence of notability, but low h index should be rejected as a standard to judge by. Gumshoe2 (talk) 10:14, 3 February 2024 (UTC)

True, but false statements about academic rank are an even worse standard. —David Eppstein (talk) 20:04, 4 February 2024 (UTC)

The PROD has been removed. In the future, proposed deletions of interest to this project are best listed at Wikipedia:WikiProject Deletion sorting/Mathematics. --JBL (talk) 17:25, 3 February 2024 (UTC)

Nothing in the article seems particularly notable here. It's just one more person who got a PhD in mathematics and the article lists irrelevant details of their personal life and the title of the thesis and name of the advisor. Not sure why that person was selected as worthy of a Wikipedia article. PatrickR2 (talk) 21:57, 3 February 2024 (UTC)

Anyone can, of course, send the article to WP:AfD if they want to. --JBL (talk) 19:40, 4 February 2024 (UTC)

Quantity of references in mathematics articles

I'm trying to get a better understanding of the content assessment criteria specifically for mathematics articles. I have noticed that mathematics articles often do not include many references. Take for example Ordinal number, many sections in this article don't have any references, or may only provide a single reference for a specific sentence or word in a section. Still, this article was once rated GA, and today is still rated B, indicating only minor problems exist. Can someone provide some advice on this? Mokadoshi (talk) 03:07, 5 February 2024 (UTC)

The Rater tool gives Ordinal number as C rating. That means it most resembles articles that humans have evaluated as C across Wikipedia.

Your observation also applies to physics article. The long-time editors have said that many articles written back in the 2000s where just typed in. But another factor is the huge number of articles.

If the content assessment for an article seems wrong, just change it. Or improve the article up to the current rating ;-) Johnjbarton (talk) 03:17, 5 February 2024 (UTC)

You are right that math articles on Wikipedia are systematically reference-light. I see two reasons.

First, mathematicians were early adopters of Wikipedia. Many math articles were written into decent shape long before there was so much insistence on reliable sources (as Johnjbarton implied above). And, in later years, many editors have not felt strong motivation to systematically add references to long-established, pretty good text.

Second, even professional math articles are reference-light compared to articles I've seen in the natural sciences, history, etc. This is because math is almost pure logic, which the diligent reader can verify or refute for themselves. (Moreover, the policy WP:CALC is interpreted to give broad leeway in math articles.) Mathematicians are simply not acculturated to reference-heavy writing.

Let me emphasize that I am not defending the lack of references in Wikipedia math articles. I am merely enunciating the reasons, as I see them. Regards, Mgnbar (talk) 03:51, 5 February 2024 (UTC)

Professional math sources also typically (not always) do a poor job of citing original authors or describing their work in its own terms: misnamed objects and ideas abound, a wide variety of mythical origin stories persist, and treatment of earlier sources is often anachronistic to the point of pure fantasy. Reading works mentioning math history requires some skepticism and care, as plenty of nonsense gets passed down uncritically. Recent professional mathematical historians have gotten better about this and are more careful to separate what is actually known from invented folklore, especially about older material. Wikipedia math articles could do a better job accurately describing (and citing original sources relevant to) the history of pretty much every topic. –jacobolus (t) 06:20, 5 February 2024 (UTC)

Of course, as soon as I posted this discussion, I came across this discussion from 2006 about this topic, which includes a link to Wikipedia:Scientific citation guidelines. If I'm understanding it correctly: On Wikipedia it is not required to provide a citation on every instance of uncontroversial knowledge. However, in scientific articles "uncontroversial knowledge" is defined broadly to be knowledge that would be known by anyone with an underground background in the field of study, and is covered in any common or obvious books on the topic -- even if this is not known by a layperson. Still, each section should have at least one reference to one of these common or obvious books on the topic, and these can be cited in the first or last sentence of a section (the rest of the section need no references if it contains uncontroversial knowledge).

Am I correct in this? If so, it might be helpful to include a link to this page on Wikipedia:WikiProject_Mathematics/Assessment. This might be obvious to many people, but that is the page I looked at before posting this discussion and found nothing there about citation guidelines. Mokadoshi (talk) 03:58, 5 February 2024 (UTC)

@Mokadoshi: I think the reader's background is supposed to be assumed to be undergraduate-level, rather than secret or subterranean! — MarkH₂₁^talk 04:12, 5 February 2024 (UTC)

My very rough personal scale is: if it supports more than one section, with more than one sentence in them and with a lead that properly summarizes those sections, it is at least start-class (otherwise it's a stub). If it covers the main ground and is adequately referenced but not very well written or organized, or (as in the case at hand) is thorough, competently written and organized, but badly sourced, it is C-class. If it is thorough, well-written, and mostly well-sourced, but maybe with a few topics missing or a few unsourced claims, it is B-class. And if it has all that, it is written as accessibly as reasonably possible, and careful read-throughs and literature searches can find nothing obvious that is still in need of improvement, then it is either GA-class or should be a nominee for GA-class. I don't consider FA-class worth the effort, so the scale stops there. As for Wikipedia:Scientific citation guidelines: I think it is outdated and should be marked historical. I don't think its recommendations to leave background material unsourced, or sourced only to general reference sections at the end, reflect current Wikipedia practice. —David Eppstein (talk) 06:33, 5 February 2024 (UTC)

Invite to join the February 2024 Unreferenced Backlog Drive

WikiProject Unreferenced articles | February 2024 Backlog Drive

1 + 1 ≠ 2

Many math articles do not have references. This drive wants to change that. The aim of this drive is to cite all unreferenced articles on Wikipedia and ensure its reliability. Barnstars will be awarded based on the number of articles cited. Remember to tag your edit summary with [[WP:FEB24]], both to advertise the event and tally the points later using Edit Summary Search. Interested in taking part? Sign up here.

CactiStaccingCrane (talk) 14:55, 21 January 2024 (UTC)

@CactiStaccingCrane: Where is the list of unreferenced mathematics articles? Michael Hardy (talk) 18:51, 21 January 2024 (UTC)

You can find them at https://bambots.brucemyers.com/cwb/bycat/Mathematics.html#Cites%20no%20sources. CactiStaccingCrane (talk) 18:55, 21 January 2024 (UTC)

I'd recommend not turning improving math articles into a race/speedrun. It would be significantly more valuable if someone picked one highly viewed start or C class math article and spent a few hours or days making substantial improvements, instead of trying to spend a few minutes each adding hastily chosen references as footnotes to sections that are already well written and describe well-known topics in a standard way. References found in haste in this way by searching (rather than either chosen by an expert who already knows the literature or carefully found by someone willing to do some significant literature research) tend to be low quality, and ticking off a binary checklist of "has a reference" vs. "doesn't have a reference" is not really very valuable to the Wikipedia project. –jacobolus (t) 20:39, 21 January 2024 (UTC)

No, we are not adding referenced to well-sourced articles. We are adding references to articles that do not have any citations at all and risk being AfDed for not demonstrating that this concept actually exist, especially for mathematics articles where "this concept exists" is not easy to verify. So yes, an article "has a reference" is indeed much better than an article that "does not have a reference". CactiStaccingCrane (talk) 00:34, 22 January 2024 (UTC)

Nevertheless, you are free to chip in at 'check for sloppy work in the drive' thread, as quality control should also play a big part in the drive. CactiStaccingCrane (talk) 00:37, 22 January 2024 (UTC)

It's really not practically helpful to readers to add shitty references to well-written articles, whether or not they already had sources. If something is verifiable it's not going to get deleted, and people sending obviously verifiable stuff to AFD based on a lack of footnotes are wasting everyone's time.

My point is: please don't try to add references to articles as some kind of speed race game in search of little meaningless wiki awards for being the fastest, but instead take the time to do the work properly so it doesn't need to be done over later.

If you (anyone reading along) want to find a reference to some mathematical article which is currently unsourced, take the trouble to find a source which is well written and respected, and then fill out a carefully written citation. This often takes skimming several sources, checking their citation counts in the academic literature, considering which one is most appropriate for the intended audience of a Wikipedia page, etc. It's even better to figure out a bit of the history of the topic and give some concept of the priority for an idea, or give multiple sources appropriate for different audiences. –jacobolus (t) 00:48, 22 January 2024 (UTC)

It might be helpful for you to read this discussion: Wikipedia:Requests for comment/Deletion of uncited articles CactiStaccingCrane (talk) 02:26, 22 January 2024 (UTC)

The tone of your response leads me to think that you care more about the superficial appearance of having little clicky blue footnotes than about the quality of the sourcing, and that you would like the outcome of the sort of speed race game that jacobolus warns against. Perhaps you can persuade me otherwise. —David Eppstein (talk) 02:34, 22 January 2024 (UTC)

Ok, just to clarify, I do agree that in the most ideal scenario, we would get people to give many citations to reliable sources for each article, enough so that the article is unambiguously notable and will be speedily keep in an AfD discussion. This drive's main goal is not to cite small percent of these uncited articles are well-written (e.g. 238 math articles/113000 total), but to cite barely notable articles that you might find in Special:Random, like articles about random places or random people. For a participant in the drive, it is much more efficient to cite these stubs to get those "little clicky blue footnote points" that you mentioned rather than citing math articles that require a lot of effort to find a reliable source. And frankly, who cares about these articles? For all we know citing these articles might not guarantee these articles will be kept. If somebody truly care about an article's existence, they would go above and beyond to cite these articles to meet GNG.

I do agree that this drive is not perfect, and I do want to say that I appreciate that you have raised concerns about the drive and about uncited articles in general. We might be relying too much on good faith here and a better solution might be needed. But it is ludicrous for us to require new articles to be fully cited while we are not making an active effort to cite our older unreferenced articles. We can do better than this. Because a lot of math articles are not cited, I want to send this notice ahead of time so that people like you who knowledgeable about the topic area can help address these articles. CactiStaccingCrane (talk) 02:54, 22 January 2024 (UTC)

@CactiStaccingCrane: As predicted: [5] —David Eppstein (talk) 08:13, 5 February 2024 (UTC)

So? CactiStaccingCrane (talk) 15:32, 5 February 2024 (UTC)

It seems like there are some editors who are really excited about deleting stuff (to rack up points?) whether or not it is notable or verifiable, and are constantly hunting for excuses to do so. That's indeed a problem, but the better solution is to educate them about the Wikipedia project's goals and community process, not to let them push you into wasting time jumping through bureaucratic hoops.

