Wikipedia talk:WikiProject Mathematics/Archive/2022

Jan 2022

Mathematically Correct

Mathematically Correct (edit | talk | history | protect | delete | links | watch | logs | views)

I've noticed that this article, about a website involved in the math wars, contains major factual errors. In particular, the article falsely claimed (until now) that the website went down c. 2013. It is scant on references, especially reliable ones. It hasn't changed much since 2009, and still lacks a content assessment rating. –LaundryPizza03 (dc̄) 03:41, 1 January 2022 (UTC)

Help needed

Talk:Original proof of Gödel's completeness theorem has a discussion that could use some eyes on it. David notMD (talk) 02:43, 31 December 2021 (UTC)

I would be happy to help, but I am not entirely sure that it is appropriate to have a separate page on Gödel's original proof of the Completeness Theorem.

To establish notability, we would need independent secondary sources treating specifically Gödel's proof of that theorem (rather than the theorem itself). I am only aware of the treatment by Jeremy Avigad in his essay (doi:10.1017/CBO9780511750762.004) and some discussions on the influence of Skolem's earlier work on Gödel. If this is deemed enough, one could try and rework our article based on Avigad's treatment. Felix QW (talk) 13:14, 4 January 2022 (UTC)

Some more research has uncovered the chapter by van Attan and Kennedy in The History of Logic (https://doi.org/10.1016/S1874-5857(09)70014-7), and there is also non-trivial coverage in the Introductory Note to Gödel's dissertation, contained in the Collected Works Vol. I. So that seems to be sufficient to pass WP:GNG? Felix QW (talk) 15:17, 4 January 2022 (UTC)

Transcendental equation

Is this a meaningful concept, treated by reliable sources? I am skeptical. The fact that only one sentence is sourced is not encouraging. --JBL (talk) 01:20, 29 December 2021 (UTC)

• Aside from being dubiously sourced, the contents are also factually dubious. Of the three transcendental equations in the lead with allegedly no closed-form solution, the first and third do have closed-form solutions involving the Lambert-W function , which is not really that obscure. Reyk _YO! 01:27, 29 December 2021 (UTC)
  • It could have meant something meaningful and correct, but just not stated entirely precisely. What's "closed form" depends on what function symbols you allow. If rephrased as "cannot be obtained from the rational numbers via elementary functions", I expect that's true. --Trovatore (talk) 20:32, 29 December 2021 (UTC)
• Even the two first sentences are factually dubious ("A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for. Such equations often do not have closed-form solutions"): it is unclear whether ${\textstyle \exp({\frac {\log x}{2}})=5}$ is transcendental, as it simplifies easily to an algebraic function; the phrase "closed form solution" is meaningless without listing the accepted basic functions.
  It seems that there are no general theory nor significant results on such non-algebraic equations. So I suggest to nominate this article at AfD. D.Lazard (talk) 10:18, 29 December 2021 (UTC)
• I believe to remember that "transcendental equation" is used for an equation (over numeric domains) that is not (equivalent to) an algebraic equation. The large number of translation links indicates that the concept is widely known. The link de:Transzendente Gleichung gives 2-3 fairly reliable sources (in German); also the depicted Herschel book looks reliable, and interesting at first glance. So, I'd be in favor of fixing the flaws of this article and keeping it as a stub. In the long run, it could accumulate methods to solve particular kinds of nonalgebraic equations, which are useful to obtain "closed-form"/"analytic" solutions in special cases. - Jochen Burghardt (talk) 11:41, 29 December 2021 (UTC)
  • I agree that I think the "right" definition of "transcendental equation" is "non-algebraic equation". And maybe you're right that an article could be written about that concept. I don't think it would include any of the material currently in the article, though; do you? --JBL (talk) 15:44, 29 December 2021 (UTC)

    Not exactly: a differential equation is a non-algebraic equation that nobody calls transcental. In fact one could define a transcendental equation as the equation for the zeros of a non-algebraic function. This point of view suggests redirecting to Zero of a function, and adding a sentence to the target article for defining "transcendental equation". Redirecting to Root-finding algorithms is another option. D.Lazard (talk) 16:13, 29 December 2021 (UTC)

    I'll try to fix the article during the next days. I suggest that after that, we can discuss whether to leave it standalone or to merge/redirect it somewhere. - Jochen Burghardt (talk) 18:19, 31 December 2021 (UTC)

    I would not be in favor of either of the redirects suggested by D.Lazard above. We shouldn't redirect a term to an article just because the article suggests ways of handling the search term. The equation is not a zero of a function, and it's not a root-finding algorithm. A redirect to a glossary article might be a possibility, though. --Trovatore (talk) 01:22, 4 January 2022 (UTC)

    Algebraic equation seems like another possible redirect target. --JBL (talk) 03:14, 4 January 2022 (UTC)

    I think it's a code smell when there are multiple, equally plausible targets for a redirect. At least we should look for the most "canonical" target. I think in this case it would probably be a glossary. --Trovatore (talk) 18:51, 4 January 2022 (UTC)

 Done Anyway, I'm through with editing. I've avoided "closed form" and emphasized the ad-hoc character of this "field of research application". It may be possible to expand the article further, based on the works by Varyukhin and Boyd (who devotes p.233-308 to "Analytical methods", including "explicit solutions", see the public), but I haven't access to any of them (except for Boyd's TOC and Varyukhin's Russian original).

I admit I'm not happy with the mess of transformation examples along Bronstein et al. in section Transcendental_equation#Transformation_into_an_algebraic_equation. They could possibly be grouped into "top-down" and "bottom-up" approaches, operating at the expression tree top (root) and bottom (leaves representing the unknown), respectively; however, we can't conceal that it is (necessarily) a catalogue of almost unrelated tricks. - Jochen Burghardt (talk) 20:25, 4 January 2022 (UTC)

Discussion on variant of infinity symbol

Please see Talk:Infinity symbol#Euler's variant and participate in the discussion if you have an opinion. —David Eppstein (talk) 20:57, 4 January 2022 (UTC)

Edit war started

Some help would be helpful for the edit-war that is starting at Inner product space. Pinging Mgkrupa. D.Lazard (talk) 15:01, 22 December 2021 (UTC)

@D.Lazard: it takes two to tango. If there are 4 reverts within a 24 hour period, that might lead to a report at WP:EWN, but not here. The edits to the article inner product space seem like cosmetic and harmless format changes (<math>, </math>, latex format vs. more primitive mathematical coding). Possibly it might be surprising that the complex conjugate of a Hilbert space is not mentioned in the article. [For a (complex) inner product space, its dual space is naturally a Hilbert space (with a canonical conjugate structure in the complex case).] Isn't it more usual to use the coding

$\int _{a}^{b}f(t){\overline {g(t)}}\,dt$

with dt instead of dt, which seems clunky? Mathsci (talk) 16:05, 22 December 2021 (UTC)

On the last point, apparently this is a known difference of conventions. The traditional usage in the States (and maybe Britain, not sure) is to use italic d, but in France and maybe some other places they prefer to put it in roman text, sometimes bold. I think the idea is to save italics for variables. Sometimes they go as far as to render e in roman, on the grounds that it's a constant rather than a variable. --Trovatore (talk) 18:00, 22 December 2021 (UTC)

@Trovatore: I thought that was more of a mathematicians-v.-physicists divide rather than a geographical difference. Michael Hardy (talk) 20:09, 22 December 2021 (UTC)

Could be. My memory of the discussions is hazy. --Trovatore (talk) 20:37, 22 December 2021 (UTC)

I don't think so. In my maths degree I have seen both $\mathrm {d} x$ and $dx$. (usually those that are very fussy about their presentation tending to use the former, many others using the latter) --George AKA Caliburn · (Talk · Contribs · CentralAuth · Log) 19:29, 24 December 2021 (UTC)

Looking at my hard copy of Laurent Schwartz's 1966 classic "Théorie des distributions", $dx_{1}$, etc, is the standard style adopted. The Notes for proofs in the article are unintelligible seas of red and blue, of little use for readers of wikipedia: Inner_product_space#Notes The French article Espace préhilbertien is fine. Mathsci (talk) 18:48, 22 December 2021 (UTC)

Hi, I'm the other editor and this 09:38, 22 Dec version of the article is what I would like to commit. After this 20:48, 21 Dec edit was partially reverted (resulting in this 21:18, 21 Dec edit that D.Lazard said was "clearer"), I changed my now-reverted 20:48, 21 Dec edit to be more similar to that of D.Lazard's 21:18, 21 Dec edit (resulting in what I consider to be an improvement) and I also made some changes that I hoped would remedy some of his concerns. Long story short, the result of my changes was this 09:38, 22 Dec edit (which I'd like to commit) that was fully reverted (resulting in the latest version of the article). Is D.Lazard right that my desired version of the article is flawed enough that it should not replace the current version of the article? Thanks. Mgkrupa 01:11, 23 December 2021 (UTC)

The eighth reference seems like a wiki, can it be used as a wikipedia reference like PlanetMath ?--SilverMatsu (talk) 13:29, 26 December 2021 (UTC)

BrilliantMath is a low-quality source. It was added (along with a bunch of other mediocre-to-poor sources) in this edit by Miaumee -- I think any of the sources added in that edit could/should be removed. --JBL (talk) 14:35, 26 December 2021 (UTC)

Thank you for your reply. A search of BrilliantMath on wikipedia found that it was used in the section of references in over 20 articles. Would you(we) like to create a new section for this? But today it takes longer than usual to load a wikipedia article.--SilverMatsu (talk) 15:39, 26 December 2021 (UTC)

Reference removal is complete in the Inner product space.--SilverMatsu (talk) 16:06, 26 December 2021 (UTC)

• User:D.Lazard seems to be edit-warring yet again. But his edits to inner product space show WP:CIR (both for language and mathematics). As background to my WP editing, in creating content on Hilbert algebras, I created the article commutation theorem, prompted by a real life friend User:R.e.b.. That is part of Bourbaki territory (Jacques Dixmier, Jean Dieudonné and Roger Godement), part of the Gelfand–Naimark–Segal construction and spectral theory. That mathematical theory and the relevant reliable sources are still valid.

Wikipedia:Babel

en-2This user can contribute with an intermediate level of English.

Search user languages

D.Lazard's mathematical specialty is outside this area. The WP:CIR problems are shown by the edit to Wikipedia talk:WikiProject Mathematics#Articles on "differential calculus" and "integral calculus", involving the phrase "The strong relation between these two subjects makes artificial to distinguish them". That can be excused on talk pages, like here, but unfortunately not for poor quality edits to main space content. In inner product space, D.Lazard has "corrected" field of real numbers to their preferred field of the real numbers without any justification. OTOH, D.Lazard's language userbox indicates an intermediate proficiency in English (en-2); D.Lazard is free to change that if he wishes. It's not hard to explain why the French phrase "le corps des nombres réels" is translated into English as "the field of real numbers". Simply use WP:RS and WP:V. Bourbaki's General Topology has a section IV.4 entitled "The field of real numbers". In the original French version, Topologie Générale, section IV.4 is entitled, "Le corps des nombres réels". The same applies to Dieudonné's Foundations of Modern Analysis/Fondements de l'Analyse Moderne. D.Lazard's edits shows that WP:CIR. Mathsci (talk) 10:29, 4 January 2022 (UTC)

This is not a place for discussing my behavior. Instead of discussing the competence of other editors, Mathsci should improve their own competence, and, in particular, learn where such a discussion may occur. Also, they should learn that the French "des" is a contraction of "de les". So, the proper translation of "le corps des nombres réels" is "the field of the real numbers", and, conversely, the proper French translation of "field of real numbers" is "corps de nombres réels". However, Wikipedia is not the place for discussing the accuracy of English translations of French books. D.Lazard (talk) 12:14, 4 January 2022 (UTC)

We are discussing your edits, that's all. User:D.Lazard is now stalking my edits.[1][2][3][4] In one of the edits, D.Lazard gives a short unsourced description as a would-be expert:{{Sort of von Neumann algebra}}. Can D.Lazard explain what Sort of von Neumann algebra means? A standard example has been given of the algebra of Hilbert--Schmid operators on a Hilbert space. It is not a von Neumann algebra. So WP:CIR, your edits are hopelessly inaccurate: they look like WP:NOTHERE. It's clear that you have not identified User:R.e.b.. Mathsci (talk) 12:22, 4 January 2022 (UTC)

It would be difficult to overstate how inappropriate and useless the linking to WP:CIR and WP:NOTHERE is in the present context -- find some less inflammatory way to make your point. --JBL (talk) 13:08, 4 January 2022 (UTC)

@Mathsci: First, as you wisely pointed out above, it takes two to tango. If you disagreed with D. Lazard's revert of your change to inner product space, you should have started a discussion on the talk page there instead of reverting his revert. Second, you clearly are discussing both D. Lazard's edits and conduct. This project page isn't really appropriate for either dispute, especially since the content dispute has not yet been discussed on the relevant talk page. Danstronger (talk) 03:24, 5 January 2022 (UTC)

Ultrapolynomial

This brand-new article is little more than a dictionary definition, with weak sourcing. Two minutes on MathSciNet convinced me that this probably is a thing, but it could use attention from a passing good samaritan. --JBL (talk) 22:46, 2 January 2022 (UTC)

When I searched for ultrapolynomial in the Anywhere field of MathSciNet, all the papers I found were by Stevan Pilipović and his students (there were 7 in total, of which 5 were by Pilipović himself). So my guess is that the definition is not common enough to justify a Wikipedia article. Ebony Jackson (talk) 01:31, 3 January 2022 (UTC)

Mmm you're right I didn't look carefully at the authors -- even the 1994 one (where the appearance is in the form "ultrapolynomial growth") is someone who heavily coauthors with Pilipović. --JBL (talk) 01:49, 3 January 2022 (UTC)

Even if it's a term used (at least so far) only by a restricted community that includes the person who coined it, it does look like there's enough peer-reviewed work to justify coverage. There are at least dozens of hits on Google Scholar. That said, it shouldn't stay a dictionary definition. Someone who understands the subject needs to explain why it's important. --Trovatore (talk) 17:47, 3 January 2022 (UTC)

It looks as if nearly all the hits on Google Scholar also are from Stevan Pilipović and his students, so can one really justify inclusion based on this? There may be other reasons to keep an article about this, perhaps with a different name - some of what I read suggests that it relates to work of Arne Beurling and others in the 1960s on generalizations of classical differential operators. I'm not an expert on this, so I'm not sure. Ebony Jackson (talk) 21:39, 3 January 2022 (UTC)

It's a judgment call of course. My sense right now is, yes, with that much peer-reviewed published work, it's likely worth keeping, even if the uses come from authors with connections to one another. --Trovatore (talk) 21:48, 3 January 2022 (UTC)

(I am the article's creator) The term's use (currently) being confined to a small subcommunity of authors is in my opinion not a valid argument for excluding this article. When a mathematical subdomain is specialized enough, then there are often only a small handful of select mathematicians working in it who, in addition, typically have some sort of connection to one another. This might be concerning if some key figures within this community are of ill repute; however, in the case of ultrapolynomials, as far as I can tell, real, reputable mathematicians put this tool to use in real, reputable, peer-reviewed work. --Fytcha (talk) 13:30, 4 January 2022 (UTC)

I have copied the article into http://Power_series#Power_series_in_several_variables https://en.wikipedia.org/wiki/Power_series#Power_series_in_several_variables (It obviously needs improvement). For such a specialized topic it probably makes sense to write a subsection of a broader topic instead of a new article. Vitamindeth (talk) 19:02, 4 January 2022 (UTC)

Honestly, I don't think it's appropriate in that location. It's not really interesting to most people reading about polynomials power series. It's interesting to people reading about the area of study of Pilipović and his group, whatever that is exactly (I suspect I could get at least a general idea of that if I wanted to spend the time, but I haven't so far).

So in my opinion it's probably fine as a standalone article, but it needs to be better contextualized. We're not supposed to have articles that just define something and do nothing else. One possibility might to write an article on that area of study and then redirect ultrapolynomial there. --Trovatore (talk) 19:42, 4 January 2022 (UTC)

I agree. I think that section explains the characteristics of the domain of convergence. (e.g.log-convex).--SilverMatsu (talk) 03:20, 7 January 2022 (UTC)

I am not part of this field of study but it seems there is no reason to think this is a notable concept by itself. There have been some two million peer-reviewed published math papers published in the last twenty years, and the argument for keeping this page seems to represent the lowest possible nontrivial standard for selecting concepts from among them. From a little searching through mathscinet and google scholar, it looks like a better case could be made for the (related?) concept of ultradistribution. Gumshoe2 (talk) 02:48, 5 January 2022 (UTC)

I agree with the last comment, as far as i can tell (from the article and looking around on Zentralblatt) this is a purely technical definition that makes no sense out of context. So if there should be an article it would be better if it was about that context (i guess the study of some class of PDEs). And if i'm wrong and these ultrapolynomials are really the crux of the matter then it should be explained why in the article. jraimbau (talk) 11:50, 5 January 2022 (UTC)

Yes, this seems very believable to me. --JBL (talk) 11:52, 5 January 2022 (UTC)

"Nonlinear algebra"

The article named Nonlinear algebra seems essentially content-free in its current version, vague to the point of uselessness in some parts and just pointing to specific topics reflecting the interests of its editors in others. By default "nonlinear algebra" should refer to all parts of algebra that are not purely linear algebra (e.g. commutative algebra, group theory, ...) and as far as i know there is no unified field of research that represents them all. So unless the term is used in a precise technical sense in some field i'm not familiar with (computational algebra?) the article would be more appropriate as a disambiguation page. jraimbau (talk) 12:04, 5 January 2022 (UTC)

The article is very incomplete, but doesn't seem wrong as far as it goes. My understanding of nonlinear algebra is as an applied mathematics field that goes beyond linear algebra to consider polynomials. Examples are the survey Nonlinear Algebra and Applications, the book Invitation to Nonlinear Algebra and the course Introduction to Non-Linear Algebra. That said, I think you make a good point, in that the topic means different things to different people. Taking the approach of a broad concept article or a DAB may be a good option. --{{u|Mark viking}} {Talk} 04:11, 7 January 2022 (UTC)

Unlike linear algebra, which is also considered a pure maths field, nonlinear algebra seems to me to be used distinctly for computational aspects.

I am not sure how exactly, but I suspect it is closely linked to computational algebraic geometry. Felix QW (talk) 05:56, 7 January 2022 (UTC)

OK, with the Michalek--Sturmfels book as support in particular i think it would make sense to attempt a re-writing of the the article with a lede like

Nonlinear algebra is a name recently used to design a collection of techniques from areas of algebra outside of linear algebra (in particular computational algebraic geometry, tensor algebra, representation theory,...) to problems in applied mathematics.

and then a more detailed list of techniques and applications. This seems much clearer than the current version. It would also make sense to put stuff like computational group theory (which seems outside the scope of Michalek--Sturmfels at least) in a "see also" section. jraimbau (talk) 09:09, 7 January 2022 (UTC)

Pentangle puzzles

Math geeks born between 1940 and 1970 may remember Pentangle puzzles, a company in Over Wallop, Hampshire, UK, which made and sold burr puzzles and other puzzles. I'd like to create a Wikipedia article about it, but have trouble finding evidence of notablity. Any help at Draft:Pentangle puzzles would be most welcome. Maproom (talk) 21:55, 9 January 2022 (UTC)

Combining dimensions

There is currently an unsourced stub at Combining dimensions which mentions combining dimensions to be the visualisation of a manifold in a lower-dimensional space. A merger into Projection (mathematics) was discussed in 2013, but no suitable merger target was identified. With the advances in data mining over the last 10 years, Dimensionality reduction is now clearly the primary topic for the search term, so I would like to create a redirect there. My question: Is it worth to disambiguate Combining dimensions as a topology concept? Or do we have a better merge target now? I am not convinced with the meaning given in the article that this is a well-defined concept at all. Felix QW (talk) 09:01, 11 January 2022 (UTC)

I have never heard this term. It does not describe either projection or dimensionality reduction well. Quick Google searches don't give any evidence for it. My gut reaction is that it's original research and should be deleted. However, if many readers are searching for it, then we should redirect it to Dimensionality reduction or whatever we think it means. Mgnbar (talk) 12:36, 11 January 2022 (UTC)

My vote would be delete, but if we end up disambiguating or redirecting, one potential target would be Embedding#Topology_and_geometry or something like that, based on the content that's there now. Danstronger (talk) 13:46, 11 January 2022 (UTC)

Thanks for the initial responses! Before we have to duplicate a longer discussion, I have taken it to AfD (See Wikipedia:Articles for deletion/Combining dimensions). Felix QW (talk) 14:22, 11 January 2022 (UTC)

Edit warring for Fundamental theorem of Riemannian geometry

Would appreciate any extra eyes at the page Fundamental theorem of Riemannian geometry, see its talk page for context Gumshoe2 (talk) 16:54, 16 January 2022 (UTC)

odd format in EB 1911

Hi. I'm proofing the math, chemistry &c articles of the 1911 EB on Wikisource, and there's something odd here (the line just above "[VALIDATOR, VERIFY ODD FORMAT]"). I am replicating apparent typos, but will fix up the formatting where it's obviously trivial. Is that an acceptable way to format the line, or am I missing something? (Please ping.) — kwami (talk) 04:33, 17 January 2022 (UTC)

Inverse functions and differentiation

I have recently discovered the article Inverse functions and differentiation. It is presently unsourced, despite having been in existence since 2002. It is rated as Start Class and Mid-Priority. It appears to me to be amateurish. What little content is truly valuable is probably already found in one of the substantial articles on inverse functions, the derivative, or the inverse function theorem. Before I start action to delete the article or merge its contents, I would appreciate some feedback on what others think about the article. Dolphin (t) 04:16, 7 January 2022 (UTC)

Two comments- 1) as written it seems more like "cheat sheet"/formula list or tutorial rather than encyclopedic; 2) it would be pretty easy to add sources. I guess I think it should be merged into other articles. Actually, all of its contents probably already appear elsewhere here. Gumshoe2 (talk) 07:45, 7 January 2022 (UTC)

We do have pages for the power rule, the product rule and so on. In fact, the article Inverse functions and differentiation is linked in the sidebar template Calculus, which is transcluded on many calculus pages. I agree that the current state is poor, though, and that the page should probably be renamed in line with the other articles on differentiation rules (the article on differentiation rules just calls it the inverse function rule). Felix QW (talk) 14:39, 11 January 2022 (UTC)

I suggest redirecting to the Inverse function theorem.--SilverMatsu (talk) 03:13, 13 January 2022 (UTC)

I agree that mathematically speaking, the interesting question is the differentiability of the inverse rather than the calculation of the derivative. However, Inverse function theorem is clearly aimed at those working on real analysis upwards, while I think there is value in having the inverse function rule covered in the set of calculus articles pitched a level lower. Felix QW (talk) 11:17, 13 January 2022 (UTC)

I have now moved the page to Inverse function rule and rephrased the lead to match. I also changed the corresponding wikilink in template:Calculus. Felix QW (talk) 10:03, 18 January 2022 (UTC)

Hawkes process

I have created an article titled Hawkes process, which could use further work. Michael Hardy (talk) 19:26, 19 January 2022 (UTC)

About modern triangle geometry

Given that wikipedia doesn't have an article the modern geometry, I wonder if it can create an article the Modern triangle geometry.--SilverMatsu (talk) 04:13, 13 January 2022 (UTC)

Probably should be merged into History of geometry. Danstronger (talk) 14:10, 13 January 2022 (UTC)

Possibly I'm just bad at reading but I cannot at all understand from that article what "modern triangle geometry" is about. The cited definition from 1887 is impenetrable to me. Also, it seems there are only three pages of google results for "modern triangle geometry". Color me confused. Gumshoe2 (talk) 18:49, 13 January 2022 (UTC)

In its current form, the article is too long for merging. Instead, a "History" section should be split off from the lead. However, like Gumshoe2, I feel unable to express the introductory description, which should make up the lead after splitting, i.e. I didn't understand what the article is about (except: an arbitrary(?) collection of triangle-geometry results obtained after 1850). I suspect the 1887 "definition" cannot be translated into formal mathematical language; but maybe the lead author just picked it unluckily. Finally, I guess the geometric results presented in the article body do deserve a Wikipedia article, but "Modern triangle geometry" may not be the best title to collect them under. - Jochen Burghardt (talk) 13:48, 14 January 2022 (UTC)

Splitting the triangle geometry that is currently redirecting to a triangle can be useful for something. --SilverMatsu (talk) 02:43, 21 January 2022 (UTC)

Article for David Cox

We are looking to clean up the article on David Cox to make sure the description of his work is accurate and cited properly. Your help would be most welcome. Joofjoof (talk) 04:46, 21 January 2022 (UTC)

Non-Hausdorff redirect nominated for deletion

Non-Hausdorff currently redirects to Non-Hausdorff manifold, which is misleading to say the least. I have nominated the redirect for deletion. Please take a look at Wikipedia:Redirects for discussion if you want to add your opinion. PatrickR2 (talk) 04:42, 20 January 2022 (UTC)

Would appreciate the opinion of others in Wikipedia:Redirects_for_discussion/Log/2022_January_20#Non-Hausdorff to build consensus, as some outsider has a different opinion. PatrickR2 (talk) 04:26, 22 January 2022 (UTC)

Mathematical errors in Fields medal commentary

I would appreciate any thoughts on this new comment on the Fields medal page. It seems to me that several mathematical achievements of Fields medalists have been misstated in various ways. It seems that the expert commentaries at ICM have been summarized by non-experts in a published non-technical book, which were then copied uncritically to the Fields medal website and then copied over to wikipedia. So the expert commentaries have become a little corrupted. But my own expertise is limited, maybe this is all my error, so I would appreciate any knowledgeable persons having a look. Gumshoe2 (talk) 07:57, 25 January 2022 (UTC)

There are no problems with the Proceedings of the ICMs. The International Mathematical Union, however, is a different organisation; it manages the online ICMs and makes its own postings. Vaughan Jones did not edit wikipedia, except here. [5] None of his students could have helped with this BLP, since it doesn't mention subfactors. That topic was first treated on WP by User:R.e.b. ... Although it's no quite clear what Gumshoe2's aim is, he has to follow WP:consensus. Polishing Fields medal (remember it doesn't tarnish), requires reading the WP:RS (the Proceedings) and summarising them carefully, possibly without direct quotes. For cosmologists (also theoretical physicists), there is a similar problem with Nobel prizes, e.g. Kip Thorne. I don't know how that works. Mathsci (talk) 20:37, 25 January 2022 (UTC)

Maybe you still do not understand the situation. Kip Thorne, to take your example, was awarded the Nobel prize "for decisive contributions to the LIGO detector and the observation of gravitational waves", and that is an officially given reason. (This is present in the opening paragraph of his wiki page and has good references, so I'm not sure how you missed it.) I have no idea what you think is the relevance of your comments on Vaughan Jones and r.e.b., so I am unable to respond to them. I recommend that you take some more time to focus your thoughts. It would be very helpful for discussions. Gumshoe2 (talk) 01:00, 26 January 2022 (UTC)

??? In RL, I was involved in organising section speakers for an ICM and was later an invited speaker — a different perspective & possibly a COI for the article. Mathsci (talk) 13:15, 26 January 2022 (UTC)

I do not understand the relevance of this remark, sorry. Gumshoe2 (talk) 14:10, 26 January 2022 (UTC)

Short Description Guidelines

I've noticed that remarkably few mathematics articles outside of very large scope articles (and bio pages) seem to have a short description in line with what's described in WP:SHORTDES. In particular, the short description

• Should provide a very brief description of the field covered by the article
• Disambiguate search results
• Avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject
• Should not attempt to define the subject of the article nor summarize the lead.

It's challenging to write about math without overusing jargon, so that one I get. However, the majority of pages I click on do not seem to align with the goals of describing the field covered by the article or to help disambiguate search results, and most of them attempt to define the subject and/or summarize the lead. I've edited many articles now to fix the short description, but there seems to be such a large proportion of articles that need adjusting (almost every article I click), that I'm seriously doubting myself. It feels like I'm being gaslit by the entire mathematics corner of Wikipedia. Is there something I'm missing, like a page somewhere that has different guidelines for the short description specifically for math articles?

I wanted to bring this up because either I am wrong about what the short description should look like (in which case I will happily revert my edits), or this is a very widespread issue throughout the mathematics articles which needs more attention. Donko XI (talk) 07:46, 21 January 2022 (UTC)

@Donko XI: The short descriptions I've seen you add to articles on my watchlist today are, pretty much uniformly, bad. The only information a reader can glean from them is that "it's mathematics". One of the main uses of short descriptions is to disambiguate search results, so (as well as being short) they need to provide enough detail about the topic they describe to distinguish it from other topics that have similar enough names to come up in the same searches. One of the worst examples of your bad short descriptions was on Lattice (order), which you changed from the informative and short-enough "Partial order having least upper bounds and greatest lower bounds" to the uninformative "Algebraic structure in order theory". Beyond failing WP:SDNOTDEF's guideline to avoid repeating article title words in short descriptions, saying that it's an "algebraic structure" fails to distinguish it from, and in fact makes it more likely to be confused with, Lattice (group), which is more clearly an algebraic structure rather than an ordering. Another bad example was logarithmic spiral which you changed to "mathematical curve", which would completely fail to clarify what kind of spiral it is among many other possible spirals in a search result. My advice would be: if you don't understand a mathematical topic well enough to formulate a short description which is sufficiently informative, you should recognize your ignorance and let someone else deal with writing its short description, rather than making things worse by reducing the short description to the level of your non-understanding. Or if you must work on short descriptions, put some effort into thinking what kinds of searches the title might come up in, and what information about the topic needs to be put into the short description to disambiguate those searches. It doesn't need to be a precise definition (those are often too long), but cutting down a definition to its essentials is often a better choice than trying to summarize the broader context, because that broader context is too often the same as other similarly-titled articles that it might need disambiguation from. —David Eppstein (talk) 08:08, 21 January 2022 (UTC)

@David Eppstein: Your character attack is unwarranted. These are good faith edits and, as an algebraist, I feel comfortable enough with these topics to describe them. I read WP:SHORTDES very carefully and looked through numerous examples of short descriptions on high profile articles before making any edits to make sure I had a good idea of what I was doing. I have immense respect for Wikipedia and take these edits seriously. In particular, the short description should not attempt to define the subject of the article. Both revisions restored a short description which defined the subject of the article rather than indicate the field the article covered. When it comes to providing disambiguation for search results, there are many articles one could be looking for with the term "lattice", some of which are not mathematical at all. For someone searching for Lattice (music), or Lattice (pastry), it is much more useful to them to see immediately that this is a mathematics article rather than be confronted with jargon like "partial order". I do agree that the short description I provided was not optimal for distinguishing it from Lattice (group) (and I'm more than open to improvements), but, taken on the whole, I do think it is an improvement and more adequately satisfies the guidelines on WP:SHORTDES. It's clear to me that your revisions (and overall Wikipedia history) are in good faith so I would much prefer this discussion to proceed civilly. Donko XI (talk) 08:38, 21 January 2022 (UTC)

@David Eppstein: Before you continue to revert my edits en masse, hear me out. The short descriptions I wrote on pages like Universal algebra and Abstract Algebra are very much in line with the standard of their peers. Abstract algebra is a branch of mathematics (like Algebraic geometry or Homological algebra, which I did not edit) in the same way Babe Ruth is an "American baseball player" instead of "American baseball player known for <whatever he's actually famous for>". The short description "American baseball player" clearly doesn't serve to define the subject of the article in the same way that "Generalization of vector spaces from fields to rings" does in your revision of my edit for Module (mathematics) does. The format "<Nationality><Profession>" is the standard for biographical articles and "Algebraic structure in Ring Theory" seems to fit in with this paradigm quite well. Again, I'm more than open to improvements, but it seems clear to me that there is an issue with the short descriptions currently used on many of these mathematics articles, and shutting down my attempt to bring them into line with the standards on WP:SHORTDES isn't productive. Donko XI (talk) 09:07, 21 January 2022 (UTC)

In the abstract, the points made by both users here seem very reasonable to me. Donko XI, do you have some particular examples in mind of obviously problematic descriptions? I would find it helpful to see. Gumshoe2 (talk) 09:29, 21 January 2022 (UTC)

I support David's reverts for the articles that are in my watchlist. Donko XI changed other short desc. in my watchlist. Some are improvements, such as, for Group (mathematics) changing "Algebraic structure with a single binary operation" into "Algebraic structure" (the long version does not distinguish groups from monoids, semigroups, etc., and this adds nothing to the short version). But, in most cases, the previous version was better, and I have restored it. In some other cases, such as function (mathematics), I have reverted Donko XI's version and edited the previous version. D.Lazard (talk) 10:15, 21 January 2022 (UTC)

@Gumshoe2: Here are a few. Most of these involve some combination of attempting to define the subject, using jargon, and being too long (more than 40 characters).

• Archimedean property - "Absence of infinitesimals in a mathematical system"
• Uniform polyhedron - "Polyhedron which has regular polygons as faces and is vertex-transitive"
• Archimedean solid - "Convex uniform polyhedra first enumerated by Archimedes with all vertices the same"
• Archimedean spiral - "Spiral named after the 3rd-century BC Greek mathematician Archimedes"
• Logarithmic spiral - "Self-similar growth spiral whose curvature pattern appears frequently in nature"
• Group (mathematics) - "Algebraic structure with one binary operation" (This one isn't that bad, but the info about having one operation doesn't seem appropriate here)
• Logarithm - "Inverse of the exponential function, which maps products to sums"

If you look at my edit history, you can see I'm not cherry picking here. This is a continuous block of short descriptions I edited. I visited these pages back to back. Here are a few more:

• Homeomorphism - "Isomorphism of topological spaces in mathematics"
• Topological property - "Object of study in the category of topological spaces"
• Function (mathematics) - "Mapping that associates a single output value to each input"

For comparison, here are some short descriptions from a few high profile articles to get an idea of the level and type of detail that's expected

• Blueberry - "Section of plants"
• Florida - "U.S. state"
• Mathematics - "Field of study"
• Number Theory - "Branch of mathematics"
• Pink Floyd - "English rock band"
• The Lion King - "1994 animated film"
• Babe Ruth - "American baseball player"

With this in mind, the description "Mathematical operation" for Logarithm, "Branch of mathematics" for Abstract algebra, or "Mathematical relationship in topology" for Homeomorphism seem perfectly in line and appropriate (even if they're not perfect). Donko XI (talk) 10:37, 21 January 2022 (UTC)

I agree with Gumshoe2 that this is hard to discuss in the abstract, and what best serves WP:SHORTDESC#Purposes is very case-specific. I'll just comment on a few:

• Abstract algebra, from "Mathematical study of algebraic structures" to "Branch of mathematics": This change looks good to me. In line with, say, Geometry. A problem is that "algebraic structures" is itself jargon. For readers who aren't sure if Abstract algebra is the article they're looking for, seeing "algebraic structures" won't help.
• Group (mathematics): In this context, "algebraic structure" actually adds value. I agree with Donko XI and D.Lazard that the shortened version is better than the longer version.
• Homeomorphism, "Isomorphism of topological spaces in mathematics" or "Isomorphism in topology (mathematics)" or "Mathematical relationship in topology": This one is tougher. "Isomorphism" is a word roughly at the same level as "homeomorphism". "Topological equivalence" might be a little more understandable, while still trying to stay descriptive technically. (Note that Topological equivalence is a redirect (WP:PRIMARYREDIRECT) to homeomorphism.) For "relationship", I guess I wouldn't use that word to describe it normally. And then of course there's always the option of "Concept in _____", which can feel like a cop-out, but is commonly used – there's nothing wrong with it, and there isn't always a more satisfactory option.

Adumbrativus (talk) 12:21, 21 January 2022 (UTC)

To me, this comparison just says that if a topic is something that one might not encounter until going to graduate school for mathematics, then a "short description" of it will be on the longer side. I can't say I find that very surprising. XOR'easter (talk) 01:57, 22 January 2022 (UTC)

I do not care enough about short descriptions to have a substantive position about this, but I would like to point out a semantic issue: "should not attempt to define the subject of the article" sounds prescriptive, but surely it should be read as "need not attempt to define the subject of the article" -- otherwise it would be objectionable if the short description on triangle were to successfully define what a triangle is in under 40 characters, and that's (obviously?) absurd. --JBL (talk) 12:13, 21 January 2022 (UTC)

This talk page is not the place for discussing specific short descriptions. For each short descriptions for which there is no consensus, the discussion must go the talk page of the article (this is stated in WP:SHORTDESC). IMO, WP:SHORTDESC is sufficient as a style guideline for short descriptions. However, I can add some specific recommendations:

• It must be clear from the title and the short description together that an article is about mathematics. As "mathematics" has 11 characters, this has the consequence that it is often very difficult to have a short dscription of less than 40 characters.
• As soon as it is clear that an article is about mathematics, there is no problem with using technical terms known by most readers who are possibly interested in the article. For example, one can suppose that a reader that has never heard of isomorphism and topology, will not be interested by Homeomorphism (he will propbaly understand nothing in the article). So "Isomorphism in topology (mathematics)" is sufficiently informative for readers interested by the article; for other readers also, since it makes clear that the article is not for them. On the other hand, "Mathematical relationship in topology" and "topological equivalence" must be avoided because "relationship" and "equivalence" have many different meanings that cannot be disambiguated in a short description, and are therefore confusing.
• Many article have a title such as "Someone theorem" or "Fundamental theorem of ..." . It is common that a reader knows the theorem without knowing its name. This must be clarified by the short description.

D.Lazard (talk) 15:37, 21 January 2022 (UTC)

I agree with most of what you bring up here and keep these points in mind in the future. However, I disagree on the Homeomorphism example specifically and it speaks to something broader about these short descriptions.

I do think "isomorphism" is too much. It's very possible that a student taking a first topology course wouldn't be familiar with the term "isomorphism" but would find the page helpful nonetheless. For someone looking to distinguish Homeomorphism from Homomorphism, knowing that the former is topological is the key piece of information, and for somebody searching for Homeopathy or Homeostasis, merely knowing it's a math article is what matters. On the other hand, I can't picture a scenario where someone will identify the article as the correct one because it discusses a type of isomorphism, but not because it's a topological relationship (even if relationship isn't the best word to use here).

This isn't intended to be a discussion about Homeomorphism specifically. WP:SHORTDES suggests avoiding jargon for a reason. Even if we, at the moment of editing, can't think of a scenario where someone unfamiliar with a piece of technical jargon would be interested in the article, that doesn't mean this audience doesn't exist. I would think first course topology students comprise a large body of readers who would find Homeomorphism useful, and turning them away is the wrong move. I've personally spent a lot of time browsing through Wikipedia articles that weren't in my technical specialty and have been reading articles beyond my technical depth since I was a kid (and this has been very valuable for me). I don't think it's right to assume the audience of these articles is a narrow group of people with a technical education on the subject. For example, an adult without an advanced mathematics background attempting to teach themselves to fulfill a lifelong dream might find the article valuable, as would a curious non-math student (or even a child) who's seen the picture of the donut-mug homeomorphism and wants to learn more.

I'm not suggesting that the short descriptions should all be fully understandable by children; that's obviously taking it too far. It should, however, be understandable at a level sufficiently below that of the article itself. There is likely an audience for a given article (or an audience attempting to navigate to a different article) that we won't anticipate while writing a short description, and the short description should be helpful to them too.

The wording on WP:SHORTDES is "avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject". I think it's safe to say that "Isomorphism" is jargon. While this guideline is particularly difficult to do justice for mathematics topics, I don't think we should ignore this. It just makes the job of coming up with a good description harder. Donko XI (talk) 21:26, 21 January 2022 (UTC)

I think the "should not attempt to define the subject of the article" is being misread. Short descriptions should not be full and complete definitions of their subjects, mostly because that would not be short enough. However, it is usually a better choice to include in the short description what makes this topic different from topics with related names rather than what makes it the same, because only what makes it different will be helpful in distinguishing it in search results. Among spirals, for instance, it is not helpful to call them "mathematical curves" (as Donko XI did) because that's true of all of them; we need some brief information about which specific spiral each one is. Summarizing a key point from the definition (not providing it in full) is often a good way to come up with distinguishing information in this way. —David Eppstein (talk) 16:48, 21 January 2022 (UTC)

Agree with that. It looks like they should be the sort of thing one sees in disambiguation pages or a list to distinguish entries frome each other. NadVolum (talk) 17:41, 21 January 2022 (UTC)

I agree with you that "mathematical curve" wasn't the best. Of each of the short descriptions I wrote, I like this one the least for exactly the point you make. When I wrote this in for Archimedean spiral and Logarithmic spiral, I was more interested at the time in disambiguating search results beginning with "Archimedean" and "Logarithmic". The previous descriptions (especially Archimedean spiral) had significant issues and were in need of adjustment, but I had difficulty coming up with something of approximately 40 characters which also indicated what type of spiral it was.

Given the descriptions for pages like Babe Ruth, Pink Floyd, and Blueberry, which make no attempt to distinguish them within a broad class analogous to "spirals" in the present discussion, I don't think I was totally off the mark, but I do agree that it should have been better. If the SD is a "concise explanation of the scope of the page" as in the first paragraph of WP:SHORTDES, it doesn't seem like distinguishing particular spirals from each other is necessarily the appropriate function of the SD. However, I do think that there is a discussion to be had, but it seems sufficiently context dependent and likely belongs over on the relevant pages. Donko XI (talk) 22:03, 21 January 2022 (UTC)

It is false that Babe Ruth makes no attempt to distinguish within a broad class. The broad-class description here would be "Biography" or maybe "human"; instead, Babe Ruth's short description makes clear that he was American and a baseball player, enough to disambiguate him from other people named George Ruth or Ruth George who might plausible come up in some searches. Please remember also that many search results come from content within the article, and not just the title words. The reason to avoid title words in the shortdesc (when reasonable) is not so much because they're the likely search terms, and more because they're automatically visible anyway in the search results, so it's better to use the limited space of a shortdesc to provide new information instead of repeating what's already there. The same reasoning also suggests avoiding the word "mathematical" in many short descriptions of mathematical topics: if other words from the article title are already recognizably mathematical, it provides no extra information. Additionally, in "concise explanation of the scope of the page", scope ≠ context. Scope is what this particular article is about; context is what broader topic it might be part of. We need to explain what this particular article is about, not set it into context. —David Eppstein (talk) 22:14, 21 January 2022 (UTC)

My general sense is that David tries to put too much into short descriptions. The main point of short descriptions is to give mobile users some very broad context, so that (to use M Hardy's favorite example) someone who's looking up psychological notions doesn't need to click on schismatic temperament. If they do that, their main job is done; more is not required.

Giving more detail is OK, possibly even useful, if:

1. It doesn't go over the "soft limit" of 40 characters
2. It doesn't confuse users who were searching for something in a completely different field

But the extra detail not being part of the core mission of short descriptions, it shouldn't be added if it violates either of those. Of course this is just my opinion. --Trovatore (talk) 01:59, 22 January 2022 (UTC)

I agree with the "soft limit" and "not confuse" parts, but disagree with "extra detail not being part of the core mission". An experiment for you to try:

1. Go into the mobile app (I think it's the same on Android and IOS)
2. Enter the word spiral into the search box

All you will see is titles and short descriptions and tiny illegible images. The first hit is for the main spiral article, with a short description that is too long (the target length is 40 characters but this one is 86). But If what you were really looking for is a specific kind of spiral (maybe the Euler spiral), but you can't remember which mathematician it was named for, you will never find it because (currently) it has no short description and you will be lost in the many other results.

For examples like this, it is essential, and part of the core mission, to have short descriptions that provide enough extra detail to find what you are looking for.

—David Eppstein (talk) 02:15, 22 January 2022 (UTC)

PS I shortened the spiral short description and added one for Euler spiral, so you won't get exactly the same results now. —David Eppstein (talk) 02:20, 22 January 2022 (UTC)

Summarizing the positions, from "most context" to "most detail":

• User:Donko XI (henceforth Dk) argues that Short Descriptions (SD) should say what field the article is part of, avoiding technical terms.
• User:Trovatore (Tr) underlines the importance of helping users who are looking for something in a "completely different field" and argues against excess detail.
• User:D.Lazard (DL) argues that the SD should include the word "mathematics"; additional detail may include technical terms.
• User:David Eppstein (DE) argues that SDs should distinguish articles from similar articles in the same field, possibly using technical terms, and prefers avoiding the word "mathematics" if other words from the title are "recognizably mathematical".

The problem is that many things are "recognizably mathematical" only to people with some mathematical background. Math loves giving specific mathematical meanings to generic terms like "field", "lattice", "structure", "kernel", and "group", as well as inventing special words not recognized at all by non-mathematicians, like "monoid", "diffeomorphism", and "tensor". For the general terms, the SD must differentiate the mathematical meaning from the non-mathematical one without using even more technical terms. For the special terms, it must point out that it's a mathematical term. It doesn't necessarily need to use the word "mathematics"; I think "algebra" and "geometry" are recognized as mathematical by the general user, though "topology" and "model theory" are surely not; "mathematical logic" must be differentiated from logic in rhetoric and philosophy.

It's certainly nice to distinguish from similar things with similar names (logarithmic spirals from Archimedian spirals), but it's even more important to clarify that they're plane figures in mathematics rather than astronomical features, software development methods, etc.

So I agree with Dk, Tr, and DL that the SD should explicitly mention that the topic is mathematical. I agree in principle with DL that additional detail can include technical terms, but the character budget is pretty tight. User:Gumshoe2 (G2) has not expressed an opinion.

By the way, many of the longer SDs still fail to actually differentiate the topic from similar topics. The SD for factorial "product of consecutive integers" does differentiate it from double factorial and the general Bhargava factorial, but not from falling and rising factorials. I don't see how to both make it clear that these are mathematical functions (and not experimental designs or data encodings) and to differentiate among the various mathematical definitions, all in 40 characters or not much more. --Macrakis (talk) 19:18, 22 January 2022 (UTC)

I wouldn't bother with making the simpler ones more complicated to distinguish from much less well known ones. And perhaps it might be enough to say variant of or something like that for special ones. It's to help someone find what they want but they'll sometimes have to look at a second article if the first isn't exactly what they wanted.. NadVolum (talk) 19:24, 22 January 2022 (UTC)

I agree. I was pointing out that even when the SD tries to clearly differentiate from other topics instead of providing context, it's well-nigh impossible in 40 characters.

SDs should stay simple. My SD for factorial, which DE reverted, was "Mathematical function on integers". --Macrakis (talk) 19:42, 22 January 2022 (UTC)

I though 'product of consecutive integers' was a good one and more descriptive. Or even just numbers instead of integers. Saying mathematical is only worthwhile for words like group or set where one genuinely has to distinguish it from oter common uses. And function is a word that people looking up factorial might not understand. NadVolum (talk) 19:51, 22 January 2022 (UTC)

I'd be happy to change it to 'product of consecutive numbers'. That's more recognizable to non-experts, and it's not supposed to be mathematically precise. In this example, "numbers" is already good enough to make it recognizable as mathematics; "mathematical" is just unnecessary and useless redundancy, and (because the other two main meanings of factorial are also somewhat mathematical) fails to distinguish it from them. Similarly, for all of the various spirals, "curve" is a familiar word that is enough to make it recognizable as geometry, leaving plenty of characters within the 40-character limit to say something more specific about which kind of curve it is. —David Eppstein (talk) 19:58, 22 January 2022 (UTC)

I'm not sure which readers are well-served by the definition "product of consecutive numbers/integers". Imagine an ag major who is told that a certain study used a "factorial design". Is that a design that has something to do with a product of numbers? Maybe?

BTW, I have updated the SD of factorial experiment, which was far too long and descriptive (195 characters!) to "Kind of experiment in statistics"; similarly, factorial should, I argue, be something like "Mathematical function", with additional optional information (like "on numbers/integers"). Interestingly, the Factorial experiment article's lead actually begins with "in statistics" and the Factorial article's lead begins with "in mathematics" -- if the article needs that level of context-settings, surely the SD does, too. --Macrakis (talk) 20:31, 22 January 2022 (UTC)

Your hypothetical ag student needs a descriptive short description on factorial design. Making the factorial short description much more vague by saying it's a "mathematical function" rather than a "product of consecutive numbers" is not going to make things any more clear for them or for anyone else. Terseness and avoiding jargon are virtues here but vagueness for its own sake is not. Also, yes, 195 characters is way too long. I don't think "kind of" or "in" add any information, so if you're going to use that short description you might as well go with the shorter "statistical experiment". Maybe "statistical experiment over all combinations of values" would still work? But it's still a little too long and I don't see a good way of packing the same information in more tightly while remaining understandable. —David Eppstein (talk) 21:38, 22 January 2022 (UTC)

I agree that factorial design needed a better description, and I provided it (with an editing glitch along the way).