Again, I don't have any problem with the goal of improving the sourcing of poorly sourced math articles. I just don't think this should be turned into a speed game where the person who adds the most footnotes wins irrespective of whether they add any value. –jacobolus (t) 02:42, 22 January 2024 (UTC)

Anyway, don't let me discourage anyone from participating here if you want. I just hope anyone trying to add sources to math articles is doing so carefully and thoughtfully rather than prioritizing speed. My personal experience is that it takes me significant amounts of time and effort to carefully add sources for one small subsection of one article, mostly spent reading and thinking. This contest has badges for adding sources to 300, 500, or 750 articles during the month of February. I can't even imagine doing good work at anywhere close to that pace, even if I spent 10 hours per day for a month doing nothing but adding sources to math articles. YMMV. –jacobolus (t) 02:53, 22 January 2024 (UTC)

I appreciate your concerns about the drive in general. I don't want to give a false assurance here and say that the reviewing process will spot 100% fake references and bogus attempts. But again, the majority of article that will be addressed by these articles are geostubs, biostubs, school/universities and obscure music bands. As an example, there are 238 uncited math articles compared to ~113000 in total. Statistically speaking it is unlikely for people to randomly come across these articles and participants who will cite these math articles are likely to be those knowledgeable about mathematics and seek for these articles deliberately. CactiStaccingCrane (talk) 02:59, 22 January 2024 (UTC)

geostubs, biostubs, school/universities and obscure music bands – what's the point of getting a lot of people to spend their time marginally improving obscure never-read articles that nobody cares about? Personally I think it would be a better use of time for anyone here to make their goal for February something like: "improve one high-importance math article from C class to B class in the next month", including doing a thorough literature review, drawing some nice diagrams, and writing a clear and concise overview of the current expert consensus. Again, YMMV. –jacobolus (t) 03:04, 22 January 2024 (UTC)

I applaud your philosophy here, but not to be condescending, people can have different interests :) CactiStaccingCrane (talk) 03:35, 22 January 2024 (UTC)

Well, despite the disagreements above, the list of unreferenced articles provided by CactiStaccingCrane does at least provide a helpful way of finding some mathematics articles that are on good topics but need help, although many others are on marginal topics (that I would rather not waste my time on). I already took advantage of that list to find and clean up the sourcing in Arithmetic–geometric mean and Basel problem. I think there are plenty of others worthy of attention there. —David Eppstein (talk) 08:42, 22 January 2024 (UTC)

I hope you find them useful :D CactiStaccingCrane (talk) 10:59, 22 January 2024 (UTC)

From my perspective, this is not about adding references, but rather improving the articles. I have seen the tables listing many bunches of articles that may need to be improved. I do think that there are many articles without being tagged that may need to be improved as well, especially with the article that contains many no-context-and-what-to-do-tables. Dedhert.Jr (talk) 03:34, 23 January 2024 (UTC)

One could also view the announcement here as a warning: fix up your unreferenced articles by the end of January, before the cleanup drive starts, or some eager cleanup drive participant will get to them without as much care for detail. —David Eppstein (talk) 04:52, 23 January 2024 (UTC)

Why do you think that adding one citation to a mathematics article so damaging? Or let me be straightforward: why do you view the drive so negatively? CactiStaccingCrane (talk) 05:39, 23 January 2024 (UTC)

I think that it is important to provide high-quality sources for stubs on significant topics in mathematics, and to do something to clean out the many bad stubs on insignificant topics. I think it is important that this be done by people who are interested in the mathematics (not necessarily professional mathematicians!), and not just those interested in getting gold stars for sourcing lots of things, because interest leads to expertise and expertise leads to better choices for the sourcing. I think that having people add low-quality sources to indiscriminately chosen articles causes problems in two directions: it does not change the need for the significant topics to have high-quality sources, but it obscures the fact that they need them, and it does not change the need to clean out the insignificant topics, but by removing them from the lists of problem articles it makes it harder to find them. I hope that the sourcing drive does not lead to this problem of adding low-quality sources to indiscriminately chosen articles but I worry that it might. —David Eppstein (talk) 05:59, 23 January 2024 (UTC)

I think that's true and I should list some examples of what sources is encouraged/discouraged from use generally. But in general, I have to admit that this drive will be a pain in the ass to manage and it will keep me busy for the rest of this and next month ;) CactiStaccingCrane (talk) 09:59, 23 January 2024 (UTC)

I have looked up the list, and it confused me: why is the article decagonal bipyramid classified as "cite no sources", although it is a redirect article? Dedhert.Jr (talk) 10:33, 23 January 2024 (UTC)

Someone has redirected it recently. CactiStaccingCrane (talk) 10:35, 23 January 2024 (UTC)

The list is only updated weekly. In this case, I judged that there were no sources giving decagonal bipyramid independent notability from bipyramid, and redirected it per WP:BLAR in preference to trying to get it deleted. —David Eppstein (talk) 17:54, 23 January 2024 (UTC)

I just redirected the heptagonal and octagonal cases as well, and shrank the still-overwide tables. If there's anything to say about one or another specific n-gonal bipyramid, it can be put in a section of bipyramid. At the point the specific information grows to more than several paragraphs it can plausibly be re-split into a new article again. –jacobolus (t) 18:07, 23 January 2024 (UTC)

While we're here, Bipyramid is very weakly sourced, if anyone is looking for a page to improve sources on. –jacobolus (t) 19:39, 23 January 2024 (UTC)

Thank you for your work! CactiStaccingCrane (talk) 01:01, 24 January 2024 (UTC)

I already have some planning about the sketch of the structure and the improvement of the content, but there are some missing topics; for example, the bipyramidal graph is missing. I remember that there is a source that mentions about the graph of bipyramids, but it is not free access. Dedhert.Jr (talk) 01:51, 24 January 2024 (UTC)

R2 values

Could someone (find a source) and add a sentence to the top of Coefficient of determination that says something like "Generally, bigger/smaller numbers are better", or whatever top-line summary might be useful for someone completely unfamiliar with statistics? WhatamIdoing (talk) 17:51, 7 February 2024 (UTC)

I added a reference in the body of article. However summarizing the meaning of R-squared in a sentence is difficult. Larger values of R-squared imply regression models that are better at reproducing the input data. But "better" is not something R-squared can tell you. Johnjbarton (talk) 18:14, 7 February 2024 (UTC)

Thank you! I really appreciate it.

Some years back, someone was saying that the most dangerous thing in the world was a spreadsheet. Among the many things you can do/screw up with a modern spreadsheet is to select some data, click two buttons to make a graph, and then click another button to fit a regression. But there are options (e.g., linear vs logarithmic), and while there are doubtless better ways to go about it, I imagine that the most common way to pick one is to try all the options and then pick the one that you think looks best. The more advanced options require knowing what you're doing – like knowing whether it's better, if you just click through all the options, to pick the option whose automatically calculated R² is the biggest or the smallest in the list. This is the level of comprehension that I was hoping to address here. WhatamIdoing (talk) 18:37, 7 February 2024 (UTC)

Conformal linear transformation

Your input is requested to settle a dispute at Talk:Conformal linear transformation. Thanks. 100.36.106.199 (talk) 11:51, 8 February 2024 (UTC)

"univalent relations"

A recent edit at partial function by User:Rgdboer claims that a partial function is a "univalent relation". I googled that term, and the first hit was an entry at univalent added by Rgdboer.

I do not recall coming across this term with this meaning in the wild. I would be interested to know if anyone else has. --Trovatore (talk) 03:24, 28 January 2024 (UTC)

On Scholar Google, there are many hits for "univalent relation" (with the quotes). I did not check whether they correspond to the definition in Univalent relation, since I do not care very much about terminology of relations. In fact, User:Rgdboer's edits consisted of changing "functional relation" to "univalent relation", and redirect univalent relation to Partial function. As the latter article is not the place for defining a specific type of relations, I have restored (an fixed) the previous target, and left the change from "functional relation" to "univalent relation". D.Lazard (talk) 12:29, 28 January 2024 (UTC)

Some care is necessary to edit accurately. Functional relation is not a term supported by WP:RSs. All mention of it should be removed from the project. Partial function is not a function except on a subset S of the source set. Thus it is a misnomer and Univalent relation is preferred. — Rgdboer (talk) 22:40, 31 January 2024 (UTC)

Rgdboer, "partial function" is entirely standard in mathematics, and I'm afraid that the fact that you wish it weren't is of no concern here. Please do not attempt to change mathematical terminology by editing Wikipedia. You can go make your case in the real world.

That said, it does appear that the term "univalent relation" has some usage in this sense. Not a lot, but enough that I can agree it can be mentioned. --Trovatore (talk) 23:20, 31 January 2024 (UTC)

As to the separate question about functional relation — I have to say I am not familiar with this as a mathematical term of art. I can imagine someone talking about binary relations in general, and saying, well, these ones here are functional because they represent functions, but I am not aware of anyone using "functional relation" as a standalone precise term. Why wouldn't you just say "function", or maybe "partial function", depending on context?

Also I think it's reasonably likely that someone typing "functional relation" into the search box, or wikilinking it, intends something non-mathematical entirely, so it may well be reasonable to delete the redirect per WP:XY if for no other reason. --Trovatore (talk) 01:10, 1 February 2024 (UTC)

We do have a related (and sourced) redirect at functional graph. —David Eppstein (talk) 01:15, 1 February 2024 (UTC)

That seems much less likely to be searched for outside of mathematics. --Trovatore (talk) 01:15, 1 February 2024 (UTC)

As far as I know, the main uses of "functional relation" occurs in physics and applied mathematics in the case of two quantities that are related in such a way that one can be expressed as a function of the other. Scholar Google search for "functional relation" function ("function" is here for trying to eliminate non-mathematical articles) provides many examples of the use of this phrase, even in article titles. Most of the examples are in applied mathematics (data analysis), but

Friedli, F. (2016). A functional relation for L-functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L-functions. Journal of Number Theory, 169, 342-352.

is an example in pure mathematics. However, I have not verified the exact meaning of the phrase in these articles. D.Lazard (talk) 11:18, 1 February 2024 (UTC)

Here's an example from the philosophy of science:

Although scientific laws may take the form of any relation between variables in some specified set of objects, causal laws represent a specific kind of relation of special interest to humans. Causal laws are relations in nature that reveal what one would have to be able to do to effect specific kinds of outcomes unambiguously. And functional relations are an appropriate form for expressing these kinds of relations. Recall that a functional relation is a relation between two sets, a first set and a second set, such that to each element of the first set there corresponds one, and only one, element from the second set. Thus, functional relations as causal relations associate with any given value of some independent variable (which may be multivariate), a unique value of a dependent variable (which may also be multivariate), revealing thus the unique outcome associated with any given value of the independent variable. So, if I want to know how to achieve a specified pressure in a gas in some container with fixed volume, then I must heat the container and raise the temperature of the gas to a specific value; or, if I cannot do that, and the container's volume can be varied, then I must decrease the volume of the container to a specific value. The pressure of a gas varies as a function of its temperature and volume. Thus, whenever I specify a causal hypothesis, I specify causal directions between variables as a part of the causal hypothesis. I do this by specifying those variables that are functions of other variables.