I would claim that "mathematical function" is about the right level of description. If I could fit in "used in combinatorics", I would, but "product of consecutive numbers" is simply a definition, and doesn't tell the naive reader what it is related to. Though "combinatorics" is a pretty fancy (and long) word, too.

"Mathematical function" is not vague. It says what kind of thing it is, which is the main goal, and is the sort of thing you might find on a disambiguation page. (cf. Γ).

I agree about "kind of". --Macrakis (talk) 23:45, 22 January 2022 (UTC)

The Gamma function is definitely a function as its primary meaning. For factorial, I'm not so sure. 5! is a factorial, but it is a number, not a function. The sequence 1, 1, 2, 6, 24, ... is a sequence of numbers, not a function, but it is the sequence of factorials. It is not wrong to think of "factorial" as defining a function rather than referring to the individual numbers that are its values or the sequence of those numbers, but I think it involves a more advanced mathematical perspective, which maybe for short descriptions we should not be doing. Also, you could just as well say that a factorial code is a function (from data values to their codes), so calling it a function fails to disambiguate. —David Eppstein (talk) 23:58, 22 January 2022 (UTC)

For Factorial, I suggest to replace "product of consecutive numbers" with "product of first consecutive numbers". This remains sufficiently short, and, by distinguishing it from falling and rising factorials, may be less confusing for people who have learnt and forgotten the definitions. D.Lazard (talk) 21:46, 22 January 2022 (UTC)

Could be "product of numbers from 1 to n"? I don't think "first" sounds very idiomatic in this context. "Initial" is better but unnecessarily technical. —David Eppstein (talk) 21:48, 22 January 2022 (UTC)

Very good for me. D.Lazard (talk) 22:21, 22 January 2022 (UTC)

Short descriptions (SD) seem marginally useful to help a mobile user pick a correct entry from a search list, but in the grand scheme of things, I think it should not matter too much if the SD is kept at a very general level for that particular purpose. If the mobile user picks the wrong entry, no big deal, they just go back and try another one, as we all do. On the other hand, something that this discussion has not adressed so far, the SD is also used more and more in "annotated link" entries in See Also sections of articles. For that particular purpose, since we are already reading a mathematics article that sets up the broad context, it seems to me that a more focused description as user:David Eppstein advocates would be much more useful. PatrickR2 (talk) 01:33, 23 January 2022 (UTC)

That would be a very minor consideration indeed when drafting a short description. The number of instances where {{Annotated link}} is used in See also sections is extremely small, and its use is never mandatory. Within mathematics it's often impossible to make careful and sometimes subtle distinctions between articles within the WP:SDSHORT soft limit of 40 characters. In this field, it's often better to continue using a wikilink with manual text (of unlimited length) in the traditional way. MichaelMaggs (talk) 15:37, 23 January 2022 (UTC)

This is a useful thread, and some good points are being made. From my perspective (significant experience with short descriptions, but not a mathematician), Donko XI is right to note that the majority of mathematics articles have SDs that are badly non-compliant with WP:SHORTDESC. Many may have been copied over from old Wikidata descriptions which are intended for a different purpose and which don't of course attempt to comply with Wikipedia's guidance at WP:SDFORMAT and WP:SDSHORT. Those ought to be replaced. The essential things to bear in mind for mathematics articles, I think, are:

• There should never be a need to go beyond the soft limit of 40 characters - WP:SDSHORT. If you feel compelled to, it's probably because you are attempting to define the subject or copying the first sentence of the lead, contrary to WP:SDNOTDEF, or trying to make some unnecessary distinction from another mathematics article.
• WP:SDNOTDEF asks editors to "avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject". That implies that the target audience is not mathematicians, or even scientists, but readers who know little mathematics apart from words in general common use. Now of course it's frequently impossible to provide "a very brief indication of the field covered by the article" without occasionally using words that are a little more technical, but that's OK if the title itself or something within the SD states or conveys that this is an article in the field of mathematics. Even then, though, avoid terms that would be known only to mathematicians, or terms that mathematicians use in a special, unexpected sense.
• Trying hard to distinguish between two specialist subjects within the overall field of mathematics really isn't something to focus on, especially at that's often impossible within around 40 characters while at the same time avoiding jargon. It doesn't matter if multiple mathematics articles end up with the same SD, any more than it matters in biology that there are tens of thousands of articles with "Flowering plant", or in geography that there are as many with "Town in <country>" – though naturally if there is enough space within the 40 character budget, more information can usefully be added.
• If an article is too abstruse to capture within around 40 characters, "Concept in mathematics" works perfectly well; or if "mathematics" is already stated or implied by the title, something slightly more definite such as "Concept within group theory" could be used. MichaelMaggs (talk) 17:10, 23 January 2022 (UTC)

Agree with MM above. Attempting to distinguish a topic from related ones sometimes requires hatnotes such as {{for}} or {{about}}. That is not the purpose of SDs. "Concept in mathematics", or "Concept in algegra" are fine, just like "University in Odisha, India" would be fine for every one of 300+ articles. In general, I agree with Donko's SDs, having made similar changes to shorten hundreds of SD in many topic areas (including some that I remember in mathematics), often imported from WD but not always. MB 18:53, 23 January 2022 (UTC)

"Concept in mathematics" is much more vague than "University in Odisha, India", more like "place in Asia". It is better than no description at all, and better than a 200-character description that attempts to define the subject in full mathematical detail, but not much better. 40 characters is plenty to both convey to a general audience that this is mathematics and provide more specificity within mathematics. What would you feel if you saw a "See also" section of a mathematics article that listed a bunch of topics related to the article, for each of them giving its title and short description, as for example Intersection (set theory) § See also does, but if all of the short descriptions were replaced by "Concept in mathematics"? Would you think that short descriptions like that were a useful piece of information for that context? —David Eppstein (talk) 20:22, 23 January 2022 (UTC)

"Concept in mathematics" isn't a recommendation by any means. I just commented that it would work perfectly well if an article is too abstruse to capture within around 40 characters. Normally there should be something that works much better, as you say. MichaelMaggs (talk) 21:39, 23 January 2022 (UTC)

There's a bit I disagree with "avoid jargon, and use simple, readily comprehensible terms that do not require pre-existing detailed knowledge of the subject". It is a good aim but I wouldn't push it too far. If jargon is obviously jargon gibberish as far as a reader is concerned then they know it probably is not what they want! Avoiding the jargon may mean too big a number of possibilities are not distinguished for someone who would understand the jargon. Of course jargon that sounds lke something the user is interested in but is in fact something completely different is bad. NadVolum (talk) 01:40, 25 January 2022 (UTC)

I think you just want too much from short descriptions. If you need to use jargon to provide value in a short description, consider just not having one (more precisely, using an empty short description), which is a perfectly fine option provided the title itself gives context. --Trovatore (talk) 01:07, 26 January 2022 (UTC)

Have a look at Homology for instance. The descriptions are fine even though many include jargon. I is pretty clear that "Homologous series, a series of organic compounds having different quantities of a repeated unit" has nothing to do with homological algebra for instance even though organic, compound and units have all sorts of different jargon meanings. NadVolum (talk) 13:29, 26 January 2022 (UTC)

My field of research directly involves homological algebra, but it would still take me a second to recognize that this article is not what I am looking for. On the disambiguation page you linked to, the situation is clear by the fact that its listed under the heading "Chemistry", but in the search results, it would take a moment to process (not long, but it wouldn't be immediate). I imagine a student learning introductory homological algebra or algebraic topology might click on that article after reading that description. Given that the disambiguation page has additional structure to complement the job of the SD, it might be more worthwhile to emphasize the role of SDs in the search results (not to discard their value in disambiguation pages, but put this at slightly lower priority).

It's worth noting that the text in the disambiguation page isn't even the short description. The article is currently missing one. That text is directly part of the disambiguation page. The fact that we can customize the disambiguation page is another reason why the use of SDs in search results should be prioritized. If the short description isn't optimal for a disambiguation page or in most other locations it might appear, the text which appears can be customized to suit that particular need.

Something that I think is being missed in this discussion is that these descriptions aren't intended to be carefully read. They're just given a glance before the article is either moved on from or clicked on. Nuance and precise content will not be very useful in this setting and are more likely to cloud the readers decision than something very simple and less detailed. That's not to say that the SDs shouldn't be well thought out, but that the effort should be in carefully choosing a wording that lends itself to immediate clarity rather than nuance or precision. On the disambiguation page, the heading "chemistry" is all that was needed for me to know that I'm not looking at a homological algebra article. The same would be true in the search results. Seeing the term "chemistry" show up at the very beginning would be far more useful than the chemistry definition which is used instead. Donko XI (talk) 01:30, 27 January 2022 (UTC)

The Homology example isn't relevant to this discussion. That is a WP:DAB page, and like almost all such pages the text there has nothing whatsoever to do with short descriptions. It has been manually added and is part of the DAB page itself. Because DAB pages need to discriminate in such a wide range of situations, the {{Annotated link}} template should not be used there, per the template documentation. MichaelMaggs (talk) 10:14, 27 January 2022 (UTC)

Requested move at Talk:Siméon Denis Poisson#Requested move 29 January 2022

There is a requested move discussion at Talk:Siméon Denis Poisson#Requested move 29 January 2022 that may be of interest to members of this WikiProject. Favonian (talk) 22:43, 29 January 2022 (UTC)

< math > produces wrong symbols

Direct sum

Earth symbol

\oplus and \otimes are used for direct sum and tensor product, but they generate the wrong symbols. They should be ⊕ (U+2295 CIRCLED PLUS) and ⊗ (U+2297 CIRCLED TIMES), but instead we get 🜨 (U+1F728 ALCHEMICAL SYMBOL FOR VERDIGRIS) -- the astronomical symbol for the Earth -- and U+1F774 LOT OF FORTUNE (in the pipeline for Unicode 15). Can they be fixed? The circle should not touch the operator -- in fact, a variation selector is provided to force a font to display properly (with a "white rim"), e.g. U+2295+FE00 produces ⊕︀. Please ping, — kwami (talk) 01:11, 28 January 2022 (UTC)

People are so weird. —JBL (talk) 01:19, 28 January 2022 (UTC)

Where by "people", maybe you mean the font designers or unicode standards-wonks who somehow decided that the LaTeX de facto standard for typesetting mathematics was not good enough and decided to introduce gratuitous differences? —David Eppstein (talk) 01:43, 28 January 2022 (UTC)

It's really specifically the idea that it's wrong to have the plus touch the circle that gets me, I think. I'm trying to imagine some linear algebra instructor somewhere carefully drawing her direct sum circles to not touch the inner plus sign, because the unicode people think it's wrong if they touch? It definitely feels weirder than the "the 'd' in dx is non-italic because ISO" thing. (As a person too young to know life before LaTeX, it did cause me to go look up a bit of history -- unsurprisingly, LaTeX is several years earlier than Unicode.) --JBL (talk) 03:38, 28 January 2022 (UTC)

The Unicode people do not think it's wrong if they touch. As pointed out above, in order for it to not touch, you need to add the variation selector (see also the PDF, plainly showing that the default/canonical (for lack of a better term) glyphs do indeed have the circle and operator touching). Not sure where kwami got the idea that they shouldn't touch from; I've never heard of that as an issue. eviolite (talk) 03:44, 28 January 2022 (UTC)

@Kwamikagami: I have to admit that I'd never heard that touching the circle was wrong; indeed I'd always drawn it that way myself when doing mathematics on paper. Where does the notion that it's wrong come from? Double sharp (talk) 10:19, 28 January 2022 (UTC)

From my understanding from Unicode, fonts vary in whether the + touches the circle or not due to poor font design, so if you want to force a font to display "correctly", Unicode supplies a fix. (Of course, the font has to support the fix, or it will just ignore the variation selector.)

Perhaps I'm wrong about this. If it's standard in Latex, then I guess it's irrelevant. There's also a second circled plus in Unicode, ⨁ (U+2A01 N-ARY CIRCLED PLUS OPERATOR).

JBL: "I'm trying to imagine some linear algebra instructor somewhere ..." Well of course. In handwriting, you're not going to bother being so careful. You won't necessarily distinguish 1, l and I in handwriting either, but that doesn't mean you should use one for the other in print. (Well, I remember an old mechanical typewriter that saved space by not having a one or zero key, and you were expected to letters instead. But that probably wouldn't have flown for most publishers even back then.)

eviolite: "in order for it to not touch, you need to add the variation selector." Actually, that's not the case. In some fonts they touch, in some they don't. On my browser, I see a "white rim" around the plus even without the variation selector. In the default math font that came with my OS, MathJax, they don't touch, nor do they in Liberation or FreeSans fonts (though they do in FreeSerif). Note that there is no variation selector to force them to touch: that is, there's a VS to "correct" the display, but not one to force the "incorrect" form. Unicode may be wrong about the touching form being wrong, but AFAICT that's the reason for the VS. I can ask someone who would know the history of it if you like. — kwami (talk) 10:53, 28 January 2022 (UTC)

Following up on eviolite's comment: Sorry, but I'm having trouble establishing the basic facts here (perhaps because of the fonts I'm using). In LaTeX the operator touches the circle, right? In Unicode the operator touches the circle by default, right? In every math book and lecture that I can remember, the operator touches the circle. What's the problem? Mgnbar (talk) 12:40, 28 January 2022 (UTC)

How do we write \bigoplus ($\bigoplus$) and \bigotimes ($\bigotimes$) in Unicode ?--SilverMatsu (talk) 01:41, 30 January 2022 (UTC)

Solution: We use the default behavior, in which they touch. Or is the issue the "big" operators as opposed to the "small" ones? Or am I still missing the problem? Mgnbar (talk) 04:02, 30 January 2022 (UTC)

Thank you for your reply. This PDF says that if we write \bigoplus in Unicode, it will be use U + 2A01, and if we write \oplus in Unicode, it will be use U + 2295. In this PDF and LaTeX, it (\bigoplus and \oplus) seems to me that the operator touches the circle. The display of my browser on wikipedia is that U + 2295 does not touch the circle and U + 2A01 the operator touches the circle.--SilverMatsu (talk) 05:25, 30 January 2022 (UTC)

Earth mass uses \oplus for the earth symbol.--SilverMatsu (talk) 08:48, 30 January 2022 (UTC)

Examples from direct sums and Earth mass

$\textstyle A=\bigoplus _{i\in I}A_{i}$ (Use bigoplus)

$\textstyle A=\oplus _{i\in I}A_{i}$ (Use oplus)

$M_{\oplus }=(5.9722\;\pm \;0.0006)\times 10^{24}\;\mathrm {kg}$ (Use oplus)

$M_{\bigoplus }=(5.9722\;\pm \;0.0006)\times 10^{24}\;\mathrm {kg}$ (Use bigoplus)

If bigoplus and oplus cannot be exchanged, I think it will be difficult to write articles.--SilverMatsu (talk) 09:21, 30 January 2022 (UTC)

In that PDF, I too see both U+2A01 and U+2295 touching the circle. In your four examples above, I see all of them touching the circle. The issue is that some browsers render U+2295 in a non-touching way? Is this a typeface (font) issue? Or does Wikipedia emit Unicode that explicitly tells them not to touch? Mgnbar (talk) 12:34, 30 January 2022 (UTC)

In that PDF and examples (mw:Extension:Math), so do I. About the "issue", I don't know the solution.--SilverMatsu (talk) 14:25, 30 January 2022 (UTC)

"Proofs involving..." articles

Lately I am tackling the backlog of unassessed mathematics articles. While doing that I encountered articles whose titles start with "Proofs involving..." and which have developed from deprecated /proof subpages.

As a way of maintaining proof archives for particular pages, they seem problematic since their development tends to diverge from the original article. As stand-alone articles, they often have an ill-defined scope. There are currently five such pages I am aware of:

Proofs involving covariant derivatives

Proofs involving the Laplace-Beltrami operator

Proofs involving ordinary least squares

Proofs involving the Moore-Penrose inverse

Proofs involving the addition of natural numbers Felix QW (talk) 19:58, 10 January 2022 (UTC)

I have just discovered WP:WikiProject Mathematics/Proofs, which confirms my suspicion that the proofs presented there are insufficiently notable to warrant their own articles.

My current plan would be to merge them somewhere where they can be of use, which may or may not be their previous superpage.

Proofs involving the Laplace–Beltrami operator can probably be merged into Laplace-Beltrami operator without too much difficulty.

I find Proofs involving the Moore-Penrose inverse to be excessively detailed for Moore-Penrose inverse, and I am not sure what others think.

I think material from Proofs involving the addition of natural numbers makes most sense in Peano axioms as a demonstration of how the definitions of addition and multiplication given there can be used to derive well-known basic properties of natural addition.

The first two sections of Proofs involving covariant derivatives could be merged into Contracted Bianchi identities and Einstein tensor respectively. The third section was never linked to another page in the first place and I am insufficiently familiar with the material to know what to do with it.

Proofs involving ordinary least squares is more difficult, since parts of the material have been merged from Linear least squares (mathematics) and split from simple linear regression in 2018.

Any thoughts would be very much appreciated! Felix QW (talk) 18:06, 18 January 2022 (UTC)

Thank you for bringing this to attention. I think the "not a textbook" principle is extremely important for maths wikipedia. Furthermore, many of these "proofs" are actually just computations, and so are especially suitable to textbooks. I think that in many cases it would be most appropriate to remove them altogether, but to provide precise references to where they appear in standard textbooks. Gumshoe2 (talk) 21:10, 18 January 2022 (UTC)

Maybe the remaining unmergeable proofs could be moved to some wikiversity page(s), so the effort that has gone into typesetting them would not be wasted? - Jochen Burghardt (talk) 06:49, 19 January 2022 (UTC)

The German Wikibooks actually has a Beweisarchiv, which is essentially an indiscriminate collection of proofs in German. I don't think that English Wikibooks has anything similar, though, and despite some searching through their catalogue I couldn't really find a place for any of our proofs in an existing Wikibook. The exception would be the addition of natural numbers, which would fit the remit of the Abstract Algebra Wikibook, but it already has a derivation of some of the identities listed here, and besides it does not include 0 in its natural numbers. Felix QW (talk) 08:21, 26 January 2022 (UTC)

I have now requested transwikiing Proofs involving the Moore-Penrose inverse to Wikibooks so that it can be used towards the Linear Algebra chapter of the (more advanced) wikibooks:Topics in Abstract Algebra. This should keep the content available in a place where it is more suitable. Felix QW (talk) 14:39, 31 January 2022 (UTC)

• Not so much a thought as a related problem: Draft:Bose integral is essentially an unsourced proof that the Bose-Einstein integral can be expressed as a product of the Gamma function and Zeta function. If this material is worth keeping, it perhaps should go somewhere in Polylogarithm, but it doesn't look like the general case and I don't know how interesting or useful this material is. — Charles Stewart (talk) 22:55, 18 January 2022 (UTC)

Feb 2022

Tool for easily converting BibTeX database entries to Wikipedia reference entries

Short question: is there a tool to easily convert BibTeX database entries to Wikipedia reference entries?

"Tool" can be interpreted broadly: web, graphical, command-line, . . .

Background: Whatever its strengths or faults as a programming language, BibTeX has the great advantage that many (most?) scholarly math websites can export bibliographic information in BibTeX format. For example, the following websites have this capability: (1) arXiv, where virtually all recent math papers are housed; (2) MathSciNet, a collection of reviews of most math papers; and (3) zbMATH, an open-access analogue of MathSciNet with slightly different coverage.

If such a tool existed, it would become very easy to make Wikipedia references to many math papers. In particular, it would become much easier for members of the professional mathematics community to contribute to Wikipedia, and this is a group whose participation we certainly want to encourage!

Since both .bib files and Mediawiki references are basically a list of key-value pairs, it should really not be that hard to write a program to convert between them. Of course, the final output might need to be tweaked slightly, for instance, to hyperlink to an author's Wikipedia page, but we should be able to get 95% of the way there through automation alone.

Follow-up question: If there is no such tool, then has anyone found a manageable workflow for making Wikipedia references to math papers? David Schwein (talk) 09:36, 30 January 2022 (UTC)

It's a good idea. One of our editors created an export template for BibDesk, but I don't know of a canonical tool. If you just want to easily import a journal or book citation, the citoid popup form in the editor (press Cite, then Templates, then pick a template) allows one to fill in the template from a URL or DOI (paste it in and press the magnifying glass icon) and works surprisingly well. WP:CITEGENERATORS has a list of citation generation tools. --{{u|Mark viking}} {Talk} 12:51, 30 January 2022 (UTC)

I'm using a home-brewn 50-line sed script for that purpose; it has several drawbacks requiring manual corrections of its outputs (such as converting BiBTeX's "and" to "author1=|author2=|..."). - Jochen Burghardt (talk) 13:51, 30 January 2022 (UTC)

I'm using a home-brewed many-more-than-50-line Python app. It does get multiple authors right but still often involves hand-correction, in many cases because the BibTeX one gets from publishers or even sometimes from MathSciNet is itself imperfect. —David Eppstein (talk) 01:27, 2 February 2022 (UTC)

Tau proposal FAQ and tau coverage on Wikipedia

From "Frequently asked questions (FAQ)" on this page:

Q: Why is wikipedia [sic] lagging behind the rest of the world in not creating an article on τ (2π)?

A: The notability of τ=2π is not yet established. Neither the mathematics community nor the math education community has responded to the proposed new constant in any notable way. τ=2π does not at this point of time meet the criteria of notability as per Notability or Wikipedia:Notability (numbers). See also Turn (geometry)#Tau proposal.

I don't think that insufficient notability is "really" the reason for opposing a creation of a $\tau$ article. Even if $\tau$ meets sufficient notability criteria, it won't have its own article. The possibility of such article is already doomed, as it would be a content fork of the $\pi$ article (with every $\pi$ expression just rewritten in terms of $\tau$).

Also, the usage of "lagging behind the rest of the world" is inconsistent with $\tau$ being insufficiently notable.

The current "answer" (and question, for that matter) is misleading and I suggest changing it. Please note that $\tau$ day and $\tau$ activism are not the subjects of this discussion ($\tau$ activism can have its own article if the notability criteria are met). A1E6 (talk) 01:18, 2 February 2022 (UTC)

See Albert Eagle, "The Elliptic Functions as They Should be", Galloway and Porter (1958); Eagle explains in gory detail why π/2 should be τ. Mathsci (talk) 02:49, 2 February 2022 (UTC)

Well, one can argue for $\pi /4$, $\pi /2$, $\pi$, $2\pi$, (etc?) That is not supposed to be the subject of this discussion. This discussion should be merely about editing the "FAQ" on this page. A1E6 (talk) 02:58, 2 February 2022 (UTC)

I am surprised this was ever considered as a serious question on the FAQ. I bought Eagle's book for £1 at G&P, when the bookshop still existed on Sidney Street; in the book (and on zbl), Eagle wanted π to be read aloud as "pie" and τ = h(alf p)i ≡ hi as "high". His proposal is mentioned in the WP article Pi. Mathsci (talk) 03:33, 2 February 2022 (UTC)

A1E6, it seems possible to me that someday we will deem tau notable (if only as a social phenomenon), and we will write an article about it, and that article will discuss the pros and cons of prioritizing tau over pi — what you call tau activism, as far as I understand. Therefore the FAQ text seems okay to me. Mgnbar (talk) 03:30, 2 February 2022 (UTC)

I want to make clear that I did not deny $\tau$ becoming notable in the future. But pros and cons of $\tau$ are already in Turn (geometry) (though I doubt that the comparison table in that article is neutral (WP:NPOV): more formulas in favor of $\pi$ are available). @Mgnbar: Did you mean turning the "Turn" article into a $\tau$ article? A1E6 (talk) 03:43, 2 February 2022 (UTC)

For the near future, Turn (angle)#Tau proposal is more than sufficient. And Tau (mathematical constant) redirects there. So I do not advocate moving (or otherwise "turning") Turn into Tau, or even anticipating that need. :)

I guess my point is this: If tau advocates (who are presumably the audience for that FAQ) got their way, then effectively the Pi (mathematical constant) article would be turned into Tau (mathematical constant), so there would be tons of material for the latter article, contrary to what you said above. (And Wikipedia's coverage of pi would be reduced to some article section that's the mirror image of the current Turn (angle)#Tau proposal.) Mgnbar (talk) 13:21, 2 February 2022 (UTC)

To put it more succinctly: It's not that there won't be material for Tau (mathematical constant). It's that there won't be material for Pi (mathematical constant). (And let me emphasize that I am not advocating for this brave new world.) Mgnbar (talk) 13:25, 2 February 2022 (UTC)

I suppose I consider myself a "tau advocate", but I certainly wouldn't advocate anything that radical. Pi is effectively the WP:COMMONNAME of the circle constant concept; that page is fine. I would argue that the section Turn_(angle)#Proposals_for_a_single_letter_to_represent_2π should be split into its own article. There is enough well-sourced content for a standalone article, and it is not really about the "turn" angle unit, so it is a bit of a WP:COATRACK problem. The new article could be called Tau (proposed mathematical constant) and be held to a high standard of NPOV regarding the goodness of tau. The page wouldn't be a fork of pi, it would be about the idea that tau is better, with the history of that idea and a description of the arguments on both sides, as appropriate. (Incidentally, I agree that the FAQ question was terrible.) Danstronger (talk) 15:02, 2 February 2022 (UTC)

@Danstronger: Don't you think that a $\tau$ article would make Turn (angle) totally unnecessary? Wouldn't it be a content fork of Turn (angle)? I mean, tauists advocate for $\tau$ because of its equivalent correspondence with a turn.

It also seems that many editors would dispute the "mathematical value" of $\pi$ vs. $2\pi$ comparison, as the factor of $2$ is a triviality. But I don't see anything wrong with an article about "$\tau$ culture" or something like that, if it becomes notable. A1E6 (talk) 15:38, 2 February 2022 (UTC)

Tau culture would be a bad name. It would really be about the advantages of using tau vs pi. Which would be one of greater simplicity/convenience, benefits in math education, making wave theory more accessible, making trigonometry more accessible (and radians vs degrees in general), etc... I doubt we have a great body of research on this, but it seems rather evident to me that the benefits of using tau in education instead of pi would be huge. Headbomb {t · c · p · b} 18:51, 2 February 2022 (UTC)

"More accessible" is a huge exaggeration. But still, this should not be the topic of this discussion. I'm just trying to reply. A1E6 (talk) 19:05, 2 February 2022 (UTC)

Forming students for using tau instead of pi would certainly have the huge benefits to have students who will be unable to find a job because the terminology used in the real world is not that they have learnt. Please, respect the future of your students. D.Lazard (talk) 20:27, 2 February 2022 (UTC)

Don't speculate about what I teach or don't teach. I'm running into issues because I'm using pi, issues which I wouldn't have with tau. The reason why I'm working with pi is because everyone else is. If tau was used instead, it would be better and we wouldn't have these issues. Were that the case, telling people "btw, some people use pi, which is half of tau" is basically all you need to do to "respect the future of students", whatever that means. Headbomb {t · c · p · b} 20:36, 2 February 2022 (UTC)

"Will produce more Field medalists" would be a huge exaggeration. "More accessible" covers anything above 0% more accessible. A person with a Ph.D. in math will see little personal benefit from this, but in high schools and first year math/physics/science courses? People there would definitely benefit. Just today I've ran into issues with plot y = A sin (2*pi*f*t) because someone had problems understanding that plot y = A sin (20*pi*t) meant a frequency of 10. These are not issues I would have had if we worked with plot y = A sin (tau*f*t). Headbomb {t · c · p · b} 19:36, 2 February 2022 (UTC)

The improvement in accessibility would be marginal at best. If trigonometry courses need to be more accessible, this is the last thing that should be done (if it is a good idea in the first place). Mathematics is not just trigonometry and you can find many $\pi$ expressions (in trigonometry as well) without that pesky factor of $2$. A1E6 (talk) 19:49, 2 February 2022 (UTC)

As a direct example, working with tau, angles of ${\frac {\tau }{4}}$, ${\frac {\tau }{6}}$, ${\frac {\tau }{12}}$, ${\frac {\tau }{3}}$, etc... are all immediately recognizable as the angles describing one quarter, one sixth, one twelfth, and one third of a circle. ${\frac {\pi }{3}}$ needs some thinking before one recognizes it corresponds to a sixth of a circle. I don't know what your area of interest is, but I'll bet it's not teaching math at the high school level / undergrad level. Headbomb {t · c · p · b} 20:44, 2 February 2022 (UTC)

Please stop using this page to debate the merits of the tau proposal. That's not within our remit. I'm more tolerant of chitchat than a lot of people, and do plenty of it myself if I'm honest, but this is starting to make it harder to use this page for what it's for. --Trovatore (talk) 20:48, 2 February 2022 (UTC)

Agreed with Trovatore, this is not the point of present discussion. My recommendation for tau enthusiasts: if/when you bring it up as its own topic of discussion, it would be useful to do so with sources showing merit. Since tau is not even purportedly based on intellectual merit, this would probably have to be something showing pedagogical merit. Gumshoe2 (talk) 04:52, 3 February 2022 (UTC)

My remark was directed at both "sides". --Trovatore (talk) 07:15, 3 February 2022 (UTC)

Mine as well (first sentence anyway). Anyhow, if this is a place where this is to be discussed, then it would be useful to know what tau-related reliable sources people are thinking of, and what specific claims they are intended to be sourcing. I am finding this whole discussion to be rather ambiguous, with people's personal opinions on mathematical form and pedagogy freely and unclearly mixed in with everything else. Gumshoe2 (talk) 17:42, 3 February 2022 (UTC)

Initially, this was supposed to be a discussion about the tau proposal in FAQ. Even though we got rid of the tau proposal question in FAQ, this turned out to be a discussion about tau coverage on Wikipedia. Tau coverage on Wikipedia alone would be suitable for a new thread, but since the stuff was quite mixed, I decided to just rename this thread instead. If anything, editors should focus on the topic of tau coverage on Wikipedia (whether pro-tau or anti-tau). A1E6 (talk) 17:51, 3 February 2022 (UTC)

@A1E6: The concept of "turn (angle)" is almost entirely distinct from the concept that is "tau (proposed mathematical constant)". One is about a unit of angle and the other is about a proposal to use tau = 2pi as the fundamental circle constant. Even tau itself (the number) is conceptually quite distinct from one turn. (Physicists might call angles "unitless", but you can't say "$1^{\circ }=\tau /360$ rad" without the "rad".) Of the content in turn (angle), the stuff in the tau section is unrelated to the content in the rest of the article. On the topic of "many mathematicians would find it trivial", it doesn't matter if some people don't like it; it's a notable, well-sourced topic. (Incidentally, I think the characterication that tau is important because of it's connection to one turn undersells it; it would be more accurate to say that there is some overlap between the reasons tau is an important number and the reasons one turn is an important angle.) Danstronger (talk) 04:07, 3 February 2022 (UTC)

@Danstronger: $\mathrm {rad} =1.$ "It would be more accurate to say that there is some overlap between the reasons tau is an important number and the reasons one turn is an important angle." Well, I agree with that. But $\pi /2$ is an important number as well. I don't understand why you linked WP:IDL – we try to discuss Wikipedia policies which seem to go against $\tau$. A1E6 (talk) 13:00, 3 February 2022 (UTC)

I suggest to just remove that question. It's been a few years since Tau was a hot topic. Certainly the question in its current form violates NPOV. —Kusma (talk) 13:43, 2 February 2022 (UTC)

I agree. Mathsci had doubts as well. A1E6 (talk) 13:48, 2 February 2022 (UTC)

Tau's notable IMO. There's certainly enough material for a standalone article, but really it's all covered in Turn (angle). Maybe it could be split, but I don't really see the benefits. Headbomb {t · c · p · b} 14:05, 2 February 2022 (UTC)

$\tau$'s notability may be sufficient for a section of some article, but it is not sufficient for FAQ. I doubt that the question has been asked frequently and it seems it was rather some sort of a "promotional vehicle" for tauists. A1E6 (talk) 14:09, 2 February 2022 (UTC)

Yeah, FAQ implies the Q is F, and it's definitely not. Headbomb {t · c · p · b} 15:47, 2 February 2022 (UTC)

Thank you for removing it. —Kusma (talk) 17:14, 2 February 2022 (UTC)

No problem. A1E6 (talk) 17:41, 2 February 2022 (UTC)

• I'm quite the opposite of a tau enthusiast, but I think the CONTENTFORK argument against the proposal is wrongheaded, simply because I think there are circumstances where biting the maintenance-headache bullet of multiple entrypoints to a topic is worth it in terms of making the encyclopedia more user-friendly to a substantial subset of readers. Two arguments:

1. If all these programming language designers can support tau enthusiasts, why can't we? Do we lack the needed editing skill?
2. We have multiple entrypoints on other topics already, e.g. Boolean structures from algebraic and model-theoretic viewpoints and we used to have an entrypoint for engineers, which we, in my opinion wrongheadedly, seem to have done away with.

Can we think like encyclopedia writers on this matter and not notability-obsessed bureaucrats? — Charles Stewart (talk) 09:15, 3 February 2022 (UTC)

In my opinion, the question is not one of notability - I am pretty sure that $\tau$ is notable as a unit - nor content - it has been discussed sufficiently in reliable sources to write about.

The point to me is that readers looking for $\tau$ are more likely than readers looking for $\pi$ to be interested in the historical, social and didactic aspects of using $\tau$, and that therefore it makes more sense to discuss $\tau$ in context. So I think integrating content on $\tau$ into our articles on Pi or Turn (geometry) is preferable to a stand-alone article. Since Pi is already quite long, and also one of our most high-profile featured articles that should probably be handled with some care, having a section in Turn (geometry) devoted to it seems very sensible to me. Felix QW (talk) 09:39, 3 February 2022 (UTC)

• And for that group, who I presume to be the majority, what we have is right. The thing is, for the minority who prefer their mathematics to be presented in terms of tau, we do not have a single article that presents the relevant mathematics in the way that is most natural for them: A single article could conceivably make a big difference to the utility of the encyclopedia for these users. It might be that it doesn't make sense to override the CONTENTFORK guideline for even one article, but I'd like us to make that decision based on a rational evaluation of the benefit to this minority of readers vs the maintenance burden for us. — Charles Stewart (talk) 11:40, 3 February 2022 (UTC)

It could be a small article just describing the history of the idea and the reasons people have put forward for adopting it. One would then only need a small section referring to it in the pi article. I'm not keen on it being in the turn article, a turn is a measurement like a radian or degree whereas tau is a constant like 2pi or 360, or 1 for turn. NadVolum (talk) 11:52, 3 February 2022 (UTC)

Turns is where tau shines most. (In most places in physics or engineering, the letter tau is so overused that the suggestion to give it a new meaning is hopeless: it looks like intentionally trying to confuse people). —Kusma (talk) 17:57, 3 February 2022 (UTC)

Abbott's reformulation of the Euler identity

Please excuse a digression, but I think it illustrates what is at stake in documenting the tau proposal correctly.

In the section Proposals for a single letter to represent 2π we have the table excerpted from, IIUC, Abbott's 'My conversion to Tausim':

Euler's identity	0       eiπ = − 1 eiπ + 1 = 0	0     eiτ = 1 eiτ − 1 = 0

While each identity easily follows from the other, they are not really the same claim: to my mind, the identities to the left document distinct facts from those on the right, each pair following from observing distinct points on the unit circle. This claim, I'm pretty confident, could be expanded to a provable proposition in type theory: it's a logical theorem about mathematical analysis. Should the identity be a new subsection in the Euler identity? Imagine we did so, and it outgrew that article, gathering clear independent SIGCOV. Would farming the article out be a content fork? — Charles Stewart (talk) 12:27, 3 February 2022 (UTC)

It shouldn't be a new subsection. You can write $e^{2\pi i}=1$, anyway. A1E6 (talk) 13:00, 3 February 2022 (UTC)

• I think you have misunderstood the point. A reliable source, attempting to translate Euler into the vocabulary of tau, misrepresented the content of Euler's observation. If you like, this is a case of mistakened identity, arising from the conufsion that effort to switch between dialects of mathematics apparently risks. — Charles Stewart (talk) 13:06, 3 February 2022 (UTC)

You can go on and rewrite the residue theorem in terms of $\tau$ (I'm kidding). Even if there is a reliable source translating the residue theorem into the vocabulary of $\tau$, it's not a good idea. A1E6 (talk) 13:13, 3 February 2022 (UTC)

• OK, let's take the scenario one step further. Suppose the article is created and then taken to AfD. After the first week, the !votes are split between those claiming falls foul of CONTENTFORK and those who say it doesn't. An admin extends the discussion and you want to participate. Can you find a winning argument that will enable us to reach consensus at AfD? — Charles Stewart (talk) 13:20, 3 February 2022 (UTC)

Danstronger recently gave a reason for an independent $\tau$ article, showing it wouldn't be a content fork of Turn (angle) and it wouldn't be a content fork of Pi. I don't think such article would be taken to AfD. But, if it is taken to AfD – editors will probably oppose the creation of that article on the grounds of insufficient notability. You know, Hartl's $\tau$ manifesto is self-published etc. My initial point about the impossibility of a $\tau$ article seems to be a bit off now, but the $\tau$ question did not belong to FAQ anyway. A1E6 (talk) 13:29, 3 February 2022 (UTC)

I haven't seen Danstronger's proposed article yet, maybe it would be considered a content fork after all. The $\tau$ article would probably be a heavily restricted version of the $\pi$ article. I mean, people would still go to the $\pi$ article for the "mathematical-value content". In fact, it would be all a matter of just using $\pi =\tau /2$. The $\tau$ article could contain information about $\tau$ culture, though. A1E6 (talk) 14:38, 3 February 2022 (UTC)

It's just an upsetting situation for tauists on Wikipedia because of WP:N and WP:CONTENTFORK. A1E6 (talk) 15:09, 3 February 2022 (UTC)

Will we need an article on seven nines in tau (currently there's not even a mention in six nines in pi)? —Kusma (talk) 15:43, 3 February 2022 (UTC)

"Froda's theorem"

There is a strange situation at Froda's theorem. As best I can tell/guess:

• a wiki editor in 2009, based on an original reading of a research article from 1929, ascribed the well-known theorem that "a monotonic real function cannot have uncountably many discontinuities" to Alexandru Froda — despite the fact that the relevant 1929 article of Froda described it as previously and widely known.
• Ten years ago there were some discussions on the talk page about this, which were inconclusive. I have recently added some links on the talk page to posts on stackexchange websites where various people, with better knowledge of historical sources, have commented on the matter (the conclusion of each being that Froda's name should not be present). These links are not meant as sources but hopefully give some helpful information to editors.
• There have been some number of books and articles which call the theorem "Froda's theorem". [6] [7] [8] [9] [10] [11].
• I have not been able to find a single such book or article from before 2009, so I assume that the naming in each of these references was inspired by the wikipedia article, which has referred to "Froda's theorem" for the last thirteen years. Nonetheless, whatever the reason, there now do exist some sources calling the theorem "Froda's theorem".

Yesterday I retitled Froda's theorem to Discontinuities of monotone functions, as I think there is no standard name for the theorem. I think there are two remaining questions:

1. is there a better name for the article?
2. should the article be completely folded into Classification of discontinuities? The given proofs can be significantly condensed and clarified, see e.g. Rudin's book or any similar textbook.

Any thoughts appreciated. Gumshoe2 (talk) 18:20, 3 February 2022 (UTC)

As Froda's theorem redirect here, this must be mentioned in the article. I have done this, but some of the above links must still be added as sources. Also, feel free to improve my wording. D.Lazard (talk) 19:06, 3 February 2022 (UTC)

Ok, I am not so familiar with these rules & regulations. Would it be a possible/better solution to just delete the Froda's theorem redirect page altogether and leave only Discontinuities of monotone functions? Gumshoe2 (talk) 19:23, 3 February 2022 (UTC)

It is not a good idea to delete the redirect, as readers who have heard of Froda's theorem may search for it. So, it must be mentioned in the article with a provisio that this is a misnomer. D.Lazard (talk) 21:12, 3 February 2022 (UTC)

Also, Alexandru Froda must be edited accordingly, and WP:PEACOCK formulations must be removed there. D.Lazard (talk) 19:11, 3 February 2022 (UTC)

Should the article include a construction of a monotone function having any given countable set as its points of discontinuity? —David Eppstein (talk) 19:15, 3 February 2022 (UTC)

Yes, I think that would be excellent to include. Gumshoe2 (talk) 19:22, 3 February 2022 (UTC)

For anyone who wishes to add it, it is done in section 2.18 of Gelbaum & Olmsted "Counterexamples in analysis". Gumshoe2 (talk) 19:28, 3 February 2022 (UTC)

As pointed out on one of the Stackexchange posts Gumshoe2 found, Ludwig Schaeffer constructed such functions in 1884: https://doi.org/10.1007/BF02421552 (Example after Theorem III) Felix QW (talk) 19:36, 3 February 2022 (UTC)

Thanks for pointing out. Maybe somebody would also like to make a wiki page for Scheeffer, they could translate his short German wikipedia page. https://de.wikipedia.org/wiki/Ludwig_Scheeffer Gumshoe2 (talk) 19:44, 3 February 2022 (UTC)

My German is not great but it seems the Gelbaum–Olmsted example is identical to the one originally done by Scheeffer. Gumshoe2 (talk) 19:52, 3 February 2022 (UTC)

I started a translation at Ludwig Scheeffer. - Jochen Burghardt (talk) 22:28, 4 February 2022 (UTC)

It seems that the theorem in Discontinuities of monotone functions is not exactly the same as the theorem called "Froda's theorem" in Alexandru Froda: the first one concerns monotone functions, and the second one concerns functions that have only jump discontinuities. I ignore whether the latter was known before Froda's proof. This must be checked. D.Lazard (talk) 21:38, 3 February 2022 (UTC)

See these stackexchange/mathoverflow answers: [12] and [13]. As far as I can see, "Froda's theorem" has no meaning except on wikipedia (and some other more recent sources as discussed in my original post above). The "Froda's theorem" wikipage has always referred to the theorem on monotonic functions, and correspondingly every reference since 2009 which I have found in the literature uses "Froda's theorem" in this way. As you indicate, on some talk pages and at least one other wikipage, "Froda's theorem" also refers to a result on jump discontinuities of general functions. According to the refs in the above SE/MO links, this result was already proved at least by 1907 (by other authors, and perhaps by Young in 1907). My impression is that Froda's original results in his 1929 paper deal with discontinuities of multivariable functions, and that he does not claim any originality on the monotonic theorem or on the more general results possibly due to Young. As far as I know, the original results in Froda's 1929 paper are not well-known or considered as particularly important.
Anyway, just to be clear on your direct question: from what I have seen, wikipedia (whether on talk pages or the Alexandru Froda page) stands completely alone in calling the result on jump discontinuities of general functions as "Froda's theorem". Gumshoe2 (talk) 22:02, 3 February 2022 (UTC)

This means that the article Alexandru Froda has to be fixed. You are much more competent than me for this. Please, go on and do it. D.Lazard (talk) 08:14, 4 February 2022 (UTC)

Courtesy of NUMDAM, the French-language dissertation is available digitally (with the orthography "Alexandre Froda"). Mathsci (talk) 10:12, 4 February 2022 (UTC)

Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/"

Hello, I need help over at Max-flow min-cut theorem. I edited the dual constraint in the section "Linear programming formulation", a <math> formula inside of a table. The preview looked fine, but after saving the actual page gives a red warning saying

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle \begin{align} d_{uv} - z_u + z_v & \geq 0 && \forall (u, v) \in E, u\neq s, v\neq t \\ d_{sv} + z_v & \geq 1 && \forall (s, v) \in E, v\neq t \\ d_{ut} - z_u & \geq 0 && \forall (u, t) \in E,u\neq s \\ d_{st} & \geq 1 && \text{if } (s, t) \in E \end{align}}

Maybe something having to do with the mathoid service is down? What to do? Thanks, AxelBoldt (talk) 21:12, 4 February 2022 (UTC)

Please ignore: after reverting the page to the previous version and then reverting again to the now current version, the error message seems to have gone away. AxelBoldt (talk) 21:20, 4 February 2022 (UTC)

This is probably a problem of internet connexion (too slow or too busy). When I get this kind of message, I generally try to save my edit again, and it works well. D.Lazard (talk) 21:36, 4 February 2022 (UTC)

They happen from time to time, due to some temporary connection fault. There is a system to detect these so they should go away by themselves. I also monitor Category:articles with math errors that show all pages with error and fix the strays. --Salix alba (talk): 22:54, 4 February 2022 (UTC)

\vphantom and others

Today I wanted to fix the Generalized continued fraction article where inappropriate markup is used, the "K" is inconsistent with \sum_{i=1}^\infty, as you can see:

The code \underset{i=1}\overset{\infty}\operatorname{K}\frac{a_i}{b_i}\sum_{i=1}^\infty\frac{a_i}{b_i} produces

${\underset {i=1}{\overset {\infty }{\operatorname {K} }}}{\frac {a_{i}}{b_{i}}}\sum _{i=1}^{\infty }{\frac {a_{i}}{b_{i}}}$

In MathJax, this can be fixed by \mathop{\vphantom{\sum}\vcenter{\huge \mathrm K}}_{i=1}^\infty\frac{a_i}{b_i}\sum_{i=1}^\infty\frac{a_i}{b_i}, but this gives error messages on Wikipedia.

Is there a workaround on Wikipedia? A1E6 (talk) 19:49, 5 February 2022 (UTC)

Not a good one, I think. See previous discussion at Wikipedia talk:WikiProject Mathematics/Archive/2020/Nov § Missing LaTeX macros: mathstrut, vphantom, vrule, and smash. —David Eppstein (talk) 20:08, 5 February 2022 (UTC)

Finite field

If you have an opinion on whether the study of finite fields should be categorized as "Finite fields" (current name), "Finite field" (proposed name), "Finite field theory" (alternative name in discussion), or something else please weigh in at Wikipedia:Categories for discussion/Log/2022 January 1 § Category:Finite fields. —David Eppstein (talk) 22:19, 6 February 2022 (UTC)

MOS:INDENTGAP bot

According to MOS:FORMULA,

"A frequent method for displaying formulas on their own line has been to indent the line with one or more colons (:). Although this produces the intended visual appearance, it produces invalid html (see Wikipedia:Manual of Style/Accessibility § Indentation). Instead, formulas may be placed on their own line using <math display=block>. For instance, the formula above was typeset using <math display=block>\int_0^\pi \sin x\,dx.</math>.

If you find an article which indents lines with spaces in order to achieve some formula layout effect, you should convert the formula to LaTeX markup." (bolding mine)

According to MOS:INDENTGAP, the usage of colons

"is not ideal for accessibility, semantics, or reuse, but is currently commonly used, despite the problems it causes for users of screen readers."

Is there a WP:BOT that would do the job, so that it doesn't have to be done manually [14]? A1E6 (talk) 16:21, 7 February 2022 (UTC)

It definitely cannot be done mechanically without producing large numbers of problems. For example, there are plenty of places where one finds a colon-indented equation with text on the same line (including possibly punctuation outside the closing math tag, or a reference). Changing these to display=block creates unintended effects (e.g., punctuation or references being bumped to the next line). --JBL (talk) 16:51, 7 February 2022 (UTC)

(edit conflict)A bot would be a convenient solution for existing indented formulas. However, for new formulas, it is boring to type "display = block" instead of ":" for every displayed formula. So, it would be useful to add entries "<math display=block>" and "<math display=inline>" to the menu "Math and logic" of the editing window.