Mulaik, Stanley A. (1986). "Toward a Synthesis of Deterministic and Probabilistic Formulations of Causal Relations by the Functional Relation Concept". Philosophy of Science. 53 (3): 313–332. JSTOR 187672.

–jacobolus (t) 16:00, 1 February 2024 (UTC)

I can also find a couple sources using "functional relation" as a synonym for what I have usually heard called a functional equation. For example: "A meromorphic function $F(\zeta )$ on this torus can be defined as a function satisfying the functional relation $F(\rho ^{2}\zeta )=F(\zeta )$ and having only poles in the annulus $\rho \leq |\zeta |<\rho ^{-1}.$ Such functions have been dubbed loxodromic functions." –jacobolus (t) 17:00, 1 February 2024 (UTC)

Let's not rabbithole on what "functional relation" means in mathematics, unless it can be established that at least the majority of uses of the term (and really we'd want a fairly solid majority) are mathematical at all. Otherwise I think it's WP:XY and probably should be deleted. That's without prejudice to the idea that there could possibly exist a functional relation (mathematics) redirect, but to be honest that sounds sort of pointless to me. --Trovatore (talk) 17:42, 1 February 2024 (UTC)

WP:XY seems totally irrelevant to this question. But anyway, the main use of "functional relation" I can find after skimming a bunch of papers, both in mathematics and in adjacent applied fields, is that it is broadly a synonym for "function", but some authors draw an explicit distinction when trying to emphasize one or another aspect of the function concept. My impression is that D.Lazard's summary above (two quantities that are related in such a way that one can be expressed as a function of the other) generally seems about right. –jacobolus (t) 18:19, 1 February 2024 (UTC)

How is it irrelevant? It seems very much on point to me. We can't know whether people linking or searching this term are looking for mathematics (or "adjacent fields") at all. If there were two or three clear meanings, we could make a disambig page, or use hatnotes if one of them is primary. But it's just all a big mush as far as I can tell, some people using it one way and some people in another, but without enough clarity to make the existence of the redirect preferable to Wikpedia's search engine. So we should delete the redirect to expose the search engine. --Trovatore (talk) 18:56, 1 February 2024 (UTC)

WP:XY is explicitly about titles of the form "X and Y", where X and Y are two things which typically go together but can also be discussed separately. As demonstrated by the examples there, sometimes it is valuable to keep a title like "X and Y" or a redirect from the name "X and Y" to a relevant section of an article (either X or Y or another) where the topic of X and Y together is explicitly discussed. Other times it is decided to delete these in cases where the existing articles cover the subject well enough independently, or where the category is inherently politically controversial, etc. WP:XY does not describe a concrete policy in which one choice or another is a priori correct – whether each such redirect should exist is decided by consensus case by case – but links to some previous examples for context, so "per WP:XY" doesn't mean anything. Either way, this has little if anything to do with whatever we're discussing here. –jacobolus (t) 20:38, 1 February 2024 (UTC)

Hmm. It didn't use to be, I think. Or maybe I misunderstood it when I saw it in an RFD discussion.

Anyway, even if I didn't have the exact right link, the substantive point stands. We don't need a redirect for every way writers have combined words together. There are many many things "functional relation" can mean, and none of them seems to be particularly "canonical". I don't see any value in keeping this redirect. Admittedly there's not a huge upside to deleting it either, but there could be some. For example users who see the term somewhere with a different meaning might not be misled by seeing it come up when they search for it, and editors who think it's a precise term with an agreed meaning might be disabused of that notion when they add the link and see it come up red. --Trovatore (talk) 21:37, 1 February 2024 (UTC)

(I might change my view if it could be established that non-mathematical uses are just using the two words in natural English but that the mathematical usage is a term of art. But it doesn't seem that the latter is true, at least not in any consistent and well-understood way.) --Trovatore (talk) 17:44, 1 February 2024 (UTC)

In the above discussion two meanings for "a functional relation" are given (another name for functional equation and a binary relation that is the the graph of a function or a partial function. None of these meanings can be easily infered from the dictionary definitions of the two words constituting the phrase.

As these two meanings refer to different concepts, I'll boldly transform the redirect Functional relation into a dab page. If there are some non-mathematical usages, they can easily be added to the dab page. D.Lazard (talk) 12:02, 2 February 2024 (UTC)

Dolciani versus Bourbaki

Mary P. Dolciani wrote textbooks where functions are defined as a particular type of relation. Millions of secondary students in North America used these algebra textbooks and learned about functions in the realm of relations. In France, Bourbaki advanced the theory of sets in French. A review of the Bourbaki approach was given by Wayne Aitken, writing in English in 2022 at California State University San Marcos. His pdf notes, on page 7, that Bourbaki used relation meaning formula, so a different slant is taken. "...each specific symbol is classified as either functional (Bourbaki: substantific) or relational."

On page 38 Aitken gives this

Remark: If (∃! x) R[x] is a theorem, then Bourbaki calls R[x] a "functional relation in x". In other words we can regard "R[x] is a function relation x" is synonymous with "(∃! x) R[x]". Recall that Bourbaki uses the term relation for our term formula.

Thus, the sources in English and French mathematics diverge, so editors with different backgrounds are in conflict. Rgdboer (talk) 02:33, 4 February 2024 (UTC)

Even in English there are two different definitions:

• The relational approach
• The categorical approach, In which a function is a triple $(D,R,F)$, where $\forall _{x}\in D(\exists y\in R)(x,y)\in F$

The categorical approach is standard in, e.g. Algebraic topology. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:09, 8 February 2024 (UTC)

Draft:Invariant set

Will someone please review this draft? Should it be accepted? Dammit, Jim, I'm a computer scientist, not a mathematician. Robert McClenon (talk) 06:06, 9 February 2024 (UTC)

The draft is a WP:REDUNDANTFORK of Invariant set. Also, it contains WP:OR terminology. D.Lazard (talk) 13:33, 9 February 2024 (UTC)

Calling this a "redundant fork" of 1–2 paragraphs in a different article seems unnecessarily sharp (and nowhere close to justified by the text of WP:REDUNDANTFORK – have you looked at it recently?). This subject can entirely plausibly be a separate article instead of a short section, if someone can find the sources to back more material. –jacobolus (t) 15:44, 9 February 2024 (UTC)

My comment in the draft is: We have already Invariant set, which covers the same subject. This is a section of Invariant (mathematics). It is possible that this section deserves to be expanded, and eventually to be split into an independent article, but this requires a WP:consensus at Talk:Invariant (mathematics). For the moment, this draft is a WP:REDUNDANTFORK. Also, the terminology ("one-sided invariant set", "two-sided invariant set", "a dynamics") of this article seems WP:OR.

By the way, I do not see any reason for not being sharp about an article where everything that is not in Invariant set is either WP:OR, or wrong (such as the sentence that follows the first "equivalently", or the generalization to categories) or very badly formulated (for example, the examples in the section 'Examples')" D.Lazard (talk) 16:38, 9 February 2024 (UTC)

The reason is that Wikipedia is a collaborative project that we want to encourage people to feel good about participating in, including newcomers and folks from different backgrounds. Ideally we can disagree about content, talk it over, and arrive at a consensus result without making it feel like a personal rejection. I agree that the business about "one-sided" vs. "two-sided" seems a bit confusing though.

@Robert McClenon, have you taken a look at Invariant (mathematics)? It seems like your interest is examples from probability theory. Does that article handle the subject well enough to explain those, or are there specific parts that you think should be expanded / split into a separate sub-article? –jacobolus (t) 18:42, 9 February 2024 (UTC)

@Jacobolus I don't see anything personal in D.Lazard's assessment of the article. It's just a statement of facts about the quality of the draft. Wikipedia is not about making people feel good. Anybody is welcome to participate, but their contributions should be up to par with the expected level of mathematical correctness and clarity of exposition, while following all the required Wikipedia guidelines, etc, etc (WP:OR in particular). PatrickR2 (talk) 07:25, 11 February 2024 (UTC)

I didn't say it was "personal" (and I don't think it was improper or done with any ill intent). I said it seemed unnecessarily sharp. I think we should try to err on the side of being as patient and generous as practical with newcomers, even when we don't want to take one or another specific contribution. Cf. WP:BITE. To elaborate: someone typically decides to make a new article or edit an existing article when they either (a) can't find what they were looking for, or (b) don't think the previous coverage sufficiently handled the specific topic/question they were concerned about. Usually those changes have their own flaws (as do many from established editors), but they can still give us valuable feedback if we try to take the effort to understand why someone thought it was important to contribute a change and reflect on whether the implicit or explicit criticism of the existing article(s) was reasonable, and start a dialog about what they think is missing. –jacobolus (t) 07:30, 11 February 2024 (UTC)

Has Bard chatbot expressed an interest in collaborating with the WMF?