By the way, all special Unicode characters whose use is discouraged should be removed from this menu, or replaced by their LaTeX macros. D.Lazard (talk) 17:03, 7 February 2022 (UTC)

display = block and dark mode

I've noticed some IP editors complaining about displayed equations (using <math display="block"> ) not working in dark mode on mobile (e.g.). I am sure that there is a place to report technical errors of this nature to WP developers; can someone help? Thanks, JBL (talk) 01:03, 12 February 2022 (UTC)

T182128 and T268279 —David Eppstein (talk) 01:15, 12 February 2022 (UTC)

Thank you! --JBL (talk) 21:24, 12 February 2022 (UTC)

Bernoulli quadrisection problem

I have created a new article about the Bernoulli quadrisection problem. It is a stub consisting of two sentences. Michael Hardy (talk) 18:01, 13 February 2022 (UTC)

Triple Equal Sign replacement of Equal Sign

I am thinking of replacing equal signs in the Dot product article with the identity sign Triple bar. I am also going to add arrows over the vectors. I am wondering if this is a good contribution or against the style guidelines. ScientistBuilder (talk) 18:55, 14 February 2022 (UTC)

Why on earth would you replace a correct symbol with an incorrect symbol? --JBL (talk) 19:02, 14 February 2022 (UTC)

Is your idea to use the triple bar to indicate that the equation holds for all values of the variables involved? Or to indicate that the equation is a definition? Or to indicate that some quantity, which appears to be a function, is constant-valued and hence independent of the arguments to that function? That triple bar has multiple meanings in mathematics. Mgnbar (talk) 20:53, 14 February 2022 (UTC)

Maybe they are doing dot products in finite fields and want to indicate that they are using modular arithmetic? —David Eppstein (talk) 20:58, 14 February 2022 (UTC)

I just knew somebody would bring that up too. :) Mgnbar (talk) 21:00, 14 February 2022 (UTC)

According to the Manual of Style, ordinary "=" is preferred over "≡" or ":=" in definitions. Instead, the prose around the equation should indicate that it is a definition. I do not know if we have an overall standard for whether to use boldface or arrows to indicate vectors, but we certainly don't need to use both at once; since the article dot product already uses boldface throughout, I don't see the purpose of changing it. Perhaps you could elaborate on what you find unclear about the article as it currently stands. XOR'easter (talk) 21:34, 14 February 2022 (UTC)

(1) Yes, some mathematicians use the triple bar for definitions, to indicate that the two sides are not only equal "by chance" (as in x = y, where this may be true in a specific case, but isn't the definition of x), but this usage is far from universal. In fact it's pretty rare in most textbooks. And in the case of the dot-product article, I think it's overly pedantic. We're here for general readers, who really have enough on their plates making sense of our maths articles. Let's keep things as simple as possible.

(2) A general principle of Wikipedia is that nomenclatures and styles are rarely fixed, provided they reflect usage in sources. Vectors are widely denoted by arrows or by bold-face in sources, so either is appropriate in Wikipedia. Consistency is important. If an article uses bold face throughout, it would be wrong to insert an example using an arrow (again: the idea is to help the reader). But if you move from one article to another, expect that overall styles may change. And they will of course change if you move to a branch of maths where the practitioners have their own preference. Elemimele (talk) 23:03, 14 February 2022 (UTC)

One thing I'll note on notation, is that it's often useful to explain that bold means vector, as done in Bouncing ball#Forces during flight and effect on motion. That's something that's obvious to mathematicians and physicists, but might not be obvious to someone new to vectors. Headbomb {t · c · p · b} 23:08, 14 February 2022 (UTC)

Unsolved problems and solved problems in mathematics

Excuse me, I would like to ask about the unsolved and the solved problems in mathematics. So, I'm asking the question: why the solved problems have been written in unsolved problems of mathematics? Is it better to make a new page about the solved problems in mathematics? Is it better to write about who's solved the problems and what are the solutions (if the idea, that is, to make a new page about solved problems in mathematics, is acceptable)? Regards Dedhert.Jr (talk) 10:24, 16 February 2022 (UTC)

There are billions of solved problems in mathematics. So listing them is nonsensical. On the other hand, readers who search a problem that they believe unsolved, would certainly be helped with a list of problems that were unsolved for a while, but have been recently solved. This the purpose of the section on recently solved problems in List of unsolved problems in mathematics. D.Lazard (talk) 11:05, 16 February 2022 (UTC)

Problems that were unsolved but interesting enough to be named and passed around and tackled are notable though and the list of unsolved problems acknowledges that by listing such problems which have recently been solved. NadVolum (talk) 21:15, 16 February 2022 (UTC)

Introduction to Linear Algebra Topics

I want to create an Introduction to article for several key linear algebra concepts:

1. Matrix
2. System of Linear Equations
3. Methods for Solving Systems of Linear Equations (LU Decomposition, Row Reduction, Gaussian Elimination)
4. Vectors
5. Eigensystems (Eigenvectors, Eigenvalues, Eigenspaces, Eigenbasis)
6. Determinants
7. Vector Spaces
8. Row Space, Column Space, Kernel
9. Linear Transformations, homogenous coordinates
10. Applications of Linear Algebra

I am going go to post this message on Wikipedia:WikiProject Mathematics as well. I do not want to have an issue with https://en.wikipedia.org/wiki/Wikipedia:Make_technical_articles_understandable's Introduction to Article's guidelines. I am wondering if there is a piece of advice anyway has. ScientistBuilder (talk) 01:01, 19 February 2022 (UTC)

It's great that you want to improve Wikipedia's accessibility on this ultra-important topic. But what you propose is huge. It's basically a first course in linear algebra, which many students learn over the course of 4-15 weeks. How will your article differ from, say, Linear algebra? Mgnbar (talk) 01:59, 19 February 2022 (UTC)

Yes, that's a big proposal! You might want to focus on a small part of it first. Remember, you can write drafts in your sandbox or in subpages within your own user space, e.g., User:ScientistBuilder/Introduction to eigensystems. It might be best to try writing a draft that way first and then ask for opinions here on whether it is a good fit for Wikipedia, since that can be hard to tell in advance. Also, you might try warming up by improving existing articles before starting new ones. There's no better way to learn than by doing! Best of luck, XOR'easter (talk) 02:18, 19 February 2022 (UTC)

Also you should understand the difference between encyclopedia articles (which are not meant to be instructional) and the kind of content found in text books. Paul August ☎ 03:10, 19 February 2022 (UTC)

Please pay particular attention to WP:NOTTEXTBOOK. PatrickR2 (talk) 23:59, 19 February 2022 (UTC)

about Cauchy's integral theorem

I started a discussion at the Talk:Ludwig Bieberbach about the Cauchy's integral theorem#Political significance. --SilverMatsu (talk) 03:38, 20 February 2022 (UTC)

New draft article that needs expansion ASAP

Please check out Draft:Comparison of number bases. It needs expanding with reliable sources ASAP. The article is currently completely empty. Thank you! 2601:647:5800:1A1F:69F6:E3D2:8BE3:ABEE (talk) 06:37, 19 February 2022 (UTC)

We already have Radix. XOR'easter (talk) 09:53, 19 February 2022 (UTC)

My article is more about their merits and flaws for human use. Username142857 (talk) 11:40, 20 February 2022 (UTC)

See Wikipedia:Miscellany for deletion/Draft:Comparison of number bases. XOR'easter (talk) 21:25, 19 February 2022 (UTC)

Discussion on Alexandrov's uniqueness theorem

In the last day there have been some discussions on talk page [15] for Alexandrov's uniqueness theorem which do not seem to be going very productively. Any thoughts or comments welcome. Gumshoe2 (talk) 21:00, 20 February 2022 (UTC)

How to space a large number

I am wondering how to put spaces every three digits in a number for example how to format 9192631770 to be formatted lik 9 192 631 770 in Wikipedia's math formatting langue. ScientistBuilder (talk) 02:21, 21 February 2022 (UTC)

Try the {{val}} template. XOR'easter (talk) 02:29, 21 February 2022 (UTC)

And that'll make sure the number isn't split at line end by spaces! NadVolum (talk) 16:29, 21 February 2022 (UTC)

Category:A-Class mathematics articles

Hello, WikiProject Math,

This category keeps popping up on the Empty Categories list and I'm just surprised that there are no A-Class mathematics articles. There are FA articles and GA articles but no A-class? Are there ones that need to be reassessed? Thanks. Liz ^{Read! Talk!} 16:38, 22 February 2022 (UTC)

Most WikiProjects don't do A-Class reviews anymore; I'm only aware of WP:MILHIST and WP:WPTC that retain it. See the subcategories of Category:A-Class articles - the vast majority are empty. Peano axioms was one of the last remaining A-Class math articles (having been assessed in 2007), but it was downgraded in January. eviolite (talk) 17:01, 22 February 2022 (UTC)

I removed the links to this empty category from Template:WikiProject Mathematics assessment and Template:WikiProject Mathematics/class. That should at least cut down the other links coming from these templates, making it easier to see what more needs to be cleaned up before we can delete the category altogether. —David Eppstein (talk) 18:04, 22 February 2022 (UTC)

Tuesday is Twosday

//

or // (dd-mm-yyyy)

Today is a palindrome and ambigram date.

Don't miss out celebrating the coolest date of the decade. Why numbers like 2/22/22 have been too fascinating for over 2,000 years. -- Basile Morin (talk) 10:31, 22 February 2022 (UTC)

I've been calling it Cantor Day. We've had a few Cantor Days over the last couple years, but this is the last one (at least sensu stricto) for quite a while. --Trovatore (talk) 00:50, 23 February 2022 (UTC)

Up-to-date information no longer exists

The page titled Wikipedia:WikiProject Mathematics/Current activity died in 2015, and now the one titled User:Mathbot/Changes to mathlists has become defunct as of October.

Will we now be deprived of these sorts of news sources forever? Michael Hardy (talk) 06:34, 21 February 2022 (UTC)

We do have Wikipedia:WikiProject Mathematics/Article alerts and User:AlexNewArtBot/MathSearchResult. XOR'easter (talk) 06:41, 21 February 2022 (UTC)

Thank you--I am subscribed to the former, but was not aware of the latter. Off to check A Subway Named Mobius. --{{u|Mark viking}} {Talk} 12:39, 21 February 2022 (UTC)

@Mark viking: Although that particular article is not new, it was recently moved (to remove the umlaut on Mobius) -- seems questionable to me. --JBL (talk) 14:06, 21 February 2022 (UTC)

Just scanning the brief discussion, it sounds like the original story was "questionably" titled, but it's not for us to correct the error retroactively. --Trovatore (talk) 19:17, 21 February 2022 (UTC)

I was myself trying to locate mathematics articles needing sources/citations some weeks ago and only had partial success with some contorted deepcat searches. Does anyone know of an accepted way to retrieve, say, all articles of interest to WPM with an Unreferenced tag? Felix QW (talk) 13:38, 21 February 2022 (UTC)

You can use PetScan. This query retrieves articles in Category:All articles lacking sources which have {{Maths rating}} on their talk page. eviolite (talk) 14:14, 21 February 2022 (UTC)

Excellent pointers all around! I have added these and more to Wikipedia:WikiProject Mathematics#Things to do. I also signed up this WikiProject for the User:CleanupWorklistBot listings, which are quite nice. If I did that right, they should appear on Tuesday, March 1. -- Beland (talk) 06:29, 23 February 2022 (UTC)

Thin spaces

I anyone wishes to offer an interpretation of the whitespace in Wikipedia:Manual of Style/Mathematics#Multiplication sign and MOS:MARKUP, we could use a third opinion at Talk:Hyperdeterminant#Thin spaces. -- Beland (talk) 06:34, 23 February 2022 (UTC)

Draft:Nth K-Permutation

If this is notable enough for an article, would someone please accept it or advise me how to handle it. DGG ( talk ) 06:49, 23 February 2022 (UTC)

Natural math

An article within the scope of this group was recently moved to Draft:Natural math. WhatamIdoing (talk) 02:09, 24 February 2022 (UTC)

Proposed merger of Differential (infinitesimal) to Differential (mathematics)

An editor has requested for Differential (infinitesimal) to be merged into Differential (mathematics). Since you had some involvement with Differential (infinitesimal) or Differential (mathematics), you might want to participate in the merger discussion (if you have not already done so). --Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:34, 24 February 2022 (UTC)

With due respect

...for the work that many must do here, that is WP policy-compliant. But I have to say this once, as an educator that has been here for a couple of decades. Despite having graduated students that are now faculty members at major universities, including in maths, and having looked in sporadically at articles here over the years, I cannot make this WikiProject a place to recommend reading or effort. The reason is very simply that we see no broadly evident commitment to the very core principle of WP, that our words have no claim to authority absent the appearance of citations from which our concepts, definitions, derivations, and examples derive.

In the maths articles here, the cases of articles with sentence after sentence, paragraph after paragraph, section after section that are either unattributed of only very poorly done—so widespread are they—means we cannot possible let students use WP maths articles. They are not in a position to differentiate between content trustworthy vs. untrustworthy, we are not in a postiion to say (damn the rules) trust it all, and otherwise, the material is generally poor as an example to offer them of secondary or tertiary academic writing. [It almost seems at times that maths article writers think they are called either to novel derivations and examples (i.e., publishing here), or to higher education teaching (where it is acceptable to approach and present content from memory, no need to present the origins of ones ideas).]

If someone wants to reply here with a list of maths articles that follow WP:VERIFY, articles that are therefore trustworthy, we will be glad to take a look. But otherwise, our sampling of this space is sufficient to allow us to conclude that it is not worth the time spent checking in on particular articles, given the likelihood that unsourced material will be mostly what students find.

Note, this is the only time in all these years I have complained in this way here. (Tried to fix things, yes. Complained here, no.) And so apologies, and good luck to those committed to the careful work of redeeming lost articles. We know, based on student initiatives, how very difficult, if not impossible it is to do such work after the fact. 2601:246:C700:558:B96E:EF41:6BF4:5C2A (talk) 06:16, 11 February 2022 (UTC)

I do not agree fully with your condemnation but I think some of what you say is quite accurate. One specific (seemingly unnecessary) problem I have found is that many editors are far too eager to add proofs or quasi-proofs to pages and nowhere near eager enough to add a specific page ref to a standard textbook where a proof is given! (the latter being one of the most valuable things any editor can do) Gumshoe2 (talk) 06:46, 11 February 2022 (UTC)

Very well said! PatrickR2 (talk) 09:42, 11 February 2022 (UTC)

I disagree. Most "reliable sources" are either unavailable (out of print or behind a high pay-wall) or contain errors just as egregious as those which appear in Wikipedia. Many are written in foreign languages or use archaic terminology which render them incomprehensible to modern readers. Although Wikipedia is far from perfect, at least it can be improved relatively easily. JRSpriggs (talk) 19:45, 11 February 2022 (UTC)

The original poster raises some good points. I've been thinking about this issue for a while. I see two big socio-cultural reasons:

1. Math papers and books have far fewer citations than publications in other sciences. Math papers don't need to cite data; they are often pure logic, which the culture of math expects the reader to painstakingly verify. WP:CALC applies of course, but a lot is left to the math reader, even in textbooks, and Wikipedia is not even a textbook.
2. Mathematicians (along with computer scientists, Star Wars fans, etc.) were early adopters of Wikipedia. In the early days, less attention was paid to good citations. Consequently a bunch of math articles got pretty decent without them. Now it's "too much" work to rewrite these articles to be organized around what reliable sources say. Or rather there are even higher priorities, or more interesting tasks?

I'm not defending the status quo. I'm just trying to understand how people I respect, including myself, produce this imperfect work. Mgnbar (talk) 20:19, 11 February 2022 (UTC)

Mgnbar, I think these are good observations. Math content can sit around a long time without significant change. When a topic is not so glamorous, the people who would have the experience to make improvements look at it and think, "Yep, that's right", then move on. It takes a certain bloody-minded persistence to plug away at standard textbook material. The Good and Featured mathematics articles are probably among the best we've got when it comes to citations, organization, etc. I don't think anyone has tried organizing an article-improvement drive along the lines of, e.g., making a list of the articles most important to the undergrad math curriculum and trying to get them to GA. XOR'easter (talk) 18:56, 12 February 2022 (UTC)

It is a worthwhile thing to do, but a lot of effort, to take on articles on widely-known basic topics in mathematics and clear out the decades of unsourced and badly-organized cruft that these articles have accumulated because they are so widely known and because so many Wikipedia editors over the years have added just this one little thing that they thought was maybe sort of relevant and that they thought they understood well enough to write about. Obscure topics with few editors are much easier to handle. That said, I think that despite the greater difficulty, effort on improving our coverage of basic and central topics is much more helpful to most readers of Wikipedia articles. —David Eppstein (talk) 21:21, 12 February 2022 (UTC)

To that end, I've taken a first crack at fixing up calculus. It's still undersourced, and crufty in places. XOR'easter (talk) 00:55, 13 February 2022 (UTC)

It's a valid observation that a large proportion of WP higher-math articles are inadequately sourced. This falls short of the standards of Wikipedia culture and of encyclopedic writing in general, and it's a problem for many excellent reasons.

That said, I'm not convinced that it's such a problem for the reason you're talking about. Postsecondary mathematics students should not be learning mathematics on the basis of "this reliable source said so". They should be learning it on the basis of "I understand the argument; I know why this is true".

Therefore, learning mathematics from an encyclopedia entry is always going to be a time-consuming process (as of course is any other way of learning mathematics). The useful thing about it is that it can give you a roadmap, showing you where the arguments are heading. But you still have to find the arguments and work through them yourself.

Sometimes you may find an error. That's fine. Part of what students need to learn is that sometimes there are mistakes. (Even harder to learn is that, if a source is generally good, you should look really hard when you think you've found a mistake, because the mistake is likely to be yours. In software engineering we call this "don't bet against the compiler". But occasionally it really is the compiler's fault.)

There's a famous quote of Richard Feynman, responding to a student who had relied on a test on something Feynman had said in one of his textbooks:

Your instructor was right not to give you any points, for your answer was wrong, as he demonstrated using Gauss’s law. You should, in science, believe logic and arguments, carefully drawn, and not authorities. You also read the book correctly and understood it. I made a mistake, so the book is wrong. I probably was thinking of a grounded conducting sphere, or else of the fact that moving the charges around in different places inside does not affect things on the outside. I am not sure how I did it, but I goofed. And you goofed, too, for believing me.

--Trovatore (talk) 20:24, 11 February 2022 (UTC)

To be honest, I'd be more worried by the fact that most of our maths articles are incomprehensible to anyone who doesn't already know what they're trying to say, and fail to include sufficient links to places where people can find out. We may not be a textbook, but we are supposed to be a generally informative place for the semi-informed who'd like to become more informed. Elemimele (talk) 23:31, 14 February 2022 (UTC)

That's a common thing that people say, but in most cases it's just not true. Wikipedia math articles are typically comprehensible by people who don't already know what they're trying to say, given that they have enough background to understand it, and given that they're willing to put some effort into comprehending it. There is no practical way to remove the "background" requirement. There's no way at all, practical or otherwise, to remove the requirement to put in effort.

That said, it is true that many articles could be written to require less background and less effort, and that would be a worthwhile thing to do. --Trovatore (talk) 01:25, 15 February 2022 (UTC)

"Wikipedia math articles are typically comprehensible by people who don't already know what they're trying to say". In my experience, the only people who seem to think that are other mathematicians. There's a few topics where the broad ideas are accessible.

Take for example In mathematics, a group is a set equipped with a binary operation that is associative, has an identity element, and is such that every element has an inverse., from Group (mathematics).

Note that this isn't necessarily something that can be fixed. It's simply that to understand what a group is, you need to first understand a) what a set is, b) what a binary operation is, c) what associativity is, d) what an identity element is, and e) what the inverse of an element is.

That means you need to understand 5 rather technical definitions to understand the very first sentence of the article.

Drop by your local coffee shop and ask if anyone knows what "a set equipped with a binary operation that is associative, has an identity element, and is such that every element has an inverse" is called and if anyone replies "that's a group!", you've found yourself another mathematician. Headbomb {t · c · p · b} 03:40, 15 February 2022 (UTC)

I think that this is not true, and that even the definition section of the Group article itself does not require pre-acquaintance except with "binary relation" (which I think is itself unnecessary and could/should be edited away). In my opinion that opening sentence is unnecessarily technical. Gumshoe2 (talk) 05:41, 15 February 2022 (UTC)

My bias is working with biologists (and organic chemists). Okay, this is a notoriously difficult group, because biology (or medicine) is what you do if you're good at sciences and can't do maths. But genuinely, these are clever people with a background in science, and yet WP articles don't help them at all. I think the problem is the "not textbook" bit, which makes it very hard for any WP editor to include background information or anything that might make the material easier to grasp, without being accused of textbookery.

I'll give an example, False discovery rate. This is a very useful and important statistical concept for biologists, but unfortunately the original authors' presentation is quite complex, though very precise and solid. Their work has been picked up by a number of secondary authors who've added graphical interpretations and simplifications that make the whole thing more accessible, and it's also been picked up by any number of nice American professors who've put their lecture notes and explanations on-line. When first I got interested in WP, I tried to insert a little more information on one of the more obvious secondary authors, but encountered a brick wall of (what felt to me) "Benjamini and Hochberg had the idea, their version contains everything, anything else is less cited and nothing new, and in any case not the same, and therefore shouldn't be here". As a result, we have an article full of formulae with not a single graphical diagram to show what it actually means. There are loads of diagrams in other sources, but no way to get them into the article because Benjamini and Hochberg didn't use diagrams, and their explanation is mathematically faultless, so why should we need anything else in the article?

The article doesn't even help biologists use the procedure. It finally defines how to do it, by writing

For a given $\alpha$, find the largest k such that $P_{(k)}\leq {\frac {k}{m}}\alpha$ (i.e., $k={\underset {j\in (1,...,m)}{\operatorname {arg\,max} }}\,\left(j\cdot I_{P_{(j)}\leq {\frac {j}{m}}\alpha }\right)$)

The bit from "i.e." onwards is a complete disaster. Stop! Less is More! When you've said something quite clearly, why say it again in vastly over-complex notation? The biologist who's just managed to grasp the first bit of the definition is going to look at the section after "i.e." and panic. And it's completely unnecessary.

I would like to see more use of External Links sections to provide links to explanatory, didactic sources for those who need help in understanding. Someone made the point, below, about explaining concepts too, such as bold-type for vectors. Yes, it's true, biologists need to be reminded of this. It may sound trivial, but which is better, to feel smug that our articles are as efficient and concise as possible, or that our articles actually help people understand things? Elemimele (talk) 08:44, 15 February 2022 (UTC)

There are two important points that are discussed in this thread. The first one is about inline citations for verifications, the second one is about comprehensiveness.

• About citations: This is true that some mathematical articles are not correctly sourced. Nevertheless the use of sources for verification is different in mathematics than elsewhere. Many mathematical articles are about concepts that are described in the same way in many text books. In such a case, the global reference to several textbooks may be sufficient, and too much inline citations may be counterproductive (why pushing the reader to consult a specific textbook for verifying something that can be found in many places?). So, inline citations are mainly needed when there are disagreement between secondary sources, or when details appear only in primary sources. There are also some case of "well known results" that are very difficult to source. This may occur for many reasons. One example that I have encountered is the discussion, in Homomorphism, on the relationship between injective and left cancellable homomorphisms, which are often both called "monomorphisms" (and the similar discussion about "epimorphisms"). As I do not know any elementary textbook that contains this general discussion, the only way that I have found for verifiability was to give explicit proof (that are collapsed, because they play the same role as a source). Nevertheless, better sourcing of our articles is an important task, and several editors spent a lot of time to it.
• About comprehensiveness. I tends to agree with Elemimele's sentence: "To be honest, I'd be more worried by the fact that most of our maths articles are incomprehensible to anyone who doesn't already know what they're trying to say,...", except that I would replace "most" by "too many". I would even add that, in the case many articles, even professional mathematicians may have difficulties to understand what is written, and to recognize concepts that they know already. Several editors (including myself) spent a lot of time for improving this, and, for elementary and vital articles, the situation is much better than, say, 10 years ago. Nevertheless a lot of work is still needed, even for elementary and vital articles. Also, the meaning of "comprehensible" must be clear. An article, or at least its lead, must be understandable by people who may be interested in. So, a technical terms must not appear without definition in a lead, unless its knowledge is fundamental for understanding the subject of the article. For group this is the case of the concept of a set (which must be linked but cannot be defined in this article) and binary relation (which must be defined; the term must be linked if used, but it seems better to not use it for avoiding pedantry). In any case, writing a comprehensible lead is a difficult task for which too few editors are competent.

D.Lazard (talk) 11:53, 15 February 2022 (UTC)

Textbooks have the advantage that they can be pitched to a specific audience (e.g., Calculus for Pre-Med or Introductory Category Theory for Physics Majors). In contrast, our articles often have to have "something for everybody", and that's not easy to manage. Being somewhat suitable for many audiences can mean being suboptimal for each specific one. That comes particularly into play when writing the lead section, I think. As you say, it's a difficult task. XOR'easter (talk) 20:13, 15 February 2022 (UTC)

This is definitely true. Often (but not always) if it is just a question of generality, it may be possible to give the main development of the text in simple terms, but in a way that makes automatic generalization natural. I mean, for example, on the page vector space it may be possible to talk mostly in terms of real vector spaces, but in such a way as to make possible a note at the top of a given section that says something like "The following material discusses real vector spaces. The discussion may be generalized by replacing the real numbers, wherever they appear, by an arbitrary field." My hope is that this would not lose any informational content but may be more accessible, and in a way which even would match several standard presentations of the material. Gumshoe2 (talk) 20:27, 15 February 2022 (UTC)

One issue, for which I see no good solution, is that the nomenclature is not standardized. Mathematicians use different names for the same concept, use different definitions for the same term, use different sign conventions, etc. A good article should mention these variations, but if it cites a source for each than it may be too cluttered with references. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:44, 24 February 2022 (UTC)

Disruptive editing by D.Lazard

D.Lazard recently removed the following sourced information from the article Linear map

A linear extension of a function $f$ refers to an extension of $f$ to some larger vector space that is also a linear map.

For context, this sentence appeared in the "Definition and first consequences" section and the symbol $f$ was used earlier to define "linear map". D.Lazard tried giving some justification on the talk page Talk:Linear map#Linear extensions. I think his reasoning is clear nonsense. I am wrong in thinking that his edit was blatantly disruptive? I'm asking because I do not want to get into an edit war. Mgkrupa 15:05, 9 February 2022 (UTC)

The provided source and a quick Google-Scholar search shows that "linear extensions" must be continuous. So, unless a reliable source is found that establishes that this term is commonly used in purely algebraic contexts, the given definition has the be considered as WP:OR. D.Lazard (talk) 15:42, 9 February 2022 (UTC)

(edit conflict) You made an edit, it was reverted, now you are discussing the disagreement on the talk page; no one is (yet) acting disruptive, and framing it that way seems unhelpful. The relevant editorial question is due weight: Giving due weight and avoiding giving undue weight means articles should not give minority ... aspects as much of or as detailed a description as ... more widely supported aspects. There are several kinds of extensions of linear maps (the one you described, but also complexification and more generally extension of scalars) and quite possibly they should be mentioned in the article Linear map and also quite possibly they do not belong in a section titled "Definition and first consequences". (In fact it looks to me like the last three two paragraphs of that section are also very questionably located; this may point to a broader question of organization of the article.) --JBL (talk) 15:46, 9 February 2022 (UTC)

References

"a quick Google-Scholar search shows that "linear extensions" must be continuous." That is not true. For example, the Hahn−Banach dominated extension theorem often uses the term "linear extension" despite not requiring the vector space to be endowed with a topology. I can give a plethora of references that state Hahn−Banach in purely algebraic terms, although "a quick Google-Scholar search" would show this as well. Mgkrupa 15:56, 9 February 2022 (UTC)

I am a little confused by the need to state the definition of "linear extension". It is just a combination of two words, the meaning of which is obtained by combining the meaning of the individual two words. Why not also insist on including the definition of (say) "complex-valued linear map" as a linear map whose outputs are complex numbers? Or of an "injective linear map" as a linear map which is also injective? Gumshoe2 (talk) 21:30, 9 February 2022 (UTC)

Many of this article's readers will be people who are taking linear algebra for the first time. When I Googled "linearly extend", the top result was a link to this stackexchange question: What does "extend linearly" mean in linear algebra? so although the meaning is obvious to us, it might not be obvious to someone who is brand new to the subject. This is why I want to include it. Mgkrupa 05:41, 10 February 2022 (UTC)

Ok, I can understand your thinking, but in my opinion that is not a good standard to follow for inclusion of material. Gumshoe2 (talk) 05:54, 10 February 2022 (UTC)

Agreed with JBL. As a different (but possibly tangentially related) issue I'd like to point out that there are many professionals (not mathematicians) who are perfectly conversant with linear maps but for whom the wiki page is largely inscrutable. I think this is a major and unnecessary problem. Gumshoe2 (talk) 21:20, 9 February 2022 (UTC)

I am very late to the discussion but there is one point no one is making: isn’t this just a categorical thing? If we are considering the category of topological vector spaces, then a morphism there is a continuous linear map and therefore a linear extension is required to be continuous (so it is a morphism in the category). I know we need some sources but the definition of a linear extension does seem to follow from this categorical thinking, and the logical reasoning should suffice when we can’t find good refs. —- Taku (talk) 18:27, 24 February 2022 (UTC)

Grassmann

Extensions are no trivial matter as we credit Grassmann for seeing that an n-space actually entails an nxn space of its extensions, or p-vectors of sub-spaces of p dimensions. See Llyodd C. Cannenberg, Extension Theory, reviewed in Isis by Gert Schubring. Rgdboer (talk) 04:42, 10 February 2022 (UTC)

Mar 2022

Meaning of "nodes" as special points in interpolation.

There are 172 articles containing node interpolation except, however, Interpolation itself. Interpolation#Example could read:

Interpolation provides a means of estimating the function between and beyond the nodes, for example, at $x=2.5.$

(as opposed to at intermediate points).

I am in doubt, because

• I cannot find a matching entry for this meaning of "node" in Node. If there are other uses of "node" with this meaning (in numerical integration?), which article should the new entry link to?
• There are only two interwiki links in de:Stützstelle.

--Rainald62 (talk) 18:40, 1 March 2022 (UTC)

Draft of Analysis of vector-valued curves

User:MarkH21 moved Analysis of vector-valued curves into draftspace in June 2020. It's since been changed substantially and is now at User:Mgkrupa/Analysis of vector-valued curves. Editing of the draft seems to have stalled. I was going to return this back to being an article so it won't be forgotten, but I wanted to give folks a chance to do further cleanup or trim any parts that were unacceptable. Does anyone want to do that in the next few days, or is it good to go now? -- Beland (talk) 21:21, 1 March 2022 (UTC)

The problem with that draft is that it looks a bit original research. The article title "Analysis of vector-valued curves" doesn't seem a standard topic name in literature (The Google search returns none). I think it's more of a part of calculus on a topological vector space. Maybe we just need to rename the draft to something like that. (The materials in the draft look legit so there is no need for deletion.) -- Taku (talk) 08:06, 2 March 2022 (UTC)

Draft:Ruler function

Via this deletion discussion, I noticed Draft:Ruler function and did some basic tidying-up and referencing. I think it would stand on its own in mainspace now, but it would have to be moved over a redirect. XOR'easter (talk) 22:55, 1 March 2022 (UTC)

I have requested the move at Wikipedia:Requested_moves/Technical_requests#Technical_requests. (Now that it has more refs, it should be able to survive in mainspace.) -- Taku (talk) 08:09, 2 March 2022 (UTC)

Never mind, actually I was able to move it myself: Ruler function. -- Taku (talk) 08:11, 2 March 2022 (UTC)

Schwarz triangle function

Asking for help with this one. The original author was Mathsci (talk · contribs), but he stopped editing the article in February of 2017, leaving it unfinished. From this discussion on his usertalk page, it appears he suffered a stroke sometime in 2017. He's still active, but seemingly in a reduced capacity.

The unfinished article has two major problems. The first is that much of its content is redundant to other articles on Wikipedia such as Schwarz triangle. This content appears to me to be introductory preliminaries that would make sense to move elsewhere. The second is that he stopped right before the section where he talks about the Schwarz triangle function itself, instead of those preliminaries. So it seems to me that aside from a small amount of text I added, this article in its present state fails to address its topic at all!

I am not an expert on this topic and I'm reluctant to radically rework the article without consensus. Mathsci expressed disagreement with me on the article talk page, although has not started working on it again (and may not be able to given the medical issues mentioned earlier). I would really appreciate another editor's view. Apocheir (talk) 01:05, 25 February 2022 (UTC)

@Apocheir: the page title has been moved to Schwarz triangle tessellation and the application to Schwarz triangle function, as a special case of uniformization, will be added be me (see below). As in the paper of Schwarz, the tessellation and uniformization have never been regarded as separate.

The theory concerns the 2 x 2 complex ordinary differential system $f^{\prime }(z)=z^{-1}Af+(z-1)^{-1}Bf$ with regular singular points at 0, 1 and ∞. There are several aspects: (a) the reduction to a 2nd order ODE, Euler integrals, hypergeometric power series and monodromy (Ince); (b) the geometric interpretation using the Schwarzian derivative, Schwarz triangle tessellation and automorphic forms (Caratheodory, Nehari, Hille); (c) the limiting case of the Farey tessellation, modular lambda function and theta constants (Ahlfors, Chandrasekharan, Hardy & Wright).

On wikipedia, many things are left incomplete. Concerti grossi, Op. 6 (Handel) [stable]]--> Concerti grossi, Op. 3 (Handel) [unfinished]; Clavier-Übung III [stable] --> Clavier-Übung I [unfinished]. Similarly here, sources have already been listed and specific page references are easy to add. New content mentioned above is easy to summarise; but the explicit formulas with quotients of hypergeometric formulas need more care; similarly the Kummer case of the Riemann sphere and finite groups. It's not clear whether Stillwell's "Papers on Fuchsian Functions by Henri Poincaré" are available online — the reference is good for further reading/commentary. Mathsci (talk) 14:24, 25 February 2022 (UTC)

I looked at the article and the one on Schwarz triangles. I was surprised not to see any images of (4,4,4), a tessellation by equilateral triangles with eight meeting at each vertex. It seems to be the most symmetrical (regular) tessellation of the hyperbolic plane. Do we not have any? Nor have I seen any of the related tiling by triangles with angles π/2, π/3, and π/8. Six of these make up one of the equilateral triangles. JRSpriggs (talk) 21:48, 26 February 2022 (UTC)

You'd have to look at Commons to find relevant images. I think I spent some time looking for examples. Mathsci (talk) 21:25, 25 February 2022 (UTC)

The image was already added to the article yesterday. The equilateral triangles with angle π/n are important because in the limit they tend to the ideal triangle. If you want images for Schwarz triangle, please look for them on Commons. Mathsci (talk) 22:07, 26 February 2022 (UTC)

To Mathsci: Thank you for adding the missing image of (4,4,4). JRSpriggs (talk) 22:18, 26 February 2022 (UTC)

I strongly agree with Apocheir's suggestions for reworking the page (same comment left at talk page) Gumshoe2 (talk) 18:58, 25 February 2022 (UTC)

• Above I mentioned a matrix-valued ODE with regular singular points at 0, 1 and ∞. In 2008, I wrote content on the Knizhnik-Zamolodchikov equations and vertex algebra formalism; by SL(2,C)-invariance of "four-point functions", this reduces to a matrix-valued ODE and its monodromy properties, part of my expertise. Mathsci (talk) 22:14, 25 February 2022 (UTC)

I strongly oppose this move. The definition of Schwarz triangle is a triangle that can be used to tesselate a sphere, the plane, or hyperbolic space. Having a page called Schwarz triangle tessellation is redundant and amounts to a WP:CFORK. -Apocheir (talk) 23:04, 25 February 2022 (UTC)

I strongly agree with Apocheir about Mathsci's move of the page Gumshoe2 (talk) 23:06, 25 February 2022 (UTC)

@Apocheir: you have stated that you know nothing about the area. But you have made a false assertion that is true by definition that any Schwarz triangle automatically defines a tessellation. Caratheodory spends eight pages showing that the tessellation can be constructed in an elementary way, using a convexity argument. Wilhelm Magnus, an expert of tessellation, then just quotes Catheodory. So there is an elementary but slightly lengthy proof; but no rabbit-out-of-the-hat easy proof. Mathsci (talk) 02:46, 26 February 2022 (UTC)

I didn't say I know nothing. I said I am not an expert. If I accidentally misstated the definition of a Schwarz triangle somewhat, that does not change the fact that the page currently titled Schwarz triangle tessellation covers much of the same material as Schwarz triangle.

I am growing increasingly frustrated with your obstructiveness and unwillingness to cooperate with other editors on this topic. Apocheir (talk) 19:58, 27 February 2022 (UTC)

John Stillwell

Bourbaki's "Groupes et Algèbres de Lie", Chapters IV & V, is one of the classic sources for "hyperbolic reflection groups", following Tits (and Vinberg). Care has to be taken not to confuse a list (Coxeter-type diagrams) and a proof (triangle/polygon tessellation theorem). The new material on Tits' theorem on fundamental domains follows the standard pattern of editing wikipedia: there is WP:NORUSH. Please see also John Stillwell's English-language "Henri Poincaré: Papers on Fuchsian functions", which contains an excellent historical survey. Thanks, Mathsci (talk) 16:11, 2 March 2022 (UTC)

Draft:Flag algebra

Can a member here take a look at Draft:Flag algebra and help to evaluate if it can go on to the mainspace? There at least three editors (including me, and the other two who have commented on the article directly) passing on evaluating the draft. Thanks! – robertsky (talk) 08:05, 6 March 2022 (UTC)

This is about graph theory (not sure that this is immediately clear, even for graph theorists). D.Lazard (talk) 09:31, 6 March 2022 (UTC)

Although I don’t have a background in this area, the notability seems ok. There are also enough refs. As Lazard points out, the intro can be improved to give a better context. I would say it’s fine to move it to mainspace. —- Taku (talk) 04:45, 7 March 2022 (UTC)

merge ?

I would like to suggest merging Cantor's theorem (disambiguation) into Draft:List of things named after Georg Cantor, but I'm wondering if the former can be merged into an article that didn't pass AfC. --SilverMatsu (talk) 02:40, 7 March 2022 (UTC)

I have moved the draft to mainspace (the afc judgment was wrong in my opinion). The disambig page isn’t really an encyclopedia article; it’s more of a navigation page. So, I don’t know if it is a good idea to merge the two pages. —- Taku (talk) 04:40, 7 March 2022 (UTC)

Thank you your reply. When I added the "Cantor's theorem" to this page, the edit history was tagged as "Tag: Disambiguation links added", which seems useful when I accidentally type only with "Cantor's theorem". So, it might be better not to merge, because I missed it. Also, I agree with moving the draft to the mainspace. --SilverMatsu (talk) 07:28, 7 March 2022 (UTC)

By the way, can Draft:List of things named after Henri Lebesgue and Draft:List of things named after René Descartes be also move to the mainspace ? --SilverMatsu (talk) 23:40, 7 March 2022 (UTC)

I have moved them to mainspace. But please know you can also move them to mainspace; any editor with some editing history can. —- Taku (talk) 07:07, 10 March 2022 (UTC)

Remind me again, what's the advantage of having these lists in separate articles versus having these as sections in the respective articles about Lebesgue/Descartes/Cantor (where it seems they would be more likely to be accessed from anyway)? PatrickR2 (talk) 19:09, 10 March 2022 (UTC)

It's essentially a matter of appearance but having a not-so-short list is quite distracting. Also, the "See also" section is generally meant to list items that are not mentioned in the body of the article; in other words, the "See also" section is not meant to be comprehensive while lists are meant to be comprehensive. By the way, List of things named after Georg Cantor is still underdeveloped; it shouldn't just list items but list them with some short descriptions. --- Taku (talk) 12:54, 12 March 2022 (UTC)

I did not suggest to put this in the "See also" section, but rather in a separate section. PatrickR2 (talk) 03:54, 14 March 2022 (UTC)

The fact that there are generally no "list named after" sections in bio articles seems to indicate that people find a list distasteful (so we put it in a separate article). I should have said it’s a matter of aesthetic. Encyclopedic articles with long lists or tables are less preferred than texts, it seems to me. —- Taku (talk) 07:38, 14 March 2022 (UTC)

It's a good use case for Wikipedia:Summary style. The biography can have a section on major accomplishments, short enough so as not to overwhelm the article and also including the major accomplishments that happen not to be named after the subject, while a more comprehensive list can be linked at the start of the section. ——David Eppstein (talk) 07:59, 14 March 2022 (UTC)

Makes sense. Thanks. PatrickR2 (talk) 22:06, 15 March 2022 (UTC)

Draft:Linear form for special categories of Pythagorean triples

Will someone please take a look at this draft? Robert McClenon (talk) 05:11, 13 March 2022 (UTC)

Never mind. I realized that this is not higher math, and so I can review it myself, and I have declined it as reading like it was copied from a textbook. Robert McClenon (talk) 05:16, 13 March 2022 (UTC)

It would certainly be much better if it were copied from a textbook. It is WP:OR, and I have explained why in a comment on the draft. D.Lazard (talk) 17:46, 16 March 2022 (UTC)

Draft:Polynomials calculating sums of powers of arithmetic progressions

Will someone please look at this draft and at the one listed above? They both look as if they were copied from a mathematics textbook. Should the submitters be asked whether this is a class exercise? Robert McClenon (talk) 16:09, 16 March 2022 (UTC)

IMO, there is nothing to keep in this draft. I have left a comment on the draft for explaining this. D.Lazard (talk) 17:31, 16 March 2022 (UTC)

User:D.Lazard - Thank you. I thought so, but I'm a computer scientist, not a mathematician. Robert McClenon (talk) 16:19, 17 March 2022 (UTC)

Elaborate code for notation

In the article titled π I found the following and thought maybe they've finally fixed a but in the way TeX code gets rendered:

$4\pi kQ=$ ${\scriptstyle S}$ $\mathbf {E} \cdot d\mathbf {A} .$

Here's the code:

 :{{oiint|preintegral=<math>4\pi k Q = </math>|intsubscpt=<math>{\scriptstyle S}</math>|integrand=<math>\mathbf{E} \cdot d\mathbf{A}.</math>}}

That someone took the trouble to create this suggests that the bug that prevented it from being done properly in TeX code is still there. Is this a bug that it is hopeless to fix between now and the end of Eternity? 15:30, 19 March 2022 (UTC)

This workaround is discussed in Help:MATH#Unimplemented elements and workarounds. D.Lazard (talk) 15:56, 19 March 2022 (UTC)

Latin Letters used in Mathematics

Dear WikiProject Mathematics,

Hello, I am a new editor on Wikipedia! When I first started editing, the Wikipedia algorithm suggested that I started referencing the Latin letters used in mathematics article. However, I was surprised to see that there were absolutely no citations. I started to add some, however, I am still in high school and I have only just finished learning about trigonometry. Therefore my knowledge is limited and I could use some help from more experienced editors, like you, to fully reference this incredibly important article. Thanks for your time Kabiryani (talk) 18:27, 23 March 2022 (UTC)

I have changed the name of the article into List of mathematical uses of Latin letters, because this reflects more accurately the content of the article. D.Lazard (talk) 20:26, 23 March 2022 (UTC)

That seems reasonable. --Trovatore (talk) 20:30, 23 March 2022 (UTC)

This change presents a problem however because scientific uses of these letters are also present in the list. Kabiryani (talk) 14:49, 24 March 2022 (UTC)

What about letters that have a special meaning when used in conjunction with an integer, e.g., $\mathrm {H} _{n}(T,G)$, $\mathbf {T} 2$, $\mathbb {R} ^{n}$? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 21:33, 23 March 2022 (UTC)

Earliest Uses of Various Mathematical Symbols may be helpful for some of this. XOR'easter (talk) 01:16, 24 March 2022 (UTC)

Thank you for this source! Kabiryani (talk) 14:49, 24 March 2022 (UTC)

"a combinatorial theory"

Our article titled Structural rigidity begins thus:

In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.

I have qualms about the phrase "a combinatorial theory". What phrase ought to be there, if any? Michael Hardy (talk) 19:36, 23 March 2022 (UTC)

Postscript in response to comments below: When I posted the above, it had never occurred to me that anyone might think I was expressing any qualms about the word "combinatorial." @David Eppstein: @Trovatore: Michael Hardy (talk) 17:40, 25 March 2022 (UTC)

Perhaps:

In discrete geometry and mechanics, structural rigidity is a theory describing the combinatorial aspects of rigidity for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.

--{{u|Mark viking}} {Talk} 20:05, 23 March 2022 (UTC)

Why do you think "combinatorial theory" is incorrect? This theory largely concerns itself with combinatorial structures (often graphs or matroids) describing which subsystems of a system of interlinked objects are rigid, and which aren't. (MV's answer above addresses the details of wording, but not really the issue of whether this theory is combinatorial, which is what I interpreted your question as pointing to.) —David Eppstein (talk) 20:11, 23 March 2022 (UTC)

I guess it comes down to what you consider combinatorics, which is one of these categorization discussions that tend to be unsatisfying. It doesn't seem to be about counting things, and most "classic" combinatorics is in one way or another about counting things. I don't really consider graph theory to be a subfield of combinatorics — it's a separate are of discrete math that overlaps with combinatorics. That said, rigid boundaries between fields tend to be unhelpful, and I can see that this is at least combinatorics-adjacent. --Trovatore (talk) 22:37, 23 March 2022 (UTC)

Our article combinatorics says that it concerns both counting and "properties of finite structures." The Mathematics Subject Classification lists counting (05Axx) as only one of five major subdivisions of combinatorics, with graph theory (05Cxx) as another. Matroids are either under a third (05Bxx, Designs and configurations) or under 52-XX (convex and discrete geometry). —David Eppstein (talk) 22:46, 23 March 2022 (UTC)

I'd need convincing with good citations to mention combinatorics in the lead. It is not mentioned elsewhere in the article nor for instance in Flexible polyhedron. Any combinatorics is a small part of it rather than anything major. The lead shouldn't say things that are completely absent in the body of the article. NadVolum (talk) 10:56, 24 March 2022 (UTC)

Agree with David Eppstein: the theory is partly or even mainly about the combinatorics of the system. Although the word combinatorial does not appear below in the article, it does appear in that for most or all of the objects described in the Mathematics of Rigidity section. I do like Mark viking's alternative wording a little better than what is in the article currently. Russ Woodroofe (talk) 12:02, 24 March 2022 (UTC)

I don't think it is a major issue one way or another; as far as I can see, the topic is combinatorial exactly in as much as it is at the intersection of discrete geometry and mechanics, so that it is justifiable but unnecessary to say. I am more dubious of the word "predicting" which seems overly specific. Maybe it could just say something like "... structural rigidity is a topic dealing with the flexibility of ensembles ..."? Gumshoe2 (talk) 12:05, 24 March 2022 (UTC)

@David Eppstein: You wrote "Why do you think "combinatorial theory" is incorrect? This theory largely concerns itself..."

This WHAT largely concerns itself....?? Maybe the theory of structural rigidity concerns itself with something. I expected to read that structural rigidity is a property of something, and that those things possessing that property are called structurally rigid things. Michael Hardy (talk) 17:32, 25 March 2022 (UTC)

@Trovatore: "I guess it comes down to what you consider combinatorics"

No, it doesn't. I never had an issue with that. You are the one introducing that issue. Seem my comment addressed to David Eppstein above. Michael Hardy (talk) 17:36, 25 March 2022 (UTC)

Ah. I completely missed that. I suppose "structural rigidity" does indeed sound like a property, though tacitly reading an unwritten "the study of" does not cause me much distress. --Trovatore (talk) 18:23, 25 March 2022 (UTC)

You can call something a geometry or you can talk about geometry, the theory of geometric objects. You can call something an algebra or you can talk about algebra, the theory of algebraic structures. In the same way, you can say that something is structurally rigid, and call the property that it has structural rigidity (although usually in this area more specific terms are used), while also talking about structural rigidity, the theory of structures that have this property. We don't need to tack on extra "theory" filler-words: "the theory of geometric theory". —David Eppstein (talk) 18:32, 25 March 2022 (UTC)

Requested move at Talk:List of linear algebra topics#Requested move 21 March 2022

There is a requested move discussion at Talk:List of linear algebra topics#Requested move 21 March 2022 that may be of interest to members of this WikiProject. Favonian (talk) 18:36, 28 March 2022 (UTC)

Draft:Glossary of linear algebra

Just to let people know that I have amalgamated the glossary of linear algebra from Wiktionary with those terms from Vector_(mathematics_and_physics)#Concepts_related_to_vector_spaces that appear to genuinely belong to linear algebra to a bare-bones glossary of linear algebra draft here. Needless to say, much that is indispensable to such a glossary is still missing. Any contributions very welcome! Glossary of linear algebra currently redirects to List of linear algebra topics, which should really be at Outline of linear algebra and currently has a navigation box leading to the Wiktionary glossary. Felix QW (talk) 15:55, 25 March 2022 (UTC)

Good work. I support to move it in the main space. Some suggestions:

• The links to dab pages that remain must be disambiguated (I did this, except for the entry "Vector space")
• Curently, some definitions contain terms of the glossary that are linked to the corresponding article. I seems better to link them to the entry in the glossary. For example, in the entry "Dual space", the phrase "linear form" is linked to Linear form instead of to the entry "Linear form" of the glossary. I did this change for two occurrences of "basis", and this required to modify the entry Basis.

D.Lazard (talk) 17:57, 25 March 2022 (UTC)

Very good suggestions! I must confess that I don't really understand the issue with the anchors though - for instance, the internal link to Draft:Glossary of linear algebra#isotropic_vector seems to have worked before and after the corresponding change by User:D.Lazard? Felix QW (talk) 21:36, 25 March 2022 (UTC)

The glossary has been moved to mainspace! Thank you everyone for your contributions! Felix QW (talk) 20:31, 28 March 2022 (UTC)

l-adic sheaf

I added a paragraph on why lisse sheaves are necessary in place of local systems here: ℓ-adic_sheaf. I read this from an article, which is cited in the entry. In the article it uses a specific scheme (a nodal curve) for demonstrating the counterexample but I found it works for general schemes (I might be wrong . Please tell me if so.) Please review this edit. Sorry in advance for this is my first edit on Wikipedia so there might be guidelines or requirements that I'm not properly following. Thanks. --Fourier-Deligne Transgirl (talk) 02:49, 26 March 2022 (UTC)

Welcome! Wikipedia is full of guidelines and requirements, most of which make sense if you think about them from the right perspective. (I wrote a brief introduction to the most common Wikipedia jargon here.) For example, Wikipedia isn't a platform for new ideas. Instead, we summarize what has already been written elsewhere. That's all we can do, given the nature of the project and the tools we have to work with. We don't have the infrastructure for formal peer review, it's hard to tell who contributed what to any article, and plenty of us are pseudonymous anyway. XOR'easter (talk) 03:36, 26 March 2022 (UTC)

Many math articles in Wikipedia lack a discussion of motivation. This is NOT because such mentions of motivations are superfluous but because no one has bothered to add such discussions. So, adding motivations is unequivocally welcome (assuming the correctness of course). As for editing Wikipedia, the way things work here is that the edits undergo the natural selection: the good edits will survive while the bad edits get slaughtered. This applies to the editors as well; if someone keeps making unconstructive edits, he or she will be banned from editing Wikipedia. In other words, as long as you are being constructive to the project, you shouldn't get into trouble or if you do, other editors will get behind you. -- Taku (talk) 11:24, 26 March 2022 (UTC)

I'll echo this -- many math articles are sorely lacking in this area and help is definitely appreciated. - CRGreathouse (t | c) 02:37, 27 March 2022 (UTC)

As an aspiring mathematician, I'm sure my intention is to add correct explanations of the topic. Yet there are times where I might be wrong and thus requires review and correction. I hope my contributions are constructive enough so that I don't get banned. That being said I'm only an undergraduate majoring in mathematics so my understanding of a lot of things will definitely be insufficient. BTW I noticed the page about pro-etale site is not created so maybe I will spend some time on creating it next few days. Thank you all for the support! --Fourier-Deligne Transgirl (talk) 08:38, 29 March 2022 (UTC)

Apr 2022

all square roots of natural numbers, other than of perfect squares, are irrational

"all square roots of natural numbers, other than of perfect squares, are irrational" is said in the article Irrational number can we provide a source for this?Immanuelle (talk) 23:42, 4 April 2022 (UTC)

This is an almost obvious consequence of the fundamental theorem of arithmetic. Suppose that

${\sqrt {n}}={\frac {a}{b}}$

where a/b is in lowest terms. Then

$nb^{2}=a^{2}.$

By the theorem, any prime factor p of b is a factor of the left hand side and thus of the right hand side and thus of a. This contradicts the fact that the fraction is in lowest terms, unless b = 1. That is, unless n is a perfect square. OK? JRSpriggs (talk) 00:02, 5 April 2022 (UTC)

That quote is from the lead. In the body of the body we state that the proof is in Quadratic irrational number. Meters (talk) 00:03, 5 April 2022 (UTC)

It is not an unreasonable request that a claim in a Wikipedia article be given a citation. The article Quadratic irrational number gives the same proof as JRSpriggs, but also without a citation. (It also gives another proof, not relying on any properties prime factorization.) --JBL (talk) 00:47, 5 April 2022 (UTC)

Chapter 4 of Hardy and Wright's "An introduction to the theory of numbers" is a good and standard reference for that, also for some of the other claims in the article. Gumshoe2 (talk) 01:07, 5 April 2022 (UTC)

Citation added MrOllie (talk) 01:08, 5 April 2022 (UTC)

I was tempted to point to Theaetetus (dialogue), but I think the following looks like another more-helpful reference:

Ungar, Peter (April 2006), "Irrationality of square roots", Mathematics Magazine, 79 (2): 147–148, doi:10.2307/27642924, JSTOR 27642924

—David Eppstein (talk) 01:10, 5 April 2022 (UTC)

Fourier series page problems

I'm concerned that Fourier Series, which covers a pretty important topic, has some issues, especially in the lead. It seems to be written with a more pedagogical, occasionally vague and "intuition-building" goal, rather than to summarize. There are objective problems, like the fact that the way the lead refers to images violates MOS:SEEIMAGE, but fixing this would require rewriting the lead wholesale. I'm inexperienced when it comes to fixing larger issues like this and hope someone would help. Wuffuwwuf (talk) 20:05, 5 April 2022 (UTC)

Thanks for calling attention to the Fourier series page. Per WP:NOTTEXTBOOK, we can't hold the reader's hand and lead them step-by-step through the subject (and since that process would be different for every reader, it would be a mistake to try). But per WP:ONELEVELDOWN, that article should at least start with material comprehensible to readers who have seen the prerequisites but not Fourier series themselves. For example, we can reasonably guess that they know what sines and cosines are and have at least a glancing familiarity with calculus. XOR'easter (talk) 06:25, 6 April 2022 (UTC)

Residual Wolfspam

I'm not quite sure which page(s) to raise this question on, since we don't have a WikiProject Grandiose Interdisciplinary Claims, but maybe the community here would be interested. Last year, we had a major operation to clean up Wolfspam — undisclosed paid editing by Wolfram employees. Some residual effects and general hyperbole may still need addressing. In particular, I've been looking lately at our article on A New Kind of Science. The "Contents" section still strikes me as rather vague, in that "created by a fan in the days before Wikipedia had citations" kind of way. It's all but footnote-free; even granting that a book is a valid source for its "plot summary", as it were, there's no indication of where in 1200+ pages the reader should look for a given claim. Further opinions would be welcome. XOR'easter (talk) 19:26, 7 April 2022 (UTC)

This article should do no more than give the reader an idea of what the book is about and where it fits into the academic landscape. IMO, the contents section should be reduced to under 10% of the size, simply describing the topic of the book. Essentially, the following would suffice to replace that section: "In NSF, Wolfram explores, as have many before, examples of how unexpectedly complex behaviour can sometimes arise from simple computational rules. He then attempts to find parallels of this behaviour in several other systems." 172.82.47.18 (talk) 22:55, 8 April 2022 (UTC)

I'd have no objection in principle to a significant shortening. XOR'easter (talk) 08:39, 9 April 2022 (UTC)

Twists of curves

Can someone figure out if Twists of curves has the right article name? None of the sources in the article use the term "twists of curves" at all, and honestly, I find the article extremely technical and understand literally zero percent of it. Ten Pound Hammer • ^{(What did I screw up now?)} 02:57, 10 April 2022 (UTC)

The second line of reference 4 begins, The study of twists of curves is a very useful tool. I don't think there's anything wrong with the current title, strictly speaking, but it could perhaps be changed to "Twists of curves in algebraic geometry" or "Twists of algebraic curves" or something like that. I've no strong feelings on the matter. (It's outside my own specialization.) As for it being "extremely technical", well, when a subject isn't likely to be encountered before graduate school, sometimes that's just the way it goes. In practical terms, it's probably more worthwhile to work on making elliptic curve a comprehensible introduction, as that is a prerequisite and more likely to be encountered. We can't build every niche mathematical topic up from Algebra 101 in its own article. XOR'easter (talk) 03:34, 10 April 2022 (UTC)

The only thing that I see that might be wrong with the article title is potential confusion with Twist (mathematics), which discusses a quantity associated with ribbons (which are essentially curves with additional structure). However, this could probably be solved with hatnoting. Felix QW (talk) 09:47, 10 April 2022 (UTC)

Good point. XOR'easter (talk) 16:29, 10 April 2022 (UTC)

The other issue is that it is plural, for no obvious reason, when one could just as well consider one particular twist rather than the whole family of twists. One possibility would be something like twist (algebraic curve). (The disambiguator needs to be very specific to distinguish it from e.g. twists of modules.) —David Eppstein (talk) 16:30, 10 April 2022 (UTC)

I thought about that and have no problems with it myself but had some vague notion that a style guide somewhere preferred non-parenthetical disambiguations when possible. I could be completely backwards on that, however. XOR'easter (talk) 16:35, 10 April 2022 (UTC)

@XOR'easter: WP:NCDAB. — MarkH₂₁^talk 22:07, 10 April 2022 (UTC)

That was probably it; thanks. XOR'easter (talk) 22:13, 10 April 2022 (UTC)

Or twist of an algebraic curve, then? "Algebraic", to distinguish it from torsion of a curve. —David Eppstein (talk) 18:54, 10 April 2022 (UTC)

Sounds good to me. XOR'easter (talk) 19:29, 10 April 2022 (UTC)

Ditto. --JBL (talk) 20:48, 10 April 2022 (UTC)

I moved boldly Twists of curves to Twists of elliptic curves. This is clearer than Twist of an algebraic curve, since there is no indication in the article that the concept extends to other algebraic curves. D.Lazard (talk) 21:01, 10 April 2022 (UTC)

In the article, no, but it is definitely applied to other related curves; see my remarks in Wikipedia:Articles for deletion/Twists of curves. —David Eppstein (talk) 21:32, 10 April 2022 (UTC)

It did mention hyperelliptic curves briefly, and I've added some further remarks. As I said, though, this is outside my own specialization, and having never tried to explain Galois cohomology before, my brain goes into a 60-hertz hum when I try. XOR'easter (talk) 21:46, 10 April 2022 (UTC)

One part in two million? What's that mean?

In YBC 7289, I've read this sentence.

...a numerical approximation of the square root of two that is off by less than one part in two million.

I still don't get it, even though I had read the cited sources before. My bad for asking this one (if this is kinda silly), cause I don't fully understand it. I appreciate that someone answers this question. Regards, Dedhert.Jr (talk) 07:21, 13 April 2022 (UTC)

The claim is that the clay tablet has a very accurate representation of the square root of 2. That value is around 1.4. Dividing 1.4 by two million gives 7×10⁻⁷. The claim is that 7×10⁻⁷ is the error in the value on the clay tablet. Johnuniq (talk) 07:53, 13 April 2022 (UTC)

Maybe, "is off by less than 0.00005%" is easier to understand, although harder to read. - Jochen Burghardt (talk) 07:59, 13 April 2022 (UTC)

I would expect "off by" to refer to absolute error, not relative error. The value on the tablet is approximately 1.414212962962963. The actual square root of two is approximately 1.4142135623730951. Their difference (absolute error) is approximately $6\times 10^{-7}$. But that doesn't match the quoted phrase, so maybe relative error was intended. —David Eppstein (talk) 08:13, 13 April 2022 (UTC)

I see, thanks. Dedhert.Jr (talk) 08:50, 13 April 2022 (UTC)

Tagged a statement in Sphere packing as dubious

I added a {{dubious}} tag to a statement in Sphere packing#Dense packing and started a discussion at Talk:Sphere packing#FCC and HCP are not both lattices?. Input is welcome. Toshio Yamaguchi (talk) 12:09, 13 April 2022 (UTC)

about Table of congruences

For the Table of congruences, I can find references for each of the content in the article, but I couldn't find any references for the list. --SilverMatsu (talk) 08:50, 11 April 2022 (UTC)

If you mean the first section "Table of congruences characterizing special primes", there is no need for a common reference for that. Each entry refers to another wikipedia article, which is supposed to contain references as needed for that particular entry (example, Wolstenholme's theorem, etc). PatrickR2 (talk) 04:16, 12 April 2022 (UTC)

Thank you your comment. I agree with your comments as to whether a comprehensive reference is required. But I think there is a comprehensive reference somewhere, like the List of definite integrals.--SilverMatsu (talk) 16:19, 13 April 2022 (UTC)

Also, I thought the meaning of the current title of the article was like a tables of logarithms, so I misundersted if the content of the article was something like this link (External link). --SilverMatsu (talk) 03:20, 15 April 2022 (UTC)

Subbase: alternate definition

There are two potential definitions of subbase in topology. The second one seems dubiously sourced. I have started a discussion at Talk:Subbase#Alternate definition section. Would appreciate any input. PatrickR2 (talk) 05:34, 16 April 2022 (UTC)

Are these edits vandalism?

[16] Doug Weller talk 08:05, 16 April 2022 (UTC)

Not really vandalism, if no error has been introduced by these changes (which I have not checked). Certainly WP:disruptive editing, as these changes of variable names would need a careful check by other editors for being sure that no error has been introduced. I have undone these changes, as MOS:VAR applies here. D.Lazard (talk) 08:43, 16 April 2022 (UTC)

Thanks. All of the first editor's edits seem dubious, and he's never edited an article on mathematics again. Doug Weller talk 09:09, 16 April 2022 (UTC)

Delete Complex conjugate vector space?

Complex conjugate vector space makes no sense. A complex conjugate vector space, as defined there, is just a complex vector space. I suggest deleting it. 172.82.47.212 (talk) 19:57, 28 March 2022 (UTC)

Or redirect it to Antilinear map. 172.82.47.212 (talk) 20:17, 28 March 2022 (UTC)

"A complex conjugate vector space" is not a thing; "the complex conjugate of a given complex vector space" is a thing. --JBL (talk) 21:07, 28 March 2022 (UTC)

Could just rename the article Complex conjugate of a vector space and be done with it? The content is important enough to warrant a mention somewhere (although it could be merged into Complex conjugate or Complex vector space). Tazerenix (talk) 10:42, 29 March 2022 (UTC)

Field automorphisms induce vector space automorphisms functorially so maybe merge some of the article content into there? --Fourier-Deligne Transgirl (talk) 08:55, 29 March 2022 (UTC)

Any thoughts on a subtle renaming to Complex conjugate (vector spaces) or similar, with a hatnote from Complex conjugate? Felix QW (talk) 09:18, 29 March 2022 (UTC)

Complex conjugate (vector spaces) must be avoided, as most readers would understand that it is about conjugation in vector spaces, which is defined in complex vector spaces with a canonical basis (matrices, polynomials, ...) and complexified real vector spaces. So, I agree with Tazerenix, including merge suggestion. D.Lazard (talk) 12:44, 29 March 2022 (UTC)

Complex vector space just redirects to vector space, and Complex conjugate is about the basic operation underlying an Antilinear map. Therefore, I prefer to merge into the latter, as suggested by 172.82.47.212. Since the article name "Complex conjugate vector space" is questionable (as discussed above), I suggest not to turn it into a redirect. - Jochen Burghardt (talk) 15:38, 29 March 2022 (UTC)

I actually think it is a mistake that there is no complex vector space article. We do have the complex vector bundle article after all, which discusses the conjugate bundle (vector bundle version of a complex conjugate vector space.) If there is the complex vector space article, stuff like conjugates or anti-linearity can be discussed in natural ways. —- Taku (talk) 19:03, 29 March 2022 (UTC)

Taku, indeed. However, you will concede that the notion of a conjugate complex bundle is indistinguishable from a complex bundle: it is only through the structure that connects them (such as duality) that one can tell that there is any antilinearity involved. I agree with Jochen: delete after merge. 172.82.47.212 (talk) 17:06, 31 March 2022 (UTC)

I have now boldly moved the page as suggested by Tazerenix above, without any prejudice to a separate merger. Felix QW (talk) 10:15, 5 April 2022 (UTC)

I agree to move the page, also I think the inner product space is one of the option for merging.--SilverMatsu (talk) 17:32, 16 April 2022 (UTC)

Examples of differential equations

I don't really know what to make of this page. It seems to be a guided walk-through of how to solve different classes of differential equations rather than a coverage of examples in the sense of the Examples of Markov chains or the Examples of groups. Everything encyclopedic here seems to overlap with the articles for the individual types of differential equation or the Linear differential equation article. I thought I'd check here to see what others think. Options I could see would include blanking and redirecting to Differential equations#Examples or starting the nucleus of an actual page of examples in the spirit of the other pages mentioned above by only retaining the barebones of the oscillating motion example. Felix QW (talk) 10:06, 5 April 2022 (UTC)

A note to anyone reading the above that the page has now been nominated for deletion. Felix QW (talk) 13:39, 5 April 2022 (UTC)

The eventual consensus was to redirect the article to Differential equation#Examples. XOR'easter (talk) 18:03, 16 April 2022 (UTC)

Uncited source of a sentence in Pythagoras

In the sentences as follow:

Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors

didn't have any cited source. And I did the same thing in Indonesian Wikipedia. But someone already reverted my edit and told me that the cited source has already been in a sentence in one of the sections, that is

Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton.

And I'm not very sure that the sentence in an introduction can be the same as that sentence in Numerology. Maybe someone can explain this thing, cause I'm afraid that I misunderstand it. Regards, Dedhert.Jr (talk) 11:41, 20 April 2022 (UTC)

Requested move at Talk:Fixed point (mathematics)#Requested move 8 April 2022

There is a requested move discussion at Talk:Fixed point (mathematics)#Requested move 8 April 2022 that may be of interest to members of this WikiProject. Favonian (talk) 08:34, 23 April 2022 (UTC)

Fellows of the AMS

Looking at some of the current drafts on mathematicians, I have been wondering whether the fellowship of the AMS satisifes Criterion #3 of NPROF. The AMS is certainly a "major scholarly society", but I was wondering whether its own admission that the goals of the fellowship program include "lift[ing] the morale of the profession by providing an honor more accessible than those currently available" means that it is not a "highly selective honour" in the sense of the notes to NPROF#3. Does anyone have any thoughts on this? Felix QW (talk) 08:42, 22 April 2022 (UTC)

If I remember right, they have no membership restriction other than paying their dues. I would not call that selective. JRSpriggs (talk) 10:14, 22 April 2022 (UTC)

AMS Membership is not selective at all. AMS _Fellowship_, on the other hand, is fairly highly selective. I believe it meets WP:NPROF C3. The acid test is that most AMS fellows appear to meet other WP:NPROF notability criteria. Comment that being more accessible than the fancier and fewer-in-number AMS awards does not mean that it is not sufficiently selective for Wikipedia notability. Russ Woodroofe (talk) 10:25, 22 April 2022 (UTC)

I agree with Russ Woodroofe here. XOR'easter (talk) 14:03, 22 April 2022 (UTC)

I think the AMS fellowships are more tied to scholarly achievement and less tied to seniority than some other societies. That's a good thing for whether it counts towards C3; it means that someone named a fellow can be more relied on to have done something important and not just been around a long time. —David Eppstein (talk) 15:57, 22 April 2022 (UTC)

I think it satisfies the criteria, although on the lower margin; of all the standard honors I can think of for professional mathematicians, it is the least selective. Also, if it is to be used to satisfy the criteria, I believe the same principle should apply to analogous honors awarded by other countries' mathematical societies (or similar organizations). Gumshoe2 (talk) 20:29, 22 April 2022 (UTC)

It is not an issue of national parity, but of how selective that individual society is in offering their analogous honors. If they are as selective, then it should probably count for the same reason. If they are not selective in offering this honor, then they should not, regardless of the prestige or national standing of the society. There are several other national-society fellowships (for instance Canadian Mathematical Society [17]) that I think do and should count. I am not entirely convinced that FIMA for the UK is selective enough, though (their criteria [18] speak of seven years of experience as a mathematics researcher, and say nothing about limits on number of fellows as a fraction of total membership, so I think that may be too low a bar). —David Eppstein (talk) 22:28, 22 April 2022 (UTC)

I agree. In part I suppose that what I implicitly had in mind is my belief that US (and British) mathematicians are somewhat disproportionately represented here, even after taking into account that this is the English wikipedia. So I should have instead just said that it would be good to find comparably prestigious honors for mathematicians based in China, Japan, South America, and others. As for those you linked, I would judge the CMS Fellows as a very prestigious list (moreso than AMS), but I actually can't find any publicly available members list for FIMA! Gumshoe2 (talk) 22:59, 22 April 2022 (UTC)

So WP:NPROF specifically gives as an example Fellow of the Institute of Electrical and Electronics Engineers, which is limited to 1/1000 of members per year. According to American Mathematical Society, the AMS has 30,000 members; there were 45 new fellows last year. So that's less selective, but basically comparable. --JBL (talk) 22:29, 22 April 2022 (UTC)

Thank you very much for your thoughts! Felix QW (talk) 08:34, 25 April 2022 (UTC)

Help with Kahn–Kalai conjecture

I've had a go at writing something on the Kahn–Kalai conjecture, but have run out of mathematical knowledge in the relevant field. Hopefully what I have written is not gibberish, but I know when I'm out of my depth. Can anybody more knowledgeable help? — The Anome (talk) 09:14, 27 April 2022 (UTC)

Need to fix Heptadecagon?

This article is very messy due to some animations having a massive scale, so I can't even possibly feel comfortable while reading. Dedhert.Jr (talk) 10:55, 24 April 2022 (UTC)

I agree that the diagrams and animations there are too complex to be helpful towards understanding. Somebody put a lot of work into them, but probably they should be removed. Ebony Jackson (talk) 03:25, 26 April 2022 (UTC)

Maybe the material could be rearranged into a gallery of some sort? XOR'easter (talk) 15:31, 27 April 2022 (UTC)

I have fixed the page in my sandbox, User:Dedhert.Jr/1st sandbox. Also, I added the properties of heptadecagon. Maybe someone can help to fix the words here, and please inform me (by ping) that I'm making mistakes. Regards, Dedhert.Jr (talk) 03:59, 28 April 2022 (UTC)

User script to detect unreliable sources

Main page: User:Headbomb/unreliable

I have (with the help of others) made a small user script to detect and highlight various links to unreliable sources and predatory journals. Some of you may already be familiar with it, given it is currently the 39th most imported script on Wikipedia. The idea is that it takes something like

• John Smith "Article of things" Deprecated.com. Accessed 2020-02-14. (John Smith "[https://www.deprecated.com/article Article of things]" ''Deprecated.com''. Accessed 2020-02-14.)

and turns it into something like

• John Smith "Article of things" Deprecated.com. Accessed 2020-02-14.

It will work on a variety of links, including those from {{cite web}}, {{cite journal}} and {{doi}}.

The script is mostly based on WP:RSPSOURCES, WP:NPPSG and WP:CITEWATCH and a good dose of common sense. I'm always expanding coverage and tweaking the script's logic, so general feedback and suggestions to expand coverage to other unreliable sources are always welcomed.

Do note that this is not a script to be mindlessly used, and several caveats apply. Details and instructions are available at User:Headbomb/unreliable. Questions, comments and requests can be made at User talk:Headbomb/unreliable.

- Headbomb {t · c · p · b}

This is a one time notice and can't be unsubscribed from. Delivered by: MediaWiki message delivery (talk) 16:01, 29 April 2022 (UTC)

May 2022

RfC: Reliability of the nLab

Some articles on Wikipedia, such as Higher category theory, Enriched category, ∞-groupoid, and Quasi-category, use the nLab as a source. However, according to past discussions on the nForum, such as [19] [20] [21] and [22] it is fairly clear that the nLab allows original research within the wiki. Because of that, the nLab is self-published content WP:RSSELF and shouldn't be used as a reliable source on Wikipedia. 96.63.208.27 (talk) 17:07, 18 April 2022 (UTC)

• This may technically be an ill-formed RfC, since RfC's are supposed to open with a neutral statement rather than advocate a particular conclusion. But setting that aside, the nLab is mostly written by subject-matter experts, so in principle it could be used in some circumstances per WP:SPS. However, because it is a wiki, figuring out who contributed what is time-consuming, and it is probably best to use it as a collection of pointers into the more formal literature. (I am adapting my remarks from my So, you've decided to write about physics and/or mathematics on Wikipedia general advice page, which I will update if the discussion here so indicates.) XOR'easter (talk) 17:27, 18 April 2022 (UTC)
  • Well as a stickler for procedure I have removed the inappropriate RfC tag. IP, if there's some place you think the nLab is being used in a way that is problematic, you are welcome to tag it, to start a discussion on the article talk-page, or to boldly remove it (with the recognition that you might be reverted). --JBL (talk) 17:33, 18 April 2022 (UTC)

    The mentioned articles don't use the nLab as an inline reference, as far as I noticed, but at the bottom as a general reference or external link. XOR'easter (talk) 17:47, 18 April 2022 (UTC)

    I noticed that as well. ∞-groupoid does use it as an inline reference. (The sentence it's attached to seems oddly placed to me, fwiw.) --JBL (talk) 17:53, 18 April 2022 (UTC)

    As an external link I think nLab is fine: generally of much higher quality than MathWorld, which we use regularly as an external link, for instance. I am not convinced it qualifies as a reliable source, though. —David Eppstein (talk) 17:55, 18 April 2022 (UTC)

    In fact it is used as an inline reference in other places: see [23]. Perhaps 250 uses in total. --JBL (talk) 18:01, 18 April 2022 (UTC)

    Thanks for checking! XOR'easter (talk) 18:27, 18 April 2022 (UTC)

As an inline reference, I think it is roughly comparable to using lecture notes that a researcher has posted on their website. That is: it's definitely better than nothing, and on some topics it may happen to be quite useful, but it should not be regarded as ideal and whenever possible should be replaced by better refs. Gumshoe2 (talk) 18:16, 18 April 2022 (UTC)

nLab is usually a mess, to be honest. Maybe refactoring some of the references to Lurie/Riehl's work might be appropriate. -- Fourier-Deligne Transgirl (talk) 07:37, 1 May 2022 (UTC)

Calculus on Euclidean space

Beland has recently moved the draft Calculus on Euclidean space into mainspace. I think that in its current state, it really can't hold its own as a published article. So I was wondering what to do with this. While the draft was clearly started with the ambition to cover more advanced topics, the current content could probably be adapted very nicely into a section for Multivariable calculus, which is surprisingly thin. On the other hand, I don't fully understand how all of our higher calculus articles fit together, so perhaps that would not be the most natural place for the material. Felix QW (talk) 21:15, 30 April 2022 (UTC)

My first instinct would be to expand the Multivariable calculus article, which briefly touches upon differential forms, rather than creating a new article. Calculus on Euclidean space should not have been moved into mainspace: multiple sections are tagged as needing expansion, one section is nothing more than a "main article" link to somewhere else, a sentence just trails off without finishing, and a subsection is completely empty.

I don't think there is a plan for how our higher-calculus articles fit together, or how any articles fit together, really. XOR'easter (talk) 22:29, 30 April 2022 (UTC)

So, I am the one who started the article (and, in a way, the fault of not expanding it sufficiently goes to me, I guess). The issue is related to the question of what advanced calculus refers to: it can often mean multivariable calculus but can also mean an elementary part of real analysis, though it currently redirects to mathematical analysis. The article title "Calculus on Euclidean space" was meant to avoid this ambiguity of the term "advanced calculus".

In my opinion, the scopes of "advanced calculus" and "multivariable calculus" tend to differ; in the US at least, multivariable calculus seems to refer to a calculus course that follows one-variable one but does not cover more advanced topics like differential forms. If the main audience of "multivariable calculus" article is undergraduates taking such calculus courses, then treating that article with the advanced calculus topics is not a good idea (whence a separate article is warranted). -- Taku (talk) 09:00, 1 May 2022 (UTC)

Thanks, I understand a bit better now. In England and in Germany, the usual progression form maths or physics students is Sixth-Form calculus (1 variable) -> Real analysis in 1 variable -> Analysis in several variables, so the specific audience for multivariable calculus did not occur to me. I do think you have a point, since presumably engineering majors would make up a large part of the readership of the multivariable calculus page.

PS Don't worry, Taku - you didn't move it to mainspace, so you can hardly be faulted :) Felix QW (talk) 10:03, 1 May 2022 (UTC)

There are issues with how the articles fit together, e.g., Tensors covers a lot of material that belongs in Tensor fields.

The modern view of calculus is centered on differentiable manifolds, but understanding and using, e.g., the definition of charts, requires a basic understanding of multivariable calculus.

The baic results of multivariable calculus don't really depend on a Euclidean metric, but at the moment I can't think of a better title than "Calculus on Euclidean space". --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:28, 1 May 2022 (UTC)

I agree with others that it should not be in mainspace. Aside from the content problems pointed out by Felix QW, the intended scope of the article should be clarified. I think it is usually accepted (and is a principle which I believe anyway) that it is not good to write wiki articles based on parameters set by university coursework, which seems to be suggested above. Gumshoe2 (talk) 19:09, 1 May 2022 (UTC)

I have just approached the mover of the draft into mainspace whether he would agree with re-draftifying the page for now. I gathered from the very restrictive language at WP:DRAFTIFY that this would be necessary. Felix QW (talk) 17:18, 2 May 2022 (UTC)

Not sure this matters to the ultimate destination of this content, but checking the history, it looks like this content was actually branched off of: https://en.wikipedia.org/w/index.php?title=Differential_geometry_of_surfaces&oldid=971313451#Function_theory_in_two_variables

I would prefer this article not be sent back to draft space. It sat there in a zombie state for years with no one working on it, getting deleted and undeleted. With due respect to good intentions, TakuyaMurata created a lot of draft articles and then left them in this zombie state, and the point of bringing the promising ones into mainspace is to get the attention and contributions of other editors.

Given that knowledgeable editors people are looking at the content now, I think it's time to decide whether to delete, merge, or rewrite it. Delete is the easy case; it could be sent to Wikipedia:Articles for deletion now. If a rewrite under this title were desired, it can either be tagged as problematic and worked on here, just like plenty of other mainspace articles that are incomplete and poorly written. Or, if there's a lot of problematic content that definitely has no place in the rewrite, that content can simply be stripped, possibly making the article a stub in the spirit of Wikipedia:Blow it up and start over.

It sounds like the preferred option is merge to Multivariable calculus. If that can be done in a few days, it should just be done. If it's going to take a long time, Calculus on Euclidean space can simply be tagged for cleanup and merge and left until someone can deal with it, possibly after trimming any content that's clearly not going to be retained. Or, the content could get a rough cleanup and be merged now, and the new content on Multivariable calculus tagged for cleanup until someone can get around to it. If none of the content here is really helpful verbatim, but the ideas expressed could guide the expansion of Multivariable calculus, I would recommend making Calculus on Euclidean space a redirect there, and adding a note on Talk:Multivariable calculus with an outline of the proposed expansion. Or if that's too much work, just add a note there referring to the edit history of Calculus on Euclidean space and maybe someone will look at it some day, or maybe Multivariable calculus will grow organically without referring to this content, but at least content editors find ugly won't be publicly visible. If content needs to be rebalanced among math articles generally, cleaning up and merging Calculus on Euclidean space does not necessarily need to wait for that, and in fact doing that may clarify how the rebalancing would work. -- Beland (talk) 17:59, 2 May 2022 (UTC)

First to respond to @Gumshoe2: no, I don't believe the principle that math articles should be organized in a mathematically natural way regardless of how materials are taught in school. In fact, we are not allowed to do that; articles in wikipedia are titled and cover what typical readers would expect (and the expectation is sharped by school works). If we were to build some treatise on math in a manner faithful to math, that has to be a different project (I have an idea of such a project but that's another story). Note that no refs cited in Calc on E have titles with "multivariable calculus", which argue against a merger. Like I said above, the question is whether advanced calculus is the same thing as multivariable calculus and, if the answer is no, the merger is probably a wrong move.

To @Beland:, to me, the simplest solution is to put back the article back to the draftspace. Yes, there would be a danger that it stays there while not being developed actively. But I do still have an intension to develop the article, although, at least for now, I am too busy with real-life stuff. -- Taku (talk) 07:37, 3 May 2022 (UTC)

Would somebody restore Draft talk:Calculus on Euclidean space for this discussion ? --SilverMatsu (talk) 16:05, 3 May 2022 (UTC)

Talk:Calculus on Euclidean space exists and is available for this discussion to be continued there. Felix QW (talk) 16:12, 3 May 2022 (UTC)

The page doesn't seem to reflect the deleted 18 revisions.--SilverMatsu (talk) 17:15, 3 May 2022 (UTC)

Ah, I understand now. Sorry, I missed your point. Felix QW (talk) 18:06, 3 May 2022 (UTC)

Don't worry about it, or rather, Thank you for telling me that we need to merge the history after this page is restored. I missed that talk page.--SilverMatsu (talk) 00:44, 4 May 2022 (UTC)

Graeme Bartlett has helpfully moved the draft talk page contents (with history) to Talk:Calculus on Euclidean space. -- Beland (talk) 09:39, 4 May 2022 (UTC)

@TakuyaMurata: If you don't have time to work on this article, it's probably best to leave it to others. I just trimmed so it looks more like an article that could grow and less like an incomplete thought. It sounds like the question of whether or not this should be merged into multivariable calculus is unsettled, so I added merge discussion tags pointing here. I can implement a rough merge if consensus favors that solution, though a math enthusiast might do a better job. -- Beland (talk) 09:51, 4 May 2022 (UTC)

@Beland: In Wikipedia, no article belongs to anyone so it makes little sense to say "leave it to others". On Thu, I have a meeting but on Fri, I will probably have more time and so will try to expand the article so to address some of concerns. Also, to me, the consensus is that the article is not ready to be put in mainspace and so putting it back to the draftspace would be a natural obvious solution (is it just me?) -- Taku (talk) 10:34, 4 May 2022 (UTC)

@Gumshoe2: An addendum to my comment above. A good example of school courses affecting the way articles are organized is the fact we have two separate Stokes theorem and generalized Stokes theorem. Mathematically, this doesn't make much sense since there is only one Stokes' formula. But presenting the general version of Stokes theorem as Stokes theorem would be contrary to the readers who expect to see a version they saw in school. -- Taku (talk) 11:06, 4 May 2022 (UTC)

Also Green's theorem. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:13, 4 May 2022 (UTC)

Pétur Blöndal

He is listed in Category:Icelandic mathematicians, but I was wondering whether he satisifes WP:PROF.--SilverMatsu (talk) 15:55, 2 May 2022 (UTC)

He may not pass WP:NPROF, but as a member of the Icelandic Parliament should be notable by WP:NPOLITICIAN. Felix QW (talk) 17:10, 2 May 2022 (UTC)

Thank you for your comment. I agree that this article meets WP: NPOLITICIAN, but I wondering whether it is possible to add Category: Icelandic mathematicians to this article.--SilverMatsu (talk) 16:52, 3 May 2022 (UTC)

@SilverMatsu Having a doctorate in mathematics does not make one a mathematician. Voting to not add to your proposed category unless you can document that he has produced substantial mathematical research output. PatrickR2 (talk) 08:28, 5 May 2022 (UTC)

Thank you for your comment. Removed Category:Icelandic mathematicians from article.--SilverMatsu (talk) 15:21, 5 May 2022 (UTC)

Getting a PhD requires writing a PhD thesis, which requires producing substantial mathematical research output. Separately, I doubt you will find consensus for the idea that "producing substantial mathematical research output" is a necessary criterion to be classified as a mathematician. --JBL (talk) 17:10, 5 May 2022 (UTC)

True about the need to write a PhD thesis, although I have personally witnessed a few cases where the corresponding research was not "substantial" (without mentioning any names, e.g., a case where the advisor moved to another school, the student was passed to another professor not really familiar with the area, and the student ended up putting in his thesis results that were not even original research but things that the first professor had mentioned and explained in one of his classes. The advising committee said it was pretty weak, but let him pass anyway, knowing he was going to go to a teaching school.) [Note I am not claiming this is the case here for Blondal, just mentioning in support of the point that a PhD does not a mathematician make.]. More of a case in point, looking at Math Genealogy project for example, you can see lots of new PhD's being granted every year. Quite a few of these don't stay in academics, move to industry, become programmers, work in finance, etc, either right after the PhD or after just a few years, realizing academics is not for them. I don't think anyone can say these people are mathematicians (not to diminish anything to what they might have done for their thesis). PatrickR2 (talk) 04:44, 6 May 2022 (UTC)

@JayBeeEll and PatrickR2: Thank you for your(s) comments. Both agree to comments. I'd like WP: PROF will give an explicit explanation for this case, but as already pointed out, there seems to be no consensus, so I think it is better to decide each case individually.--SilverMatsu (talk) 03:25, 7 May 2022 (UTC)

I think the relevant policy here is WP:Categorization of people, which states:

"For example, a film actor who holds a law degree should be categorized as a film actor, but not as a lawyer unless their legal career was notable in its own right or relevant to their acting career. Many people had assorted jobs before taking the one that made them notable; those other jobs should not be categorized."

So the question is whether our mathematician-turned-politician was notable as a mathematician. And this notability may come from WP:NPROF, but in our case the subject is almost certainly not notable by WP:NPROF standards. So on that basis I would remove him from the category. Felix QW (talk) 15:19, 7 May 2022 (UTC)

WP:COP is just what I was looking for. Thank you so much !--SilverMatsu (talk) 01:09, 8 May 2022 (UTC)

Labeling "press recognition" and "a proof" based on Quanta & press releases

See Talk:Jinyoung Park (mathematician)#"Widespread recognition" for a content dispute about a recent arXiv preprint that has been discussed in a Quanta article (link) and two department/institute press releases (link 1, link 2).

The dispute is on whether:

1. The Quanta article and press releases can be summarized in WP:WIKIVOICE as Park having received recognition for her preprint
2. The preprint contents can be described as a 6-page proof or a 6-page proposed proof

Any input is much appreciated. Thanks! — MarkH₂₁^talk 05:50, 9 May 2022 (UTC)

Agree with MarkH21's comments at the link, particularly that the IAS and Stanford press releases are not good sources. The Quanta article is solid verification that the paper is of interest. But it is probably too early to say unambiguously that the result is proved, although (just making educated guess as non-expert in combinatorics) it seems very likely. Gumshoe2 (talk) 06:39, 9 May 2022 (UTC)

Thank you for the input here! Resolved. — Preceding unsigned comment added by Caleb Stanford (talk • contribs)

Chinese Postman Problem and other arc routing Variants

I am reading a lot about the Chinese Postman problem, which is NP hard for mixed graphs that contain undirected edges and directed arcs. These arcs and edges can be weighted, and solving the mixed Chinese Postman is something I've been working on a lot recently its possible to fit everything about the Chinese Postman Problem in to the article Route Inspection. I would like to suggest a series or template on operations research and arc routing problems. I would like to make the documentation of the Chinese postman problem more comprehensive. ScientistBuilder (talk) 23:24, 9 May 2022 (UTC)

Vertical alignment of \overrightarrow

Tracked in Phabricator
Task T308188

The latex command \overrightarrow is used many times in Euclidean space, affine space, and other articles of geometry. It is awfully aligned when used with two letters, as in ${\overrightarrow {PQ}}$ (to compare with ${\overrightarrow {P}},$ which is correct). This misalignment is less visible in displayed formulas. However, if the vector in enclosed with brackets, the brackets are much too long below the line, as in

$$\left\|{\overrightarrow {PQ}}\right\|.$$

Also, in some cases, the upper part of the arrow is not displayed, as in

$${\overrightarrow {PQ}}.$$

Does anybody know some work-around, and/or asking for fixing the bug? D.Lazard (talk) 16:51, 4 May 2022 (UTC)

It may be too short … :

$${\vec {PQ}}.$$

$$\left\|{\vec {PQ}}\right\|.$$

--SilverMatsu (talk) 15:11, 5 May 2022 (UTC)

The image below is what I see when I look at the posting by D.Lazard above. I suspect others looking at that, including D.Lazaard, see something different because of different settings. @D.Lazard: Is something "awfully aligned" about the arrows as they appear in this screenshot, or do you see something different when you look at the articles and at your own posting above? Michael Hardy (talk) 17:44, 5 May 2022 (UTC)

To editor Michael Hardy: The screenshot is correctly formatted, except maybe that the vertical lines are too long toward bottom. On my screen, in the inline formula ${\overrightarrow {PQ}}$, the bottom of P is aligned with the middle of text characters such as "n". For the displayed formula with brackets the bottom of PQ and the period are aligned with the middle of the brackets, when the formula should be centered with respect to the brackets. In both displayed formulas the upper part of the arrowhead is lacking. I ignore which sort of setting can produce this sort of display errors. D.Lazard (talk) 20:01, 5 May 2022 (UTC)

Apparently, this is a bug in "MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools)", as, when I change my math preferences to "PNG images", I get the same rendering as you. D.Lazard (talk) 20:11, 5 May 2022 (UTC)

I think the svg fallback is likely to look more or less the same as Michael Hardy's screenshot, so my guess is that Wikimedia thinks your browser can properly render mathml and is not using the fallback, but your browser's rendering of mathml is bad (as is most browsers' renderings of mathml). —David Eppstein (talk) 21:40, 5 May 2022 (UTC)

@D.Lazard: Why don't you post a screenshot, as I did, so that we can tell what you're trying to say? In your comment saying "the upper part of the arrow is not displayed, as in", I see something displaying the entire arrow normally. You require us to take on faith that you see something of which you offer this verbal description but no image matching the discription, while at the same time you appear to intend to show us an image. It's not working at all. Michael Hardy (talk) 18:09, 11 May 2022 (UTC)

I see the same problem as D.Lazard. Here is my screenshot:

Example of a badly rendered \overrightarrow

. Note that the connection between arrow and extension line is also misaligned. It looks bad. --{{u|Mark viking}} {Talk} 19:22, 11 May 2022 (UTC)

This is a problem with the SVG rendering, you can tell this by looking at the code in the developer console. It seems like somewhere in the process, the vertical-align style attribute is incorrect. I've added a Phabricator bug T308188. --Salix alba (talk): 21:19, 11 May 2022 (UTC)

Hole

The article Hole (topology) seems to revolve around an idiosyncratic definition which is better subsumed in the homology (mathematics) and homotopy groups articles, the term hole is often used in a colloquial sense to give an idea of what these notions mean but presenting it as a formal notion as in done in the article seems to be counterproductive to me (and it is not supported by the given reference). I think the article should be deleted or made a redirect (probably to the article on homotopy groups or homotopical connectivity ; it may also make sense as a disambiguation page). jraimbau (talk) 07:40, 3 May 2022 (UTC)

Just to clarify: Did you check the offline reference (If not, I could do so at some point this week in our library)? Felix QW (talk) 07:57, 3 May 2022 (UTC)

Never mind, I managed to check it and you are right. It doesn't support the formal definition. Felix QW (talk) 08:15, 3 May 2022 (UTC)

I blanked and redirected. I'll notify the page creator, if they disagree i'll make an afd. jraimbau (talk) 12:02, 8 May 2022 (UTC)

I feel like the original redirect target was better. —JBL (talk) 20:32, 8 May 2022 (UTC)

The reference defines "a hole in dimension $\ell$ is something that prevents some suitably placed $S^{\ell }$ from shrinking to a point". While the definition is not written in mathematical notation, it is clear and accurate. The way to write it in mathematical notation is indicated at the bottom of the same page (specified in the opposite sense): it is "a continuous map $f:S^{\ell }\to X$ that cannot be extended to a continuous map ${\bar {f}}:B^{\ell }\to X$", or equivalently "a continuous map $f:S^{\ell }\to X$ that is not nullhomotopic". It is not colloquial - it is completely formal. The advantage of this definition over the one using homotopy groups is that it requires less previous knowledge - it does not require any background in group theory. In contrast, while the page on homotopy groups mentions that they are somehow related to holes, it is not clear from this page what a hole is.

If you still think that the concept of a "hole" does not deserve a page on its own, then I think it is better to merge it into homotopical connectivity. --Erel Segal (talk) 04:48, 9 May 2022 (UTC)

References

Since there was no objection, I changed the redirect to homotopical connectivity. --Erel Segal (talk) 11:24, 15 May 2022 (UTC)

I do strongly object to the mention of "hole" as a formal object in mathematics, be it on its own page or on the page about homotopical connectivity.

Here is the relevant excerpt from Matoušek's book :

Informally, a topological space X is k-connected if it has no “holes” up to dimension k. A hole in dimension k is something that prevents some suitably placed S^k from continuously shrinking to a point (...) Of course, things can be more complicated: A torus certainly has a hole in dimension 1 in this sense, but what about dimension 2? Fortunately, we need not contemplate such fine points here, since the formal definition is simple

and a proper definition of a k-connected space follows. It is clear from this excerpt that there is no formal definition of "hole", as opposed to one of k-connectivity, in this reference and that it actually provides a rationale against such a formal definition: "things can be more complicated", meaning that there is no reason that a "hole" in a topological space should be a missing ball rather than something else; the word is employed here as an intuitive explanation bulding on the (deceptively) simple 2-dimensional case (what is the "number of holes" in a 3--manifold?).