This question is motivated by something Bard said at:

v:Chatbot math/Bard/Unitary Transformation & Matrix Symmetry#I will post this on Wikiversity and leave a note on a Wikipedia talk page. Don't worry, this problem will get solved. Goodbye, for now. I will sign off as I would on Wikipedia/Wikiversity --user:Guy vandegrift

I contribute to Wikipedia mostly by adding images (see list). But I mostly edit Wikiversity because I am too fun-loving to follow your editorial rules (rules of which I strongly approve!) Recently I have been playing with Bard, and am convinced that Bard's and Wikipedia's future are closely linked. I am not here to make any proposals regarding chatbots and Wikipedia. But I do invite you to think about this. And you might want to look at two conversations I recently had:

• v:Quantum mechanics/A conversation with Bard has a sister link on Wikipedia's History of quantum mechanics, but I made it clear to the editors of that page that I have no objections to deleting the link.
• v:Chatbot math/Bard/Unitary Transformation & Matrix Symmetry is an extremely long conversation in which I unsuccessfully resolve a question about symmetric matrices. A brief commentary is available at v:Chatbot math#Unitary Transformation & Matrix Symmetry

I am not ready to make any proposals or give any advice. But if anyone is interested in looking into the question of chatbots and Wikipedia, let me know.--Guy vandegrift (talk) 00:47, 7 February 2024 (UTC)

If you are treating anything a chatbot says as anything other than telling you what you want to hear, you are making a mistake. —David Eppstein (talk) 01:15, 7 February 2024 (UTC)

Please please please don't ever try to add AI-generated output to Wikipedia. What a disaster that would be. We have enough problem as it is with humans pretending to be bots; we don't also need bots pretending to be human. –jacobolus (t) 01:19, 7 February 2024 (UTC)

Ha ha ha. It looks like there will be very good AI/Proof Assistant combos available in a couple of years for maths. But we're not there yet, certainly not with ones like Bard. Yes it can help you with what yo're doing but I'd be very careful to check everything. We're not supposed to engage in any original research here so at most you're talking about using it for spotting problems and cheking citations and stuff like that. Generating good maths images from descriptions sounds like it could be a good use though of course it would have to be checked - but once proof checkers ae incorporated that should be a fairly reasonable job. NadVolum (talk) 12:58, 7 February 2024 (UTC)

I wonder - perhaps it would be possible to add a checker for normal reasonng as well which would staep through the rasoning and flag and maybe helps correct the various types of false arguments in what an AI comes up with. The problem with just training on what is out there like an LLM does is it copies all the bad reasoning and biases of humans. NadVolum (talk) 15:44, 7 February 2024 (UTC)

My experience with using AI assistants for "Generating good maths images from descriptions" has been...not good. I needed an image of a solid cone for a paper. I asked Adobe's AI assistant to generate one for me. It was unable to generate anything that looked like a cone. I had to figure out how to do it myself with gradients. Then, for a separate mathematics blog post, I wanted a picture of a pencil being sharpened with a long shaving coming out. The AI could draw pencils, and pencil sharpeners, but not believable shavings, and it insisted that the pencils went into the sharpener eraser-end first. In that case I gave up and found a close-enough photo from Commons. —David Eppstein (talk) 16:20, 7 February 2024 (UTC)

I just asked Google for images of 'pencil sharpener in acion', and Wow! I think I can see the problem an AI might have in getting a basic model of what one looks like! NadVolum (talk) 17:00, 7 February 2024 (UTC)

I've not tried Bard or math questions, but physics questions to Google's generative AI echo back Wikipedia content that I personally typed in. So it seems to me the collaboration is well underway ;-) Johnjbarton (talk) 16:16, 7 February 2024 (UTC)

The encyclopedic value of stochastic-parrot output is zero at most. XOR'easter (talk) 18:38, 14 February 2024 (UTC)

Can you please review Draft:Mathseeds

It's been a while since I submitted it for review, and I've tried the Education WikiProject. Faster than Thunder (talk | contributions) 03:33, 17 February 2024 (UTC)

I would say this does not belong to Wikiproject Mathematics. The Education WikiProject seems the right place for it. PatrickR2 (talk) 04:01, 17 February 2024 (UTC)

After you strip out the primary and poor-quality sources (like prweb, blogs), what are the WP:THREE best sources that remain? 100.36.106.199 (talk) 13:05, 17 February 2024 (UTC)

evaluation map

Currently, Evaluation map is a redirect to Initial topology#Evaluation. However, I think it may also refer to Apply#Universal property. What would you suggest I do? SilverMatsu (talk) 05:26, 18 February 2024 (UTC)

It may also refer to Polynomial ring#Polynomial evaluation or Polynomial evaluation, or also to function evaluation. (By the way, the definition given in Apply#Universal property seems to be nothing else that an abstract version of that of function evaluation).

So, the current target is certainly not a primary topic (I do not understand why is map is called an evaluation map). I'll rename Evaluation map as Evaluation map (topology), and create a dab page for evaluation map. D.Lazard (talk) 10:09, 18 February 2024 (UTC)

Thank you for creating the dab page. Also, I agree with clarifying the page name. By the way, I accessed the Apply#Universal property via the wiki-link in the Exponential object. --SilverMatsu (talk) 15:38, 19 February 2024 (UTC)

Drawing polyhedron

I would like to draw any polyhedron or group of polyhedron modeling on computers or laptops. Stella is the first software I searched on Google (as far as I remember), but some of the polyhedrons in this software have silver balls representing their vertices, so I prefer to find another one. Are there other recommendations for apps or software? Dedhert.Jr (talk) 12:13, 19 February 2024 (UTC)

I like https://prideout.net/blog/svg_wireframes/ — it generates images in vector rather than bitmap formats, which I think is better for Wikipedia illustrations when possible. It can do shading and lighting effects but I usually use it with a plainer style in which all faces are the same color and somewhat transparent, as in for instance File:Triaugmented triangular prism (symmetric view).svg and File:Translucent Jessen icosahedron.svg. —David Eppstein (talk) 19:50, 21 February 2024 (UTC)

Perhaps I would say that this is difficult to create using Python, and I can't do Python. But I think I will give it a try in the future. Dedhert.Jr (talk) 15:18, 23 February 2024 (UTC)

Edit warring and content disputes on Hindu–Arabic numeral system

Are any other folks interested in the history of number representation willing to wade into an ongoing content dispute / edit wars at talk:Hindu–Arabic numeral system? Sorry to drag anyone into what has become a bit of a mess, but this and related articles are in my opinion pretty mediocre (incomplete, poorly organized, poorly sourced, misleading, ...), but efforts to make even modest improvements are getting hit by instant reversion, and discussion gets repeatedly diverted away from content disagreements toward unproductive meta conversations. –jacobolus (t) 19:16, 25 February 2024 (UTC)

List of Johnson solids

The reviewer has gone AWOL during the nomination of List of Johnson solids. I welcome someone who is in favor of replacing the reviewer and providing comments for the sake of improvement. Dedhert.Jr (talk) 13:36, 26 February 2024 (UTC)

Mar 2024

Notability of John H. Wolfe

The article John H. Wolfe has gone through a PROD, but still has issues as it is based on one secondary textbook claim that his work on model-based clustering matters. It was created directly by a novice editor (Stat3472 33 edits). The article model-based clustering supports him as the inventor, but whether this is big enough for notability is unclear. Comments on that talk page please. Ldm1954 (talk) 09:57, 2 March 2024 (UTC)

≙

There is a discussion about the ≙ character that needs attention from mathematical editors at Wikipedia:Redirects for discussion/Log/2024 March 2#≙. Thryduulf (talk) 12:35, 2 March 2024 (UTC)

Mental calculation

Does anyone feel like cleaning up Mental calculation? It's roughly as disorganized as one would expect. XOR'easter (talk) 18:35, 3 March 2024 (UTC)

any, every, some

• For every number $\varepsilon >0,\ldots$

• For some number $\delta >0,\ldots$

It is clear that in standard English usage, the words "every" and "some" as used above are respectively universal and existential quantifiers.

"Any" can be a universal quantifier, as in:

"Any fool can see that."

(But "Anyone can be elected chair of the committee" doesn't mean the same thing as "Everyone can be elected chair of the committee.)

"Any" can also be an existential quantifier, as in:

• There isn't anyone here who can answer that question.

• Is there anyone here who can answer that question?

• If anyone knows the answer, please step forward.

I thought that there are three contexts in which "any" is an existential quantifier:

• negations,
• questions, and
• conditional clauses,

those being the three exhibited above.

But then in the article titled Causality conditions, I found this:

• A manifold satisfying any of the weaker causality conditions defined above may fail to do so if the metric is given a small perturbation.

Here, "any" is used as an existential quantifier, and it is not clear to me that it is one of those three kinds. Thus my list appears to be incomplete.

A grammar question rather than a math question, but one to which mathematicians are in more desparate need to pay attention than is perhaps anyone else.

What should be added to this list? Michael Hardy (talk) 18:51, 21 February 2024 (UTC)

In the above quotation, "any" is a universal quantifier. D.Lazard (talk) 19:02, 21 February 2024 (UTC)

You can still see "any" here as a universal quantifier, in the sense that "for all of these weaker causality conditions, a manifold satisfying said condition can fail to do so if <rest of sentence>." I would argue that the existential quantifier here is actually hidden in "can", in the sense that "a manifold satisfying said condition can fail to do so if..." is shorthand for "there exists a manifold satisfying said condition that fails to do so if..." GalacticShoe (talk) 19:09, 21 February 2024 (UTC)

Because pushing a negation through a $\forall$ flips it to a $\exists$ and vice-versa, examples involving negation — including "not", "fails", "never", etc. — can be argued about endlessly. It seems to me that math textbook authors solve this problem by stating each definition and theorem as clearly as they can, relying on the proof to clarify the exact meaning of a theorem in a pinch, and tolerating looser talk in discussions between theorems. Mgnbar (talk) 19:30, 21 February 2024 (UTC)

The correct phrasing is "for any (every) said condition, there exists a manifold satisfying it that fails to do so if...". So the hidden existential quantifier does not refer to the same thing. D.Lazard (talk) 19:36, 21 February 2024 (UTC)

The meaning of the expression "a manifold satisfying any of the weaker causality conditions defined above" is a manifold which falls into one or more of the classes defined by the previous causality conditions; as previously stated in the article, if it falls into one of them, it also falls into the previous classes, as they are nested with stricter conditions listed later. But the manifolds of particular interest for that section are the strongly causal ones (the immediately preceding condition). My understanding based on the article's text is that "stably causal" means a strongly causal manifold which remains strongly causal under any possible perturbation of a chosen (arbitrarily small) magnitude. Or another way of saying this: if a manifold is "stably causal", then there exists some specific size of perturbation for which every smaller perturbation of the manifold preserves the strong causality property. From what I can tell the perturbations of other kinds of causality-condition-satisfying manifolds are not at issue (beyond the initial mention, for context, that for each of the earlier conditions there exists some manifold satisfying it which can be perturbed into not satisfying it by an arbitrarily small perturbation). –jacobolus (t) 19:41, 21 February 2024 (UTC)

Some months ago, the was consensus that "any" should be avoided (in order not to require the reader to be familiar with discussions like the above one), see MOS:MATH#ANY. - Jochen Burghardt (talk) 20:10, 21 February 2024 (UTC)

Rephrasing this particular passage is more complicated than the examples given there, as it expresses a somewhat tricky logical claim. I don't think this one is really ambiguous in context, but it could be rephrased as e.g. "For each of the weaker causality conditions defined above, there are some manifolds satisfying the condition which can be made to violate it by arbitrarily small perturbations." –jacobolus (t) 21:43, 21 February 2024 (UTC)

Jacobulus last suggestion is perfect. To answer Micheal Hardy's original question, there is yet another sense of any: in this case, it's "menu choice": "pick any one item from this menu". Menu choice is similar to exclusive-or, but is not truth-valued, it is object-valued. Menu choice shows up as a fragment of linear logic (for example, the quantum no-cloning theorem, which says "you can only have one of these") but also in vending machines "for a dollar you pick one item" and in mutex locks in computing (one user at a time.) Menu choice is a really cool tool in foundational logic. 67.198.37.16 (talk) 07:34, 4 March 2024 (UTC)

Brouwer–Hilbert controversy

Should this article be renamed to Grundlagenstreit? This is the name often given in the literature to this debate. I do not know much about it but it seemed odd when I was looking for it. See for example Brouwer's biography ReyHahn (talk) 10:01, 4 March 2024 (UTC)

For me, naming an obscure topic from 100 years ago using an unfamiliar non-English word (German?) is the same as deleting the article.

Maybe "Grundlagenstreit, the Brouwer–Hilbert controversy"? Johnjbarton (talk) 15:45, 4 March 2024 (UTC)

Maybe the term Grundlagenstreit should be included in the lede; it seems common enough in writings about the topic. XOR'easter (talk) 16:18, 4 March 2024 (UTC)

Apparently Grundlagenstreit means "foundational debate", and was related to Hilbert's book Grundlagen der Geometrie. Seems fine to me to create a redirect and mention the name in the lead section (doesn't need to be bolded in my opinion). –jacobolus (t) 16:30, 4 March 2024 (UTC)

No, but theree should be a printworthy redirect from Grundlagenstreit to the article. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:28, 4 March 2024 (UTC)

Thank you all, I prefer to keep it bold but that can be discussed. As for the main topic I consider this  Done.--ReyHahn (talk) 21:06, 4 March 2024 (UTC)

Merge?

On pl wiki, User:Epsilon598 suggested AM–GM inequality, QM-AM-GM-HM inequalities and Generalized mean may need a merge. Thoughts? _{Piotr Konieczny aka Prokonsul Piotrus| reply here} 02:07, 26 February 2024 (UTC)

Actually, Pythagorean means should also be at least linked to the others. In Polish all of these inequalities are usually called simply "inequalities among means", which is also used in at least one of these articles. This name is not nearly as fitting in English as it is in Polish, but would be my first guess. Epsilon598 (talk) 02:45, 26 February 2024 (UTC)

I usually hear this called "Power Mean Inequality" in English (which is currently a redirect to Generalized_mean#Generalized_mean_inequality). Elestrophe (talk) 16:38, 7 March 2024 (UTC)

Notice of discussion

 Note: A discussion at Wikipedia talk:Good article nominations might be of interest to members of this project. ~~ AirshipJungleman29 (talk) 22:23, 7 March 2024 (UTC)

Inconsistent

In the interest of keeping this Project rational, it can be noted that as things stand, a function may be partial or total or multivalued or univalent. The terms "partial function" and "multivalued function" are self-contradictory, they are oxymorons. According to WP:Article names, consistency is one of the parameters of evaluation. Tolerating contradiction, as in the two article names, invites arbitrary deductions since any proposition may be deduced from a contradiction. A function is a type of relation so its variants are best described with properties of relations. A partial function is a univalent relation, and a multivalued function is a relation. Rgdboer (talk) 01:09, 10 March 2024 (UTC)

It's established mathematical terminology, and it's also pretty common in English generally (see, for example, Subsective modifier). - CRGreathouse (t | c) 01:17, 10 March 2024 (UTC)

Lots of things have names of the form [modifier] [something] to indicate that it is a generalization or variant form of something or something modified in a certain way rather than a special case of something. A Reuleaux triangle is not actually a triangle. A truncated icosahedron is not actually an an icosahedron, and a snub cube is not a cube. "Partial function" is no different. There is nothing inconsistent about this naming convention. See also WP:COMMONNAME and WP:NEO. —David Eppstein (talk) 01:29, 10 March 2024 (UTC)

Well put. I would add that a skew field may be a field but is not necessarily a field, which maybe is more directly analogous to the case at hand, since a partial function may be a function but is not necessarily a function. --Trovatore (talk) 03:28, 10 March 2024 (UTC)

I don't believe Wikipedia claims to be "rational", nor would we want it to be. Rationality has its limits; irrationality knowns no bounds. Johnjbarton (talk) 01:56, 10 March 2024 (UTC)

It's also often much harder to keep things rational. — MarkH₂₁^talk 03:51, 10 March 2024 (UTC)

You could argue that irrationality has its limits too :P GalacticShoe (talk) 04:09, 10 March 2024 (UTC)

The first goal of article names should be reflecting common usage among reliable sources, especially those from professional practitioners, with common alternative names listed/explained in the article text. This helps the widest range of readers to get up to speed with the terminology and conventions they will find in other sources. Other goals are subsidiary to that, and any "irrational" features of the most widely used and accepted nomenclature can be explained in text.

If you have a problem with widespread mathematical conventions, the place to fix it is in the mathematical literature, not in Wikipedia. (But making an explicit note when terminology is confusing, ambiguous, historically revisionist, politicized, a misattribution, etc. could be helpful.) –jacobolus (t) 04:27, 10 March 2024 (UTC)

Also, for considering the original example, the general meaning of "function" refers to univariate total function, but, in many texts, partial functions and multivariate functions are simply called functions. These generalized functions may be considered as functions in the first sense, by changing of domain. This is for this reason that I have added recently the subsections "Partial functions" and "Multivariate functions" to Function (mathematics)#Definition, with explanations on these terminology shifts. D.Lazard (talk) 09:54, 10 March 2024 (UTC)

Requested move at Talk:N = 2 superconformal algebra#Requested move 7 March 2024

There is a requested move discussion at Talk:N = 2 superconformal algebra#Requested move 7 March 2024 that may be of interest to members of this WikiProject. Killarnee (talk) 23:44, 14 March 2024 (UTC)

Torsion tensor

Could you join the dispute at Talk:Torsion tensor?

The summary of the discussion (in my view point) is written in the section Discussion between Tito Omburo and Idutsu.

---Idutsu (talk) 14:20, 14 March 2024 (UTC), editor of japanese Wikipedia.

I've spent a long time trying to make sense of the torsion tensor in terms of normal coordinate systems. I came to the conclusion a long time ago that the #Twisting of reference frames section of the torsion page was wrong. Not in interpretation, but literally mathematically incorrect. The relationships asserted between the torsion tensor and the development of a frame along a curve don't match: the expression people think of for the rotational development of a coordinate frame correspond only to the covariant derivative of the frame along the curve, not to the difference of covariant derivatives as appears in the torsion tensor.

I've never seen any source which actually went through the details of this interpretation and explained it, and I've seen many mathoverflow posts just like Bill Thurstons which wax lyrical about interpretations of torsion without ever explaining in mathematical detail how the formula of torsion relates directly to the development of a coordinate frame along a curve.

I don't have any skin in the game of your discussion but if it were me I would try to hold this to a very high standard of reference because it is a notoriously wishy-washy subject in differential geometry. The conclusions of Tu & Spivak that there is no actual detailed mathematical link between the name torsion and some of the more elementary interpretations of twisting of a frame around a curve seem to hold up to my scrutiny at least. Tazerenix (talk) 06:23, 15 March 2024 (UTC)

Is this the part you disagree with?

The foregoing considerations can be made more quantitative by considering a small parallelogram, originating at the point $p\in M$, with sides $v,w\in T_{p}M$. Then the tangent bivector to the parallelogram is $v\wedge w\in \Lambda ^{2}T_{p}M$. The development of this parallelogram, using the connection, is no longer closed in general, and the displacement in going around the loop is translation by the vector $\Theta (v,w)$, where $\Theta$ is the torsion tensor, up to higher order terms in $v,w$.

Gumshoe2 (talk) 13:36, 15 March 2024 (UTC)

No, that's the standard interpretation of the torsion tensor geometrically. However I reject that it has much to do with the english word "torsion". The section of the page I was referring to has since been removed. My comments were just general that care should be taken with this subject to get high quality sources! Tazerenix (talk) 22:09, 15 March 2024 (UTC)

The article has been substantially revised since the bad version that User:Tazerenix is referring to. I wrote the above description in terms of the tangent bivector to replace the mathematically wrong section that had been there before. What I wrote is correct and supported by sources. There may however be different factors of two in place in the article, which I have not checked in detail. So this interpretation is satisfied up to a factor of two that is subject to checking conventions.

The connection with development, however, is well-known and easily understood. I have given a detailed example in the image in the lede. Basically the idea is to take a closed curve $\gamma$ in the manifold, and a parallel coframe $\theta ^{i}$ along $\gamma$, and then solve the ODE $dx^{i}=\gamma ^{*}\theta$ for coordinates $x^{i}$. When the torsion vanishes (and the curve is null homotopic), the developed curve is also closed (a consequence of the Ambrose-Singer theorem, or alternatively even Stokes' theorem is sufficient.)

When the torsion does not vanish, it means that there is a non-trivial translation component to the holonomy for the affine group, and so the developed curve need not be closed. I think the current image at the top of Torsion tensor nicely illustrates this, and as a bonus shows the connection to Frenet-Serret torsion. Tito Omburo (talk) 20:15, 15 March 2024 (UTC)

Tom Ilmanen

Good day! Is there some experienced editor interested in helping me create an article about Tom Ilmanen? He seems like notable enough (many papers cited by hundreds each), but it's hard to find sources about him (not about his work). :( I've made a beginning draft: Draft:Tom Ilmanen. Thanks! Gererhyme (talk) 10:27, 15 March 2024 (UTC)

I wouldn't say that "his best known mathematical works are in cooperation with Gerhard Huisken," since they only have two research papers together. It would be better to say something like: "Huisken and Ilmanen used inverse mean curvature flow to prove the Riemannian Penrose conjecture, which was resolved at the same time in greater generality by Hubert Bray using alternative methods." This article could be used as a reference.