I do support the suggestion of putting the original redirect, to Hole#In_mathematics, back (i chose "homotopy groups" as a target because i was not aware of this original redirect). jraimbau (talk) 16:03, 15 May 2022 (UTC)

I agree wholeheartedly with Jean Raimbault and Felix QW -- the presentation of this as a formal definition of "hole" is deeply misleading at best, close to source falsification (even if not intentionally so). JBL (talk) 17:16, 15 May 2022 (UTC)

I have gone ahead and restored the earlier redirect. --JBL (talk) 17:17, 15 May 2022 (UTC)

Question: the "main article" link is to Homotopy group, but the text at Hole#In_mathematics is about homology. (The latter usage is what I have always heard!) Should there be multiple main article links, and/or should the text under Hole in mathematics be adjusted? Russ Woodroofe (talk) 17:38, 15 May 2022 (UTC)

I added some stuff about homotopy in the hole article (i think the Matoušek quote given by Erel Segal actually fits perfectly there). jraimbau (talk) 18:13, 15 May 2022 (UTC)

Deletion of "Greatest integer" proposed

Greatest integer redirects to Floor and ceiling functions. Deletion of the redirect is proposed. Post opinions at Wikipedia:Redirects_for_discussion/Log/2022_May_19#Greatest_integer. Michael Hardy (talk) 23:47, 20 May 2022 (UTC)

Need to rephrase Commutative property

I think this article needs to rephrase, for example, the section in Commutative property#Example made the reader, probably, confused to read what it means. It's not also be made confused to read, but it also didn't well written. I'm afraid that this GA will be delisted due to didn't meet one of the criteria of GA. Dedhert.Jr (talk) 13:15, 11 May 2022 (UTC)

Your concern is not written in coherent English, but it lacks references and does seem to contain original research. –LaundryPizza03 (dc̄) 20:52, 19 May 2022 (UTC)

EDIT: Partially redacted per WP:BITE rule. –LaundryPizza03 (dc̄) 01:26, 21 May 2022 (UTC) 03:37, 21 May 2022 (UTC)

Dedhert.Jr No disrespect meant, but I would like to suggest a serious improvement of your English capability before editing anything yourself in Wikipedia. Your English is just not grammatical. In a Talk comment we can figure out what you mean, but it would not be acceptable in a wikipedia article itself. In the long run this will be very beneficial to you, to allow you to interact in a more meaningful way with other folks. PatrickR2 (talk) 20:21, 24 May 2022 (UTC)

Connes embedding problem

I have discovered several articles which have become outdated since the Connes embedding problem was answered in the negative in 2020; in particular, I just updated Tsirelson's bound regarding an equivalent conjecture. Make sure that all of the articles that link to this conjecture are updated. –LaundryPizza03 (dc̄) 10:33, 24 May 2022 (UTC)

LaundryPizza03 Has this actually been proved, or is it only a preprint? The Quanta magazine article was written in March 2020, based on the arxiv article from Jan 2020. Later on (Sep 2020), a new version of the arxiv article was published based on another preprint https://arxiv.org/abs/2009.12982, where they say "Unfortunately a mistake was recently discovered in the latter result, invalidating the main result of ... as well as its use in subsequent works, including ...". I am in no position to judge the validity of this work, but it may not have been fully peer reviewed and fully accepted yet by the research community at this point? PatrickR2 (talk) 20:36, 24 May 2022 (UTC)

I found [24] which also postdates the erratum, but it is not yet peer-reviewed. I have several articles to scrub as premature. –LaundryPizza03 (dc̄) 08:04, 26 May 2022 (UTC)

@PatrickR2: Should the Connes embedding problem be removed from List_of_unsolved_problems_in_mathematics#Problems_solved_since_1995? I added disclaimers to several articles. –LaundryPizza03 (dc̄) 08:16, 26 May 2022 (UTC)

Not sure. I'll leave that decision to others more qualified. PatrickR2 (talk) 07:53, 28 May 2022 (UTC)

Seeing as the preprint and submissions have yet to complete the peer-review process, the problem should not be described in articles as having been solved (using wikivoice). Once it has been published in full peer-reviewed form (i.e. not counting research announcements like this), then the articles can be updated. — MarkH₂₁^talk 08:13, 28 May 2022 (UTC)

References

Homotopy groups of spheres GAR

Homotopy groups of spheres has been tagged for a Good Article Review in Wikipedia:Good article reassessment/Homotopy groups of spheres/1, mostly because at the time it passed GA it was acceptable to write things that were common knowledge in sources on the topic using general references at the end of the article, and nowadays we expect every individual statement^[1][2][3] to have these little footnote markers on it^[4][5][6] so that we can believe what it says by syntactically checking for the presence of footnote markers instead of by reading the sources. Regardless of that, it does have many statements that probably should be given inline sources, and doing so expeditiously might help save its GA status. Anyone wishing to pitch in to help, please do. —David Eppstein (talk) 08:07, 30 May 2022 (UTC)

Jun 2022

Jörg M. Wills

I recently created a draft for German mathematician Jörg M. Wills. Any help would be appreciated. Thank you, Thriley (talk) 03:28, 7 June 2022 (UTC)

"The most remarkable formula in mathematics" listed at Redirects for discussion

An editor has identified a potential problem with the redirect The most remarkable formula in mathematics and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 June 7#The most remarkable formula in mathematics until a consensus is reached, and readers of this page are welcome to contribute to the discussion. By the way, I don't know the format for adding RfD to Wikipedia:WikiProject Deletion sorting/Mathematics. Sorry … SilverMatsu (talk) 09:21, 7 June 2022 (UTC)

Update: Add "The Most Remarkable Formula In The World" to the list.--SilverMatsu (talk) 06:29, 8 June 2022 (UTC)

Lobachevsky

Could somebody with rollback rights revert the edits made to Nikolai Lobachevsky by Truthtellinggoat (talk · contribs)? (plain vandalism, but spread around enough that it's best not to undo by hand). jraimbau (talk) 05:12, 10 June 2022 (UTC)

Done. Rollback wouldn't help. For this sort of thing, the easiest thing to do is look back through the history for the last good version, edit that version, and save it over the vandalized versions. —David Eppstein (talk) 07:23, 10 June 2022 (UTC)

Thank you! that makes sense, i'll keep that in mind. jraimbau (talk) 13:09, 10 June 2022 (UTC)

Mathematician ITNRD nomination needing attention

There is an ITN RD nomination regarding the recent death of Aleksei Parshin which has not seen much input, perhaps due to the technical nature of some of the article content. The nomination may be of interest to this WikiProject, so your additional input is appreciated. Thanks. — MarkH₂₁^talk 08:47, 23 June 2022 (UTC)

Euler-alpha equations ?

I don't think Euler's formula are also known as Euler-alpha equations. So I think it needs to be retargeted, but I don't know the target. --SilverMatsu (talk) 04:24, 22 June 2022 (UTC)

@SilverMatsu: Then take it to RfD. –LaundryPizza03 (dc̄) 06:33, 22 June 2022 (UTC)

There appears to be something called the Euler alpha equations in fluid dynamics, some kind of perturbation of Euler equations (fluid dynamics), but they don't seem to be mentioned at that article. In any case that meaning, if it is notable, is unrelated to the current link target. —David Eppstein (talk) 07:43, 22 June 2022 (UTC)

Thank you for your comments. I will report when RfD is ready. --SilverMatsu (talk) 08:25, 22 June 2022 (UTC)

@LaundryPizza03 and David Eppstein: Done ! (Wikipedia:Redirects for discussion/Log/2022 June 22#Euler-alpha equations) thanks !--SilverMatsu (talk) 08:43, 22 June 2022 (UTC)

Content dispute at Sine and cosine

The Sine and cosine article is now fully protected because I and MrOllie can't reach an agreement. It concerns an inclusion of this article [25]. This [26] is the difference between the version proposed by MrOllie and the version proposed by me. Please help us to resolve this dispute on the relevant Talk page [27]. A1E6 (talk) 14:37, 22 June 2022 (UTC)

"Complex exponential" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Complex exponential and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 June 23#Complex exponential until a consensus is reached, and readers of this page are welcome to contribute to the discussion. SilverMatsu (talk) 03:49, 23 June 2022 (UTC)

Malfatti circles

I've been trying to beat back a very stubborn and very promotional editor on Malfatti circles who insists that all previous papers claiming a certain theorem are somehow unsatisfactory, that all later papers referring to those previous papers as being rigorous solutions are incorrect, that only a brand-new publication from 2022 (presumably, by the editor in question) counts as a valid solution, that their own edits to other-language Wikipedias count as evidence for these assertions, and that more than merely citing this new publication among others claiming solutions we must proclaim it to be the only true solution in the text of the article. Assistance here would be welcome. —David Eppstein (talk) 17:20, 22 June 2022 (UTC)

Is there an openly readable version of this work somewhere? It’s paywalled, not in sci-hub, not yet in Google Scholar or other indexes, and I don’t feel like shelling out $40 to read it. With nothing more substantial than a link getting added to Wikipedia, it’s impossible to evaluate any claims the anonymous contributor makes here. –jacobolus (t) 19:22, 22 June 2022 (UTC)

I have subscription access to it and could email a copy if you want. (Obviously, I don't think it would be a good idea to make a copy public rather than merely emailing privately.) It is a published paper, clearly relevant, so I think it should be cited. It is the claims that all previous solutions were faulty and now is the first solution of the problem that I find overblown. —David Eppstein (talk) 19:27, 22 June 2022 (UTC)

That's okay. I am happy to take your word for it. –jacobolus (t) 21:50, 22 June 2022 (UTC)

meta:The Wikipedia Library. --SilverMatsu (talk) 01:33, 23 June 2022 (UTC)

Having access to the article as well, I briefly looked through their claims. As far as I can tell, the numerical calculations that the 1994 paper rely on are involved and not pretty, but they are not "simulations" in any sense of the word which would detract from their propriety as steps in a mathematical proof. They seem to be just numerical approximations "to n decimal places", which is a precise fact with precise consequences. So I agree with David Eppstein on both counts: The new proof is clearly worth a mention, but not as the "first published proof" of the conjecture, at least unless future third party sources (ideally surveys or review articles) agree with IP's reading of the situation. Felix QW (talk) 20:05, 22 June 2022 (UTC)

Agreed. It seems to be like saying that it isn't rigorous to use a computer to say that $\sin(12.8)>e^{-\pi }.$ (I believe it is almost inarguably rigorous and formal to do so.) Gumshoe2 (talk) 04:06, 23 June 2022 (UTC)

Geometric algebra as a duplicate article of Clifford algebra

The article Geometric algebra is about the same object as the one covered in the article Clifford algebra, but presented using different notation and perspective. Should the two article be merged according to WP:OVERLAP? Should Geometric algebra be turned into something more clearly separate in scope like Geometric models of Clifford algebras?

Both article are quite long, but it looks like unnecessary material from both current articles can be easily cut to form a single well-written article from a quick glance. — MarkH₂₁^talk 09:46, 27 June 2022 (UTC)

• As someone who is not a mathematical physicist, I cannot really judge the potential of a separate article on 'geometric models of Clifford algebras', but I certainly agree that the current state is untenable. So I would support a merger of what we have, if someone were willing to take on the requisite cutting of material. Felix QW (talk) 10:04, 27 June 2022 (UTC)
• I think the way the object (the exterior algebra of a vector space) is talked about is very different from the two perspectives. The "Clifford algebra" language is all very geared towards describing spin representations and Dirac operators, whereas geometric algebra is very oriented towards describing the extended geometric constructions that an inner product on a vector space gives you. The fact that from one perspective you can understand spinors as certain objects in geometric algebra is interesting, but not really the way they get thought about (rather as certain representations of Spin groups, which the "Clifford algebra" language always emphasizes).

For example, I'm sure it would be very confusing for physics articles if the page on Clifford algebras spent half its time talking about unrelated geometric algebra constructions before completely shifting the language to describe the spin representations in the Clifford algebra (and similarly anyone looking for a fun introduction to geometric algebra would be very confused by all the detail about Spin/Pin groups and other language clearly set up for someone studying Dirac operators on manifolds).

• Whilst the actual object (exterior algebra of a vector space with inner product) is the same in both articles, I think the topic is different. I don't really think they should be merged unless someone can find a very good source which manages to explain in a way that isn't confusing to spin geometers/physicists or elementary geometric algebra people how the two subjects are the same. I seriously doubt the existence of such a source. Tazerenix (talk) 10:10, 27 June 2022 (UTC)
  • I see your point, but I do want to at least say that we shouldn't be writing the articles as a textbook-like fun introduction. An encyclopedic article can cover multiple perspectives in different sections. Also, re spent half its time talking about unrelated geometric algebra constructions before completely shifting the language, sections can be definitely self-contained and introduce new notation; this is quite normal in my experience (as long as it is made clear that there is a shift and a brief indication of why there is a shift). — MarkH₂₁^talk 05:24, 28 June 2022 (UTC)
• Geometric and Clifford algebras are not the same object. In physics, the Hestenes-type of geometric algebra is a type of Clifford algebra with a real-valued vector basis. See the papers [28] and [29] for a comparison of the two types of objects. Because geometric algebras in physics are a subset of Clifford algebras and as Tazerenix notes, they are typically used for different purposes in physics, I think it would be better to keep the topics as separate articles. There is already a section Clifford_algebra#Real_numbers on geometric algebra in the Clifford algebra article, which I think is the right approach to linking them. Part of the challenge is that some people do talk of complex geometric algebras and so "geometric algebra" means different things to different groups. --{{u|Mark viking}} {Talk} 17:23, 27 June 2022 (UTC)
• The point of view is quite different. Books about “Clifford algebras” start from a pure math grad student kind of audience (say, someone who has taken courses in linear and multilinear algebra, abstract algebra, complex analysis, differential geometry, Lie theory, ...), defining very general/abstract objects in terms of tensors and dual spaces using highly abstracted proofs, and typically starting from complex numbers as a scalar field; Clifford algebra are then seen as a niche special-purpose tool, just one among many others. Hestenes’s “geometric algebra” (Clifford’s own name for the subject, btw) can start as a subject aimed at a high-school-level audience building on the basic notions of vectors and introductory geometry (and even for more advanced audiences, eschewing abstract machinery to the extent possible), and always using “real” numbers as scalars; it considers geometric algebra to be a fundamental and unifying single language, in terms of which most (all?) other geometric tools can be built or described. Cf. “Reforming the Mathematical Language of Physics”, “Grassmann’s Vision” “Mathematical Viruses”. –jacobolus (t) 22:46, 27 June 2022 (UTC)
  • Aside: No offense intended to the authors, but the current lede for geometric algebra is incredibly unfriendly to a lay Wikipedia-reader audience, while also largely of missing the point of GA: In mathematics, a geometric algebra (GA) is another name for a Clifford algebra Cl(V, g) of a vector space V with a quadratic form g over a field of scalars F. It is an algebra over F generated by the vector space V.... The first few sentences here should have no mention of quadratic forms or fields (and the whole article should focus primarily if not exclusively on “real” scalars), and does not need letters or symbols. Vector division should probably be mentioned somewhere near the top. It might instead say something along the lines of “In mathematics, geometric algebra (also known as real Clifford algebra) is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric algebra is noteworthy for supporting vector division and addition of objects of different dimensions....” The rest of the lede section that I didn’t quote here is way too long and link-heavy (most of it can be transplanted to later sections or removed), and the early sections of the article are too jargony, technical, and unfocused. –jacobolus (t) 00:46, 28 June 2022 (UTC)
  • For anyone from a mathy background who wants to learn about GA, let me recommend Chisolm (2012) “Geometric Algebra”. –jacobolus (t) 01:05, 28 June 2022 (UTC)
• Thanks for all the replies! I'm not very familiar with the perspective given in geometric algebra, so this has been quite helpful. The suggestions of jacobolus sound quite good. If it is indeed the case that geometric algebra is mostly used in RSes for Clifford algebras over the real numbers, then I think that the article (or at least the lead) should be revised so that this restricted scope is clear from the beginning. — MarkH₂₁^talk 05:18, 28 June 2022 (UTC)
  • I think it's important to distinguish a geometric algebra (the type of structure) from geometric algebra as a mass noun (presumably the equational theory of those structures, or some such). At least it's really important for Boolean algebras, because the structures differ in important ways, whereas there's only one equational theory. I don't know nearly as much about geometric algebra(s), but if there's a distinction to be made then it should be made clearly, and the structures would likely merit a separate article, along the lines of Boolean algebra (structure). --Trovatore (talk) 06:55, 28 June 2022 (UTC)

    I think it is important to elide/suppress this difference for the article geometric algebra, because (a) it is irrelevant and confusing to lay / nonspecialist readers and emphasizing it clutters the narrative, and (b) a focus on “a geometric algebra” as some particular precisely defined formal structure obscures the fundamental point that “geometric algebra” is a common unifying language which can be widely employed under multiple interpretations in different contexts, but using common algebraic identities/manipulations (revealing some commonality in apparently different situations), and (c) if you really want to you can think of any “a geometric algebra” as a sub-algebra of a single universal geometric algebra which encompasses it and all the others (though I think a discussion of this should be considered out of scope for the wikipedia article). –jacobolus (t) 07:14, 28 June 2022 (UTC)

    As I say, I'm not an expert in this area, but I have trouble believing that it's ever irrelevant. A theory and its model are utterly different things. If you want to talk about the language, fine, but the structures are something different. --Trovatore (talk) 07:16, 28 June 2022 (UTC)

    To put it another way, you can just not talk about the structures in a particular article if you don't want to. But you can't "elide the distinction". That's like eliding the distinction between words on the page and the things the words are talking about. --Trovatore (talk) 07:18, 28 June 2022 (UTC)

    It’s more like eliding the difference between “language” and “a language”. –jacobolus (t) 16:16, 28 June 2022 (UTC)

    No, it's not like that at all. --Trovatore (talk) 16:21, 28 June 2022 (UTC)

    A closer analogy would be it's like conflating elementary algebra with the real numbers. --Trovatore (talk) 21:09, 28 June 2022 (UTC)

    No, the analogy would be conflating “elementary algebra” (a language) with “the algebra of real numbers” (a formal structure relating objects on which that language can be used); both of these are different than a real number. A geometric algebra (a formal structure establishing a domain in which the language of geometric algebra can be applied) is not the same as an element of that algebra (typically called a “multivector”). –jacobolus (t) 22:09, 28 June 2022 (UTC)

    I didn't say "a real number"; I said "the real numbers". --Trovatore (talk) 22:18, 28 June 2022 (UTC)

    Okay, but here “the algebra of the real numbers” and “the real numbers” formally mean the same thing (I guess up to isomorphism). The distinction is certainly important and meaningful, and it’s fine to talk about a formal definition for a geometric algebra. It’s just not that helpful to belabor the point in an article aimed at newcomers. If you started an introductory algebra course for middle school students by first coveringthe material from an undergraduate level abstract algebra course to make sure they had their terms formally precise, most of them would be bored and confused. –jacobolus (t) 22:29, 28 June 2022 (UTC)

    I'm not distinguishing between "the field of the real numbers" and "the real numbers". I'm distinguishing both of those from "elementary algebra" (meaning the symbolic manipulations). This shouldn't even be a question; of course those are not the same thing, not even remotely comparable, and writing that confuses them is only going to lead to misconceptions. --Trovatore (talk) 22:59, 28 June 2022 (UTC)

    I feel like you are missing my point. The subject of the article at geometric algebra should be geometric algebra (analogous to elementary algebra), not a geometric algebra (analogous to the field of real numbers, if you like). In the context of that topic, it maybe worth defining what a geometric algebra means somewhere (just as it might be worth defining, somewhere in elementary algebra, what the field of real numbers is – though note that article currently does not do so), but the point should be to describe the language of geometric algebra, and to that end belaboring the details of the formal definition of a geometric algebra is a distraction. –jacobolus (t) 23:12, 28 June 2022 (UTC)

    As I said, if you want geometric algebra to be about the symbolic stuff, and not about the structures, that's potentially OK. In that case you probably need a separate geometric algebra (structure) article, or some such, and a hatnote pointing to it. I don't have any strong opinion on that. I have a very strong opinion that we must not confuse the two. --Trovatore (talk) 23:23, 28 June 2022 (UTC)

    I think it is sufficient to leave Clifford algebra as a topic specifically about the formal structure. –jacobolus (t) 00:14, 29 June 2022 (UTC)

    Mm, maybe so. As an aside, though, it's a little odd to me that you keep associating the word "formal" with the structures. Aren't the equations more "formal"? The structures seem more Platonic than formal. --Trovatore (talk) 00:26, 29 June 2022 (UTC)

    But in any case, yes, I agree, it's the same as conflating elementary algebra with the field of real numbers ("field" is a better choice than "algebra" here; it's also "an algebra" in some sense but not a very relevant one). And that is an absolutely unacceptable conflation! We must not do that. --Trovatore (talk) 22:22, 28 June 2022 (UTC)

A fresh perspective: a Clifford algebra is a mathematical structure, and abstract mathematicians seem to know exactly what they mean by the term. Keeping aside for the moment "geometric algebra", nominally the study of "geometric algebras", it seems to me that those that use the term "a geometric algebra" usually think they are talking about a structure, namely a Clifford algebra (usually over the field of real numbers). They do not appear to realize that they really seem to mean the use of a Clifford algebra as a representation of a geometry with its properties – that is, the correspondence of features of an algebra to model aspects of a geometry. For example, by a CGA is meant a specific mapping between elements of a Clifford algebra and points, circles, etc., and the transformations of a conformal geometry. As such, the subject area "geometric algebra" is the study of such correspondences and their application, which one could regard as belonging to applied mathematics. Given this perspective (which I do not claim to be able to source), the most valuable article Geometric algebra that we could have would deal with the application of Clifford algebras to express geometric problems (for which vector algebra, Pauli algebra, Dirac algebra, etc., are also used). An introduction of geometric algebra that addresses vector algebra problems alone would be very helpful to the lay reader – which is something that would not belong in Clifford algebra. With the intuition of bivectors (oriented areas) to replace pseudovectors, etc., this article could act as a reference for people who want to find out about what geometric algebras are good for. I agree with jacobolus that the current lead totally misses the right approach, however one looks at it. 172.82.46.195 (talk) 00:17, 29 June 2022 (UTC)

Seems reasonable. Though I would spend the first few sections primarily talking about the “vector model” of Euclidean / pseudo-Euclidean geometry in 2–4 dimensions, and put discussion of using GA to represent other kinds of geometric objects later (can later discuss projective geometry, affine geometry, the outermorphism of a general linear transformation, conformal geometry, multivector-valued functions on manifolds, etc.). –jacobolus (t) 01:22, 30 June 2022 (UTC)

Jul 2022

RFC at Fields Medal

Since I saw today that the Fields Medals will be awarded next week, I was reminded of an issue I brought up here earlier this year, without resolution. I've opened a RFC at the Fields Medal talk page to do with erroneous commendations, please feel free to comment there Gumshoe2 (talk) 20:24, 30 June 2022 (UTC)

@Gumshoe2: I started RfD related to Fields Medal. Should I withdraw this once and wait a while before re-nominated it? --SilverMatsu (talk) 05:00, 1 July 2022 (UTC)

Because Kodaira embedding theorem is one of the Fields commendation errors? I don't see any necessity to withdraw, I don't think either discussion has much effect on the other. Gumshoe2 (talk) 05:19, 1 July 2022 (UTC)

Thank you your reply. I'm worried about breaking the wiki-link in Fields Medal because RfD temporarily broke the redirect (example: "Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds.").--SilverMatsu (talk) 05:53, 1 July 2022 (UTC)

Editor adding junk content to 177 (number)

I have been working to remove huge piles of cruft that have been added over the years to many of our number articles (example diff). On 177 (number), Radlrb (talk · contribs) has been edit-warring to add back the cruft. I've reached the limit of my reverts. Help wanted. —David Eppstein (talk) 18:15, 28 June 2022 (UTC)

Yes, please help. See my comments on the Talk:177 (number). I am copy-pasting the non-junk David Eppstein does not understand to include. He reverted my edits 4 times.

I suggest we have the following properties for 177, since David Eppstein is warring my edits:

• A Blum integer: 11th and less than 60 below 1000.
• A Leyland number as there are very few below 1000.
• A 60-gonal number as there are very few below 1000.
• I added 177 as the sum of the three prime factors (41, 59, 71) whose product make the minimum faithful complex representation of the Monster group. This is not trivial, it is another set value of these digits. I.e. the group 2.B has a faithful representation under 96,256 dimensions, whose sum of digits is 196,560, the kissing number in 24 dimensions. Aliquot sums and sums of divisors are common properties of numbers, and 196,883 is a particularly important number within the monstrous moonshine as it is linked with the j-invariant under its 196,884 dimensional representation - if this is too OR then I am perfectly fine with not including it. It seems to me that David Eppstein just wants to remove "cruft" he doesn't like because, well, personally he doesn't like it. He removed plenty of other information like examples of .177 guns. It makes very little sense. People who come here and read these pages are often times not mathematicians, so yes, including information of numbers being odd, composite, and even semiprime, are important tidbits of information that inform people not well acquainted with mathematics.

These values are not unimportant. They define some of the characteristics of the number 177. To take out these properties leaves this number less notable. I am seeking mediation, as I have needed to continue reverting misguided edits by David Eppstein. He alone is not one to choose what goes on a page, or not; and neither am I. So if we can get proper input that would be great. Radlrb (talk) 18:24, 28 June 2022 (UTC)

I'd like to also add that he does not have a proper definition of that "cruft" entails, he seems to be the only person in all of Wikipedia enamoured with that phrase. Per Wikipedia:Notability (numbers), these sequences are in OEIS and have proper identifying names, and 177 is in their lists early on. Also, I tried to find middle ground and removed two properties, however it seems to not be enough for him, he wants to appropriate the page entirely. Radlrb (talk) 18:43, 28 June 2022 (UTC)

In fact, I do have a definition of "cruft": it is anything that would not be relevant to Wikipedia:Notability (numbers) and its requirement for "three unrelated interesting mathematical properties" or "obvious cultural significance". That notability guideline gives, for instance, the example of the number 9870123 as not notable. Yet, one can say many of the same things about it: it is odd, it is semiprime... the conclusion is that being odd and semiprime is not an interesting property of 3290041, one that makes it notable. In many AfDs, I have repeatedly expressed a specific and quantifiable version of this formulation: that to be interesting, the property must either have its own article here (or be deserving of an article through multiple in-depth publications) or be labeled as nice by OEIS, and the number having that property should be among the first half-dozen or so numbers with that property. The version of 177 that I cut it down to includes only properties meeting that criterion. The additional properties you have been adding do not. Therefore, they are cruft, as useless as stating on every biography on Wikipedia that the subject is human, with a head and two eyes. —David Eppstein (talk) 18:51, 28 June 2022 (UTC)

Ok. Radlrb (talk) 20:56, 28 June 2022 (UTC)

"they are cruft, as useless as stating on every biography on Wikipedia that the subject is human, with a head and two eyes." Well said! PatrickR2 (talk) 23:56, 28 June 2022 (UTC)

Just because other sums of prime factors are important when it comes to the Monster group, it doesn't follow that this sum of prime factors is important; that would have to be established and documented independently. So, it's very hard to see a case for why we should include that property. As for the others: OEIS does call the Blum integers a "nice" sequence, but 177 is 11th on the list, and while this will inevitably come down to a judgment call, it's not unreasonable to say that's too far down the line to be noteworthy. (I tend to find position in an OEIS list as more meaningful than how many there are below 1000, since the former is about the sequence itself.) 177 is the 8th Leyland number, but David Eppstein's most recent revision includes that property, so maybe we don't have a substantial disagreement there. XOR'easter (talk) 18:59, 28 June 2022 (UTC)

It's fine. No issue. I disagree, but agree to disagree - except for the point on the Monster I agree it's OR. To me, an 11th Blum integer is definitely noteworthy. In fact, I think any studied and well-defined detail is noteworthy as long as they can be incorporated in groupings if possible, even if it takes an extra 3 lines. This obsession with only highly distinguishable properties is absurd, and hurts the content of the page. A distinguishable property of say, polite numbers, or square-free numbers is precisely that they incorporate such a large universe of numbers - and I would like to know personally whether a property is unique or shared by many other numbers. That is my personal philosophy, and usually having a pool of data that is well organized and diverse tends to be of greater service than limiting it to only the most notable examples.

This is basic research philosophy, and the best way to present information - giving a comprehensive, and dynamic list of properties, even if some seem less important, there is still plenty learned from the way numbers mix with other numbers. Knowing 177 is a Blum integer and a polygonal number tells me that this number has geometric and arithmetic properties that otherwise I might be entirely unaware of. For a number like 177 it might not seem impressive, but over time one compounds properties of different numbers and one is able to make quick connections because one recognizes properties shared with other numbers. If you take these away, then you take away the possibility of making these connections. I've always appreciated and learned best when I am presented with a more universal structure of whatever I am learning. If it's too limited, then I get a perspective that is not true to the subject. Even if the notability of some points might be less than others, comparative analysis permits you to surmise a nuanced nature of the number that otherwise would be nearly impossible to feel. At the very least, every single page should explain whether a number is prime or not, since it is not evident immediately for numbers even above 20 for most people - and whether it has 2, 3 or x amount of prime factors matters, since this is the very basic elementary definition of a number. Without this, no one can really know if for example 101 is prime or not, even though those who are experienced mathematicians might recognize that it is. And let's be honest. There would not be a gargantuan amount of lesser-important sequences that we can tie with given numbers. There really, are a very few amount of such "bad examples" to include. I imagine that, say, some numbers above 30 have about an average of maybe 5 lesser important sequences and properties that could be included. Is it really destructive at all to include many of them if they're so minimal in count (they can take 1 single line - i.e. a simple list in one sentence)? This is why I think it's very silly to not include these properties - there won't be very many attributable minor properties to these larger numbers anyways (like parts of sequences, types of numbers, etc.). So why not include them to give a more holistic background of a number? It let's people know they are part of other large sets, which yes, it is important! Uniqueness and shared-properties are opposites, however they can be equal in power insofar as what they communicate. Radlrb (talk) 21:20, 28 June 2022 (UTC)

Mathematics is infinite. There are infinitely many properties, and infinitely many held by any number like 177. Even if one only goes by properties in OEIS, a search finds 6433 OEIS sequences matching 177. That is far too many to list. Your philosophy that we should list everything on the off chance that it sparks a connection is untenable, and more than that, wrongheaded: the more unimportant properties we list, the less likely that a reader coming to the article will notice and learn about the important ones, because they will be overwhelmed with unimportant minutiae. As for Blum numbers: their main significance comes in choosing keys for the RSA cryptosystem, for which the two prime factors should be large and independently random. Combining smallness and being a Blum number subtracts from the meaningfulness of the combination, rather than adding. So that is not a sequence where I am inclined to give a little leeway and say that maybe 11th is still early enough to be interesting, as I did for Leyland numbers. —David Eppstein (talk) 21:34, 28 June 2022 (UTC)

Sure. I rather choose to incorporate some minor points. Gladly you changed your mind on two properties you originally were against including. That's a win-win IMO. Radlrb (talk) 22:34, 28 June 2022 (UTC)

If we have an article on a natural number, then I think that that article should contain, near the top, its factorization into prime numbers. This is a property which is not dependent on an arbitrary choice of base. It is frequently needed and not obvious. JRSpriggs (talk) 22:41, 28 June 2022 (UTC)

That's done in {{Infobox number}}, which seems a reasonable place for it, though of course of a factorization has a further interesting property then we can expound upon that in the prose. XOR'easter (talk) 22:56, 28 June 2022 (UTC)

To XOR'easter: Thanks for pointing that out. I am afraid that I have gotten into the habit of ignoring infoboxes. JRSpriggs (talk) 23:00, 28 June 2022 (UTC)

That's true, I also forget to look at infoboxes. Thank you for reminding me as well. Looks like we're set there. Radlrb (talk) 00:00, 29 June 2022 (UTC)

Ah, I read David's's last response wrong, I was busy working. Well, it doesn't matter, given that he thinks he owns these articles himself, per how he says im giving leeway, as in "oh, let's please this little guy who doesn't know what he is saying;" and even worse, suggesting that I actually meant I would put thousands of minor points on a Wikipedia article, without realizing that I meant to add only several minor points, and then further saying I am wrongheaded. Ah, that passive aggressive nonchalance and condescending talk that just makes me think I wasted my time. Oh well, keep scruffing your cruft away, David. My time is better spent than trying to even bother with someone who is quite selfish as you are with coming to an agreement. But because you're an administrator, and I can tell you won't stop being selfish with your edits when others have a different perspective, I'm just going to spend my time otherwise. I hope you open your eyes to how rude you really can be on this platform, regardless of how much you have contributed here. Ciao. Radlrb (talk) 07:27, 29 June 2022 (UTC)

If others are interested in keeping the point on 177 as a Blum integer, feel free to edit it back if David removes it, and if you think it's notable enough. Else, I think this case is closed. Radlrb (talk) 07:48, 29 June 2022 (UTC)

And yet, despite claiming that you consider the matter closed, and resorting here to uncivil personal attacks rather than content-based discussion, you are still adding more uninteresting properties back to the article. —David Eppstein (talk) 19:36, 29 June 2022 (UTC)

I have to agree that both "60-gonal number" and "arithmetic number" fail the test of appearing early in a sequence the OEIS designates as "nice" (or interesting in any other way, like being related to a hard open problem). In the latter case, 177 is so late in the sequence it's not even in the part that the OEIS prints explicitly. The 60-gonal numbers are easy to calculate and don't seem to be among the polygonal numbers that have been written about; contrast, for example, how much the OEIS has to say about them with what it has on the hexagonal numbers, or the depth of coverage available for square triangular number and cannonball problem. XOR'easter (talk) 19:56, 29 June 2022 (UTC)

If a disagreement happens here, I rather speak of it here than move it elsewhere if there is a need of perspective for others to see abject behavior present. Moving it to another space for these types of issues I'd do if they continue, to take the matter at hand more directly if normal conversation fails to produce results. I'm trying to move on from trying to make sense of why others see notability where you/anyone would maybe not, and vice-versa, whether it's light notability, or even two minor points which together might bring some interest to a number that has such few highly notable examples (some of the examples you chose to include, as Gumshoe2 pointed out, could be interpreted as having average, or even no real notability - though I think they are good examples) - i.e. 60-gonal is a geometric representation of 177 in which its arithmetic average of its divisors also happens be a representation of 60, here as an integer itself. I find that interesting personally, especially since they arise from different operations. Take the example that 177 being a Leonardo number is 11th in its sequence (after two 1s), while the Blum example I wanted to include is also the 11th on its sequence.

The funny thing, is that, in fact, as math evolves and we learn more about large numbers, large numbers will have properties themselves that require relatively large numbers also to describe. So these numbers above 150 or so tend to have scant significant properties, and the ones that do have significant properties tend to come in sets, like for say the number 240, which is a geometrically important number (in E₈ and icosahedral symmetry for example) as well as a number that is highly composite. So my internal intuition is to include minor examples not as fillers per se, but as giving at least some color to these 100s and 200s numbers that can be exceedingly bland. Now, I want to apologize because I usually try not to be so rude myself, usually I prefer to have a more civil conversation, and I become irritated when my edits are just blanketed with a negative tone - there are also more civil ways to express disagreement than by asking a rhetorical question that is afixed to an edit. If you think I do not enjoy contributing meaningful edits, see 15, 24, or even the golden ratio which I am trying to slowly bring to good article standing. I love editing here, and I love making these pages better. And I do actually appreciate you David (if I may refer to you with your first name). And maybe I am a little bland on some of these properties, however I try to provide good improvements. That is always my goal. Radlrb (talk) 05:43, 30 June 2022 (UTC)

Well, for what it's worth, I largely agree with Radlrb that David Eppstein can be rather condescending and rude in disagreement, sometimes not very nice to interact with as a fellow editor and especially not as an admin.

Anyway, as for the matter itself, radlrb's preferred version [30] (with exception of monster group sentence, although I personally happen to like it) is perfectly concise/readable and the properties seem to all have their own wikipage (and are well-cited). This is precisely what I as a wiki reader would hope for from a page like 177 (number). The four mathematical facts in David Eppstein's preferred version [31] seem just as randomly selected as any of radlrb's (and arguably even moreso). So I agree with radlrb's edits. From reading David Eppstein's replies here, it seems his main contention is that radlrb's properties fail to, in and of themselves, make 177 a notable number, and I agree with him on this. But I think it is a bad standard to use for the question at hand. Gumshoe2 (talk) 20:23, 29 June 2022 (UTC)

This is not the correct forum for making drive-by personal attacks. Perhaps a better forum, if that's what you want to do, would be WP:ANI. Also, given that the version you linked has an entire unsourced paragraph, multiple unlinked properties, and a WP:EL violation, I do not find your assertions that "the properties seem to all have their own wikipage (and are well-cited)" particularly convincing. —David Eppstein (talk) 20:55, 29 June 2022 (UTC)

Not any kind of personal attack, my action is only to support other editors having similar difficulties to what I have had in the past. For what it's worth, I think you make a lot of valuable edits to the website.

Anyway, the "entire unsourced paragraph" you refer to seems to be "177 is an odd composite semiprime with 3 and 59 as its prime factors" which as we are all aware amounts to totally rudimentary/routine computation on the elementary-school level. On the other hand, I see now that you are correct that "digitally balanced number" misleadingly links to external website, and so I agree with you that that sentence could/should be removed. I'm not sure what other unlinked properties you refer to. Gumshoe2 (talk) 21:09, 29 June 2022 (UTC)

One thing I don't like as a Wikipedia reader is indiscriminate piles of trivia. When an article is just a heap of factoids, it's darn near impossible to tell what is important — or, in this area, what mathematicians have agreed upon as important. The goal here is to build an encyclopedia, not the TV Tropes of math. The apparent concision of "it's a Leyland number, a square-free number, an Ulam number..." is an illusion; parsing it requires traversing the graph of bluelinks, and sifting the properties that are trivially verifiable from those that are not. XOR'easter (talk) 21:11, 29 June 2022 (UTC)

I strongly agree that indiscriminate piles of trivia are terrible on wikipedia, but strongly disagree that this counts as such (to the extent that I almost wonder if we're looking at the same thing). The "graph" (?) of bluelinks has as little complexity as ever present on wikipedia (you just have to click on one thing to have the concept explained). I think it would be fine and good to rephrase to clarify which properties are trivial and which are not. Gumshoe2 (talk) 21:17, 29 June 2022 (UTC)

Having to click on a link every three or four words to make it through a sentence is, I submit, not a good use of the hypertext medium.

If a property is trivial, why write about it? The only justification I can think of is if the number is an oft-cited example of having a property. (It is commonplace for natural numbers to have irrational square roots, but the fact that ${\sqrt {2}}$ is irrational has been much remarked upon.) This is what the "does it appear early in the OEIS list?" question is trying to get at. XOR'easter (talk) 21:25, 29 June 2022 (UTC)

I agree with you for usual sentences, except that it would be strange to read the sentence in question in the usual way one reads sentences, as it is effectively (and very clearly, no matter one's comprehension of the content) a list only in sentence format. (It would be ok to convert to a literal bulleted list, but in my opinion it would not be an improvement.) Anyway, it seems we fundamentally have different criteria for what should go on a wikipage like 177 (number). For instance, given that a number page like 177 exists, I think it is totally irrelevant/uninteresting whether that number is early or late in an OEIS list. Also, I think it is universally accepted to include "trivial" information on wiki, and that the website is better for it. The question is which trivial information should be included or excluded.

It seems that the only relevant official wiki-rules (as linked above on this thread) are for whether such a number page should exist in the first place, and is not very well-suited for advising on page content itself. Maybe a RFC (on the issue of content of general number pages) would be the best way forward? Gumshoe2 (talk) 23:59, 29 June 2022 (UTC)

Given that there are 6433 OEIS sequences matching 177 (noted above), and others under dispute where 177 is too far along the list to even be mentioned at OEIS (e.g. odd numbers), we obviously cannot include them all. We need some standard. As a general principle, I think that properties that are more important as mathematical properties (say, being odd) should be preferred over properties that are unimportant (say, being a 60-gonal number) and that properties for which the number is particularly salient, likely to be cited as an example of that property, should be preferred over properties where the number is just one among many. My choice of "first half dozen members of an OEIS-nice sequence" is idiosyncratic, and I don't expect everyone else to agree with that exact choice, but it meets those principles. It also has the advantage of being somewhat objective; if we were going by my own opinion of what's interesting, for instance, I'd get rid of a lot more of the decimal-based properties (like "digitally balanced number"), but I recognize that others may find those more interesting than I do, and that's reflected in the fact that many of them are OEIS-nice. But obviously, you seem to think that my standard is the wrong standard. So can you please articulate a clear standard for what to include instead, one that is actually tenable rather than making a big pile of all properties that can either be sourced or calculated? It would not work to have an RFC with only a vague question rather than a clean yes-or-no question of whether some particular standard is a good one. My suspicion is that a general RFC is going to attract a lot of the kind of editors who have contributed to content like the current state of 155 which mixes easy-to-calculate unsourced mathematical properties held by most numbers with a large disambiguation-page-like random selection of links to bus routes numbered 155 and the like. The result of such an RFC could well be that any attempt to clean up this sort of mess would then have the weight of consensus against it. —David Eppstein (talk) 00:38, 30 June 2022 (UTC)

I see, perhaps you are right about RFC. Anyway, although I agree with OEIS that many of their nice sequences are actually nice, it seems that their deployment thereof is based on an informal poll of their mailing list (I may be wrong, I couldn't find clear info), so I don't think it's a good basis for anything here. And as I said before I also don't think that numbers towards the beginning of a sequence are more noteworthy. Anyway, my immediate thought is that it's reasonable to include named properties which have their own wikipage. Using [32] as a basis, here's where that would leave us for 177: (and just for fun, I have roughly ordered by how interesting I personally find each property)

• 177 is an evil number, i.e. the binary expansion has an even number of ones; it is a sorting number, i.e. it arises as the worst-case number of iterations needed for certain non-optimal sorting algorithms; it is an Ulam number and Leonardo number, meaning that it comes up in certain recursions (the latter being small modification of Fibonacci); it is a Hilbert number, meaning that it is of the form 4n+1; it is polite number, meaning that it is not a power of two; it is an equidigital number, meaning that it and its prime factorization have the same total number of digits
• 177 is an arithmetic number, so that the average of its divisors (1, 3, 59, 177) is an integer
• Its prime factorization is $3\times 59,$ which makes it semiprime (synonymously 2-almost prime). Since both prime factors are of the form 4n+3, it is the special kind of semiprime called Blum integer. The same fact makes it a nonhypotenuse number, so that it is not the hypotenuse of any integer-sided right triangle.
• It is a Leyland number as $177=2^{7}+7^{2}$. It is a cyclic number (group theory) since all groups of order 177 are cyclic. And it is an idoneal number, which seems particularly interesting as a (to my non-expert eyes) natural number-theoretic condition with only 65, 66, or 67 of them existing.

(I am not proposing the above text for inclusion on the page, it is just raw data for discussion.) These are (unless I miss a couple) the fourteen named properties which are satisfied from the linked list of 215 potential ones. I think that all of us present will agree that a couple of these "named" number types are totally uninteresting and perhaps should not even have their own wiki page!

However I believe that all of the above (in terms of basic content) is appropriate for inclusion, although I am sure some here will call it "crust". It is all very easy to absorb (with one or two more complicated things), easily citable to oeis, would take up only little space (couple of paragraphs) to write out well, and on a page which contains practically no other information anyway. I like the graph enumeration properties presently given but I think they are less appropriate. The monster group properties are original research and should not be present.

Two extra thoughts:

• it seems some users here are using the criteria "what properties make 177 an interesting number". I am not using this criteria, since I think no natural numbers except probably 0 & 1 are themselves interesting. I think there are some interesting sequences (primes, Ramsey theory, etc) but the individual numbers seem not so interesting. The whole 177 page (along with many others analogous) could be deleted altogether without any real mathematical loss to wiki. But taking as given that we are talking about 177, the right choice is to send the reader to other pages for which 177 has some relevance. I may have no idea why someone would single out "Hilbert numbers" for significance, and it is absolutely not something which makes 177 interesting (I defer to previous few sentences), but wiki has singled it out so I think it is appropriate to send reader to "Hilbert number" page, despite my own distaste for the concept.
• the criteria I suggest (properties with their own wiki-page) is almost certainly not practical for some very common numbers like 0, 1, 2, etc. But such wiki pages probably have to be written by a different standard anyway, being as they are at the intersection of many different things. In present case, and for similar numbers, I think it leads to a reasonable amount of information.

Apologies for the long message, I try to stay concise but it does not come natural to me Gumshoe2 (talk) 04:41, 30 June 2022 (UTC)

I don't think there's any need to apologize; it was interesting. I think idoneal should definitely be listed (finite sets of mathematical importance are different from the infinite and dense ones). Your approach is not unreasonable, but I think more difficult to implement: it takes a lot of effort to go through all of our number property articles (not all of which are listed on that template) and figure out which ones apply. You did miss some: it is also a deficient number and (as discussed above) a square-free integer. I do think there is actually a usefulness justification for including the combinatorial enumeration properties that would be dropped by your criterion: if one has a collection of 177 things, and looks up 177 to find that there are also 177 of some other kind of thing (star polygons, say), one might get a hint that the first kind of thing is secretly the same kind of thing as the second. —David Eppstein (talk) 05:34, 30 June 2022 (UTC)

Just to clarify two things: (1) if I were writing the page myself (and I do not anticipate making any edits) I probably would not include the graph enumeration properties but as is I have no strong suggestion on if they should stay or go; (relatedly, 2) I consider my proposed criteria as more if than iff -- to phrase the if/then carefully: I think that if someone adds a reasonably written sentence or two relating in this kind of totally direct way to the topic of another wikipage, then it is good/reasonable policy to leave it in. I don't consider it imperative to add such material, or that it should exclude against other content. (As I see it, my essential point is just that the suggested criteria does not let in an unmanageable mess of content, at least for numbers like 177) Gumshoe2 (talk) 06:13, 30 June 2022 (UTC)

I would tend to have the same opinion as David Eppstein in this matter. The page 177_(number) seems to be an accumulation of random (trivial?) facts about that number, which may not all be notable enough to be in this encyclopedia. But just for comparison, I wandered over to 178_(number), the next one in the sequence. And here it's becoming downright ridiculous. One of the claims of fame for that number 178 is that someone in 1946 claimed that there were 178 equivalence classes of something, and later that number was found incorrect. Makes no sense to have this in there. PatrickR2 (talk) 04:08, 1 July 2022 (UTC)

Suggestion to add for notability of the number 4: it's equal to the sum of the number of eyes and the number of ears of most vertebrates. :-) PatrickR2 (talk) 04:11, 1 July 2022 (UTC)

I have moved the information about the incorrect number of ... from 178_(number), where it did not belong, to Margaret Willerding. PatrickR2 (talk) 22:33, 1 July 2022 (UTC)

Recording the history of such things seems to make as much sense in 178 (number) as it does in Margaret Willerding, I think. Four_color_theorem#Early_proof_attempts covers failed proofs, i.e., "facts" about maps that turned out wrong; 178 (number) can record a "fact" about 178 that turned out wrong. XOR'easter (talk) 22:42, 1 July 2022 (UTC)

There's really very little to distinguish 178. If not for the history of quadratic form enumeration, we might better not have an article there at all. Only one of the other listed properties is OEIS-nice, and neither has its own article. Anyway, I think any reader likely to be misled by the claims in the literature on the number of forms, and in need of correction, is more likely to find that correction at the 178 article than at the article on Willerding. —David Eppstein (talk) 22:45, 1 July 2022 (UTC)

An analogy that just sprang to mind is that we wouldn't remove $10^{10^{10^{34}}}$ to the biography of Stanley Skewes just because that bound has been improved. XOR'easter (talk) 22:53, 1 July 2022 (UTC)

This is not the same situation at all. We are talking about whether a certain statement is a "mathematical fact" that belongs in one on the "number articles". Not other contexts. PatrickR2 (talk) 23:34, 1 July 2022 (UTC)

Not a problem to record this somewhere, and the Willerding article is a good place to mention this. But it is certainly not a "mathematical property" of the number 178, hence does not belong in that article. And let's be realistic, I doubt that any reader interested in integral quadratic forms would get their first information on that topic from the article 178_(number). Any reader interested in that topic would access detailed references to this topic from other articles. No need to clutter these number articles with more non-mathematical facts. PatrickR2 (talk) 23:25, 1 July 2022 (UTC)

"Kodaira embedding theorem" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Kodaira embedding theorem and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 July 1#Kodaira embedding theorem until a consensus is reached, and readers of this page are welcome to contribute to the discussion. SilverMatsu (talk) SilverMatsu (talk) 04:43, 1 July 2022 (UTC)

I believe the redirects are to Kodaira embedding theorem and are being discussed in the section Wikipedia:Redirects_for_discussion/Log/2022_July_1#Hodge_manifold. XOR'easter (talk) 16:08, 1 July 2022 (UTC)

@XOR'easter: Thank you for fixing the link. --SilverMatsu (talk) 00:07, 2 July 2022 (UTC)

Topology of ...

Topology of pointwise convergence redirects to an eponym section of Pointwise convergence.

Topology of compact convergence redirects to Compact convergence.

But Topology of uniform convergence does not redirect to Uniform convergence. Instead, it redirects to Topologies on spaces of linear maps. Moreover, the topology of uniform convergence is not explicitly mentioned in Uniform convergence.

This sets several issues:

1. Coherency of redirect targets
2. As far as I know, the topology of uniform convergence is defined for a much larger class of functions than the linear maps.
3. Topologies on spaces of linear maps is an article almost entirely written by Mgkrupa. This article is awfully written: almost no context provided; much too WP:TECHNICAL; for finding the definition of the topology of uniform convergence (the subject of the first section), one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before. So, for understanding the definition, one needs to be an expert of the subject, or to spend several hours of hard work.