I also wouldn't refer to "the Huisken-Ilmanen conjecture" unless grammatically in the particular context of talking about a particular conjecture by Huisken and Ilmanen. As far as I know, there has not been anything widely known as "the Huisken-Ilmanen conjecture." Even the article by Dong and Song resolving the conjecture says only "This confirms a conjecture of G. Huisken and T. Ilmanen." (It's not clear to me how significant the conjecture or its proof should be regarded as being.) Gumshoe2 (talk) 13:31, 15 March 2024 (UTC)

Wow!!! Thank you very much, Gumshoe2!!! Gererhyme (talk) 13:34, 15 March 2024 (UTC)

Happy to help. Not sure what can be done to help establish wiki-notability, although I believe it's fully orthodox to regard Huisken-Ilmanen's paper as seminal and the other three publications you've listed as highly notable as well. (Speaking of which, his book should be regarded as a research contribution and not as a textbook.) You might have to just hope to come across a sympathetic admin when submitting the draft. Gumshoe2 (talk) 13:49, 15 March 2024 (UTC)

It may be a small help to cite Yau's well-known list of open problems where the Riemannian Penrose inequality is the fifteenth problem. Gumshoe2 (talk) 14:05, 15 March 2024 (UTC)

Thank you so much!!! "Review waiting, please be patient. This may take 8 weeks or more." EIGHT WEEKS OR MORE....... ZZZzzzzzZzZZzZ "be patient" hahaha. :) Gererhyme (talk) 14:30, 15 March 2024 (UTC)

And now in mainspace, and passed through NPP. A nice short article. My one constructive suggestion would be to use the Quanta article as a source to say something meaningful about Ilmanen, rather than just dump it into a "further reading" section. --JBL (talk) 23:00, 15 March 2024 (UTC)

Nice suggestion, JBL!! Thank you! ^^ I'll follow it, but I need some rest before doing so (yesterday I edited Wikipedia for something like 12 straight hours!). In fact, it was from Quanta Magazine I first heard of Ilmanen! Gererhyme (talk) 11:18, 16 March 2024 (UTC)

"Idealwise separated" listed at Redirects for discussion

The redirect Idealwise separated to the article Completion of a ring#Krull topology 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/2024 March 18 § Idealwise separated until a consensus is reached. Kk.urban (talk) 06:22, 19 March 2024 (UTC)

Draft:Bianticupola

I have been looking for sources for my article on Bianticupolae. However, even after practically scouring the internet, the only mention I can find of them is on the Wikipedia article for cupolae. If anyone knows a good place to look, I would greatly appreciate that. Thank you! — Preceding unsigned comment added by Toxopid (talk • contribs) 17:32, 17 March 2024 (UTC)

@Toxopid please use the Add Topic button in Talk pages.

I fixed your problem: I deleted the word "Bianticupolae" from the article Cupola (geometry) so now the internet will not mention it.

Ok, sorry, that was mean. But the line was not sourced so we have no way to know if someone just made it up. The point of Wikipedia is to summarize knowledge: if you have no source then don't write an article. Move on to another topic. Every single wikipedia article has many ways to improve it, including I'm sure Cupola (geometry). Find some good sources and edit! Johnjbarton (talk) 21:43, 18 March 2024 (UTC)

Cupola (geometry) § Anticupola has no sources, and the only mention I can find in the academic literature is from a 2023 arXiv preprint. Perhaps the section should just be deleted as original research. "Bianticupola" does not seem like a notable topic. –jacobolus (t) 22:24, 18 March 2024 (UTC)

I just deleted the section. If someone can find reliable sources, feel free to restore it. –jacobolus (t) 22:40, 18 March 2024 (UTC)

@Jacobolus I added the tag unreferenced, because there are lot of sections that do not have any sources to cite the facts. Is there any possiblity that they could be removed? Dedhert.Jr (talk) 11:24, 19 March 2024 (UTC)

Levi-Civita symbol

I just reverted a pile of COI edits at Levi-Civita symbol and made some other small fixes. It currently has 3 {{citation needed}} tags; in particular, there's a long stretch of $n$-dimensional calculations without any indication that going beyond 3 dimensions is a thing that warrants all that detail. (Like a lot of math pages, the increase in verifiability between one reference per section and one reference per sentence would not be that great in practice. But it needs a little work to get up to the former standard.) XOR'easter (talk) 17:32, 17 March 2024 (UTC)

Looks fine to me in it's current form (but I only skimmed it). The 4-d version sometimes shows in general relativity contexts, and the n-dimensional version sometimes shows in riemannian geometry and differential geometry textbooks where the author wants to perform some detailed, explicit calculation showing the gory details of Poincare duality or maybe how to use the Hodge star to define some inner product on some space of forms or weak derivatives or something. Perhaps Jurgen Jost "Riemannian Geometry" textbook, he likes to do explicit calculations; but my memory is faulty. When I was in school, one homework problem was to take the n to infty limit of this tensor; turns out it is the same as some harmonic oscillator over grassman variables, a determinant of some feynmann path integral. I forget; it has some famous name attached to it - Berezin integral or something like that. The joke is that physicists know how to do only one integral. 67.198.37.16 (talk) 00:16, 22 March 2024 (UTC)

Confusing image at Quadratic formula

Quadratic_function_graph_key_values.svg is garbled in Firefox. Looking at its history, the previous version was fine, but the change to "fix rendering issues in Chromium" seems to have broken it. XOR'easter (talk) 15:33, 21 March 2024 (UTC)

For me, both versions seem to look fine (i.e. the same to each other), on both Firefox and Chromium. Felix QW (talk) 15:43, 21 March 2024 (UTC)

It's also ruined in my computer, for both Firefox and Chromium. Note that if I click through to the actual svg file it renders correctly, it's only garbled when I see it in the Wikipedia article or the Media Viewer. Tercer (talk) 15:50, 21 March 2024 (UTC)

Maybe we should just replace it with a PNG? XOR'easter (talk) 16:01, 21 March 2024 (UTC)

That would be a depressing choice. Clearly SVG is the appropriate format for this image, and by now it is very old technology. We should be capable of getting it to render correctly. Tercer (talk) 18:28, 21 March 2024 (UTC)

There's relatively little advantage to SVGs here for most readers. Wikipedia/Mediawiki renders them as a PNG image anyway, both in a thumbnail and when clicked to view larger on screen, and very few readers click through to the source file. The Mediawiki SVG renderer doesn't do a great job with antialiasing so the lines often look better when downscaled from a highish resolution raster image.

SVGs including text (including mathematical formulas) have to be carefully encoded/exported to make the font render properly, and the safest is often to resort to converting all of the fonts to explicit outlines. Getting the layout to exactly match the author's intentions can take extra work in an SVG. Wikipedia doesn't support any of SVGs interaction features that could plausibly make it an attractive format for animation or interactivity.

The main benefits of using an SVG are (1) if there is explicit English text, it can be more easily translated, and (2) if someone wants to take the image and print it in a book or put it on a billboard or something they might get a marginally better result. In practice many of our SVG images have ugly color and font choices, poor layout, etc., all of which are more important to get right than the choice of raster vs. vector format. –jacobolus (t) 18:50, 21 March 2024 (UTC)

As an explicit example, here are two images which nominally show the same subject (used in logarithm), but where the PNG image is significantly better than the SVG based on other graphical choices:

–jacobolus (t) 18:57, 21 March 2024 (UTC)

So what you are saying is that MediaWiki should stop ruining perfectly good SVGs and just deliver them as-is to the browsers, which do a good job of rendering them. Unlike MediaWiki.

One can make bad choices of font and colour in either format; the difference is that in a SVG it is trivial to fix them, whereas in a raster format it is not.

The fundamental point is that an SVG encodes information as what it is: paths as paths and text as text. This makes it much easier to do anything with it. (I have in fact used those capabilities. A PNG erases all the underlying data and gives us just a representation of the information.

The low resolution can be mitigated by using larger file sizes, as you say, but this is just another instance of an inferior solution. Tercer (talk) 21:04, 21 March 2024 (UTC)

Mediawiki has not changed in this regard in like 15+ years, so I'm not holding my breath.

My point is just that there's nothing magical about one file format or another, and the choice of format is not the most important feature of an image. All else equal, the vector image would have some advantages, but often there's a trade-off and the choice isn't quite as clear cut. For instance, if a raster image saves any appreciable amount of effort, it can be an advantage to spend the time saved on making more images instead of fiddling with the file format of a few. File:Regular tetrahedron inscribed in a sphere.svg is a good example of an image with a lot of problems, some of which are unrelated to the format such as illegibly small labels which are partly blocked by lines and a poor choice of bright pink color for radii, and others of which might be improved by using a raster image, e.g. shading the sphere (you can get somewhat acceptable sphere shading using SVG gradients, but it's not obvious, kind of tricky, and often done poorly). –jacobolus (t) 21:37, 21 March 2024 (UTC)

Well have you opened a ticket in Phabricator? They won't change anything if people don't ask for it.

As for my figure, since it's an SVG you can easily change everything you dislike about it. If it were a PNG you wouldn't be able to. Tercer (talk) 21:52, 21 March 2024 (UTC)

What makes images easy to edit or not is only tangentially related to the output format. Most images are created using some other software application (or applications), and the best way to help someone edit them is to include a link, textual description, file, etc. of the original input format. For example this might be tikz source, POV-ray source, raw PostScript code, a Blender file, a layered Photoshop document, an SVG with Inkscape-specific editor metadata, or a link to a Desmos or Geogebra plot. What tools other editors can work with or find familiar is going to vary depending on their experience and available software. –jacobolus (t) 22:27, 21 March 2024 (UTC)

Anyway, sorry, I'm not trying to give offense. My point is not to call out this particular image, which I'm sure is much more helpful than not having an image, but only to point out that the file format is way down the list of important features, and argue that people shouldn't be "depressed" to see high-quality images of any format created for the project. –jacobolus (t) 02:29, 22 March 2024 (UTC)

It is depressing to let the technical flaws of MediaWiki dictate our choice of file format. I searched a bit on Phabricator, and I'm afraid you are right: they are never going to fix their SVG rendering T40010 and nor are they going to allow browsers to render SVGs instead T5593. Tercer (talk) 08:56, 22 March 2024 (UTC)

It also seems they are stuck on an old version of librsvg, so even smaller improvements (than native rendering or a better library) are blocked: T265549 —David Eppstein (talk) 16:13, 22 March 2024 (UTC)

And that's since 2020. It's frankly ridiculous. WMF can't do even the bare minimum to keep the website running. I'm going to stop donating. They are clearly not using my money for what matters. Tercer (talk) 16:24, 22 March 2024 (UTC)

Taking arbitrary user-generated files and serving them up is a huge new "attack surface" which most sites serving SVGs are not affected by, and I'm not sure there's a super obvious existing set of tools for mitigating it. So it's definitely not a trivial thing to tackle. But it would be nice if someone would devote some resources to this, since the potential of SVGs is also pretty big.

I'd love to work with people on making interactive math diagrams for Wikipedia, if it were possible. I think the best bet is to just host anything animated or dynamic off-site and include a static version in articles. –jacobolus (t) 17:43, 22 March 2024 (UTC)

Telling readers to go look at some off-site resource is an equally large attack surface, to be fair. At least if it were served up on Wikipedia it might be expected to have passed some sanity checks. —David Eppstein (talk) 22:58, 22 March 2024 (UTC)

Regular tetrahedron inscribed in a sphere.svg also has an issue unrelated to its format: the use of quantum mechanics notation for its labels makes it unsuitable for topics beyond quantum mechanics. —David Eppstein (talk) 22:12, 21 March 2024 (UTC)

The topic is quantum mechanics, the filename is a misnomer. Tercer (talk) 22:43, 21 March 2024 (UTC)

All the files in the history look equally useless to me. Far too many equations on the graph. Johnjbarton (talk) 16:11, 21 March 2024 (UTC)

For me, on Safari, there are two problems: Firstly, on all versions, commas are vertically misplaced (At the level of denominators instead as at the level of fraction bars). On most versions, the horizontal bars (fraction bars and vincula of square roots) are horizontally misplaced with respect to the remainder of the formula. This misalignment disappears when clicking on the image or on thumbnails of the history. So, the problem seems to come from the method of writing and inserting formulas.

I agree with Johnjbarton that there are too much formulas in the image. Moreover, the directrix, the focus and the vertex of the parabola, and their coordinates are clerly out fo the scope of ths article.

So, I recommend to remove this image. D.Lazard (talk) 16:37, 21 March 2024 (UTC)

OK, I have removed it from Quadratic formula and also from Quadratic equation. An improved version (reliable rendering, leaving out the focus and directrix, etc.) would be nice. XOR'easter (talk) 17:28, 21 March 2024 (UTC)

I tried purging the image (Commons:Help:Purge) but that didn't help, so it's not a caching issue. I think the file itself is not good. —David Eppstein (talk) 17:50, 21 March 2024 (UTC)

I think it's related to this regression in SVG rendering: https://phabricator.wikimedia.org/T97233 –jacobolus (t) 19:25, 22 March 2024 (UTC)

Argh this only gets more infuriating. The bug was reported upstream, who fixed it in 3 days. That was 4 years ago. WMF couldn't care less, apparently upgrading a library is too much work. They said they will only upgrade it together with the whole Debian distribution. The thing is, they can't be arsed to do that either. The Debian stable with the fix was released 3 years ago. Nothing. There was even another Debian stable release after that, last year. Nope. They are still on Buster, that was released in 2019. Fun fact, that will be end-of-lifed in 3 months, so we will have one the largest websites in the world running on unsupported software.

What on Earth are these clowns doing with out donation money? Tercer (talk) 21:12, 22 March 2024 (UTC)

@XOR'easter I've been working on this article recently, and intend to replace this image with several related images made in Desmos (I'm not sure if readers will notice, but anyone clicking through will then find a link to an interactive version), and also move the relevant section up toward the top and expand it. It will probably just be PNG images from a screengrab, since it takes at least twice the effort to get an SVG to render the same, and the benefit is relatively marginal. –jacobolus (t) 17:48, 21 March 2024 (UTC)

I'd welcome any other questions/requests/comments/recommended sources/collaboration on this article. It should be a high priority for us, as it gets a lot of page views (60k/month), more than related articles like quadratic equation, quadratic function, completing the square, or parabola, and seems likely to be routinely consulted by middle/high school students. –jacobolus (t) 17:49, 21 March 2024 (UTC)

I've put up a proposal on VPWMF to solve this issue. Tercer (talk) 16:06, 23 March 2024 (UTC)

I replaced the top image of this article, which wasn't very clear, and also added an image to the derivation by completing the square section, both shown here:

After looking at again it though, I think including the formula in the middle of the first image is too much text, and it would probably be better to cut out the explicit quadratic formula part, even though that's the article. I'll try to figure out how to clearly (but not too busily) show the analytic-geometry meaning of the discriminant and other parts of the quadratic formula in another image or two; it's hard to make such images simple and legible while still trying to demonstrate more than one thing in a figure. –jacobolus (t) 19:01, 23 March 2024 (UTC)

The middle of the first image does look a little text-heavy. (Maybe remove the $y=0\Rightarrow x=$ part and just show the evaluation of the formula?) But thanks very much for working on this. XOR'easter (talk) 20:26, 23 March 2024 (UTC)

Requested move at Talk:Flatness (mathematics)#Requested move 19 March 2024

There is a requested move discussion at Talk:Flatness (mathematics)#Requested move 19 March 2024 that may be of interest to members of this WikiProject. Favonian (talk) 10:17, 24 March 2024 (UTC)

Is Wolfram Mathworld reliable?

Related to the previous discussion, is Wolfram Mathworld reliable? I took the reviewing Talk:Arithmetic/GA2, and I claim that Wolfram Mathworld is not reliable sources, but the nominator claimed the otherwise. Now I'm very confused. Dedhert.Jr (talk) 07:12, 2 March 2024 (UTC)

I believe it's been discussed here before, although I can't find it now. In my opinion a mathworld source is better than no source, but not much beyond that. (I think that was also the general consensus from previous discussion.) Gumshoe2 (talk) 17:01, 2 March 2024 (UTC)

It seems to never have been discussed at WP:RSN, but it has been discussed here many times, including the following:

• 2006/04 (several threads on that page are relevant)
• 2011/01
• 2011/06
• 2011/12 (also mentioned in two other threads on that page)
• 2014/01
• 2016/01
• 2019/04
• 2019/10 (two consecutive sections mention it)
• 2021/03

I would say that these threads indicate a consensus among math editors that MathWorld is a usable but mediocre source, reliable for basic factual questions, but questionable as an indicator of notability and questionable when it comes to issues of terminology. --JBL (talk) 18:57, 2 March 2024 (UTC)

Mathworld usually doesn't make outright false mathematical claims, but has a tendency to repeat (or invent?) dubious historical/naming claims. –jacobolus (t) 19:40, 2 March 2024 (UTC)

It is now open for discussion. Dedhert.Jr (talk) 13:50, 28 March 2024 (UTC)

I agree with the above two comments. It is not so unreliable that it must be immediately removed and replaced by a [citation needed] tag, as some sources are, but it is so frequently error-riddled that it is almost always better to use a different source. For a Good Article review, in particular, I think that better sources should be used. For Arithmetic, I replaced one MathWorld source by a much better one (a chapter in The Princeton Companion to Mathematics) and removed the other one as it was redundant and used only to source some alternative terminology, the sort of thing MathWorld is worst at. There still remains a MathWorld external link, of dubious value according to WP:ELNO #1. —David Eppstein (talk) 19:37, 2 March 2024 (UTC)

It seems Eric Wolfgang Weisstein created and maintains MathWorld, which is licensed by Wolfram Research. It is not self-published and from Weisstein's credentials, I don't see a good reason for categorizing this as an unreliable source. Are there any obvious points from WP:RS that suggest otherwise? Phlsph7 (talk) 13:39, 6 March 2024 (UTC)

It's not the worst ever source (Weisstein doesn't write outright nonsense and usually cites some other sources), but I'd put it on par with some professor's blog, course notes, math overflow answers, or similar: content written by someone with expertise in the general topic, but not vetted or carefully fact-checked. It's much less reliable as a source than e.g the articles by O'Connor and Robertson at MacTutor, and even those are often not a perfect reflection of the current scholarly consensus. Where possible it's best to compare multiple recent sources by subject-specific expects. –jacobolus (t) 15:19, 6 March 2024 (UTC)

Weisstein's degrees were all in astronomy. And I'm not even aware of anybody trained in mathematics who could be a reliable source for so much mathematical material. Gumshoe2 (talk) 17:44, 6 March 2024 (UTC)

I don't particularly care about Weisstein's credentials, but I have too often found mistakes and neologisms in MathWorld to give my full trust in it. There are of course also many mistakes in Wikipedia itself, but we don't allow Wikipedia to be used as a reference. —David Eppstein (talk) 18:29, 6 March 2024 (UTC)

@David Eppstein I'm curious now. Can you give me an example of some mistakes in MathWorld? Also, what about external links? Can MathWorld be used for external links as well? Dedhert.Jr (talk) 04:02, 7 March 2024 (UTC)

Mathworld can be used as either a source or in the 'exernal links' section, but also doesn't have to be. If a particular Mathworld page doesn't add anything that isn't in an article or other accessible sources, I'd take it out from the external links section. If another better source can be cited for any particular claim, I'd cite that one instead of Mathworld. Any claim sourced to Mathworld should be double checked in better sources anyway, as it's often a bit sloppy. At that point you can just cite the other source you found. –jacobolus (t) 05:04, 7 March 2024 (UTC)

@Jacobolus Ahh. I see. What I meant is not for Arithmetic, but for whole articles in general. An example is GA Malfatti circles, or GA Square pyramid in which two MathWorlds being used in external links. Should they (as well as the rest of them, if possible) be excluded in this case? How did one know that whether some kind of website or any sources will be included as external links? Dedhert.Jr (talk) 05:44, 7 March 2024 (UTC)

I wouldn't rush out to automatically remove Mathworld from all articles; that would be controversial and probably harmful. But if I'm otherwise looking at an article and its sources, I'll click the mathworld link and review whether it really seems helpful to readers to include, and when it doesn't I just take it out. –jacobolus (t) 05:56, 7 March 2024 (UTC)

One example of a mistake in MathWorld, since you're focused on polyhedra: at the time I brought Jessen's icosahedron up to GA status, the MathWorld article gave an incorrect construction based on the coordinates of a regular icosahedron. The current version fixes that.

Another example of what I think is a mistake, of terminology for polyhedra: Isohedron describes as a "trapezoidal dodecahedron" (bottom right corner of table) a shape that I think is properly called a "deltoidal dodecahedron" [6]. The trapezoidal dodecahedron is something else, not an isohedron [7]. See Special:Diff/1150447755.

Again, it is not hard to find similar mistakes in Wikipedia itself, but that is not the same kind of problem because we don't use Wikipedia as a reference. When we use MathWorld as a reference we need to be careful, more than with some other sources. —David Eppstein (talk) 07:34, 7 March 2024 (UTC)

Ahh... I see, then. Just in case, I think I prefer to find better sources for the external links. Dedhert.Jr (talk) 12:32, 7 March 2024 (UTC)

Just realized the article Triaugmented triangular prism, where MathWorld says that it is constructed by erecting regular tetrahedron onto each square faces of an equilateral triangular prism. [8]. I remember you have explained this in the edit summary before you nominated it to GA. Dedhert.Jr (talk) 13:54, 28 March 2024 (UTC)

Yes, Special:Diff/1112387125. They still haven't fixed that, I guess? —David Eppstein (talk) 17:44, 28 March 2024 (UTC)

I wanted to check this against my field of expertise and found this article: https://mathworld.wolfram.com/ProofTheory.html

It currently starts with "Proof theory, also called metamathematics", which is just bs. The Wikipedia articles are much better.