What should be done with these issues? D.Lazard (talk) 17:18, 30 June 2022 (UTC)

"one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before." I moved the section. Problem solved. Mgkrupa 17:45, 30 June 2022 (UTC)

"the topology of uniform convergence is defined for a much larger class of functions than the linear maps." Yes, there should be an article about this topic. I suggest that someone (not me) change "Uniform convergence" from a redirect into an article about this topic. Or maybe change it into a disambiguation page. Mgkrupa 17:45, 30 June 2022 (UTC)

Side note: I think that part of the reason by the article Topologies on spaces of linear maps is so technical is because there is no article dedicated to the more general theory of Uniform convergence for arbitrary classes of functions. If an article on this topic is created then we could link to it and simplify the presentation in Topologies on spaces of linear maps. Mgkrupa 18:12, 30 June 2022 (UTC)

"much too WP:TECHNICAL" The article Topologies on spaces of linear maps was intended to be about the various topologies that are used in functional analysis, which necessarily involves concepts such equicontinuous sets, bounded subsets, the Mackey topology, the ε-topology, and so on. I would like the article to be less technical and would love to hear suggestions on how to accomplish this. Mgkrupa 18:00, 30 June 2022 (UTC)

"almost entirely written by Mgkrupa. This article is awfully written" The article does need improvement. I suggest that we work together to improve it. Perhaps we can start by determining the best way to organize it? Mgkrupa 18:00, 30 June 2022 (UTC)

The material is too specialized for the subject matter. So I think that the solution is to not give the most general formulation possible. For instance, the primary context could be the weak convergence of continuous linear maps between Banach spaces, as is the context for many of the most standard textbook references on functional analysis. (At present, it seems Banach spaces are not even mentioned on the page.) Having said that, I personally like the nature of much of your contributions to this page and other similar ones. But I might suggest it is more appropriate somewhere like nlab, where it is still easily accessible to those who want it, but where wiki can have a space for (what I would call) writing more encyclopedia than knowledge database. Gumshoe2 (talk) 19:16, 30 June 2022 (UTC)

The Banach space cases should be mentioned. However, there are already multiple articles dedicated to such topologies. The article Operator topologies#List of topologies on B(H) lists many of them, including: Strong operator topology, Weak operator topology,Norm topology, Ultraweak topology, Ultrastrong topology, Weak convergence (Hilbert space), Weak topology. If I remember correctly, the reason why I originally created the article Topologies on spaces of linear maps was precisely because there was no article discussing uniform convergence in the general (non-normed space) setting of TVSs, and this was also why I did not add (norm space)-specialized content like what you suggested (i.e. weak convergence of continuous linear maps between Banach spaces). Having said that, this omission should be corrected as these cases are very important. I also suggest that links to articles like Operator topologies, Strong operator topology, etc. be mentioned early in the article (maybe the introduction) to help readers who are only interested in these special cases (and not the more general case) navigate to their desired article. [Update: I changed the introduction to contain a link to Operator topologies.] Mgkrupa 19:50, 30 June 2022 (UTC)

One comment about Topologies on spaces of linear maps, but which also applies to other articles written by you. The references are not targeted enough. Example: footnote 6 refers to "Narici & Beckenstein 2011, pp. 371–423.", and is refered to from about 7 places. Pages 371-423 is a huge range of pages, a whole chapter maybe? Each place that refers to something in that chapter should refer to a specific result on a specific page of that chapter, instead of forcing the interested reader to read the whole chapter to figure things out. PatrickR2 (talk) 04:30, 1 July 2022 (UTC)

You're right that large page ranges is bad practice. I have experienced the same problem you have (embarrassingly, a couple times with my own citations, which is why I've been doing that less frequently recently). But as you say, I should (and will) start making the page ranges more targeted. However, I sometimes include the proof or relevant definitions/author comments in a citation's page range. Is that considered bad practice?. Mgkrupa 21:42, 1 July 2022 (UTC)

Not sure I understand what the last sentence is referring to. Can you give an example? PatrickR2 (talk) 23:30, 1 July 2022 (UTC)

Consider "Grothendieck's Completeness Theorem" here: Complete topological vector space#Topology of a completion. The statement of the theorem was on page 176 (the proof is on the pages immediately after it). The citation for the theorem is given as "pp. 175−178" and this page range includes some - but not all - of the definitions/notation that are needed to understand the theorem as stated in that reference. The definitions of some the terms and notation that the reference used were defined elsewhere in hard to find locations (in this case as far away as pp. 151 and 157). If I didn't include these 2 pages then I think it likely that it would have been difficult for another person to verify that the statement and definitions were copied correctly. Now although in this particular case I used two separate citations (because of how many definitions were needed), there are occasionally other situations where this is not necessary and it would make much more sense to just use a single citation e.g. such as "pp. 151, 157, 175-176". I wish I could give a better example but I can't think of a better one off the top of my head. But did that clarify my question? Mgkrupa 08:15, 2 July 2022 (UTC)

Mgkrupa That sound ok in this case. But in general, if we don't refer to other concepts defined elsewhere in the book, I think it would be perfectly fine to just cite the page where the theorem in given. It's up to the interested reader to figure out where the proof is and where the definitions of any used concepts are in that source. No need to do it for them. The interested reader will learn more by looking things up themselves. PatrickR2 (talk) 04:35, 5 July 2022 (UTC)

RfC on Glossary of areas of mathematics

Glossary of areas of mathematics is an article that should concern all of use. Its state is presently awful. I have started an WP:RfC on inclusions criterias for this stand-alone list, at Talk:Glossary of areas of mathematics#RfC on inclusion criteria. Contributions are welcome. D.Lazard (talk) 15:28, 5 July 2022 (UTC)

Some verifiable explanation or definition of what constitutes an "Area of mathematics" would be useful if such exists. This appears to be the main subject of contention. Cheers · · · Peter Southwood ^(talk): 07:10, 6 July 2022 (UTC)

Endomorphism ring of an elliptic curve

The link in the title (as you can see) is red. I thought of redirecting it to elliptic curve, but as far as I can tell, that target has no info on the endomorphisms of elliptic curves (so the redirecting is unhelpful at best and misleading at worst). Is the topic not covered at all in Wikipedia (if so, that's very surprising.) -- Taku (talk) 08:32, 4 July 2022 (UTC)

Incidentally, the ring of differential operators also doesn't exist either (a special case is in differential operators but not the general one with the product given by the Leibniz rule with variable coefficients.) -- Taku (talk) 08:38, 4 July 2022 (UTC)

• @TakuyaMurata: The ideal target right now would be Complex multiplication or Complex multiplication#Abstract theory of endomorphisms. — MarkH₂₁^talk 13:42, 4 July 2022 (UTC)

  Thank you. As a short-term fix, this does seem to work although it probably makes sense that there is a standalone article or a section in the elliptic curve article on this topic. —- Taku (talk) 08:23, 5 July 2022 (UTC)

  Taku, When you create a redirect that you think should be expanded into an article, you can tag it with {{R with possibilities}}

  I do not know enough about the topic to create a short description for the redirect. Maybe someone from the project could take a look. · · · Peter Southwood ^(talk): 07:27, 6 July 2022 (UTC)

  Thank you for letting me know about the tag. I have added the short description. —- Taku (talk) 13:21, 7 July 2022 (UTC)

Deletion review of Łukaszyk–Karmowski metric

This discussion may be of interest to the community here. XOR'easter (talk) 14:26, 14 July 2022 (UTC)

Move of "Poincaré conjecture" to "Perelman's theorem"

A new user 廖培 (talk · contribs) has recently moved Poincaré conjecture to Perelman's theorem, since it is no longer a conjecture. I think this is unambiguously a bad move, since it is still (despite its status) universally called Poincaré conjecture and never called Perelman theorem; the user has simply decided that it ought to now be known as Perelman theorem instead. I don't understand well the technology of reverting page moves, hopefully someone else here does? Gumshoe2 (talk) 03:23, 10 July 2022 (UTC)

Thanks for flagging this. I have reverted. Presumably bots will clean up the redirects. --Trovatore (talk) 03:52, 10 July 2022 (UTC)

I suggest delete the Perelman theorem, because, as another example, I think the Geometrization conjecture are also known as Perelman theorem.--SilverMatsu (talk) 04:16, 10 July 2022 (UTC)

Much thanks, Trovatore! SilverMatsu, I believe there is absolutely nothing called Perelman theorem with any consistency. From google search "Perelman theorem" could be a classification of Ricci solitons, sometimes it is the existence of Ricci flow with surgery, in principle it could be either the geometrization conjecture or the Poincaré conjecture, and (by same principle) could be many other major results from his papers besides. I think there should not be any redirect or disambiguation page for "Perelman theorem." Gumshoe2 (talk) 14:20, 10 July 2022 (UTC)

Nominated for RfD. --SilverMatsu (talk) 16:37, 11 July 2022 (UTC)

I’d make Perelman's theorem and Perelman theorem redirect to either Poincaré conjecture or to Grigori Perelman#Geometrization and Poincaré conjectures. –jacobolus (t) 17:42, 11 July 2022 (UTC)

Is there evidence that these phrases are used in the wild for that? --Trovatore (talk) 19:32, 11 July 2022 (UTC)

Searching Google scholar for "Perelman's theorem" finds it continued:

• ...that the metric projection of a non-negatively curved open manifold onto its soul is a well-defined Riemannian submersion (ProQuest 304537849, [33]); this seems to match Grigori Perelman#Comparison geometry.
• ...that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons (doi:10.1007/s12220-017-9974-1)
• ...that positively curved ancient solutions have vanishing asymptotic volume ratio and infinite asymptotic scalar curvature ratio ([34])

So it definitely seems incorrect to redirect to Poincaré conjecture. If we had enough links for these other things we could consider making a dab page. —David Eppstein (talk) 20:25, 11 July 2022 (UTC)

As a comparable example, both Wiles's theorem and Wiles theorem redirect to Fermat's Last Theorem (even though those terms are extremely rare in the literature even 25 years after the proof). The Poincaré conjecture is by far the most famous theorem proven by Perelman (since the mid 2000s and into the future, I would expect any use of the generic "Perelman theorem" to mean this, with other "Perelman theorems" named something more specific; for example in the three examples that David Eppstein found, the theorems there are explicitly called “Perelman’s Rigidity Theorem”, “Perelman's No Local Collapsing Theorem” and "Perelman’s Theorem on Shrinking Breathers in Ricci Flow" when introduced; none of these is presented as "Perelman's Theorem" without qualification). In a brief search of the current literature, there are a bunch of uses of "Poincaré–Perelman theorem" and a few direct uses of "Perelman theorem" to mean this result, but it is still commonly called the "Poincaré conjecture" after the proof, out of historical inertia. –jacobolus (t) 20:32, 11 July 2022 (UTC)

OK, if/when that happens, we can make those redirects. Wikipedia is not supposed to drive adoption of terminology. (By the way, I don't think it's wrong to keep calling it the Poincaré conjecture, given that Poincaré did in fact conjecture it. The assertions that it "was" a conjecture and "is now" a theorem are, I think, just wrong; if it's a theorem now then it has always been a theorem, even before there were humans. The proof has always existed; the only thing that has changed is that we now know a proof. Being a conjecture is more temporal; it's not a conjecture until someone conjectures it. Still, I don't think it stops being a conjecture just because we now know that it's also a theorem. --Trovatore (talk) 20:49, 11 July 2022 (UTC)

Adding redirects here seems easy and low-cost (low chance of causing confusion; does not make false implications; as just a redirect, does not give “undue weight” to some fringe/unestablished usage), while potentially helping some readers. If nothing else, it prevents people from trying to "helpfully" move the page there in the future. Titles to be redirected have a much looser standard than the text of articles: redirects are about helping people find what they are looking for, not telling them what terms are standard usage. If you think there will be some confusion about whether Perelman theorem should refer to Poincaré conjecture or Geometrization conjecture, then a redirect to Grigori Perelman#Geometrization and Poincaré conjectures should eliminate that concern. –jacobolus (t) 21:02, 11 July 2022 (UTC)

"The Poincaré conjecture is by far the most famous theorem proven by Perelman". That does not preclude a disambiguation page. That can be the bolded primary meaning (cf the treatment at Rabbit (disambiguation)). SpinningSpark 17:44, 13 July 2022 (UTC)

The fact that it's the most famous theorem he's proved (so far) doesn't make it the primary meaning for "Perelman's theorem". --Trovatore (talk) 17:51, 13 July 2022 (UTC)

If we called Poincaré conjecture as Perelman's theorem, I think we miss the contributions of Stephen Smale and Michael Freedman.--SilverMatsu (talk) 04:36, 14 July 2022 (UTC)

It really doesn't make any difference at all, for our current purposes, whether "Perelman's theorem" would be a good name. We shouldn't even be talking about that. I'm not at all a stickler for the rules on talk pages; I'm not objecting to you talking about what you find interesting. I just don't want it to get confused with what our articles should be called or what redirects/disambigs we should have and where they should point. --Trovatore (talk) 15:48, 14 July 2022 (UTC)

While I agree that a move of Poincaré conjecture to Perelman's theorem is inappropriate, a disambiguation page with links to, e.g., Poincaré conjecture, Thurston geometrization conjecture, might be appropriate. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:18, 12 July 2022 (UTC)

σ

• Sigma-additive set function
• Sigma-ideal
• Sigma-ring
• σ-algebra
• σ-compact space
• σ-finite measure

Looks like these should be unified. 1234qwer1234qwer4 20:49, 20 July 2022 (UTC)

I don't think so. At least σ-compact space is a concept from topology and should be kept separate from the other topics from measure theory. PatrickR2 (talk) 04:42, 21 July 2022 (UTC)

I'm talking about the naming of the articles; not sure how your point is relevant. 1234qwer1234qwer4 10:46, 21 July 2022 (UTC)

The naming is merely a matter of directions of redirects. In your above order, the following redirects exist (blue) resp. don't exist (red):

• σ-additive set function, σ-additivity
• σ-ideal
• σ-ring
• sigma-algebra
• sigma-compact space, sigma-compact
• sigma-finite measure, sigma-finite

Moreover, I found Sigma-algebra of tau-past redirecting to σ-Algebra of τ-past (no idea what that is about). I suggest to create the red redirect. As for the direction of redirects, I don't care too much; either direction is ok (, and unification is nice to have, but not necessary). - Jochen Burghardt (talk) 11:14, 21 July 2022 (UTC)

You might pick one of these articles and start a discussion on the talk page, then put a link on all of the other talk pages directed at that one, to see if anyone has a preference between σ vs. "sigma" in the title or minds unifying the titles. –jacobolus (t) 21:46, 21 July 2022 (UTC)

If by "unified" you mean all of them should be merged into just one article, that seems like a very bad idea. Michael Hardy (talk) 00:16, 23 July 2022 (UTC)

I think he means, not merger nor any content change in the articles, but to change the titles to either (1) all use "σ" or (2) all use "sigma". JRSpriggs (talk) 05:55, 23 July 2022 (UTC)

My impression from glancing at some books is that "Sigma" is more likely to be used in titles and headings, "σ" in the body of texts. Am I correct about such usage? Limit-theorem (talk) 15:05, 23 July 2022 (UTC)

Colons

I may get around to fixing this eventually, but perhaps someone else would like to get there first: in Imaginary unit, one finds the amazing three-colon sentence The issue can be a subtle one: The most precise explanation is to say that although the complex field, defined as R[x]/(x² + 1) (see complex number), is unique up to isomorphism, it is not unique up to a unique isomorphism: There are exactly two field automorphisms of R[x]/(x² + 1) which keep each real number fixed: The identity and the automorphism sending x to −x. (It would also be nice if this statement were supported by a citation.) --JBL (talk) 22:09, 22 July 2022 (UTC)

Impressive!

The citation in complex number for that definition is actually to Bourbaki, which may be pedagogically suboptimal. XOR'easter (talk) 22:21, 22 July 2022 (UTC)

Thanks! I made a go at stripping out unnecessary technicality (after all, the property in question doesn't depend on how one chooses to represent C), so it's now a bit blander but perhaps more comprehensible. --JBL (talk) 17:44, 23 July 2022 (UTC)

Use of Latin in Mathematics

I was surprised that I couldn’t find any article concerning the use of Latin for writing European mathematics. From what I can tell the word “mathematics” does not occur in any of Medieval Latin, Renaissance Latin, Vulgar Latin, Ecclesiastical Latin, or History of Latin, and these articles have little if any discussion of the use of Latin for science in general. The article History of mathematics doesn’t really describe this in any detail. (There is an article Botanical Latin, and about 2 relevant sentences at Lingua franca#Historical lingua francas, and a somewhat related article at Latin translations of the 12th century.) I don’t read/speak Latin and know very little about this subject so I don’t feel I can meaningfully contribute about it. But it seems like a topic that belongs in Wikipedia, and I am sure there is a significant amount of secondary literature in English for anyone willing to hunt for it. Anyone knowledgeable about mathematical history want to take a crack at writing at least a few paragraphs? Edit: perhaps at Mathematical Latin or some similar title. –jacobolus (t) 21:25, 23 July 2022 (UTC)

See related discussion. In that discussion, the most recent mathematics paper I could find written in Latin was from 2006 (MR2214259). —David Eppstein (talk) 21:37, 23 July 2022 (UTC)

Bad typesetting

See this edit and the ones right after it. The typesetting in many many many places in the article is wrong by the standards of [[WP:MOSMATH]] and of standard typesetting conventions. Michael Hardy (talk) 00:41, 23 July 2022 (UTC)

Your changes are an improvement. But as an example, when changing the original ''n+2'', instead of manually inserting HTML "&nbsp ;" around each side of the plus sign, wouldn't be easier to just let Latex do the job with <math>n+2</math> PatrickR2 (talk) 02:39, 24 July 2022 (UTC)

Counting argument

Counting argument, a disambiguation page, currently links to two topics: the pigeonhole principle and combinatorial proof (mainly about bijections and double counting). There is another type of counting argument that is not linked: proof of the existence of an A that is not B, by counting both kinds of objects and finding that there are more A's than B's. Is there a good name for this type of argument, or better an existing article on it? —David Eppstein (talk) 01:05, 24 July 2022 (UTC)

Isn’t this just an application of the pigeonhole principle? –jacobolus (t) 17:41, 24 July 2022 (UTC)

It is related but I think not the same. The pigeonhole principle is about proving that functions from A to B are non-injective; here I'm more interested in proving that functions from B to A are non-surjective. —David Eppstein (talk) 18:09, 24 July 2022 (UTC)

Pigeonhole_principle#Alternative_formulations also mentions that version. —Kusma (talk) 18:25, 24 July 2022 (UTC)

So you think it would be enlightening to readers to link the phrase "counting argument" as occurring in Garden of Eden (cellular automaton)#Proof sketch or in the lead of P/poly? Probabilistic method seems closer in spirit (and would work for the P/poly example, at least). My feeling is that such a link would be baffling, because you have to pore very carefully through pigeonhole principle to find the relevant part. —David Eppstein (talk) 19:04, 24 July 2022 (UTC)

I don't really see a good place where the general argument "set B is contained in A, and strictly smaller in some sense (measure, cardinality, whatever), so A\B is not empty" is described, so perhaps better not to link it. For infinite sets (a typical application is that the algebraic numbers are countable, but the reals are uncountable, hence there exist transcendental numbers), this isn't covered by the pigeonhole principle. —Kusma (talk) 19:59, 24 July 2022 (UTC)

Moving Spinger series articles to new names

I think we should rename these two articles

• Undergraduate Texts in Mathematics → Undergraduate Texts in Mathematics (book series)
• Graduate Texts in Mathematics → Graduate Texts in Mathematics (book series)

to disambiguate them and then make the uncapitalized

• Undergraduate texts in mathematics
• Graduate texts in mathematics

names the "main" redirect" (with article possibility) or a disambiguation page.

There's a reason danger here of a person thinking these lists are a general listing of mathematical textbooks, e.g., "Undergraduate texts in mathematics" rather than the series "Undergraduate Texts in Mathematics". Since there are also similarly named series by publishers other than Springer, e.g., the Graduate Studies in Mathematics series, it also seems biased to me to have Springer capitalize on such general phrases. There a bit of tension here in our article title policy between our goal to be concise with titles and quickly get readers to the best article and our goals to be neutral and clear and unambiguous.

Similarly, I propose

• Graduate Studies in Mathematics → Graduate Studies in Mathematics (book series)

with Graduate studies in mathematics becoming the "main" redirect (with article possibility).

Thoughts? Ideas? Jason Quinn (talk) 03:13, 28 July 2022 (UTC)

This seems like a bad idea. These are well-known book series, and nobody ever says "undergraduate texts in mathematics" when talking about anything other than the Springer books. You can easily come up with another title if you want to talk about generic undergraduate textbooks. There's a reason danger here of a person thinking these lists are a general listing. These articles state clearly at the top what they are about. Doesn’t seem like a real danger. –jacobolus (t) 03:34, 28 July 2022 (UTC)

[edit conflict] Wikipedia only allows disambiguators on article titles when there is some other article that they disambiguate against. It generally only allows disambiguation pages when there are at least three ambiguous meanings for the title. These things are based on syntax (the wording of the title), not semantics (the meaning of the title). Wikipedia rules also generally allow different articles to have titles that differ only in capitalization, as long as they have hatnotes pointing to each other (see WP:DIFFCAPS). So, in order to move these series names to disambigated titles, we need something else that would also be titled with the same exact wording and capitalization. What is that something else that you are thinking of? —David Eppstein (talk) 03:36, 28 July 2022 (UTC)

I was thinking that I would start new articles at the previous titles with a more general scope. But maybe you two are right. Perhaps it's a bad idea. Jason Quinn (talk) 03:47, 28 July 2022 (UTC)

Exterior of a set

The article Exterior (topology) has nearly identical contents with the section Interior (topology)#Exterior of a set. Should Exterior (topology) be merged into that section of Interior (topology) and then deleted? PatrickR2 (talk) 01:22, 28 July 2022 (UTC)

Not deleted, but redirected. Yes, given the article contents, that seems reasonable (and if someone later finds more to write about exteriors, they can expand it out again later). --JBL (talk) 19:11, 28 July 2022 (UTC)

Yes, I meant redirected. PatrickR2 (talk) 01:51, 29 July 2022 (UTC)

I simply redirected it, as there is no information for merging. Most of the Exterior article was taken from the Interior one in 2009, and the bulk of the remainder was added to both articles in 2021 in parallel edits. Felix QW (talk) 08:27, 29 July 2022 (UTC)

Aug 2022

Weierstrass substitution → Tangent half-angle substitution

Just a heads up, since I know this came up a few times here before. I just restored Weierstrass substitution → Tangent half-angle substitution, after doing a fairly exhaustive search of old Calculus textbooks and other sources. Cf. Talk:Tangent half-angle substitution#Common name. I am now quite convinced that James Stewart was the source of this name (no other source before 1990 of the dozens I examined ever mentions Weierstrass in this context). Stewart’s (unsourced) claim that Karl Weierstrass originated/popularized this method is revealed by closer investigation to be clearly false (Euler first used it ~2 centuries before, and it was well known by Weierstrass’s time), but a few other authors in the 1990s took Stewart’s word for it and republished the claim uncritically, then it made its way into Mathworld and Wikipedia, whence it has spread widely. However, even today this remains minority usage (between them, descriptive terms like "tangent half-angle" and variants still outnumber "Weierstrass substitution" by at least 4:1 in recent academic literature, and the "Weierstrass" term didn’t exist at all in the pre-internet age). At some point in the indefinite future it’s possible the "Weierstrass substitution" name will proliferate to the extent it becomes commonly accepted throughout math/science/engineering; at that point Wikipedia can switch the name per WP:COMMONNAME. But today is not that day. –jacobolus (t) 01:14, 29 July 2022 (UTC)

I called this the "Weierstrass substitution", having learned that name from Stewart's book, in a very short publication in the American Mathematical Monthly, and Prof. Fred Rickey of the United States Military Academy at West Point wrote to me to say that that is a misnomer, and that he had thoroughly searched through Weierstrass's writings and had not found it, and that Euler had used this substitution in the 18th century. (Recall that Euler died some decades before Weierstrass was born.) I then sent an email to Steward asking about it. He replied that he was not the originator of the name, but he cited no earlier sources. I think he died shortly after that. Sone time after that, I sent an email to Rickey suggesting that he publish his findings. I never heard from him. Michael Hardy (talk) 06:10, 29 July 2022 (UTC)

Thanks for shedding more light here. I wonder where Stewart got that from. While you’re here Michael Hardy, I might mention that I started working on a draft of a more general article about the "half tangent" (that was the original name from the 17th–18th century but also has some currency in modern robotics and elsewhere; a.k.a. "semi-tangent" in the 18th–19th century, "half-angle tangent", "stereographic projection", many variations ...) in user namespace at User:Jacobolus/HalfTan. You might be interested in light of e.g. your AMM paper "Stereographic Trigonometric Identities". Right now I am mostly just gathering sources so the top part of the page there is not really reflective of what I am hoping to write (I haven’t yet started trying to make figures, structure sections, flesh out the history/applications, etc.) I wonder if you [or anyone else reading here] has any advice for sources to look at, esp. about historical sources, survey papers in fields where this is used regularly, etc. –jacobolus (t) 17:38, 29 July 2022 (UTC)

Ha ha.! :-) I think if we used Bayes' theorem we'd probably find that having something named after a mathematician is evidence somebody else discovered it first! NadVolum (talk) 10:08, 29 July 2022 (UTC)

Perhaps we're noticing Stigler's law of eponymy? Dicklyon (talk) 18:12, 29 July 2022 (UTC)

Thanks for that. NadVolum (talk) 23:46, 31 July 2022 (UTC)

Here is the publication of mine that I mentioned above: Hardy, Michael (2013). "Efficiency in Antidifferentiation of the Secant Function". The American Mathematical Monthly. 120 (6): 580. doi:10.4169/amer.math.monthly.120.06.580.
There I used the following variant of the tangent half-angle substitution:

$x={}\underbrace {\tan \left({\frac {\pi }{4}}+{\frac {\theta }{2}}\right)=\tan \theta +\sec \theta } _{\left({\begin{array}{l}{\text{Privately I think of this as}}\\{\text{the ``cartographers' tangent }}\\{\text{half-angle formula.''}}\end{array}}\right)}$

which leads to

$\sin \theta ={\frac {x^{2}-1}{x^{2}+1}},\quad \cos \theta ={\frac {2x}{x^{2}+1}},\quad d\theta ={\frac {2\,dx}{x^{2}+1}}$

and then to

$\int \sec \theta \,d\theta =\int {\frac {dx}{x}}.$

Is this variant worth mentioning in the article? Michael Hardy (talk) 18:59, 31 July 2022 (UTC)

Yes, if you explain how you derive the formulas. JRSpriggs (talk) 20:28, 31 July 2022 (UTC)

Yes, the stereographic projections from all 4 cardinal points are worth mentioning (cf. User:Jacobolus/HalfTan#Supplement and complement half-tangents). It’s also worth discussing branch cuts and other discontinuities resulting from such integrals, and possible ways of making integrals continuous (https://dl.acm.org/doi/pdf/10.1145/174603.174409 https://www.maa.org/sites/default/files/0025570x43754.di021186.02p0083t.pdf). (Though perhaps further discussion should be moved to talk: Tangent half-angle substitution.) –jacobolus (t) 16:07, 1 August 2022 (UTC)

is there any way to access NCTM journals without being an NCTM member?

Every once in a while in researching elementary-ish mathematical subjects I come across interesting looking paper titles in literature searches (or citations from other papers) in NCTM (current or former) journals, e.g. in The Mathematics Teacher. But it seems the only way to access these as an individual is to pay $150/year for an NCTM membership. Does anyone here know of alternatives? (This has come up several times in the past few months, but the specific paper I was curious about just now is Garfunkel & Leeds (1966) "The Circle of Unit Diameter"; just a one-sentence teaser isn’t enough information to assess whether there’s anything relevant in there though.) –jacobolus (t) 05:02, 8 August 2022 (UTC)

To answer my own question, they are apparently on JSTOR. Accessible from wikipedialibrary.wmflabs.org. –jacobolus (t) 05:43, 8 August 2022 (UTC)

Deleted drafts and the list thereof

At Wikipedia:Articles for deletion/Schneider's sine approximation formula, David Eppstein, XOR'easter, and I agreed that if drafts on Wikipedia:WikiProject Mathematics/List of math draft pages are deleted (usually because they were abandoned for 6 months), they should be removed from the list. Sometimes editors come by and do that, and TakuyaMurata typically reverts this. Taku will also often request undeletion for drafts that have been deleted just because they have been abandoned for 6 months. This means that if I want to get an incomplete draft out of an endless cycle of undeletion and re-deletion (which I think the three of us would argue goes against the consensus on how to use Draft: space), I either need to trim it enough to get it into article space, which seems to annoy editors with high standards, or it we need to have an affirmative deletion discussion. Many of the drafts stuck in this loop seem to be highly technical, and individual editors including some at Articles for Creation aren't necessarily able to discern whether the topic is worthy or the content is reasonable. This leads to the draft or trimmed down article being sent to a deletion discussion for discernment as the only way to get rid of it, which also annoys people for different reasons.

The practice of keeping redlinks and of undeletion was previously discussed at Wikipedia talk:WikiProject Mathematics/List of math draft pages#Keep redlinks?, and we revisited that. Other than Taku and XOR'easter (who said they were reconsidering their "keep" vote), the only other "keep" vote on deletion discussion for this list was Felix QW, who said they use Category:Draft-Class mathematics articles instead. This category is available as an alternative that does not require manual pruning when a draft gets promoted or deleted, and which also has a much more comprehensive list of math-related drafts. (It could be divided into subcategories if people think that would be helpful for navigation.) Looking at the edit history, Taku is the only editor that seems to be using the list for drafts other than their own anymore, and is certainly the only editor who needs a list because they want to undelete other editors' abandoned drafts.

It sounds like instead of making some policy about how the list should be used with respect to deleted drafts, the proposed solution coming out of the "Keep redlinks?" discussion seems to be to redirect the list of math drafts to the category of math drafts, and ask Taku to keep any list of drafts they need for undeletion or personal prioritization in their own User: space. This would save other editors the overhead of trying to use a list which is full of links to things that aren't drafts anymore or that should have been deleted by default or that actually have been deleted and are thus unreadable; the overhead of pruning the list to try to make it useful; and the unpleasantness of getting reverted when they try.

David Eppstein suggested this is the correct forum to get consensus for implementing this, so here we are. Apologies if my summary did not adequately convey anyone's opinions; I hope folks will speak for themselves here since now they've all been pinged. What are your thoughts? -- Beland (talk) 02:01, 3 August 2022 (UTC)

Incidentally, there are also many threads in the WP:AN and WP:ANI archives on Taku's misbehavior with respect to drafts (search for TakuyaMurata). This is not a new problem. —David Eppstein (talk) 02:37, 3 August 2022 (UTC)

If people want to keep draft articles around indefinitely perhaps they should use their own user namespace? –jacobolus (t) 04:11, 3 August 2022 (UTC)

If it's labeled as a draft (with an AFC template) in userspace, then it's also subject to the six-month limit. But it's easy to keep partial and not-ready-for-mainspace draft-like material on your own computers offsite (I have roughly 100 of them on my laptop). So the insistance that they must be kept on-wiki, when they really only have one person working on them, baffles me. —David Eppstein (talk) 05:09, 3 August 2022 (UTC)

I already replied but, to repeat (for others), that’s against the spirit of Wiki: in Wiki-way of development, we always make incomplete materials public. This helps feedbacks and also, for example, avoid duplicate efforts. This is why userspace drafts are not preferable, since they are less visible. Anyway, your argument is simply an argument against the draftspace per se. —- Taku (talk) 05:14, 3 August 2022 (UTC)

Sort of, yes. My general feeling is that the draftspace should be avoided by good-faith and serious editors. It is mostly a honeypot used to direct spammers to create their spam somewhere relatively harmless where it can be more easily cordoned off and disposed of. It needs some attention because some worthwhile content from naive editors (or inappropriate draftifications of good article content) ends up there as well, and should be skimmed off, but that's not its main purpose. —David Eppstein (talk) 05:19, 3 August 2022 (UTC)

"that's not its main purpose". I (and the other advocates of the draftspace) obviously disagree. Anyway, all I am saying is that there is a reason for the draftspace. —- Taku (talk) 05:38, 3 August 2022 (UTC)

To jacobolus, there is an issue of ownership and copyright: most of the drafts in the list are not started by me. So, it is tricky and controversial to move them to my userspace. If I keep them in my computer (really my iPad), then the copyright info gets lost and that could be a problem. -- Taku (talk) 05:24, 3 August 2022 (UTC)

The copyright issue is the main reason I haven't moved the three drafts I've been keeping alive off-wiki. —David Eppstein (talk) 05:31, 3 August 2022 (UTC)

If I understand, to keep track of the edit history, you need to maintain a draft in Wikipedia. Maybe there is a way to keep the edit history off-site; but that’s tricky and more work (I don’t know how to do it easily). —- Taku (talk) 05:38, 3 August 2022 (UTC)

I concede the list is mainly maintained by me. I maintain that it shouldn’t just list all the math drafts; that’s what a category is for. Therefore, if the project prefers to keep the list in my userspace instead of the project space, I do not object that. It’s not too important for me where the list is placed. (In fact, I already have a list of Japan-related drafts in my user space). —- Taku (talk) 05:18, 3 August 2022 (UTC)

I like to use LaTeX or other special mathematical formating which is available to pages in Wikipedia. I am not aware of any way to get that functionality on my own computer or elsewhere. This is a major reason why I like to keep my writings in Wikipedia, even if not in the articles themselves. JRSpriggs (talk) 07:50, 3 August 2022 (UTC)

It relatively trivial to get MathJax to render maths formula in a local webpage. Just add

<script>
MathJax = {
  tex: {
    inlineMath: [['$', '$'], ['<math>', '</math>']]
  },
  svg: {
    fontCache: 'global'
  }
};
</script>
<script type="text/javascript" id="MathJax-script" async
  src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js">
</script>

to the start of a page should kind of work. You would need a local webserver like xampp for it to function. Getting other Wikitext formatting to work is much more of a problem.--Salix alba (talk): 08:52, 3 August 2022 (UTC)

I use preview in a local sandbox when I need it. That doesn't require actually storing anything on-wiki. —David Eppstein (talk) 16:21, 3 August 2022 (UTC)

Same here, most of the time. (Writing offline reduces distractions.) XOR'easter (talk) 19:17, 3 August 2022 (UTC)

Just some observations (not proposals). What David is suggesting sounds like a Nupedia model to me, which was not a wiki and editors are supposed to submit a complete article developed privately. That model didn’t work and as an experiment Wikipedia was introduced (the rest is history). The draftspace supports two models in a sense. One aspect is an AfC; like a Nupedia, especially one editor develops a draft and submit it to be reviewed and, if passed, promoted to mainspace. On the other hand, the draftspace is also a place to develop new materials for established editors, who can just move materials to mainspace when they are done.

Editing through a preview cannot store editor history and even only one editor is editing an article, the edit history is useful (to restore previous discarded materials, etc.) Also, it is not reasonable to ask to run a local website in order to develop an article. (Doesn’t work for me, for example, as I usually edit on an iPad.)

It seems clear that the draftspace should be reformed in some fashion (but not sure how). In any case, we got to work with the system we got right now. So, for example, a list like the one in question is one tool for that. — Taku (talk) 05:52, 4 August 2022 (UTC)

It's not especially difficult to write a preliminary version of an article in a form that can survive in article space rather than draft space, and then let the collaboration with other editors begin from that point. Draft space is unnecessary for article creation, and the draft/article creation process (especially the long wait for a reviewer and the lack of subject expertise of reviewers) makes it a hindrance rather than a constructive way to work. The fact that the draft fragments you so cherish are languishing without edits for more than six months and getting deleted should be a hint to you that the draft process is not working for you, either. —David Eppstein (talk) 06:31, 4 August 2022 (UTC)

Just one more response. Like I said above, there is a problem but we got to work with what we got. I think, given what we got, the process is working: we are still getting drafts promoted to mainspace and, without my and some others’ works, a lot of valuable works would have been lost. “hints” are that we need to understand that, as is current the case, the draftspace is an article creation process we got and we simply have to do our best to work with it. It is time for you to realize the draftspace is here to stay if you like it or not. —- Taku (talk) 06:25, 5 August 2022 (UTC)

OK, since Taku is not objecting to userifying, unless someone in the next two days objects or wants to tweak the details or beats me to it, I will:

• Move Wikipedia:WikiProject Mathematics/List of math draft pages to User:TakuyaMurata/List of math draft pages
• Put a redirect from Wikipedia:WikiProject Mathematics/List of math draft pages to Category:Draft-Class mathematics articles and clean up incoming links.

-- Beland (talk) 18:28, 4 August 2022 (UTC)

Ah, I think we should at least keep the link since there might be someone interested in the list. There is no rule that we can’t link a userspace page in the project space. Ditto for redirects. I mean how is making it less visible makes our work more productive. —- Taku (talk)

It would make the math WikiProject more productive because the list is not well-maintained, and incurs maintenance overhead for anyone who attempts to use it that the category does not, including perennial disputes over the removal of redlinks. The point of userifying it would be to disaffiliate it from the WikiProject, while keeping it visible to you because you actually use it. Linking to the category makes it more visible to other WikiProject participants, who seem to prefer it over the list. -- Beland (talk) 07:01, 5 August 2022 (UTC)

No one is forcing anyone to use the list. I disagree it is not well-maintained; the list is selective and categorized, this makes it more convenient for, for example, me. Especially if it is in the userspace, it incurs no maintenance cost on the project. I am only talking about keeping the link: why it is necessary to hide the existence of the list? At least you need a consensus for that. —- Taku (talk) 07:10, 5 August 2022 (UTC)

I mean, I am a member of the project and so my list cannot be completely divorced from the project. I get you prefer a category to a list: but that preference should not be forced. —- Taku (talk) 07:20, 5 August 2022 (UTC)

I for one am quite happy to have the list in projectspace. Precisely because there is a large number of drafts that are not worth much, it seems valuable to me if a member of this project puts together drafts (initiated by him and others) that contain material they consider potentially worth having. I am also fine with not wanting half-baked articles in the encyclopedia that lead to eventually unproductive deletion discussion when the material could be used in a better way, either by potentially incorporating it somewhere else or by expanding into a well-sourced article.

I have certainly worked on some of these in the past and they have certainly enriched the encyclopedia when they reached mainspace. Felix QW (talk) 07:44, 5 August 2022 (UTC)

Like I said above, a list like this is a tool to work on the draftspace: nothing more. It’s mainly maintained by me so it may make sense to put in my userspace. But there is no need to make it secret to the others. —- Taku (talk) 07:42, 5 August 2022 (UTC)

@TakuyaMurata: If we point project participants at a userspace list that has redlinks and links to drafts that have already been turned into articles (which is what I see on the current list every time I clean it), then we will waste their time suggesting drafts they can't or don't need to work on. If they try to update the list to make it more useful for their future selves or the next editor who comes along, their time will be wasted when they get reverted because of the redlink dispute.

@Felix QW: You wrote in February on Wikipedia:Miscellany for deletion/Wikipedia:WikiProject Mathematics/List of math draft pages that you personally used the category instead. Has that changed?

What about a compromise where this list is kept but red links are allowed to be removed on sight and won't be re-added unless they turn blue again? That would eliminate the main source of conflict and the reason drafts have been getting pushed into article space or XFD. Taku can keep a secret list of deleted drafts if he wants, but the Requests for undeletion editors can also complain if the same draft is being undeleted several times, or decline an undeletion request if that keeps happening. It sounds like multiple undeletions will happen less often in the future because people have already done a lot of complaining, and the number of drafts stuck in this cycle is dwindling? Not sure how David Eppstein and XOR'easter feel about such a compromise. -- Beland (talk) 01:58, 6 August 2022 (UTC)

I wouldn't say it changed in that I now use it regularly, but since the last AfD brought the list to my attention I have looked over it to see if there is anything there which matches my interests or expertise. At any rate, I am very busy with real-life academic commitments over the last weeks and the foreseeable future, so I will probably not be using Wikipedia regularly, let alone a list of drafts... Felix QW (talk) 08:29, 6 August 2022 (UTC)

Either red links should be removed, or they need to be clearly marked with the reason for their deletion. I think the former is simpler. Either way, having to play a guessing game about what is listed and why makes the list counterproductive. I mean, it's way, way down the list of time-wasting things even just on Wikipedia, but still, creating the false impression that there's a community working on a draft or actively wanting to keep it around just leads to weird little squabbles that we could do without. XOR'easter (talk) 18:06, 6 August 2022 (UTC)

I thought we are discussing red links due to G13, automatic deletion of 6 month inactive drafts. If the deletion is due to MfD, say, then obviously the red links should be removed as not needed. Also, I don’t think the list gives a false impression. Perhaps it should be clarified but the list should only include drafts that the project think are worth working on, not mere fact it is math-related. So, there is only one reason and is really no guessing game. —- Taku (talk) 05:07, 7 August 2022 (UTC)

I can agree to remove red links as a compromise if the other members prefer that way. I didn’t know keeping red links is controversial (and those links are still in old revisions anyway so the links are not really gone.) —- Taku (talk) 07:12, 6 August 2022 (UTC)

Great. There was one redlink on the list today, so I deleted it. Can we consider this solved? -- Beland (talk) 06:52, 8 August 2022 (UTC)

Oh, and I changed the instruction on the list page that said not to remove red links; it now just says "Remove red links." -- Beland (talk) 06:56, 8 August 2022 (UTC)

"Vertex (topography)" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Vertex (topography) and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 August 8#Vertex (topography) until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Shhhnotsoloud (talk) 11:46, 8 August 2022 (UTC)

By the way, Triangulated irregular network (target of the above redirect) seems related to Simplicial complex but does not mention it. JRSpriggs (talk) 14:24, 8 August 2022 (UTC)

A TIN is of course a very specific kind of simplicial complex, but simplicial complex is a much more general type of object. More closely relevant articles include triangulation (geometry), polygon triangulation, surface triangulation, point-set triangulation triangulation (topology), Delaunay triangulation, triangle mesh, chordal graph. –jacobolus (t) 23:19, 9 August 2022 (UTC)

Construction animations

I have produced these animations to replace two of the images on the Straightedge and compass construction page - the first one was only intended to be demo (according to the original author) and the second was an overly convoluted construction according to some Wikipedians. Can anyone give me some feedback on these before I add them to the article, and can anyone suggest any other articles which might benefit from animations like these?

Basic constructions animation with labels

A straightedge-and-compass construction of a pentagon

Spiritual Directive (talk) 20:19, 4 August 2022 (UTC)

While I like animations in general, I don't think they should be added to Wikipedia articles. They distract from the text (cf. Motion perception), which can be annoying in particluar when I have to try hard to understand the text. However, this may be a matter of personal taste. - Jochen Burghardt (talk) 08:48, 5 August 2022 (UTC)

I think it's certainly a matter of topic, which is why I started with geometry/constructions. Spiritual Directive (talk) 13:47, 5 August 2022 (UTC)

Nice production value! What did you use to make it? Since you asked for feedback, here are some comments, which I hope are... constructive :)

• I think it would be more useful if the pentagon animation was less eager about erasing. The more important lines that are used in intermediate stages should stay visible for most of the time (at least until after the first edge of the pentagon is drawn). That is, we shouldn't erase them all immediately after they're no longer strictly needed for later steps. The minor details should still be erased immediately once they've served their purpose. If you're not sure how to decide what parts to keep visible and what to erase as you go, imagine what an uncluttered non-animated diagram of the same construction would contain. Like this: [35] (not 100% the same as your construction; I just mean roughly this level of detail).
• I think it's more familiar to viewers to have points drawn as dots instead of as X shapes. (Also, there was one part I especially thought was unnecessarily distracting: near the beginning, where two points drawn as + shapes rotate to become X shapes. If the points were dots, this wouldn't have been a problem.)

Adumbrativus (talk) 09:16, 5 August 2022 (UTC)

Thank you for your feedback! I used Manim to make these.

• Yes, I understand what you mean about erasing things: the segment bisector can stay, but the construction lines can be erased once the bisector is drawn.
• Using dots has occurred to me, but I found it difficult to make them stand out against the lines - maybe all dots can be another colour to make them easier to see? Not sure whether adding too much colour will be distracting - I also considered making old circles and lines grey as new ones appear to indicate the current step. This is also helpful if the animation is playing as a video and the viewer decides to pause it.

I will probably reduce the thickness of the lines if I substitute the crosses for dots and erase construction lines a little less readily, maybe that might help, although I think I'll still need a different colour for the dots. Spiritual Directive (talk) 14:00, 5 August 2022 (UTC)

@Adumbrativus, XOR'easter, and JayBeeEll: I've updated the animation, using points instead of crosses and retaining some construction lines where I deemed necessary. I also added some more colours to try and help differentiate the lines from the points - I didn't want to decrease their thickness/size because the diagrams have to be visible at a small size too. I don't think I can do anything about the zooming though, because otherwise it's unclear where the large arcs/circles are coming from.

I didn't bother updating the thumbnail yet, but you can click the old thumbnail beside this post to be taken to the new version of the file (there are no animated thumbnails for animations of this resolution, so you'll have to click on the gif again to view it on a separate page). Spiritual Directive (talk) 00:18, 10 August 2022 (UTC)

Your lovely animations are making me wish again that Wikipedia was not so completely incapable of rendering interactive content and multimedia in general. It would be really nice to have a version that could be clicked through step by step with description alongside, but Mediawiki sadly doesn’t have the tools for producing/rendering such a thing. –jacobolus (t) 10:31, 5 August 2022 (UTC)

Thank you! I think WebMs are decent for things like animations, but yeah, I wish there was a way to upload multiple versions of the same diagram/animation without just linking to different files in 'other versions'. Uploading is also a pain in that regard... Spiritual Directive (talk) 14:03, 5 August 2022 (UTC)

I agree with Adumbrativus's comments. I also found some of the abrupt zooming in and out to be distracting & in some cases disorienting. --JBL (talk) 18:04, 5 August 2022 (UTC)

Same here. This is a good start (and a good use of Manim), though. XOR'easter (talk) 17:53, 6 August 2022 (UTC)

Watch out for the file size on those gifs, because as of writing this your example is at 32.5 MB (6x higher than originally, and definitely not publishable). Depending on the tools you're using, you could address issues of both file size and motion distraction if you either used video files instead (which only load if the user clicks on them), or alternatively an interactive SVG (the latter is used for some circuits). Fwiw I liked the crosses over the dots just because that's sort of how the points would look if you were to actually construct them, but it's not a big deal. SamuelRiv (talk) 00:41, 10 August 2022 (UTC)

Thank you for the suggestion! I'll definitely upload a webm version - the large file size is just because I used the gif from Manim itself, rather than processing it myself with ffmpeg. Once I'm satisfied with the result I'll upload all 3 versions (gif, thumbnail gif and webm) properly. Spiritual Directive (talk) 01:41, 10 August 2022 (UTC)

Urysohn space vs. Urysohn universal space

Up until 8 Aug 2022 the page Urysohn space used to redirect to Urysohn and completely Hausdorff spaces (which covers the two concepts "Urysohn space" and "completely Hausdorff space"). Then recently someone had the idea to replace the redirect with a disambiguation page, disambiguating between "Urysohn space" and Urysohn universal space. (And then some well-intentioned editor went on a spree editing a bunch of other articles trying to bypass that disambiguation page, but that's beside the point.) As far as I can tell, there is no need for this disambiguation page. The "Urysohn universal space" is always specified under that name, and "Urysohn space" refers to the topological property instead.

What I am asking here is what the recommended procedure would be to undo the disambiguation page (because there were two edits A and B on the disambiguation page). Should I just do an undo of B and then an undo of A, or something else to get back to the previous state in one shot? PatrickR2 (talk) 04:11, 10 August 2022 (UTC)

You can just change the content back to #redirect [[Urysohn and completely Hausdorff spaces]] and if you want to be extra nice you can leave a message at the user talk page of Tosha who changed it. –jacobolus (t) 04:33, 10 August 2022 (UTC)

Thanks. I already left a message for Tosha on the talk page of the page. So I'll just change the contents directly then. PatrickR2 (talk) 05:53, 10 August 2022 (UTC)

Arthur Rubin

There’s been a few comments on the page Arthur Rubin regarding whether he’s actually notable enough to warrant an article. As far as I can tell his only significant accomplishment is being one of the only four-time Putnam Fellows. My feeling is that that alone probably wouldn’t make him notable, and the article should be deleted, but I figure folks here might have a more informed opinion. Thoughts? Isomorphic (talk) 15:36, 9 August 2022 (UTC)

I think some personal value judgment is unavoidable; some people find awards/competitions like Putnam and IMO to be significant, others (myself included) don't. It seems about half of the eight Putnam fellows have had notable careers, half have had basically ordinary ones. If it were up to me only the first half would have pages but I think enough people find Putnam excellence to be important/significant that it's ok to keep pages for the other half also. Gumshoe2 (talk) 17:22, 9 August 2022 (UTC)

Please review Wikipedia:Articles_for_deletion/Arthur_Rubin_(6th_nomination) before moving forward. --JBL (talk) 17:37, 9 August 2022 (UTC)

In particular, please see David Eppstein's carefully-reasoned !vote there. Without having a horse in this race, I think it's fairly clear that the article should stay. - CRGreathouse (t | c) 15:08, 10 August 2022 (UTC)

Wikipages for highly notable math papers

I recently became aware of a small number of wikipages for specific math papers [36]. There are surely a decent number of equally important papers that could be added. However I could not find much relevant information/advice on wiki notability guideline pages; has the question of such notability been discussed somewhere? For example, would papers receiving the AMS Seminal Research award [37] be considered automatically notable enough for a page? (In my opinion this would be reasonable) Gumshoe2 (talk) 18:40, 6 August 2022 (UTC)

By the strict letter of the General Notability Guideline, thousands of papers probably qualify, just for getting significant follow-up in papers by other authors. But that goes to show that strict GNG fundamentalism is a little silly, more than anything else. When it comes to textbooks, we can write about them as books, because reviews cover things like their organization, intended audience, writing style, idiosyncratic choices of topics included or excluded, etc. I'm not sure how often we can do something like that for individual papers. My guess is that often, even for important papers, there isn't a lot to write in that regard, and so it makes more sense to cover them in biographies of their authors or in articles on the subject matter. For example, "The Sphere Packing Problem in Dimension 8" is an important paper, but I'd be inclined to write about it in the articles Maryna Viazovska and Sphere packing.