Metamathematics is much more general, e.g. it includes semantics from model theory, whereas proof theory is syntactic. The latter two fields are subfields of mathematical logic, but metamathematics does not even stop there. It was mostly subsumed by mathematical logic to increase rigor, so I guess this is where the confusion originates.

Apart from this mistake, the author seems to know barely anything about proof theory. The description is more one of metamathematics. Formal proofs and their systems, the only things being examined in proof theory, are not even mentioned by name. 134.61.97.95 (talk) 13:13, 18 March 2024 (UTC)

I linked to a few other discussions in my general advice essay. MathWorld being untrustworthy for terminology has been an ongoing theme. XOR'easter (talk) 17:20, 6 March 2024 (UTC)

I'd agree with assessment above that Mathworld is a mediocre but usable source and one needs to apply some common sense when using it. But imho it isn't really worse than many other (properly) published mediocre math sources out there such as various small math dictionaries and lexicons. Much of the Mathworld content is also published in book form for by CRC press btw.. For a freely accessible online resource for math history topics the MacTutor History of Mathematics Archive is usually a better alternative.--Kmhkmh (talk) 08:49, 7 March 2024 (UTC)

It seems to conflate distinct concepts and to make general statements that are only true in specific contexts. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:33, 7 March 2024 (UTC)

While in my experience MathWorld is particularly bad (on terminology issues; the actual math is usually right), even if it were better on that, it would still be a tertiary source, as is MacTutor, as is Princeton Companion (at least arguably), and as are "various small math dictionaries and lexicons". We should really strain to avoid using tertiary sources when good secondary sources are available. (Though it's reasonable to point readers to a link inside a tertiary source in "Further reading", as an aid to readers who want to look something up quickly.) --Trovatore (talk) 22:44, 7 March 2024 (UTC)

While often very useful, I wouldn't characterize MathWorld as a WP:RS. I would presume that for "basic" stuff it would be relatively accurate, but less so the farther afield one goes. I personally wouldn't use it to cite something I didn't already know to be true. Paul August ☎ 15:53, 18 March 2024 (UTC)

Draft:Orientational terms

I have the opposite of the usual problem. We have articles on technical concepts of orientation in math and science, but no article on the basic concept of "some things have a top and bottom and front and back". I'm trying to write something that is very everyday life/explain it like I'm five-oriented. Who's good at that? BD2412 T 02:47, 19 March 2024 (UTC)

Take a look at Anatomical terms of location § Main terms. –jacobolus (t) 07:13, 19 March 2024 (UTC)

The challenge, I think, is describing what it means for something to be the front or back of an object without just repeating that it is in front, and without using more complex and technical terminology to describe the relation. The anatomy article may at least provide some inspiration. BD2412 T 15:10, 19 March 2024 (UTC)

I had similar challenges when editing Shape. It can help to look at how the brain psychologically maps out directions; a quick google search brought this up as an example, it may be worth pursuing this vein of research further:

[9]https://econtent.hogrefe.com/doi/abs/10.1027/1864-9335/a000065?journalCode=zsp Brirush (talk) 16:03, 19 March 2024 (UTC)

Excellent, thanks. This is very useful, and I can see how challenging it would be to write a topic like Shape. BD2412 T 17:42, 19 March 2024 (UTC)

I have worked the draft up some. What do you think? BD2412 T 20:11, 29 March 2024 (UTC)

Piecewise

I'm confused by Set theorist's recent move of Piecewise to Piecewise-defined function. Shouldn't we have an article about the general concept "piecewise" (when applied to some property of a function, rather than a definition), which subsumes piecewise linear function, piecewise constant function, piecewise continuous function, piecewise differentiable function, etc.? (The last 2 links redirect to Piecewise-defined function which I consider misleading since the properties are independent of the way in which a function is defined.) - Jochen Burghardt (talk) 11:11, 29 March 2024 (UTC)

I agree, and I have reverted back to the previous title. D.Lazard (talk) 11:46, 29 March 2024 (UTC)

I have rewriten the lead for making clear that "piecewise-defined function" and "piecewise property of a function" are essentially the same concept. Much further work would be useful for this article. D.Lazard (talk) 12:36, 29 March 2024 (UTC)

Someone should write something about the higher dimensional case, especially surface interpolation and connections with many areas (e.g., computer graphics). Tito Omburo (talk) 15:06, 29 March 2024 (UTC)

Higher dimensional examples are significantly more complicated/diverse; I'm not sure if the name "piecewise" is ever used for this per se, but perhaps. E.g. in the 2-dimensional case there are some such functions based on regular square or triangular grids, some based on arbitrary triangulations or division into assorted rectangles, and some based on arbitrary divisions into regions of other shapes. –jacobolus (t) 17:17, 29 March 2024 (UTC)

This concept is not only about functions. See piecewise linear manifold and piecewise linear curve, for instance. —David Eppstein (talk) 19:13, 29 March 2024 (UTC)

Generally adjectives make bad article titles (see also WP:NOUN). In mathematics specifically, they often seem to be explanation-of-jargon articles, which in my opinion we should generally not have. I'm not convinced there's a good rationale to explain all the different mathematical uses of "piecewise" in a single article. A blurb in glossary of mathematics might be OK, and the search term could redirect there. --Trovatore (talk) 19:50, 29 March 2024 (UTC)

Since the article, as it now stands, is only about piecewise defined functions, it should be moved to Piecewise-defined function and then a new Piecewise disambiguation page should be created, with links to Piecewise-defined function, Piecewise linear manifold, and other "piecewise" things. Michael Hardy (talk) 02:24, 30 March 2024 (UTC)

I disagree: The lead of the article defines and is linked to piecewise linear function, and I have just added in this article a hatnote linking to piecewise linear (disambiguation). As Piecewise linear manifold is about a very advanced matheatical concept, one can presume that interested readers will not search for "piecewise", and that the new hatnote is sufficient. D.Lazard (talk) 11:05, 30 March 2024 (UTC)

Piecewise linear 2-manifolds, as polyhedral surfaces, are actually a quite familiar and not very advanced concept. Similarly piecewise linear curves are commonplace and familiar. It is only in higher dimensions that they get more advanced. —David Eppstein (talk) 20:06, 30 March 2024 (UTC)

Moreover, all articles whose name begin with "piecewise" refer to the same meaning of this adjective. In this case, WP:DABCONCEPT discourages to create a dab page, and recommends an article on the general concept (WP:Broad-concept article). D.Lazard (talk) 11:25, 30 March 2024 (UTC)

The big risk with "broad-concept articles" is that we might be abstracting out a "broad concept" on our own, that sources have not isolated as a particular object of study. We are not supposed to do that. Can you find sources that bring together all these meanings of "piecewise" in a single place? If not, then we shouldn't either. --Trovatore (talk) 18:36, 30 March 2024 (UTC)

Apr 2024

How to deal with this example/proof heavy article? (Cauchy's theorem)

I was asked to edit the article on Cauchy's theorem (group theory). There are two example sections which are earmarked for lack of citations. But when I read them, they do not seem particularly appropriate for the encyclopedia format at all. Putting aside typoes and poor grammar for a moment, the examples are both presented like problem book exercises, and could be shortened to a one-sentence description, if they are even interesting enough to warrant inclusion at all.

I'm also surprised that the article includes not one, but two entire proofs of the theorem. There must surely be textbooks online with complete proofs of their own. The style manual suggests "as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result." - by this metric I would vote to remove proof 1 entirely, and heavily abbreviate proof 2.

I have ideas for content that could be added, but I thought before removing 50% of the article I should get a second opinion. Danielittlewood (talk) 21:02, 1 April 2024 (UTC)

I also am a fan of proof 2. As far as a citation for this proof goes: it is an exercise in Isaacs _Finite Group Theory_. The original proof is by J McKay in a 1959 article in the Amer. Math. Monthly. Russ Woodroofe (talk) 21:23, 1 April 2024 (UTC)

Thank you very much for that reference. I managed to find the exact reference (although I can't access it, I'll take your word for its content). I'll add that to the article.

https://www.jstor.org/stable/2310010 Danielittlewood (talk) 21:07, 2 April 2024 (UTC)

A few examples showing some basic consequences of a theorem generally seems like a good idea to include. It would be nice to show some picture with these. Any wikipedia article explicitly about a theorem should include at least one proof if it is not inordinately long, or a proof sketch if all of the proofs are extremely cumbersome. If there are multiple proofs with substantially different ideas, then including more than one proof is nice. The style guide you are quoting is discussing the use of proofs in articles that aren't explicitly about particular theorems. In an arbitrary mathematical article (something like Circle or Matrix (mathematics) or Differential calculus or Real number), including a proof of every statement would be a distraction. –jacobolus (t) 22:43, 1 April 2024 (UTC)

In this case i completely agree with removing (at least most of) the examples. The first one has nothing to do with Cauchy's theorem: it should be removed. The second one uses it (in a confusingly oblique way) while usually the result is deduced from Lagrange's theorem; it can conceivably remain if it is rewritten correctly. jraimbau (talk) 05:06, 2 April 2024 (UTC)

I'm certain there are better applications. I think the ones in the article currently can be abbreviated to a single sentence while losing nothing of value. I'll try to find some better examples, ideally that lead to proofs of deeper theorems. Danielittlewood (talk) 21:08, 2 April 2024 (UTC)

I think both proofs are good to include, since they're very short and the page is about the theorem. To my personal preference the second proof could be written a little condensed, something like this:

Given any group G, the cyclic group Z_p acts on the set of tuples (g₁,...,g_p) in G with g₁...g_p = e, by cyclic permutation of the elements. If p is prime and G is finite, it follows from the orbit-stabilizer theorem that each orbit of the action has size either 1 or p. Orbits of size one are in natural bijection with group elements g such that g^p = e. If there is no such element other than e, it follows that the cardinality of the set of tuples is not divisible by p (since it is equivalent to 1 modulo p); since it can be checked that the cardinality of the set is divisible by the order of G, it follows that the order of G is not divisible by p. So if the order of G is divisible by p, then there must exist a non-identity element g with g^p = e.

(with obvious room for improvement, and provided there's a reference given with details). If there's a similar way to slightly reduce the first proof, I think that would be ideal. But I also think that both as currently written are acceptable in terms of detail. Gumshoe2 (talk) 23:37, 1 April 2024 (UTC)

Inner measure

The inner measure article had an unsourced and incorrect definition from almost 14 years ago, which I have now removed. It leaves the article pretty spare. Thoughts on what to do are invited on the talk page. --Trovatore (talk) 05:50, 3 April 2024 (UTC)