I do, however, confess a great sentimental fondness for the idea of articles on specific math papers, just like I have for articles on textbooks. XOR'easter (talk) 18:55, 6 August 2022 (UTC)

I agree. However I think paper-specific wiki pages give a natural opportunity to go in some greater depth than would be more appropriate than biography pages (where, at the least, pretty much any formulas whatsoever would be out of place) or more general-purpose pages (where content has to be balanced with all other material on the page). For instance Viazovska's paper (disregarding the question of whether it is notable enough for a standalone page) already occupies a dense paragraph on the sphere packing page which I think is already somewhat unbalanced relative to the rest of the page. Gumshoe2 (talk) 19:08, 6 August 2022 (UTC)

To spring back at you with a question: why would formulae be out of place in a biography of a mathematician? The Featured article Leonhard Euler has several, for example.

Perhaps the best thing to do is to write an example of the kind of article you have in mind. At worst, the result would probably be suitable for merging if people don't like it as a stand-alone. XOR'easter (talk) 19:16, 6 August 2022 (UTC)

Good suggestion!

I suppose formulas in principle can be ok (and I have even added some formulas to bio pages), but I think should be generally avoided if possible in the interest of accessibility. The formulas on the Euler page can be understood by anyone who has taken calculus, so by my own standards they are very minimal offenders. (Although one of them, in the music section, is a little inscrutable to me.) When it comes to more modern (last 50 years) works it is significantly harder to use formulas or symbols which are understandable by any remotely broad kind of audience. Gumshoe2 (talk) 19:24, 6 August 2022 (UTC)

True, although the verbal jargon is likely not much better! XOR'easter (talk) 19:58, 6 August 2022 (UTC)

My feeling is that for a paper to have an article, there should be something about it that stands out separately from the research that the paper presents, enough to make a standalone article on the paper rather than on the mathematics. Maybe there are publications about the paper and its history (not just about the mathematical results it presents), it won a major award, it has a particularly unusual publication history, something like that. But ultimately the real standard is: some Wikipedia editor feels strongly enough about it to write an article, and the sourcing is independent and in-depth enough for it to survive deletion attempts. —David Eppstein (talk) 20:08, 6 August 2022 (UTC)

I'm thinking along similar lines: what makes a paper encyclopedic in a manner that should justify an article separate from its subject and/or author? I can think of two definites offhand: The Spandrels of San Marco and the Panglossian Paradigm, and A Structure for Deoxyribose Nucleic Acid for the famously understated foreboding: "It has not escaped our notice...." There's plenty of seminal papers out there, but how many of them present a moment greater than themselves that is iconic in this way?

Of the math-related papers I know offhand there's famously "In this paper, we present Google" (arguably performative, no more meaningful than what's on the tin), and Ramanujan has famously indecipherable papers which skip way too many steps (but is there a single iconic one?). James Gleick accused Newton in his bio of faking the experiment in his monograph on the visible spectrum, among others. I can think of clever jokes in titles, abstracts, and authors of some notable papers, but they do of course still have to be notable. Also there's iconic articles related to weapons tech and censorship, such as Morland's in The Progressive; I vividly remember the first time I saw dimensional analysis demonstrated on photos of the Trinity Test, and went looking for the original paper, but also found the popular story is riddled with myth. SamuelRiv (talk) 21:57, 6 August 2022 (UTC)

I just want to point out we have articles on mathematical manuscripts; e.g., Esquisse d'un Programme and Pursuing Stacks. So, it seems math papers should be treated similarly. I would argue that Grothendieck's Tohoku paper or Hironaka's paper on the resolution of singularities, or Mochizuki's (in?)famous papers on abc conjecture are surely of encyclopedic interests. -- Taku (talk) 08:09, 7 August 2022 (UTC)

I didn’t answer the original question. I think these articles can be handled case-by-case, as there are not many. —- Taku (talk) 19:48, 7 August 2022 (UTC)

Regarding the list of papers currently under Category:Mathematics_papers [38] it seems that one of them should probably removed from there and migrated to Category:Biology_papers [39], namely The Chemical Basis of Morphogenesis. It was written by Alan Turing, and it does use mathematics, but it seems the main purpose and contents of the paper is about biology/chemistry. Papers from other sciences routinely make use of mathematics, but that does not make them primarily mathematics papers, in the same way that not every paper written by Newton or Gauss is necessarily a mathematics paper. PatrickR2 (talk) 03:13, 8 August 2022 (UTC)

The article doesn't really give a justification, either in prose or references, for why that paper should have its own article separate from what's covered in Alan Turing and Turing pattern.

Also in browsing around it I found a very longstanding unsourced animation, if someone is familiar with the topic: Talk:Belousov–Zhabotinsky_reaction#12_years_an_orphaned_gif. SamuelRiv (talk) 04:35, 8 August 2022 (UTC)

I think it's arguable either way. It can be viewed as a paper on the theory of reaction-diffusion systems in partial differential equations, which happens to have some motivation from biology. (Or at least this is how I view it.) In my opinion it is more of a math paper than a biology paper, although the biological motivation is very interesting and strong. But I wouldn't argue if someone were to move it to the biology category. Gumshoe2 (talk) 04:43, 8 August 2022 (UTC)

Turing's paper is about the mathematical basis of pattern generation and therefore fits well as applied mathematics. Also it has huge citation counts and multiple sources specifically devoted to it as a publication, concerning its "its background, immediate reception and subsequent impact" (doi:10.1007/978-4-431-65958-7_3, doi:10.1007/978-3-642-70911-1_16, doi:10.1098/rstb.2014.0218, hdl:10776/2036, etc). So although the two articles as they stand don't clearly differentiate the publication and its background and impact from the patterns it describes and their subsequent development, I think there is clearly scope to do so. —David Eppstein (talk) 06:12, 8 August 2022 (UTC)

Sometimes books are produced which talk about specific papers or even reprint them. There's reprints in histories of maths and physics and economics and computing and even specific subjects like general relativity or quantum mechanics and there's lots in other subjects too. The ones that are reprinted definitely would qualify for having articles about them I'd have thought. NadVolum (talk) 09:31, 8 August 2022 (UTC)

I think merely being reprinted might not be a good reason to have a stand-alone article, because the mere fact of reprinting doesn't give us much more to write. But it is a signal of a paper's historical importance, and the prefaces to such collections may have information about their background and influence. XOR'easter (talk) 14:49, 8 August 2022 (UTC)

A Mathematical Theory of Communication is an example wiki article about a math paper. –jacobolus (t) 20:27, 8 August 2022 (UTC)

As soon as I read the initial posting above, I looked at the category and I did not find "Hearing the shape of a drum", so I went to that article and added the category. Moral of the story: This is, so far, incomplete. Maybe I'll start a list article for these. Or is there one already? Michael Hardy (talk) 22:18, 10 August 2022 (UTC)

. . . and now I've also added An Essay towards solving a Problem in the Doctrine of Chances. Michael Hardy (talk) 22:23, 10 August 2022 (UTC)

It's not so clear to me that Hearing the shape of a drum should be regarded as a page about Kac's article, as opposed to being about the topic of Kac's article. But I don't have a strong opinion Gumshoe2 (talk) 00:10, 11 August 2022 (UTC)

I agree that the subject of the article is broader than the paper introducing the subject, but if I were looking at that category I think this is indeed the sort of article I would be looking for, so I think the category is appropriate. - CRGreathouse (t | c) 03:18, 11 August 2022 (UTC)

That's a fair and convincing point Gumshoe2 (talk) 16:19, 11 August 2022 (UTC)

Suita conjecture

I am wearing my New Pages Patrol hat. I am requesting some editors from this project look at this recently created page and see if it qualifies for inclusion. I don't have the expertise in mathematics to determine anything about this topic. Do the references support this as a topic? Thanks in advance for any help. ---Steve Quinn (talk) 23:26, 17 August 2022 (UTC)

The classical Suita conjecture, a conjecture related to open Riemann surfaces, but technique of the L² extension theorem was used to prove it. So, I was wondering whether to create a separate article from the extension theorem, but since there seems to be a proof of the Suita conjecture that does not use the extension theorem, I decided to create a draft. --SilverMatsu (talk) 03:59, 18 August 2022 (UTC)

I have moved this draft to mainspace since the development of it seems complete (so no point to having it in the draftspace). One potential issue I can see is that WP:TOOSOON; some references in the article are only a year or two old (it is not uncommon someone announces a result and but retracts it soon after). But the conjecture itself is sufficiently old so maybe it's ok. -- Taku (talk) 07:32, 18 August 2022 (UTC)

Thanks very much for your help. I have marked the article as reviewed (and with no issues). ---Steve Quinn (talk) 17:17, 18 August 2022 (UTC)

Create a shadow angle article

Hello dear users, the shadow angle is one of the important topics of mathematics. I suggest that an article on the shadow angle be made. What do you think? AHEJJWILEMAMALIDGED (talk) 08:22, 5 August 2022 (UTC)

Can you elaborate? It's not clear just what topic you have in mind. Michael Hardy (talk) 17:23, 5 August 2022 (UTC)

See, I suggest you create the Shadow angle because this topic does not exist in mathematics. AHEJJWILEMAMALIDGED (talk) 19:09, 5 August 2022 (UTC)

Your initial post is vague and cryptic. If you want anyone to help you, then instead of repeating the same vague and cryptic statement, you should explain more clearly what you are talking about. JBL (talk) 19:43, 5 August 2022 (UTC)

By “shadow angle” are you talking about the length of a shadow cast by a gnomon? For instance as seen in Al-Battani’s “shadow table” (in modern times called the “cotangent” function). –jacobolus (t) 20:14, 5 August 2022 (UTC)

Shadow angle(به فارسی:زاویه ظلی)It is an angle drawn in a circle,I suggested that we create this article.Because this topic did not exist in mathematics.Now I wanted to ask your opinion.Did you all understand? — Preceding unsigned comment added by AHEJJWILEMAMALIDGED (talk • contribs) 04:26, 6 August 2022 (UTC)

No. Try explaining rather than just repeating the name of the topic. —David Eppstein (talk) 05:52, 6 August 2022 (UTC)

Articles can only be created in Wikipedia if there are notable sources about the topic. This means at the very least we need some book or place on the web that talks about shadow angle before anythng can be done about the topic. Can you point to something like that? NadVolum (talk) 11:13, 6 August 2022 (UTC)

This topic is in the book wiki. AHEJJWILEMAMALIDGED (talk) 11:36, 6 August 2022 (UTC)

Found out what is happening. It seeming is a literal translation from Arabic, like talking about water sheep in hydraulics. [40] shows it as the angle A between a chord and a tangent. In fact I very possibly got the wrong illustration there - thinking about it they're probably thinking of the alternate segment theorem. NadVolum (talk) 13:34, 6 August 2022 (UTC)

I believe AHEJJWILEMAMALIDGED is talking about the page b:fa:ریاضیات_پیشرفته/زاویه_ظلی in the Farsi Wikibooks. I’m not sure there’s any specific name in English for the angle between a tangent and a chord, but I agree it would be a useful angle to give a name to. –jacobolus (t) 15:27, 6 August 2022 (UTC)

It's briefly mentioned at Inscribed angle and Tangent lines to circles, but offhand, I don't recall there being a name for it. XOR'easter (talk) 20:52, 6 August 2022 (UTC)

Besides inscribed angle, this is also relevant to bipolar coordinates, Apollonian circles, radical axis, and pencil of circles. But I am not sure it needs its own article. –jacobolus (t) 00:01, 7 August 2022 (UTC)

I'm now reminded of an interesting opinion I once read at User:Colin_M/soapbox: whether we have an article on a topic may be too greatly influenced by whether it has a name. And, to add to that, whether it has a name in English. Given that notability isn't (supposed to be) English-centric, the idea of "Sapir–Whorf notability" is a little unsettling. Not necessarily an opinion on this specific topic, just a general thought. Adumbrativus (talk) 00:55, 7 August 2022 (UTC)

This is of course true. Things that have clear and widely adopted names get used where appropriate under those names; things that don’t have clear or widely adopted names get ignored, written about under a mishmash of ad-hoc names which are often either obscure or cumbersome, or just used without being named. In all of these cases until a good name emerges, those concepts are held back because relevant results are hard to search for, hard to link together, and hard to develop a coherent and cohesive body of knowledge about. Same story for good notation. –jacobolus (t) 23:08, 9 August 2022 (UTC)

Since this topic is mentioned in the Persian book wiki, it is good to make this article as well AHEJJWILEMAMALIDGED (talk) 20:24, 6 August 2022 (UTC)

Why don't you add it to the Farsi wikipedia then? PatrickR2 (talk) 02:26, 8 August 2022 (UTC)

In my opinion, we should create it first, so that other wikipedias will create it later. AHEJJWILEMAMALIDGED (talk) 11:16, 9 August 2022 (UTC)

In searching I couldn’t find any use of the phrase “shadow angle” in English, except in the context of literal shadows (like the angle of the shadow in a photograph of a crater on the moon, or the angle of the shadow of a gnomon on a sundial). So it wouldn’t really make sense to add an English wikipedia article under the name shadow angle. I personally don’t think the angle between the tangent and chord is noteworthy enough for its own article, you could try adding more detail about it at inscribed angle if you want. –jacobolus (t) 13:20, 9 August 2022 (UTC)

Do we have a mathematician, fluent in both Farsi and English, who is willing to do the translation? If not, then this is all moot. JRSpriggs (talk) 21:57, 9 August 2022 (UTC)

I think this is an important issue. This topic has been brought up in the circle chapter of the 11th grade geometry book of mathematics and physics and the theorem has been proven. There are many different types of this angle, I'd say there's nothing wrong with creating it.what is your opinion? AHEJJWILEMAMALIDGED (talk) 05:26, 10 August 2022 (UTC)

You should go ahead and create the article on the Farsi Wikipedia, citing reliable sources written in Farsi. Nobody here is going to make an article about this on the English Wikipedia, because there are no relevant sources in English. If you like you can also add material to inscribed angle as long as it is encyclopedic and based on reliable sources. –jacobolus (t) 17:57, 10 August 2022 (UTC)

Thank you very much, I write this topic in this article. The issue is resolved. AHEJJWILEMAMALIDGED (talk) 19:12, 10 August 2022 (UTC)

Just to make things very clear, we told you to write this in the Farsi wikipedia, not in the English wikipedia. PatrickR2 (talk) 02:49, 12 August 2022 (UTC)

That means they accept my theory? AHEJJWILEMAMALIDGED (talk) 04:38, 12 August 2022 (UTC)

If you want to add something to inscribed angle it needs to be based on reliable sources. Those could plausibly be in Farsi, but Wikibooks doesn’t cut it. The ideal would be something like a scholarly article describing the history of the term "shadow angle". Then you could add to the section mentioning the angle between the chord and the tangent something like "In Farsi and Arabic the angle between a tangent and chord was named the "shadow angle" (word in Farsi) by astronomer ABC in the YZ century". –jacobolus (t) 04:48, 12 August 2022 (UTC)

In the name of of Allah the Merciful

Helllo.I read several articles in English about the shadow angle, but not much about the circle, and its content is about spherical coordinates and the aspect of applied mathematics in astronomy, and it also has generalization content. In terms of application, it deals with the sun, earth, eclipse, lunar eclipse, etc. If you want, I will post the contents of other sites. AHEJJWILEMAMALIDGED (talk) 08:13, 23 August 2022 (UTC)

Just to be clear, leave that contents in the other sites and don't import it to the English wikipedia. Any such attempt will be rejected, for reasons already explained above (and specifically the arguments provided by jacobolus). PatrickR2 (talk) 05:04, 1 September 2022 (UTC)

Creation of Fourier Series Integral Essay

Hello again, the subject of Fourier series integral is based on the combination of Fourier series and integral. In general, integration is based on Fourier series and its transformation. This topic is available in English and Farsi on Google. I recommend that this article be made. — Preceding unsigned comment added by AHEJJWILEMAMALIDGED (talk • contribs) 11:16, 11 August 2022 (UTC)

Please stop telling people to create articles. We are all volunteers here. We cannot not tell anyone to go and create an article just because we think it would be useful. PatrickR2 (talk) 02:51, 12 August 2022 (UTC)

No, I do not order, it is translated into this verb in the translation. AHEJJWILEMAMALIDGED (talk) 04:49, 12 August 2022 (UTC) Please reply to my text AHEJJWILEMAMALIDGED (talk) 12:46, 14 August 2022 (UTC)

We already have Fourier series, Fourier transform, Fourier analysis, and other pages. What are you suggesting we write? XOR'easter (talk) 20:10, 14 August 2022 (UTC)

See, my suggestion is to create a Fourier series integral. Fourier series integral is related to Fourier series and Fourier transform, Fourier analysis, etc., but this topic has a separate topic and integration of Fourier series and Fourier transform or a combination of these two topics. If this science is created, it will provide more information for the concepts of Fourier series and Fourier transform, etc., there is no problem in creating it. AHEJJWILEMAMALIDGED (talk) 05:31, 15 August 2022 (UTC)

Please list at least one English-language reliable source that treats the material in the way that you want. By doing so, you help us understand what you want, and you help us avoid original research. Mgnbar (talk) 13:26, 15 August 2022 (UTC)

At least how many English sources should we bring? AHEJJWILEMAMALIDGED (talk) 03:38, 16 August 2022 (UTC)

In the name of Allah

Hello, the topic of Fourier series integration can be included in the Fourier series article, and I have seen several sources of it, you can search. AHEJJWILEMAMALIDGED (talk) 08:32, 23 August 2022 (UTC)

We can't tell what you're talking about unless you point to the specific sources that you have seen. XOR'easter (talk) 17:54, 23 August 2022 (UTC)

I have reached such sources

• https://math24.net › ...

Differentiation and Integration of Fourier Series - Math24.net

• https://uwaterloo.ca › files › a...PDF

5.3.2 Integration of Fourier series AHEJJWILEMAMALIDGED (talk) 03:30, 24 August 2022 (UTC)

You have to include the whole URL. I’m not sure where you got the part you copy/pasted here, but nobody else can make use of it. I would recommend again that you ask for help on fa.wikipedia.org where Farsi speakers can help you figure out how to use your web browser and operating system if you run into technical difficulties. You are wasting your time and other people’s time struggling with this in English. –jacobolus (t) 18:00, 25 August 2022 (UTC)

@Jacobolus: AHEJJWILEMAMALIDGED was blocked two days ago. JBL (talk) 18:59, 25 August 2022 (UTC)

Creation a general page for two articles, area and volume

Hello, excuse me, I had two arguments for two theories and these two theories are very important, one for Fourier integral series and one for this topic of area and volume.

I believe that the concepts of volume and area in the article are not continuous and all of them are scattered and discrete, as well as the concepts of surface and volume such as era, enclosure, three-view drawing... are they even discrete or not. I recommend that we create a general article for volume and area and write their concepts such as period and enclosure, etc., so that there is a general and continuous concept for these two topics and the concepts of these two topics compared to the rest of the article. Through their discrete and reading through their reference or continuous article.Thanks AHEJJWILEMAMALIDGED (talk) 11:48, 11 August 2022 (UTC) Please reply to my text AHEJJWILEMAMALIDGED (talk) 12:47, 14 August 2022 (UTC)

What is wrong with the existing articles on area and volume? You are free to improve them, if you want to. JRSpriggs (talk) 20:04, 14 August 2022 (UTC)

Given the patchy grammar of AHEJJWILEMAMALIDGED's contributions here, I would suggest instead improving the coverage for the Wikipedia in a language they are more fluent in. —David Eppstein (talk) 21:36, 14 August 2022 (UTC)

There is no problem with two articles, area and volume, I say to add a general page for these two sciences and their concepts for more information. Like the analysis of mathematics, which defined its branches and wrote the main article of these concepts.that both the area and volume and their concepts should be in the form of separate articles and in the form of a general article and a complete and continuous reference. AHEJJWILEMAMALIDGED (talk) 05:21, 15 August 2022 (UTC) Mr. David Eppstein Hello, I am fluent in English AHEJJWILEMAMALIDGED (talk) 05:43, 15 August 2022 (UTC)

Sorry, but this is incoherent. --Kinu ^t/_c 12:20, 15 August 2022 (UTC)

I think a link to whatever it is that is wanted in Arabic was put here that would be best. Probably Google translate is being used and it isn't getting the meaning over properly. Too many words in mathematics mean smething quite differentin other contexts. NadVolum (talk) 12:47, 15 August 2022 (UTC)

Please list at least one English-language reliable source that treats the material in the way that you want. By doing so, you help us understand what you want, and you help us avoid original research. Mgnbar (talk) 13:27, 15 August 2022 (UTC)

Perhaps you a looking for something like Measure (mathematics). JRSpriggs (talk) 02:12, 16 August 2022 (UTC)

Hello, this article does not have any incoherent or unrelated topics. I can create a list of sources through English websites and books to write this page. I mean the area and volume article is not a measurement (mathematics) article, but related to It is.I am sure that this article will be widely viewed. We collect articles about volume and area and other concepts that are not made in this wiki from other sources and then create them. — Preceding unsigned comment added by AHEJJWILEMAMALIDGED (talk • contribs) 04:03, 16 August 2022 (UTC)

I think it would be best if you supplied something in a language you are proficient in rather than trying to do something in English. NadVolum (talk) 21:55, 16 August 2022 (UTC)

In addition to Persian, I am also fluent in English AHEJJWILEMAMALIDGED (talk) 04:15, 17 August 2022 (UTC)

You are not able to talk about mathematics in English with proficiency. It would be much easier for us to see what you are talking about in Persian and try and work out what you want from that. NadVolum (talk) 09:53, 17 August 2022 (UTC)

Yes, you are right, I am not very fluent, but I know to some extent. AHEJJWILEMAMALIDGED (talk) 14:21, 17 August 2022 (UTC)

Now let go of this issue. Our most important topic is about volume and area, not about mastering the English language, it is important that you present the main idea in any way. I told you my idea with this level of English. AHEJJWILEMAMALIDGED (talk) 14:31, 17 August 2022 (UTC)

I am grateful for the volume and area article that you are reviewing. However, it would be very good if the article that covers both area and volume and their concepts is created because:

• Through a general article and at the same time, we have a reference on the two topics of volume and area, and its topics are fully explained, and by reading it, people get to know their concepts in addition to area and volume. *We also have a separate article on volume and area and its concepts.AHEJJWILEMAMALIDGED (talk) 14:39, 17 August 2022 (UTC)

AHEJJWILEMAMALIDGED, I would recommend you you try working on the Farsi wikipedia instead; or if you insist on discussing here, perhaps you could find a fluent bilingual friend who can clearly relay your thoughts to an English-reading audience. English Wikipedia already has articles about area and volume, and nobody here understands what you are trying to say. –jacobolus (t) 17:54, 17 August 2022 (UTC)

Well, tell me from the beginning, my dear Now I will explain to you clearly and completely AHEJJWILEMAMALIDGED (talk) 04:41, 18 August 2022 (UTC)

It is true that the article on area and volume has already been made. But I say that we shall we come create an article that collects all the principles and concepts of area and volume, as well as other concepts such as:

• Rotation
• surrounded volume
• Drawing three views
• Extensive drawing of geometric *volumes
• section
• Cutting and...

It is also written in it.

This article is intended to be a complete and reference article on area and volume. AHEJJWILEMAMALIDGED (talk) 04:41, 18 August 2022 (UTC)

Why don’t you stop discussing possibilities here and go ahead and write that article in Farsi (or write a blog post or pamphlet or something in some other venue), and then people can look at it under machine translation or you can perhaps find someone fluent in both Farsi and English to translate it. From your brief description here, this sounds like a mishmash of several unrelated or loosely related topics that would be a nightmare to integrate as a Wikipedia article. Nobody here thinks this is an article that needs to be written, has any idea how to structure or write that article, or is going to write one for you based on a loose request. You are wasting your time. –jacobolus (t) 07:00, 18 August 2022 (UTC)

I understand completely What is You mean

1. People think I use machine translation
2. I need to find someone who is fluent in English and Persian to create this page I gave few ideas
3. I didn't fully explain how this article is
4. I am wasting time with mysterious and complicated words — Preceding unsigned comment added by AHEJJWILEMAMALIDGED (talk • contribs) 08:17, 18 August 2022 (UTC)

No, you did not understand what I meant; you are misunderstanding nearly every point. I didn’t say you are using machine translation or should find someone else to create your page. I said you should write something in Farsi, and then afterward someone could use machine translation to read it or you could find a translator. Your further efforts to “fully explain” are not clear and coherent enough English for people to understand what you are aiming for, which is why people are recommending you write your imagined article in Farsi instead. You are wasting time (yours and other people’s) not because of “mysterious words” but because nobody here is going to act based on comments of this type even if you repeat them a few more times. –jacobolus (t) 06:13, 19 August 2022 (UTC)

Oh, you mean that I should speak in Persian, right? AHEJJWILEMAMALIDGED (talk) 11:11, 19 August 2022 (UTC)

Not on this talk page. But perhaps you would find it easier to make yourself understood on https://fa.wikipedia.org/ rather than here on en. —David Eppstein (talk) 16:02, 19 August 2022 (UTC)

Yes, I also participate in Persian Wikipedia and I said my argument, but I also contribute in Persian and English. AHEJJWILEMAMALIDGED (talk) 04:09, 20 August 2022 (UTC)

It is an idea for this article.

1. The article must have a History.
2. The article should also have a topic such as definitions
3. The article should also explain other concepts (such as rotation, section, perimeter, etc.)
4. Then the article should show the area and volume of geometric volumes and explain the method of proving it.
5. The article should have a gallery to show the overall picture of geometric volumes.
6. The article should have a topic called application and importance
7. The article should be useful at the same time
8. The article should also have a bibliography for area and volume.

The area and volume article should have a history because people should know how area and volume were created and what are their other events and also get information about the scientists who worked in the field of area and volume. The article must also have definitions, because the definitions must explain about area and volume, about geometric volumes and non-geometric volumes, about prismatic, spherical, pyramidal volumes, etc.

The article should also have concepts that are about concepts such as rotation, circumference, section, etc., so that people can know more about them.

The article should also show the formulas of area and volume of geometric shapes and write their proof methods. This topic is an important topic in the article.

The article should have a gallery containing photos of geometric shapes such as prisms, pyramids, spheres, etc. so that people can get to know them more.

The article should have a topic called importance and application, that is, people should know what is the use of area and volume in life and what is its importance in mathematics and life.

The article should also be useful so that people use it more. Because one person may use it for conferences for example.

Nair article should have a bibliography topic so that people can read other topics through other references. AHEJJWILEMAMALIDGED (talk) 05:14, 19 August 2022 (UTC)

The articles area and volume are adequate as presented, and despite the OP's (repetitive) arguments, I see no logical reason for an article that redundantly shoehorns the two topics (along with other seemingly tangential information) into one. --Kinu ^t/_c 16:00, 19 August 2022 (UTC)

Why doesn't it make sense? I have already said what my purpose is and explained it in general — Preceding unsigned comment added by AHEJJWILEMAMALIDGED (talk • contribs) 03:57, 20 August 2022 (UTC)

I have to agree with the other users. area and volume already exist and seem to be quite reasonable articles, and I don't understand what AHEJJWILEMAMALIDGED is trying to accomplish. Meters (talk) 05:33, 21 August 2022 (UTC)

AHEJJWILEMAMALIDGED, at the moment, you literally have only eight contributions to the Article namespace, and basically all of the ones to mathematics-related articles have been reverted. Perhaps something is being lost in translation; despite what you say, I am concerned (as are other editors, based on their comments here) that you are not able to communicate effectively about mathematics in English. It's not that your ideas are bad, per se; it's just that they don't seem to be an improvement on what exists. Given that, I would recommend that you drop the stick and try to focus on improving the encyclopedia (perhaps not necessarily this one, but the Farsi one) in other ways that you are comfortable based on your knowledge and communication skills. --Kinu ^t/_c 05:50, 21 August 2022 (UTC)

I have to agree with others here and say that I cannot understand what AHEJJWILEMAMALIDGED is trying to communicate. My best guess is that they want a page which illustrates area and volume as being two particular manifestations of one single framework (such as Hausdorff measure?) Gumshoe2 (talk) 06:58, 21 August 2022 (UTC)

Hello,Gumshoe2 you almost understood my theory My theory is to create an article that includes the concepts of area and volume and other concepts in the context of the article. this article should also have a topic generalization and general structures. — Preceding unsigned comment added by AHEJJWILEMAMALIDGED (talk • contribs) 19:02, 21 August 2022 (UTC) AHEJJWILEMAMALIDGED (talk) 07:16, 21 August 2022 (UTC)

In the name of God

The article on area and volume was found in many sources, which has both theoretical and practical aspects and has the formula of area and volume and their proof method. About other concepts such as: Rotation, encirclement, three-view drawing, section, etc. have separate sources. Another source also said about its generalization. AHEJJWILEMAMALIDGED (talk) 08:26, 23 August 2022 (UTC)

Saying that you have seen a source, without any details, is not helpful. Please specify the URL or at least give the name so that we can find it with Google or in a library. JRSpriggs (talk) 17:47, 23 August 2022 (UTC)

We can collect area and volume content And the formulas of area and volume of geometric volumes and the method of proving them and the contents of period, section, conic section also created this article. I found all the materials of three-dimensional drawing, perimeter, section, etc.

• Area
• Volume
• rotation (geometry)
• Conic section

This content can be selected as a source. I have to refer to other sources. AHEJJWILEMAMALIDGED (talk) 03:53, 24 August 2022 (UTC)

We keep asking you for clarification and sources, yet you keep posting the same almost incoherent ramblings over and over again, both here and in other threads. I'm sorry, but this is basically disruptive editing at this point, and I am blocking as such per WP:IDHT. We've wasted enough time here. --Kinu ^t/_c 04:04, 24 August 2022 (UTC)

Blowing up in differential equations

Do we have an article to which the general concept of blowing-up in differential equations can be linked? For instance it is mentioned (without a link) in point five of Navier–Stokes existence and smoothness § Partial results, at Harmonic map § Singularities and weak solutions, at Differential inclusion § Theory, at Method of averaging § Example: Restricting the time interval, etc. It needs to be disambiguated at Blowing up (the unrelated concept in algebraic geometry) for which at least some of the incoming links are wrong (for instance one at Saruhashi Prize) but to do so we need an article to link in the hatnote and on blow up (disambiguation). —David Eppstein (talk) 20:45, 20 August 2022 (UTC)

Are you referring to what happens when the Taylor series no longer converges to the function? See Natural_logarithm#/media/File:LogTay.svg. JRSpriggs (talk) 22:15, 20 August 2022 (UTC)

I'm referring to a phenomenon where the solution to a differential equation blows up to an infinite (in some sense) value in a finite time. It is not about approximations to the solution; the solution itself blows up. Another relevant example is alluded to near the end of Painlevé conjecture. —David Eppstein (talk) 23:17, 20 August 2022 (UTC)

It may not be the best location, but would you like to add it to the Glossary of calculus ? --SilverMatsu (talk) 01:21, 21 August 2022 (UTC)

Comment-- to my knowledge "blowup" is in general (even beyond PDE) only a piece of colloquial/informal vocabulary which analysts use to say that something converges to infinity; in certain contexts it takes on a basically fixed meaning. For instance I would have no idea what someone really means if they just refer to "a PDE which blows up" or a "solution of a PDE which blows up"; I know exactly what someone must mean if they say "a Ricci flow on a closed manifold with finite-time blowup"; I could not be sure if they say "a Ricci flow on a noncompact manifold with finite-time blowup" although I could probably guess what they have in mind. A more general phrase like "blowup of Navier-Stokes" or "blowup of Ricci flow" has pretty much no 'a priori' or inherent mathematical meaning, although of course they might happen to be defined 'de facto' by general agreement in research community; this seems to be the case for Navier-Stokes. (Some people also talk about blowup at infinite time, e.g. [41].)

Give such context-dependence, it might be inappropriate for its own page. Maybe I agree with SilverMatsu that it is best to add to some glossary page, with an appropriately loose definition in the spirit of what you provided above to JRSpriggs. And then on each particular wikipage (e.g. Navier-Stokes, harmonic map, Ricci flow, etc) to specify what exactly it is typically taken to refer to in that context.

I should also point out the the very closely related phrases "blowup analysis" or "blowup limit" by which solutions which "blowup" are often studied. However these are also used equivalently in situations where it would be a little unusual to refer to "blowup" directly. For instance (starting with Sacks-Uhlenbeck) one may study singular points of weak harmonic maps by blowup analysis and blowup limits. This is exactly analogous to studying singular points of harmonic map heat flow, also by blowup analysis and blowup limit. However only the latter (I conjecture: only for psychological reason that former does not involve a variable commonly called "time") is commonly referred to as having a PDE solution which blows up. However in both cases one could specifically say "the gradient of the solution blows up along a certain sequence of points", and this would be well-understood (simply in the most general sense of convergence to infinity), and coincides with the commonly-understood notion of "solution blowup" in the heat flow case (when on a closed manifold). Gumshoe2 (talk) 06:47, 21 August 2022 (UTC)

This detailed and careful answer is very helpful; thanks! It is also why I didn't just go ahead and do something about this myself: getting the subtleties of this terminology right is beyond my expertise. But even if it is not well formalized as a general term, I think the lack of disambiguation of it at the algebraic geometry page and the disambiguation page is a problem, one that has led to wrong links. If there's something we could link to at those two pages, even a glossary page, that would help. —David Eppstein (talk) 07:00, 21 August 2022 (UTC)

Yes, completely agreed! Gumshoe2 (talk) 07:06, 21 August 2022 (UTC)

Calculus

I put some time into brushing the cobwebs out of the calculus article, since it looked both important and highly visible (in excess of 800K views per year). However, I'm increasingly busy and increasingly burned out. Would anyone like to try picking it up and getting it to GA status? XOR'easter (talk) 21:38, 14 August 2022 (UTC)

This article seems to me to have the wrong scope and organization for an article called "calculus". History is interesting and important but should be deferred, and the first few sections should try to introduce calculus in a more general way and describe how it is used in the world. In particular, there should probably be a more substantial discussion of differential equations as a basic tool of science and engineering. There should be some discussion of the calculus of variations. There should be more coverage of the calculus of finite differences and multivariable calculus ("multivariable", "differential form", "Stokes’s theorem" are not anywhere mentioned). The history section itself is also far too focused on (a) a priority dispute between Newton/Leibniz, and (b) disputes among mathematicians about axiomatic foundations, while almost entirely neglecting the history of the *use* of calculus (Euler and the Bernoullis are more important to the history of calculus than Weierstrass or Lebesgue). I don’t know if there are any good model articles out there with the right scope, but folks might want to start from the perspective of http://www.science.smith.edu/~callahan/intromine.html –jacobolus (t) 17:41, 16 August 2022 (UTC)

The history could be cut down drastically as there is a good separate article on the history. The history article has rather too short a lead, if it was given a proper summary in the lead that could be used in the calculus article. NadVolum (talk)

The existing sections of history could be cut down (as a somewhat unbalanced) but the history section overall could be expanded. I just think it should go in the middle or end of the article rather than the very beginning. The history of calculus article could be very dramatically expanded. –jacobolus (t) 01:08, 17 August 2022 (UTC)

What's the point of expanding the history section? It should just be a summary without any sections and point off to the proper article on the history of calculus. As it is at the moment a person is liable to do changes to the section on history in the calculus instead of the proper history article. It harms both articles to have a long section on the history in the wrong place. NadVolum (talk) 08:27, 18 August 2022 (UTC)

As a general rule, I’d prefer if Wikipedia authors tried to figure out the amount of material and the appropriate structure in any particular section likely to best serve the expected audience(s) for the article. So far as I know there’s no manual of style rule/guideline that a section summarizing a longer sub-article be of any particular length or structure. In the case of calculus the history is relevant and important and a summary that takes several paragraphs and maybe a few sub-sections seems fine. The article about history of calculus would ideally be greatly expanded; it currently mostly cuts off at ~1700. –jacobolus (t) 17:30, 21 August 2022 (UTC)

I'll have a go at updating the History of calulus article with the various different bits in the history section of calculus. It is not trivial, they have diverged quite bit and I'm not a fast worker. NadVolum (talk) 09:49, 18 August 2022 (UTC)

In my opinion, we should create a topic in this article called concepts so that the concept of integral, differential calculus, derivative, etc. will be presented in it.what is your opinion? AHEJJWILEMAMALIDGED (talk) 04:20, 17 August 2022 (UTC)

The naming of cats

There is a discussion on renaming Category:Set families at Wikipedia:Categories for discussion/Log/2022 August 17 § Category:Set families. More input from people with some mathematical expertise and less from Wikipedia category naming specialists might help. —David Eppstein (talk) 07:32, 23 August 2022 (UTC)

Reconstruct

I feel that this GA article, Derivative, has many problems which need to reconstruct as soon as possible. I'll make a new section on a talk page once I reread it. Do you mind if I ask? Dedhert.Jr (talk) 03:15, 24 August 2022 (UTC)

The article does look under-footnoted, by modern standards. My guess is that much of it dates back to the early years of Wikipedia. (Its GA reassessment was in 2007.) Fortunately, finding references for standard material is not so difficult; mostly it's a matter of picking which of the many books on the shelf are decently readable and not too hard to get hold of. The textbooks referenced in the Calculus article would be a good start. XOR'easter (talk) 16:18, 24 August 2022 (UTC)

XOR'easter I already gave my opinion and commentary on a talk page. And actually, there are a lot of things that I have to discuss it. You can reply here. Regards, Dedhert.Jr (talk) 15:38, 25 August 2022 (UTC)

Metric space and Metric (mathematics)

Recently I started trying to spruce up the metric space article. The more I think about it, the less the split between that and metric (mathematics) makes sense. For example, the section on examples of metric spaces, if it were better organized, could have a subsection on different metrics on $\mathbb {R} ^{2}$. But then those are examples of metrics on the "same" space!

The reasons for the split are summarized on a talk page, but I don't think they're great reasons. The articles duplicate each other to some degree and would have to duplicate each other even more to achieve really good exposition. The main topic that's covered in metric (mathematics) but not metric space is various weakenings of the metric axioms. Does it make sense to rename that article to something like generalized metric to focus it on this topic, and merge the rest into metric space? I would just go ahead and do it but I'm not sure about the naming, plus it's marked as a "high priority" article so someone obviously thought it was important.

Any comments or better naming suggestions? --platypeanArchcow (talk) 03:28, 24 August 2022 (UTC)

I am in complete agreement with you, and the given reasons for splitting are very weak. In my opinion the articles should just be merged, although I think it would also be ok to keep the second article purely for generalized metrics. Gumshoe2 (talk) 03:56, 24 August 2022 (UTC)

What Gumshoe2 said. I too find it is hard to justify having separate articles. However, it does seem to be a case that a metric can mean something more general than one in a metric space; just as a space can mean more than a topological space. For example, it seems a bit weird to have a discussion on a metric tensor in a metric space article. (I am not specialist) but a metric that varies from a point to a point should be discussed in some geometric fashions, the metric space article is not a good place for that. Maybe we need metric (geometry) or something, which discusses Riemannian metric, Kahler metric, etc. —- Taku (talk) 09:31, 24 August 2022 (UTC)

There is a difference between how the term metric is used in Geometry and in Differential Geometry. In the former a metric is a distance function on the space, while in the latter a metric is a family of inner products on the tangent spaces of the manifold, or the equivalent rank two tensor field. Both of these are distinct from a metric on a vector space, although the second is obviously closely related to it. Shmuel (Seymour J.) Metz Username:Chatul (talk) 15:49, 25 August 2022 (UTC)

Hartshorne here says “A distance function on a Hilbert plane is a function d that to each segment assigns an element of an ordered abelian group G such that ...” – is it worth mentioning such definitions? Everything on Wikipedia defines distances as real numbers under addition rather than elements of an arbitrary ordered abelian group. –jacobolus (t) 10:11, 24 August 2022 (UTC)

I would say yes, although I'm not sure where. IAC, wiki discusses, and should discuss,complex inner products. A case could be made for discussing generalizations to vectors spaces with normed scalar fields or to modules with normed scalar rings, but generlizing to arbitrary groups is a bit dicier. IMHO, we need to hear from a SME on such topics. Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:03, 25 August 2022 (UTC)

Good points from everyone, thanks. I like the idea of just merging the articles. There are several separate "related topics" that need to be discussed or at least mentioned and linked in this article:

• The relationship between metric spaces and topological spaces, as well as in-between structures like uniform spaces
• Metric spaces with additional structure (e.g. Riemannian, sub-Riemannian, and Finsler manifolds, length spaces, normed vector spaces)
• Weakenings of the metric axioms, like quasi-, semi- etc. (I'm still tempted to silo detailed discussion of those into a separate article, maybe after merging with pseudometric space, because they don't feel important enough to me to discuss at length in the main article)

and optionally also

• Other modifications of the axioms (like metrics on multisets and the abelian group-valued metrics mentioned by jacobolus)

I think metric tensor is the right place for what Taku is proposing. We already have a metric disambiguation page which links to both concepts. --platypeanArchcow (talk) 15:44, 24 August 2022 (UTC)

I think manifold-specific discussion (metric tensors and so on) is pretty remote from what the metric space article should be. Sure, manifolds should be mentioned, but only briefly. I don't think there's any warrant to start talking about tensors in an article called "metric space". The topology discussed in the metric space article should be mostly point-set topology.

I guess maybe that means I'm against the merge. What might make sense to do is to move the more general content from metric (mathematics) into metric space, and the manifold-related content into metric tensor. Then the metric (mathematics) redirect could probably be deleted or disambig-ified. --Trovatore (talk) 16:07, 24 August 2022 (UTC)

To be clear, I agree with this. And metric (mathematics) currently has only a brief two-paragraph discussion of Riemannian manifolds, about as much as I intend to put in metric space. --platypeanArchcow (talk) 16:38, 24 August 2022 (UTC)

As analogy let me point out that a topological space defines a homology group, and that this is an important source of groups. But it would be misuse of language to conclude that a topological space is an example of a group, or that it is an example of something like "generalized group".

In exactly the same way, a (continuous) Riemannian manifold defines a metric space, i.e. a (continuous Riemannian) metric tensor defines a metric. Also in exactly the same way, it misuses language to say that a Riemannian manifold is an example of a metric space, or that a metric tensor is an example of a metric, or that a Riemannian manifold is an example of "generalized metric space". Just pointing this out in case there is any confusion.

Anyway, I agree with trovatore that a disambiguation page could be good, since differential geometers often use "metric" to implicitly refer to a Riemannian (or Finsler, etc) metric. But I think the material presently on this page about Riemannian metrics is all appropriate to a metric space page. However (per the above comments) I think it should be phrased and contextualized in a more proper way. Gumshoe2 (talk) 16:46, 24 August 2022 (UTC)

This brings up a good point: should metric (mathematics) redirect to metric space, or to metric (disambiguation) (which already exists)? --platypeanArchcow (talk) 16:48, 24 August 2022 (UTC)

Another article in the same general semantic space is distance. Obviously this should be a more informal article aimed at people with less math background, but covering overlapping ground. That said, I don't have a clear sense of what it should cover. It would be nice if someone could take the lead in making it coherent and useful. --platypeanArchcow (talk) 18:24, 24 August 2022 (UTC)

One potential difficulty with reorganization seems to be what to do with incoming links. There are a lot of links to "metric (mathematics)"; many refer to metric in a metric space but some other use metric in a (differential) geometric context. Redirecting metric (mathematics) to metric (disambiguation) means all of those links need to be modified, which actually is a right thing to do since "metric (mathematics)" is too generic and there shouldn’t be links to it. -- Taku (talk) 05:30, 25 August 2022 (UTC)

Well, I just did my part: Global LGBTQI+ Employee & Allies at Microsoft no longer links to that page. LOL. --platypeanArchcow (talk) 06:06, 25 August 2022 (UTC)

In all seriousness, the topic of that page is/was metrics in the metric space sense, not the differential geometry sense, so if there were incoming links referring to differential geometry sense they were already incorrect. --platypeanArchcow (talk) 06:10, 25 August 2022 (UTC)

Given what you all said above, I think the best solution is to merge the material at metric (mathematics) into metric space, and to allow metric tensor to continue to be the article covering the (quite different) notion of metric on a Riemannian manifold. Any link to metric (mathematics) should then link to either metric space or metric tensor, depending on what is intended. Ebony Jackson (talk) 21:40, 25 August 2022 (UTC)

OK -- the deed is done. I did a big rewrite of metric space and incorporated almost all the material from metric (mathematics). I also cleaned links to metric (mathematics) that needed to go somewhere else (though I may have missed some). Physicists were the big offenders, most of the wrong links needed to go to metric (general relativity). I redirected metric (mathematics) to metric space for now in order for link cleanup to happen. Eventually it can be redirected to metric (disambiguation) after the dust settles. As for metric space, it still needs some work: expanding the history section, adding more references and cleaning up the references that are there. But I need to get back to my actual job. Please let me know if you have any comments on the rewrite! --platypeanArchcow (talk) 01:10, 30 August 2022 (UTC)

Recent addition of fringe definition of Dirac delta as function to hyperreal numbers

I just came across Dirac delta function, where somebody has just added a reference to a paper proposing to define it as a function to hyperreal numbers in a very prominent fashion (it's the very second sentence on the page, as well as later on). This should probably be reverted, or the mention of it at least downgraded to a side remark somewhere in the history part, as it in my estimation is an unknown, fringe interpretation of an otherwise very widely used tool, and thus misleading to the general audience. As I am not too familiar with the English Wikipedia conventions for mathematics, I don't want to get involved in a dispute myself, but as the page is marked as a Good Article, I thought I would flag it here. --Clickingban (talk) 15:31, 27 August 2022 (UTC)

Thanks to pointing this. I have reverted this addition. Apparently, the editor who added this reference ignored that this was already discussed in section Dirac delta function § Infinitesimal delta functions. D.Lazard (talk) 15:58, 27 August 2022 (UTC)

It's not even altogether clear that this fringe definition is workable. Michael Hardy (talk) 19:00, 27 August 2022 (UTC)

Well it was published in a journal by a garbage publisher (MDPI) so there's no particular reason to suspect it would be correct, valid, or even sensible. JBL (talk) 20:33, 27 August 2022 (UTC)

Clarification in case anyone else goes through same confusion I just went through for a few minutes- the added intro text (presently removed from page) is to a MDPI publication but the original text linked to by D.Lazard is from a reputable journal, the Journal of Mathematical Physics. Gumshoe2 (talk) 23:17, 27 August 2022 (UTC)

This is also an odd citation though, somehow. It is a citation to a 1-page commentary on a paper by the same author in the same journal in 2006.

Maybe someone with a bit more clue in this area than me could check that this is actually a sensible citation, rather than citing the original paper (or another paper cited in the commentary note)? Felix QW (talk) 09:50, 28 August 2022 (UTC)

I don't know anything about nonstandard analysis but it looks to me like the wiki page correctly says exactly what the article contains. Of course, there could still be better references. Gumshoe2 (talk) 19:24, 28 August 2022 (UTC)

Just some remarks. (1) There is no such thing as a "fringe" definition in mathematics. Either it is a correct definition of an object (or space or whatever), or it is not a definition at all. There is nothing in between. Your personal dislike does not make a definition "fringe": your personal opinion is irrelevant. (2) The definition of the Dirac delta as an ordinary function is published in the journal Axiom which is indexed by the Science Citation Index of Clarivate. That makes it a recognized journal: there is no other criterion of demarcation between "good" and "bad" journals. Your personal dislike of the publisher doesn't make it a garbage journal: your personal opinion is irrelevant. (3) The definitions of the Dirac delta referred to in the section section Dirac delta function § Infinitesimal delta functions concern definitions as a function on the hyperreals. The definition in Axioms is a definition on the reals, which is not the same. (4) This is a wiki page about the Dirac delta, not your personal textbook on analysis. As such a new introduction should be included, even it makes other info obsolete. Such is the nature of scientific progress. For these reasons, I have restored the version with the new definition. — Preceding unsigned comment added by SwissGuy22 (talk • contribs)

"There is no other criterion of demarcation between "good" and "bad" journals." -- there are plenty. For example, Axioms is not indexed by Mathematical Reviews, which I and many other mathematicians would trust over SCI. Regardless, it is Wikipedia policy not to give undue weight to particular topics. Until this new definition is used in many other papers and (for a subject as basic and important as the Dirac delta function) textbooks, it should not be in the first paragraph of the article. --platypeanArchcow (talk) 00:24, 29 August 2022 (UTC)

You may have a fair point with MR but in the whole of science, being indexed in Clarivate's SCIE is widely regarded as a criterion for recognition or reliability of a journal. There is not a single professional scientist who would say that a journal indexed in Clarivate's SCIE is fraudulent or garbage. Then we might as well say that inclusion in the Ivy League is not a sufficient criterion for recognition of a university: why not start claiming that Harvard is a garbage university because anyone with money can get in and it sells courses that one can get for less than 1% of the money at a European university? You also may have a fair point with your comment about undue weight. But if we want to apply that policy consequently, we should start deleting references to isolated works of (often American?) scientists who use wikipedia as a PR forum. SwissGuy22 (talk) 12:02, 29 August 2022 (UTC)

If your assertions were valid then you would have a point, but (1), (2), and (4) are all certainly false. --JBL (talk) 00:42, 29 August 2022 (UTC)

If you say that (1) is false then you say that there *is* such a thing as a fringe definition in mathematics. That is utter nonsense and you know it: there is not a single scientific publication (article, textbook) where objective conditions have been established under which the predicate "fringe" applies to a mathematical definition. The predicate "fringe" is merely a pejorative used outside the framework of a scientific discussion to express one's personal dislike of something. SwissGuy22 (talk) 11:36, 29 August 2022 (UTC)

See WP:Fringe theories for a general definition of "fringe" that applies here. The aim of your edit is to replace the standard definition of Dirac delta (the one that appears in every textbook) by a different one that is not even mentioned in any textbook. This suffices definitively to qualify your definition as fringe. This has nothing to do with any personal dislike of something. D.Lazard (talk) 13:27, 29 August 2022 (UTC)

+1. JBL (talk) 17:05, 29 August 2022 (UTC)

The aim was not to replace the standard definition of the Dirac delta, but merely to mention that there is a new definition as an ordinary function on the reals. Good to know that Perelman's proof of Thurston's geometrization conjecture was just fringe mathematics before 2010 (when it appeared in a textbook). SwissGuy22 (talk) 08:58, 30 August 2022 (UTC)

People who solve millenium problems generally have a degree of self-respect that precludes publishing their work with MDPI and trying to self-promote on Wikipedia. --JBL (talk) 17:15, 30 August 2022 (UTC)

Then talk to your buddy D.Lazard who created his own wikipedia page Daniel Lazard SwissGuy22 (talk) 16:09, 31 August 2022 (UTC)

I don't know if it helps but there is a definition of Dirac delta in the framework of Sato's hyperfunction. This definition does not appear in the intro and I wouldn't say it is a *fringe* definition. The point is that the intro should only mention the standard definition and the body of the article can and should mention other definitions. In other words, reputations of journals, etc. aren't too relevant here; simply whether a definition is standard or not. -- Taku (talk) 09:48, 30 August 2022 (UTC)

Fair enough. I added the new definition to the body of the article. SwissGuy22 (talk) 11:51, 31 August 2022 (UTC)

The edit has immediately been reverted (twice) by D.Lazard; apparently D.Lazard and JBL think that the two of them having the same opinion means that there is consensus about this article; I can do other things with my time so goodbye! SwissGuy22 (talk) 16:15, 31 August 2022 (UTC)

Perfect, it sounds like everyone is in agreement about what would be best. JBL (talk) 17:28, 31 August 2022 (UTC)

Sep 2022

Classification of torsion-free abelian groups

This rather vaguely written popularization says it was recently proved that the classification of torsion-free abelian groups is a "hard" problem. Should our article titled Torsion-free abelian group mention the classification problem?

I have never thought about torsion-free abelian groups, so in reading this, my first thought was "Isn't every torsion-free abelian group a direct product of infinite cyclic groups?", but then I thought: The rationals with addition are a torsion-free abelian group, and so is the group of binary rationals with addition (i.e. rationals whose denominator is a power of 2). This raises another question: Even if the answer to the first question above is "no", should we add a diversity of examples to the article? Michael Hardy (talk) 02:35, 31 August 2022 (UTC)

If I remember, the classification of torsion-free abelian groups is very difficult and it is a field itself. By Googling, at least I found this [42]. The Wikipedia article certainly doesn’t do the justice and it’s one of those that require expertise to have an adequate treatment. —- Taku (talk) 06:33, 31 August 2022 (UTC)

Paolini and Shelah's result seems too technical to state properly in this article as there seems to be no articles on wikipedia covering the relevant background on model theory and descriptive set theory in sufficient depth. It seems reasonable to add more non-finitely generated examples and a few more elementary definitions, as the article could include some of Baer's theory (https://zbmath.org/?q=an%3A63.0074.02), in particular the classification of groups of rank 1 (subgroups of the additive group of the rationals). jraimbau (talk) 07:15, 31 August 2022 (UTC)

There is actually the article torsion-free abelian group of rank 1, which covers the classification in rank 1. I am not too sure if it should be a separate article; as far as I understand it doesn't generalize to higher ranks -- Taku (talk) 07:55, 31 August 2022 (UTC)

I think this should be merged into the torsion-free abelian group article, since as noted in this discussion it suffers from lack of content rather than overabundance thereof. Maybe some of the content of the article on Rank of an abelian group#Groups_of_higher_rank could also be mentioned in this article. jraimbau (talk) 08:05, 31 August 2022 (UTC)

The classification result is for finitely generated torsion-free Abelian groups. In general one expects more complicated behaviour. It is similar to (more or less the same as) trying to understand how operators behave as finite-dimensional matrices (where the Jordan decomposition completely answers the question) vs infinite dimensions (the entire field of functional analysis). Tazerenix (talk) 09:35, 31 August 2022 (UTC)

This is not about a classification result but a classification problem. I'm not a specialist but it seems that people think that the classification problem for countable torsion-free abelian groups is intractable beyond rank-1 groups, and so have taken to the approach of trying to quantify its "difficulty" using descriptive set theory. If i understand it correctly the theorem of Shelah and Paolini that started this discussion states that in this sense the problem for torsion free abelian group is hardest possible among classification problems for structures on countable sets.

I don't find your analogy with finite dimension/functional analysis to be very convincing, is it backed by an actual result? jraimbau (talk) 12:28, 31 August 2022 (UTC)

I was merely replying to the sentence "Isn't every torsion-free abelian group a direct product of infinite cyclic groups?". My comment is just about the proof of the classification for finitely generated Z-modules using the existence of Jordan decompositions. I agree the article should mention the classification problem beyond the finitely generated case. Tazerenix (talk) 17:48, 31 August 2022 (UTC)

I took a swing at editing the article following this conversation (my thanks to the participants). I did include a small paragraph on what prompted it---the Paolini--Shelah preprint---but it is not very good and anybody with working knowledge of the relevant fields would be welcome to improve on it (i find that very interesting but i don't have the time to delve into it now). Maybe writing an account of the Friedman--Stanley paper somewhere on wikipedia would also be useful (maybe it's already here, didn't have the courage to look for it). jraimbau (talk) 13:26, 2 September 2022 (UTC)

Harmonic function vs. Laplace's equation

There is at present one wiki page for harmonic function and one for Laplace's equation. I take these two topics to have purely grammatical difference (a harmonic function is defined as a solution of Laplace's equation), and no mathematical differences. (There are very likely some generalizations or modified contexts with a difference, probably for instance in graph theory or functions valued in metric spaces, but that is not presently relevant to either page - generalizations present on the harmonic function page all satisfy generalizations of Laplace equation.)

So I propose the two pages should be merged. Any thoughts? If agreed, the obvious followup question is whether the page should be called "harmonic function" or "Laplace's equation"? Both are extremely fundamental and widespread vocabulary.

Relatedly, there is also some content split between Laplace's equation and Laplacian, and I would also argue some material presently in the former page (such as fundamental solution) is actually about the Laplacian, and not Laplace's equation. (A differential operator has a fundamental solution, a PDE doesn't have a fundamental solution - although admittedly it is common to misspeak in that way.) Gumshoe2 (talk) 19:27, 7 September 2022 (UTC)

I would say all the content of the Laplace's equation page needs to be found somewhere on the wikipedia, even not on that page. Right now the situation is there are three separate pages which roughly cover:

• the properties of the operator at Laplace operator including generalisations
• the properties of the equation at Laplace's equation. This should include the common set ups of boundary value problems, descriptions of the equation in different coordinates (things which are likely to be incredibly useful and commonly looked for for visitors of that page)
• properties of solutions to the equation at Harmonic function including generalisations.

I think I believe these three topics are different enough that they should either have 3 separate pages, or combined into a single page. In particular I think the content on Laplace's equation is important enough to the average visitor that it doesn't make sense to bury it in either harmonic function or Laplace operator without making it abundantly clear where you would find it. If I had to choose it would be absorbed into Laplace operator almost entirely. Tazerenix (talk) 22:51, 7 September 2022 (UTC)

I agree that essentially all material on Laplace's equation page is significant and would be looked for by someone going to that page (the Schwarzschild section is an exception - it seems wrongly stated and is of dubious significance) - or moved elsewhere and, as you say, clearly linked to. But I think all that material, with possible exception of "boundary conditions" section, would be equally looked for by someone going to the harmonic function page.

For completeness, here is virtually all material on Laplace equation page (except "boundary conditions" section), minimally rephrased so as to be a fundamental aspect of harmonic functions: that the real and imaginary parts of a holomorphic function are harmonic, that any harmonic function is analytic and hence has locally has a conjugate harmonic function, that harmonic functions have a particular type of Fourier series expansion, that the Cauchy-Riemann equations arise in fluid flow and hence that the derivatives of a harmonic function appear as the velocity field, that harmonic functions describe electrostatic configurations, that the only rotationally symmetric harmonic functions are $c_{1}\log |x|+c_{2}$ and $c_{1}|x|^{2-n}+c_{2}$, that any harmonic functions on any region is represented by a certain kind of convolution of a certain region-dependent function with the boundary values, that harmonic functions can be expanded by spherical harmonics, and that harmonic functions describe gravitational vacuum in classical field theory.)

And even the content of "boundary conditions" section is equally fundamental as a statement directly about harmonic function, i.e. a harmonic function on any compact region is uniquely determined by its values along the boundary, and the choices of boundary values parametrize the harmonic functions on interior. It is just a little verbally clunkier to describe this way. (It can also be phrased as a bijection between function space of harmonic functions and function space of boundary values, although this is a little nonstandard and so not good for wiki.)

Conversely, if I were looking for information about Laplace equation, I would want the information on harmonic function page.

By contrast I think the scope of Laplace operator/Laplacian is rightfully broader, as it belongs equally well to Poisson equation, heat equation, Schrödinger equation, wave equation, etc. Gumshoe2 (talk) 00:56, 8 September 2022 (UTC)

So, I don't have a strong opinion on the matter but one thing that comes to mind: we have separate articles for holomorphic function and Cauchy–Riemann equations. If we were to merge harmonic func and Laplace equations into one article, then it seems logical that they too should be in one article. Maybe they should. It's essentially the question of what style editors (really math editors) would like to adopt (I am not sure what style is good). -- Taku (talk) 07:16, 9 September 2022 (UTC)

From a physics POV, identifying a PDE and its set of solutions as the same thing doesn't make a lot of sense--the PDE, and its symmetries, are the fundamental objects in a physical model of say, electric fields. How to calculate solutions, whether analytically or numerically, is a conceptually separate topic. But if you all wanted to go the unification route, I think you would need to consider the potential theory article as well. --{{u|Mark viking}} {Talk} 17:34, 9 September 2022 (UTC)

I essentially agree with what you say in and of itself, but it does not seem to describe the actual difference between these two pages, even in the form they are currently written. But thank you for pointing to potential theory page. So my issue is if I want to add material to wiki about harmonic functions, I would have no clue which of these three pages to add it to.

For instance, consider the Cheng–Yau estimate for harmonic functions. Its proof and reasoning is entirely a manipulation of the equation itself and the key point is about its symmetry of commutation with the derivative, so perhaps it should go to Laplace equation; however the property itself is very purely about solutions of the equation, so maybe instead to harmonic functions; however in Davies' book (a standard ref), it is the primary topic of a section called "potential theory".

I think this example is characteristic and there is no natural/obvious division between these pages. And if there is to be a division then it should be made clear to readers and editors on each of the three pages. Gumshoe2 (talk) 19:02, 9 September 2022 (UTC)

A note on the relationship between holomorphic functions and Cauchy–Riemann equations is the Looman–Menchoff theorem. However, currently the redirect target of holomorphic is a holomorphic function, but I think the Cauchy–Riemann equation might be a better target. --SilverMatsu (talk) 03:53, 11 September 2022 (UTC)

As a general rule I think it’s just fine to keep such subjects separate, even if they are largely overlapping. –jacobolus (t) 04:04, 11 September 2022 (UTC)

I agree; I also think that as a reader it's helpful when each article in such a grouping links the others in fairly prominent ways. --JBL (talk) 18:08, 11 September 2022 (UTC)

There is no way we are going to eliminate all overlaps in Wikipedia articles, and an overlapping style is even encouraged by some Wikipedia editing guidelines (notably Wikipedia:Summary style). I don't have a strong opinion or knowledgeable point of view on this specific case. But it is an obvious principle that when overlaps occur the articles should point to each other. —David Eppstein (talk) 20:23, 11 September 2022 (UTC)

I agree that overlap is ok, and in many cases desirable. My problem here is that three different pages (harmonic function, Laplace equation, and potential theory) are about exactly the same topic, to the extent that they are (to my eyes) indistinguishable, something like having one page for "mathematical constant e" and another page for "Euler's number". (caveat: I do have expertise on the mathematics involved here, although embarrassingly "potential theory" is new to my vocabulary!)

But I can see that I have a minority point of view. So in terms of adding content I will just try to select which of the three pages already has content with the closest fit. But the minimum to ask for is that each page very clearly link to the other two, perhaps via a note at the top, above the main text. I'm not sure specifically of the most appropriate format. Gumshoe2 (talk) 20:54, 11 September 2022 (UTC)

Fair enough, but we do have e (mathematical constant), Natural logarithm, Exponential function, List of representations of e, Proof that e is irrational, List of logarithmic identities, Characterizations of the exponential function, Exponential growth, Exponential decay, Matrix exponential, Logarithm of a matrix, Exponential map (Lie theory), Derivative of the exponential map, Exponential map (Riemannian geometry), Exponential map (discrete dynamical systems), History of logarithms, Slide rule, Logarithmic scale, Logarithmic derivative, Logarithmic differentiation .... (see List of exponential topics for a longer list). There is significant overlap involved in many cases here. Some questions: can these separate articles be extended in different directions? Would either article be improved by cutting down an extended section into a simple summary and including a link to a fuller treatment at the other page? –jacobolus (t) 00:42, 12 September 2022 (UTC)

As an example, I think Potential theory could include more discussion of its applications to approximation theory that would not necessarily be appropriate to include in harmonic function. Cf. literature search for «"potential theory" approximation». –jacobolus (t) 00:45, 12 September 2022 (UTC)

Well, again, my issue is with synonymous topics (Laplace equation and harmonic function), not overlapping topics. None of those topics (aside from the first itself) are synonymous with Euler number itself, or reasonably interpretable as such.

Anyway, on inspection, I think that the opening sentence of potential theory wikipage (copied from planetmath) is incorrect, and so perhaps potential theory should be excluded from consideration here. See for instance short discussion in example 9.13 in Renardy & Rogers "An introduction to PDE". Classical potential theory seems to be about newtonian potential; if this is the case, then harmonic functions are certainly very relevant to potential theory but far from the whole story. Poisson equation (with Laplace equation as only a special case) would be a closer point of reference; however it seems that modern potential theory or nonlinear potential theory contains an even broader section of equations than Poisson. See e.g. section 2.6 of Morrey's "Multiple integrals in the calculus of variations" in dealing with what it calls "generalized potential theory" (here standard potential theory, in section 2.5, is indeed about Newtonian potential, and the relevant PDE is indeed Poisson equation, not Laplace equation/harmonic function) Gumshoe2 (talk) 21:24, 12 September 2022 (UTC)

Numerical methods for PDE

I would like to propose that WikiProject Mathematics take a more deliberate approach to talking about numerical methods for PDE. Especially for non-linear PDE, I suspect that many people who search for e.g. Burgers' equation, the Monge-Ampere equation, or the Korteweg–De Vries equation are interested in numerical methods. However, the vast majority of articles on PDE only address analytical aspects, like well-posedness, etc. (None of the articles for the aforementioned PDE examples speak at all about numerical methods, as of 2022-9-12.) I'm only a casual Wikipedia editor, so I'm not sure how to implement this administratively, but I strongly believe it would be a very useful feature of WikiProject Mathematics.

I'm also not sure what would be the best way to summarize numerical methods for a given PDE, but I can propose some ideas:

• If a survey article exists in the literature, simply linking to it would be most useful.
• If there are only a few methods proven to converge, then it seems reasonable to mention them directly. E.g. "Such and such researcher has provided a wide-stencil method with proven convergence properties."
• If there are many methods proposed in the literature, but no available survey article, then it is usually possible to extract general features of the known solution methods from e.g. the introductions to papers on the subject. In such a case, it would be nice to recapitulate such general features, along with a few links to example literature. E.g. "Many methods proceed by converting the elliptic equation into a time dependent parabolic equation and solving the latter by finite difference schemes [refs]."

--171.64.108.74 (talk) 03:27, 13 September 2022 (UTC)

What is stopping you from adding that material to the relevant Wikipedia pages (besides the obvious: research and writing takes a lot of work)? Edit: For anyone who likes clicking links more than typing into search boxes, relevant pages here might include Nonlinear partial differential equation, pages linked from List of nonlinear partial differential equations including Burgers' equation, Monge–Ampère equation, Korteweg–De Vries equation, and perhaps other pages linked from List of partial differential equation topics. –jacobolus (t) 04:48, 13 September 2022 (UTC)

It is partly "the obvious" which is stopping me, and partly the lack of precedent. I would expect that I am a typical user of these articles on non-linear PDE; I have subject matter knowledge on some of them, but I rarely make edits which are not incremental. My main purpose in raising this issue here is to alert more experienced editors--people who are invested in WikiProject Mathematics--that there is a big gap between what is offered and what is needed for these articles. If there were any sort of established template for how to write about numerical methods for a given PDE, I would probably contribute to those articles for which I have knowledge. I was hoping that this would be an OK place to alert the community that this is desired change, and to start a discussion on how to go about it. I am not qualified to implement this myself. I can add knowledge, but I do not wish to invent the paradigm for writing about numerical methods for PDE all by myself. --171.64.108.74 (talk) 19:35, 13 September 2022 (UTC)

If you did a careful survey, I imagine you’d find that the majority of the content of articles in Wikipedia about every technical field are written by (more or less) amateurs such as hobbyists and students. There are surely some excellent professional mathematicians around here but most tenured professors are busy with other projects. In an ideal world perhaps every world-class expert would write (or at least review) the article(s) about their specific topic of study as a public service, considering that the Wiki page is likely to have at least an order of magnitude more readers than any of their papers. But since that doesn't happen, even relative novices shouldn’t hesitate to make "non-incremental" edits if they think they are warranted, without worrying too much about "precedent". The additions are (hopefully) still helpful compared to nothing. –jacobolus (t) 00:50, 14 September 2022 (UTC)

Is this perhaps a proposal to create *separate* articles for numerical methods in PDE? I noticed we have Numerical methods for ordinary differential equations, while we don't have a corresponding article for PDE. That sounds quite reasonable. (We have an article titled Numerical Methods for Partial Differential Equations, but that article is about a specific journal.) -- Taku (talk) 11:26, 13 September 2022 (UTC)

Sorry we have Numerical methods for partial differential equations, which is about numerical methods in PDE. So maybe that article covers what is to cover? -- Taku (talk) 11:52, 13 September 2022 (UTC)

No, this is definitely not a proposal for an article on numerical methods for PDE. The difficulty is that numerical methods for non-linear PDE are very much tailored to the specific details of the PDE. This is precisely why it is very important for the numerical methods to be discussed on the same page as the PDE itself. What I would like is (1) community guidance (or precedent) on how to write a "Numerical Methods" section for a given non-linear PDE article, and (2) for this to be considered a priority by the community for PDE articles. --171.64.108.74 (talk) 19:35, 13 September 2022 (UTC)

Generally this is a glaring missing feature of the analysis articles on the wikiproject (there seems to be quite a bias towards pure methods). I think adding sections to the relevant pages even with one or two sentences of content and a banner indicating a need to expand would be appropriate. Tazerenix (talk) 22:50, 13 September 2022 (UTC)

I wholeheartedly support this. It would be an excellent start. 171.64.108.74 (talk) 00:50, 14 September 2022 (UTC)

Although I agree, as far as I know there are not any very active editors here who are knowledgeable about numerical analysis of PDE. And there is danger of doing more harm than good when people try to add content about material they don't understand very well, even if following good references and guidelines. With this in mind, I think Tazerenix's suggestion is good. Gumshoe2 (talk) 02:11, 14 September 2022 (UTC)

Geometric examples in composition function

I had read this section, but it was confusing me until now. As a matter of fact, I don't know that there were other examples of geometry in composition function. Dedhert.Jr (talk) 05:35, 14 September 2022 (UTC)

I have reverted the (recent addition) of this section. D.Lazard (talk) 09:34, 14 September 2022 (UTC)

@D.Lazard Thanks a lot. I was trying to restore those edits, but then I was afraid that my edit become considered disruptive. In this case, I had to cancel it and then discuss this problem here. Dedhert.Jr (talk) 11:47, 14 September 2022 (UTC)

My eyes are bleeding from the style violations by Arthur Baelde at Rotational symmetry, Wallpaper group#What this page calls pattern, and Multiview orthographic projection. 171.66.135.140 (talk) 12:29, 14 September 2022 (UTC)

I removed the addition at Rotational symmetry which, in addition to being impenetrable, was entirely off-topic. 100.36.106.199 (talk) 12:40, 14 September 2022 (UTC)

Also at Multiview orthographic projection, for the same reasons. Someone else will have to consider Wallpaper group. 100.36.106.199 (talk) 12:43, 14 September 2022 (UTC)

Someone should do something about the caption on the remaining geometric image at Function composition, too, it's a real formatting nightmare. 100.36.106.199 (talk) 12:47, 14 September 2022 (UTC)

Yet again "weierstrass substitution"

Sigh. Continuing on the discussion/disputes from prior years (Cf. WikiProject math talk archives from 2013, 2020, 2022), we again have disagreement at Tangent half-angle substitution about how to present Weierstrass’s (lack of) involvement. Does anyone else want to weigh in at Talk:Tangent half-angle substitution#Name? (Also see Talk:Tangent half-angle substitution#Common name for context.) –jacobolus (t) 20:48, 21 September 2022 (UTC)

So far XOR'easter and I have weighed in, but I do think this dispute would benefit from broader input. JBL (talk) 00:58, 23 September 2022 (UTC)

Fractal articles

Hello WPM. Could someone with some expertise on fractal analysis please have a look recent edits to analysis on fractals, and the new article fractal calculus? There appears to be significant overlap, and a conflict of interest by the new article's creator. The older analysis article currently opens with "Analysis on fractals or fractal calculus..."

Should the two articles be merged? At the least, the newer article needs cleanup for essay tone, but I lack the subject knowledge for a good rewrite. Thanks for any help with this. Storchy (talk) 08:36, 20 September 2022 (UTC)

It seems like the same editor added a bunch of stuff to analysis on fractals back in 2020. Here's what it looked like before he weighed in. The "seminal" 2009 article does have a lot of citations but (at the risk of sounding elitist) none in journals I've heard of. It's also only applicable to fractal subsets of the real line. Given the cited earlier books by Kigami and Robert Strichartz, overfocusing on the 2009 article would seem like an due weight issue.

That said, I also lack subject knowledge. We might not even have any active Wikipedians with the right subject knowledge. I can try to put it on my to-do list and read some survey articles, but I also need to cut back on my Wikipedia editing... —platypeanArchcow (talk) 16:34, 20 September 2022 (UTC)

The fractal calculus article is a mess and appears unsuitable for wikipedia in any case. I'm not sure whether the contents should be incorporated into the analysis on fractals article, and i don't have anything substantial to add to what @PlatypeanArchcow: wrote above, lacking as he does the relevant expertise.

I'm going to make some proposals to advance the conversation: that the fractal calculus be AfDed and the legitimate article about analysis on fractals be reverted to its state previous to the edits by Golmankhaneh, perhaps adding a short sentence mentioning the development of a "fractal calculus" by Gangal--Parvate. It could also be useful to add some content from Strichatz's 2006 survey that is cited in the article. jraimbau (talk) 06:21, 22 September 2022 (UTC)

I believe that analysis on fractals needs a {{stub}} template and fractal calculus needs a definition of nomenclature, e.g., $S_{F}^{\alpha }(x)$. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:13, 22 September 2022 (UTC)

Fractal calculus hypes up the work of cranks (Nottale, Hameroff) and is full of word salad (e.g., In this model, time deepens into timelessness as energy folds back on itself in repeating cycles building matter, building time). Recommend killing with fire. XOR'easter (talk) 21:16, 25 September 2022 (UTC)

That's very poetic! JBL (talk) 23:36, 25 September 2022 (UTC)

"In this model, time arises from the enfolding of non-time and the erasure of points that do not become matter, as in the construction of the Cantor set. Hold on, I'm taking a hit..."

Oh, and it's copyvio. XOR'easter (talk) 01:42, 26 September 2022 (UTC)

Thank you for the work! i restored the old version of analysis on fractals. jraimbau (talk) 13:43, 26 September 2022 (UTC)

Thanks everyone for your help with this. Storchy (talk) 05:25, 29 September 2022 (UTC)

Working on a draft: Ordinal Priority Approach

Hello everyone,

I hope you are having a great time. I'm working on this draft right now. Please feel free to help me to improve it. Thank you so much for your great help in advance. Scholartop (talk) 16:00, 29 September 2022 (UTC)

I'd like to read a simple introductiory example there, if possible. - Jochen Burghardt (talk) 19:04, 29 September 2022 (UTC)

This sounds like it is about business management rather than mathematics. JRSpriggs (talk) 21:14, 29 September 2022 (UTC)

Thank you for your comment. Actually, I agree with you. I will remove it from this category and will discuss on the new one. Scholartop (talk) 21:19, 29 September 2022 (UTC)

Scholartop This does not seem to be a mathematics article. It makes use of mathematics, but it seems to be more of an applied science thing. Not sure how to categorize it (statistics?, engineering, management science?) , but I don't think it should be categorized as a mathematics article per se. PatrickR2 (talk) 21:15, 29 September 2022 (UTC)

Thank you. I will remove it from this category. You are completely right. Scholartop (talk) 21:20, 29 September 2022 (UTC)

Oct 2022

Working on a draft: Cartwright's Theorem

Hi all,

I am currently working on this draft currently. Please feel free to help me to improve it. Thank you so much for your great help if possible. Also, can I know if the stub holds general importance? Aitzaz Imtiaz (talk) 01:00, 2 October 2022 (UTC)

The lead says this is about graph theory and that it is about set theory. Both are incorrect. A hint: when you do something with graphs of functions you are not doing graph theory, and when you are using sets as part of the description of other kinds of mathematical object. you are unlikely to be doing set theory. Where are you getting this incorrect information? It does not appear to be in the sources you are using. The actual mathematical content of the draft stub also appears to be stated in a somewhat incoherent way, making it difficult to understand the actual statement of the theorem without going back to the sources and reading them instead. —David Eppstein (talk) 01:53, 2 October 2022 (UTC)

hey thanks! The following is a part of Graph theory, what think, sorry if I am wrong, but basically I tried saying that the following theorem has an application in Set Theory doesn't means it is a part of it. Aitzaz Imtiaz (talk) 02:04, 2 October 2022 (UTC)

Fixed point requested move

Hi all, I requested a move of Fixed point (mathematics) to Fixed point which is currently a disambiguation page for Fixed point (mathematics), Fixed-point arithmetic, and a few other topics. This move is somewhat controversial as several editors have objected that Fixed-point arithmetic precludes Fixed point (mathematics) from being a primary topic. A few months ago a similar move request was closed as "no consensus", so please join in at Talk:Fixed point (mathematics)#Requested move 4 October 2022 so that this discussion can reach a definitive conclusion. Mathnerd314159 (talk) 20:46, 6 October 2022 (UTC)

Discussion needs input from editors with subject knowledge

 You are invited to join the discussion at Wikipedia:Redirects for discussion/Log/2022 October 8 § Locally small category.
The redirects Locally small and Locally small category currently point to different places (Glossary of category theory#small and Category (mathematics)#Small and large categories respectively). 1234qwer1234qwer4 believes they should target the same place and has nominated them for discussion at RfD to determine what the best target is. That discussion needs input from editors familiar with the topic area. Please comment in the linked discussion rather than here. Thryduulf (talk) 22:13, 8 October 2022 (UTC)

Closed merge discussions

Working on the merging backlog, I recently closed some merge discussions involving mathematics articles. This includes the proposal to merge Polynomials calculating sums of powers of arithmetic progressions into Faulhaber's formula, which I believe had been discussed here some months back. Interested editors are invited to implement the merger! Felix QW (talk) 08:12, 14 October 2022 (UTC)

Move discussion for 142,857

There's a Requested Move for 142,857 to be renamed to 142857 at Talk:142,857#Requested move 14 October 2022. Please join the discussion if you're interested. Thank you. --Paul_012 (talk) 10:58, 14 October 2022 (UTC)

If a discussion about whether or not to have a comma in a page name doesn't go to an RfC and at least two ANI threads, I will be very disappointed in Wikipedia. XOR'easter (talk) 18:09, 14 October 2022 (UTC)

Awesome - (I am uncertain about the veracity of the following, but maybe there are other reasons for the removal of the comma, Wakelamp d[@-@]b (talk) 02:17, 18 October 2022 (UTC)

VP Idea discussion on ESL user preferring Britannica to WP

Suggest people comment. I think the points are well made.Wikipedia:Village_pump_(idea_lab)#Wikipedia_in_More_"Simple"_Languages, I like the way this site handles it (Note its called skeptical science because it's skeptical about anti-climate change science - confuses everyone), THey have basic, advanced, and intermediate levels as tabs. Wakelamp d[@-@]b (talk) 02:36, 18 October 2022 (UTC)

I don’t think having several entirely separate articles at different “levels” about each technical topic seems necessary, but many mathematics (and other technical) articles would benefit from having a more accessible top few sections, more figures, more motivation and context, some historical discussion, additional narrative explanation stitching technical details together, and so on. If you find one that you know about, please be WP:BOLD and start making improvements. If you find a specific article that you think should be more accessible than it is but you don’t know enough about the topic to improve it yourself, please start a conversation on the talk page or here. –jacobolus (t) 04:03, 18 October 2022 (UTC)

Apologies, there are two similar topics, i meant this .

Wikipedia:Village pump (idea lab)#Wikipedia should be redesigned into a much more user-friendly and dynamic site...

I have noticed that WIkipedia is no longer appearing first on google search for some maths article (eg algebra) . Links for Algebra

Brittanica

Simple English

Algebra Wakelamp d[@-@]b (talk) 04:53, 18 October 2022 (UTC)

This is just your (algorithmically personalized) Google. As a not-logged in user, Wikipedia is the first result for "algebra" in Google, Bing, Yahoo, and DuckDuckGo. –jacobolus (t) 18:39, 18 October 2022 (UTC)

@Wakelamp Quoting some of the items in the discussion that you mentioned:

If the article is too difficult, maybe there is a reason for this? Not everything can be explained in easy terms (ELI5), but simplicity would kill all the meaning that will be perfectly understandable for an appropriate audience. (I wouldn't understand an article about chemistry/abstract math/etc, but my unpreparedness is mot the reason to cut the article and explain it shallowly).
— User:Artem.G

It is true that some articles' lead sections (and sometimes the whole article) may benefit from simplification and pruning in general, but this simplification should not be at the expense of removing technical information that will be useful to experts within that particular field. Often, there is simply no way to compress an article any further without losing crucial technical precision. Additionally, many extremely technical articles (for example, articles dealing with genes, specific organic/inorganic molecues etc) are almost exclusively accessed by readers who have at least some expertise in their relevant field, so there is little need to simplify the article for the general public.
— User:Rob3512

I wholeheartedly agree with their sentiment. Some articles are just too technical due to the nature of the topic, and will not be of interest to most mathematics learners. That does not mean there is a need to "dumb them down". And on the other hand, other articles more accessible to beginners/laypeople can absolutely have a lead/sections that explain the topic in simpler terms before going into more technical details. But that should not apply to all mathematics article across the board. PatrickR2 (talk) 05:26, 20 October 2022 (UTC)

it's quite tricky to write things for students. It would be nice to ask a mathematics teachers association to review all the article ledes. Wakelamp d[@-@]b (talk) 09:30, 20 October 2022 (UTC)

You could pick a few articles and try to ask a math teacher (or a few) who teach those concepts to comment. –jacobolus (t) 16:02, 20 October 2022 (UTC)

Good idea, I have sent emails to a few classmates. Wakelamp d[@-@]b (talk) 21:59, 20 October 2022 (UTC)

rough rough draft, few links, I haven't copied the latex, I decided to have a go without a teacher, and then checked.

The aim is to provide a mental map by linking between paragraphs, what they know, where it gets them

Underlines are just summaries of the point of that section, and are not intended for the article

'Maps to Place in maths

In the branch of mathematics called linear algebra,

General form - details many readers will skim this, but use simple words for the simple cases and then formal words for the general, many exceptions should be hinted at, or should be mentioned in the body instead, forms map for the article. With definitions, the aim should be not to list all exceptions, but hint at them , and mention them in the body.

A linear equation has the general form

where are the variables (or unknowns), and

are the coefficients (or parameters).

These coefficient may be arbitrary expressions, provided they do not contain any of the variables (see polynomials). The solutions of a linear equation are the variable values that make the equality true. Each solution may be interpreted as Cartesian coordinates, and all solutions may be visualised as forming a line with 2 variables, a plane with 3 variables, and with n variables forming a hyperplane (a subspace of dimension n − 1). A linear equation can also be considered a polynomial of degree 1 which is equal to 0.

' Purpose of the article- Is/Is not, use (The chart shows simultaneous linear equations)

'This article discusses single linear equations with real coefficients and real solutions, but it is applicable to those involving complex numbers,

The normal pre-requisites are an understanding simple algebra, of cartesian co-ordinates, and x-y line charts

Linear equations in used all of mathematics, sciences , and finance can be used to approximate non-linear systems, and these equations often involve complex numbers.

When there is more than one equation , these are called simultaneous linear equations, or a system of linear equations.

Being able to solve and visualize linear equations is needed for the study of simultaneous linear equations,

Student students see an example in their text, how readers remember it, map to general form, Equations for students should be in colour in the lede - so it draws their eye, and they are not overwhelmed by the latex.

Students are initially taught to solve linear equation in the form

y = mx +c,

where m is describe as the gradient, and c is where line crosses the y axis crosses, and relation, Expressing this in the form of the original def

definition

a1x1 + a2x2 + 01 = mx -y +c =0,

The term linear equation is often assumed by students to refer to 1 or 2 variables (with the the solutions forming a line on a chart) but it also applies to 3 variables (the solution forming a plane on an x y z chart) or more, Wakelamp d[@-@]b (talk) 07:27, 21 October 2022 (UTC)

There are some amazingly well done technical articles on Wikipedia, but there are also many existing technical articles at all levels which are dramatically less accessible than they could be, and currently mostly serve as a technical reference (or list of sources) for people who have already studied the topic.

In my opinion, ideally any technical topic should be made accessible (to a basic degree) to someone with a couple years less technical background than usually assumed for first studying it. So for instance topics usually learned by advanced mathematics undergraduates should be made accessible to first-year physics or computing students. Etc. Not the whole article necessarily, but the basic motivation, some simple examples, the conceptual idea behind the definition, some historical background, etc. The main thing lacking is volunteer effort; it takes a ton of work to write excellent articles for a wide audience.

(This is not only a problem on Wikipedia. Mathematics as a field is notorious for not making results accessible to non-specialists.) –jacobolus (t) 16:13, 20 October 2022 (UTC)

As a concrete example, the notion of the "continuity" of the real numbers should be a fundamental idea made accessible at a basic level to a high-school audience, and that article should discuss (early and in as non-technical a way as possible) what continuity means in this context, why the rational numbers are not continuous, and how the real numbers are set up to fix that. The article defines: a real number is a value of a continuous quantity (wikilink on quantity but not "continuous), but continuous is not ever accessibly explained. Though it discusses the topic a few times in different ways, each version is overly technical and full of inaccessible jargon linked to articles which themselves also do not discuss the basic idea. I would have hoped that continuity (mathematics) would explain the basic idea, but it redirects to List of continuity-related mathematical topics which does not provide any basic conceptual description of what continuity means but just links to more advanced articles like continuum (set theory) and linear continuum which circularly describe a continuum as being "like the real numbers", continuous variable which just describes having an uncountable set of values (not quite technically correct, or helpful as a basic idea), continuum (topology) which is absurdly terse and technical, the kind of definition you’d find in a journal paper for an audience of mathematicians, etc. The link real line redirects to number line which again only addresses continuity using inaccessible jargon. The overall result is that an e.g. high school calculus student hearing about the "real numbers" is never going to get a clear answer about what they are or why they exist unless they go find some external source. –jacobolus (t) 16:48, 20 October 2022 (UTC)

I agree with your points. On the other hand, if the wikipedia article references these external sources as you mention, it's perfectly fine for interested people to go read these sources to get a better understanding. Wikipedia is not necessarily in the business of premasticating and regurgitating information to make it accessible to people without the necessary background. The main thing is to provide links where people can deepen their understanding. Although I do agree that some articles here are too technical. (Some technical articles have been transformed (I have in mind one editor in particular, who will remain unnamed here) to a state of technical jargon and presentation that makes them close to unreadable, even by mathematicians). PatrickR2 (talk) 21:07, 20 October 2022 (UTC)

Wikipedia is not necessarily in the business of premasticating and regurgitating information to make it accessible to people without the necessary background – where practical Wikipedia absolutely should be in that business. The concept of a real number is regularly taught in late high school or early college, and the article should very broadly accessible, and self-contained enough that someone with an ordinary high school education can follow most of the basic ideas involved without needing to go on a scavenger hunt. It is an utter cop out to pass the buck to other sources, especially since the ones linked in a 'Sources' section are a Cantor paper from the 1870s in German and several graduate level textbooks. jacobolus (t) 21:44, 20 October 2022 (UTC)

The problem with WP:BEBOLD is that it is frustrating to put a lot of time in an edit only to have it reverted for lack of WP:RS, especially in areas where many sources are proprietary. The lack of an effective dispute resolution mechanism is also discouraging. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:04, 19 October 2022 (UTC)

This seems like a bit of a tangent, and is pretty vague. Do you have a concrete example or some more specific detail? What kind of dispute are you thinking of, and how was it resolved? I will grant you that sometimes Wikipedia can be frustrating or discouraging. Getting pseudonymous strangers with widely varying backgrounds to agree can be a challenge.

You can certainly also start a talk-page discussion, make an outline, etc. if you don’t want to lead off with putting weeks of work into changes that might be opposed by other wiki authors.

What do you mean by “proprietary” sources? Mathematics doesn’t generally involve proprietary material. You can’t patent a mathematical formula or concept, and there are few if any trade secrets per se. Are your sources secret NSA documents or something? Or do you just mean papers in journals that are not freely available online? There is nothing wrong with citing paywalled papers in Wikipedia articles. Someone who really cares can usually find a copy, e.g. through their public library, a university, asking for help online, directly emailing the authors, or sci-hub. –jacobolus (t) 16:10, 19 October 2022 (UTC)

@Chatul I feel your annoyance. But then the next day something good happens. The day after that is crud.

@Jacobolus "Someone who really cares can usually find a copy, e.g. through their public library, a university, asking for help online, directly emailing the authors, or sci-hub" I agree with what you say, but that is bit bitey. Although "pseudonymous strangers with widely varying backgrounds" made me laugh,

So, what has been the past consensus of having a simpler lede? Wakelamp d[@-@]b (talk) 16:34, 19 October 2022 (UTC)

Headbomb's answer a month ago was definitive. JBL (talk) 21:18, 19 October 2022 (UTC)

I can't find his reply on special search. May I have a link? TA Wakelamp d[@-@]b (talk) 05:15, 20 October 2022 (UTC)

It's the first link in this thread, and the first reply in that link. —David Eppstein (talk) 06:01, 20 October 2022 (UTC)

@David Eppstein The first link in this thread Wikipedia:Village_pump_(idea_lab)#Wikipedia_in_More_"Simple"_Languages

Is this what you mean For 1, there's 6 millions+ articles out here. Feel free to start. For 2, that's what the lead section already does. For 3, what skin is best is subjective. That's why we have preferences. Wakelamp d[@-@]b (talk) 07:48, 20 October 2022 (UTC)

Yes. JBL (talk) 17:12, 20 October 2022 (UTC)

See WP:VPIL#Wikipedia should be redesigned into a much more user-friendly and dynamic site... for Headbomb's reply. JRSpriggs (talk) 23:16, 20 October 2022 (UTC)

I didn't have that problem with articles on Mathematics, but rather with articles on computers. Computer vendors and software vendors often have documents that they consider trade secrets, and even if an editor has a copy, readers cannot verify the relevance of the citation.

As for the issues with dispute resolution, the obvious processes explicitly require the consent of all parties. I've thrown in the towel on some topics becaus of that.

Mathematic has a different issue. As has been attributed to Albert Einstein, things should be as simple as possible but no simpler. It is difficult to write a concise lead without assuming background knowledge. A lot of articles have leads that I consider too long, but I am by no means sure that it is possible to shorten them while still leaving them intelligible to neophytes. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:36, 21 October 2022 (UTC)

If unpublished corporate documents are considered trade secrets, Wikipedia articles obviously can’t cite those... See Wikipedia:Verifiability. –jacobolus (t) 17:13, 21 October 2022 (UTC)

Planet Math links

I noticed all of the Planet Math links are now broken (or at least every one I've tried). Does anyone know if this is a temporary situation? If it's a permanent situation, is there any plans to systematically fix it? Walt Pohl (talk) 22:07, 26 October 2022 (UTC)

If it is a permanent situation, see Wikipedia talk:WikiProject Mathematics/Archive/2021/May#about Template:PlanetMath --SilverMatsu (talk) 03:47, 27 October 2022 (UTC)

Are there any examples where PlanetMath is the best (or even a particularly good) source for some topic? Another possibility would be to just look for a better source any time PlanetMath is cited. –jacobolus (t) 04:29, 27 October 2022 (UTC)

I think they are ok in "External Links" sections, not so much otherwise Gumshoe2 (talk) 04:38, 27 October 2022 (UTC)

As external links they could also just be removed without doing much harm. If someone cares enough to add it back, they can look up the proper link. But I’m not sure these are all that helpful for readers. –jacobolus (t) 06:37, 27 October 2022 (UTC)

I tend to agree that they are not great; removing or replacing the links is probably the best way forward. - CRGreathouse (t | c) 05:03, 27 October 2022 (UTC)

Template:PlanetMath attribution/doc says that; "This template should be placed on the main page of the article.", but is it possible to place this template on the talk page like Template:Merged-from ? --SilverMatsu (talk) 16:42, 27 October 2022 (UTC)

AfD for Strictly non-palindromic number

See Wikipedia:Articles for deletion/Strictly non-palindromic number, where I have stated why I believe that the term fails the notability guideline. GeoffreyT2000 (talk) 01:01, 29 October 2022 (UTC)

Page name ∂∂̅-lemma

I've just made a new page at ∂∂̅-lemma but am preemptively posting in case people have opinions about the name. It is technically the valid unicode for expressing a character with an overline, except the italic nature of ∂ as a unicode symbol causes it to be rendered slightly off (and it may be bad practice to have wikipedia pages whose names are such esoteric combined unicode characters). Alternatives are ddc-lemma or ddbar-lemma or deldelbar-lemma or ∂∂bar-lemma. The first one is an alternative mathematical name $dd^{c}$-lemma, whereas the others are just phonetic. If anyone has a particularly strong objection then feel free to move the page to one of the suggested names. Tazerenix (talk) 06:23, 27 October 2022 (UTC)

Thanks for making the page! It is a very good addition. The title rendering strikes me as very strange, so I think there must be a better alternative. If I had to choose myself, I would suggest "d-dbar lemma" but this is obviously also not perfect.

Side note, the second paragraph is wrong, its characterization of the Poincaré lemma is of the form "A implies A" since the conclusion is just rephrasing the assumptions – exactness is the very meaning of being zero in De Rham cohomology, no lemma needed! The Poincaré lemma says that any closed differential form on Euclidean space is exact. Gumshoe2 (talk) 08:10, 27 October 2022 (UTC)

Yes thanks. I guess it should just be compared to just the notion of an exact differential form. Tazerenix (talk) 09:03, 27 October 2022 (UTC)

I don't have expertise in this area, but just a general question about presentation. I see some mathematics articles quote theorems and try to give full proofs of them. Other articles don't give proofs and instead give authoritative references where proofs can be found. Unless a result is really simple and has a one or two line proof that can help the reader better grasp the concepts involved, I was under the impression that it is in general preferable to give external references instead of proofs in wikipedia itself? (I can't quote the guidelines about this, but I thought that was covered somewhere.) PatrickR2 (talk) 06:50, 28 October 2022 (UTC)

You should try to make the article legible and useful to readers. If the proof is long, tedious, and not very insightful, you can refer to an outside source, hide it by default (e.g. using Template:Collapse or similar), or move it to a footnote. If the proof is shorter / more insightful, you could put it directly in the article body copy. What is most useful and/or most legible is a judgment call, and sometimes there might be disagreement. If you can’t reach consensus, asking here is a good way to get more eyes on it. –jacobolus (t) 07:01, 28 October 2022 (UTC)

There is some discussion at Wikipedia:WikiProject Mathematics/Proofs. –jacobolus (t) 07:04, 28 October 2022 (UTC)

Thanks for the link. PatrickR2 (talk) 18:51, 28 October 2022 (UTC)

In this case the topic is of interest because of its applicability to Kahler manifolds. The most interesting part of the lemma, apart from the fact that it is true and very useful, is how the proof relies on the Kahler identities and Hodge decomposition. This is demonstrated in how the failure of the lemma is used to study non-Kahler manifolds (as mentioned on the page). Thus it seems of particular interest to produce the proof (which despite not being one or two lines, is still only 6 or 7 lines). Also the lemma is similar in theme to the Poincare lemma and Dolbeault-Grothendieck lemma, both of which appear with full (and in fact more technical/detailed, albeit slightly more elementary) proofs. Tazerenix (talk) 06:14, 29 October 2022 (UTC)

@Tazerenix: The characters ∂∂̅ probably fall under the "Symbols (avoid them)" part of WP:TSC. Either ddbar lemma, ddbar-lemma, or d-dbar lemma (as suggested by Gumshoe2) strike me as the best alternatives. — MarkH₂₁^talk 00:31, 29 October 2022 (UTC)

I've moved the page to ddbar lemma. Thanks for the comments. Tazerenix (talk) 06:01, 29 October 2022 (UTC)

Nov 2022

Wikipedia talk:WikiProject Mathematics/Archive/2022/Nov

Dec 2022

Wikipedia talk:WikiProject Mathematics/Archive/2022/Dec