Wikipedia talk:WikiProject Mathematics/Archive/2024/Jun

Degenerate bilinear form is unreferenced

Request for an esteemed colleague from WikiProject Mathematics to please review and find a source for Degenerate bilinear form, which has been tagged as "Unreferenced" since August 2008. Cielquiparle (talk) 09:58, 25 May 2024 (UTC)

I see this has been fixed; surely though the right title for this topic is Nondegenerate bilinear form? They're the important ones .... 64.26.99.248 (talk) 18:24, 30 May 2024 (UTC)

I'm guessing there is a stupid Wikipedia reason for this bizarre state of affairs. Tito Omburo (talk) 21:35, 30 May 2024 (UTC)

The reason is probably history rather than policy. IAC, rather than renaming the article it might be better to merge it into Bilinear form with {{R to section}} in the redirects. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:39, 31 May 2024 (UTC)

That sounds reasonable. XOR'easter (talk) 00:26, 6 June 2024 (UTC)

Uncited statements at 0#Computer science

A few statements at 0#Computer science need support from manuals, textbooks, and/or histories. I know math people aren't necessarily computer people, but it seemed a good idea to raise the signal here too. XOR'easter (talk) 02:42, 6 June 2024 (UTC)

Doi will be added to the Theory and Applications of Categories

See this blog post. SilverMatsu (talk) 15:31, 6 June 2024 (UTC)

SVG rendering bug is fixed

I'm happy to announce that MediaWiki has finally updated their SVG rendering library to a less obsolete version, and as a result plenty of bugs were fixed, including the one that sparked a discussion here back in March. Tercer (talk) 20:23, 6 June 2024 (UTC)

Thanks for the good news! —David Eppstein (talk) 20:31, 6 June 2024 (UTC)

History of the definition of the real numbers

I am confused by the Wikipedia description of the history of the definition/construction of real numbers:

• In Real number § History: The first rigorous definition was published by Cantor in 1871. No indication on the method (infinite decimals?)
• In Construction of real numbers: Nothing
• In Foundations of mathematics § Real analysis: In 1858, Dedekind proposed a definition of the real numbers as cuts of rational numbers
• In Dedekind cut, the note 3 refers to Dedekind, Richard (1872). Continuity and Irrational Numbers. Apparently, 1972 is the date of the English translation, not of the original in German. This seems confirm that Cantor's definition was not the first one.
• In fr:Charles Méray (translated): In 1869 he is the first to give a rigorous construction of the real numbers. This construction is based on equivalence classes of Cauchy sequences of rational numbers.

Similarly, it depends on the Wikipedia article whether the first (ε, δ)-definition of limit must be attributed to Bolzano, Cauchy or Weierstrass.

Could someone provide a clarification? D.Lazard (talk) 18:28, 12 June 2024 (UTC)

I'd hazard that the 1858 date is the erroneous one for Dedekind. Stetigkeit und irrationale Zahlen was published in 1872 [1]. However I think the question of priority is the wrong frame for the construction of the real numbers. One first needed integers (Peano), rationals (maybe Dedekind), infinite sets (Cantor), by which point of course "the real numbers" were already in some sense defined! Tito Omburo (talk) 22:20, 12 June 2024 (UTC)

According to Kline, Dedekind had given lectures in 1858 where he realized real numbers hadn't been properly formalized, but these ideas weren't published until 1872. It also looks like Meray (1869), Heine (1872), Cantor (1871) and Dedekind (1872) all published some constructions of the irrationals in around the same time frame, but its difficult to locate the primary sources. Weierstrass claimed to have presented a rigorous construction in 1859 that was never published. Tito Omburo (talk) 22:39, 12 June 2024 (UTC)

Clarification should be in the form of a reference to a history. Johnjbarton (talk) 22:25, 12 June 2024 (UTC)

There's an issue of publication vs. discovery. See the following (bolding for emphasis):

Dedekind worked out his theory of Dedekind cuts in 1858 but it remained unpublished until 1872.

Weierstrass gave his own theory of real numbers in his Berlin lectures beginning in 1865 but this work was not published.

The first published contribution regarding this new approach came in 1867 from Hankel who was a student of Weierstrass. Hankel, for the first time, suggests a total change in out point of view regarding the concept of a real number [...]

Two years after the publication of Hankel's monograph, Méray published Remarques sur la nature des quantités in which he considered Cauchy sequences of rational numbers [...]

Three years later Heine published a similar notion in his book Elemente der Functionenlehre although it was done independently of Méray. [...] Essentially Heine looks at Cauchy sequences of rational numbers. [...]

Cantor also published his version of the real numbers in 1872 which followed a similar method to that of Heine. His numbers were Cauchy sequences of rational numbers and he used the term "determinate limit". [...]

As we mentioned above, Dedekind had worked out his idea of Dedekind cuts in 1858. When he realised that others like Heine and Cantor were about to publish their versions of a rigorous definition of the real numbers he decided that he too should publish his ideas. This resulted in yet another 1872 publication giving a definition of the real numbers.
— O'Connor, John J.; Robertson, Edmund F. (October 2005), "The real numbers: Stevin to Hilbert", MacTutor History of Mathematics Archive, University of St Andrews

I think this is also covered in some of MacTutor's cited references. So Dedekind is often credited with the first construction in 1858, the first publication is credited to Hankel in 1867, the first publication with a "rigorous construction" is credited to Méray in 1869 or Cantor in 1872 or Dedekind in 1872. — MarkH₂₁^talk 22:44, 12 June 2024 (UTC)

Many thanks (I have fixed the parameters in your reference to Mac Tutor). D.Lazard (talk) 08:29, 13 June 2024 (UTC)

Can someone explain what Riemannian circle is supposed to be?

My guess is that the article Riemannian circle has an incorrect definition; as it is described there it seems like an obfuscated synonym for great circle, which should just be redirected there. But it wouldn't make any sense to call a great circle a "Riemannian circle" instead, so I imagine the term is probably supposed to mean something different instead. However, I don't really have the background or patience to sift through old sources trying to figure out precisely what. Can someone who knows about Riemannian geometry figure out what is going on there? –jacobolus (t) 02:40, 13 June 2024 (UTC)

Just WP:BOLDly redirect. The article has offers references and even if it did the content would be better in great circle. Johnjbarton (talk) 03:01, 13 June 2024 (UTC)

I don't want to do that because my expectation is that Riemannian circle means something different; if so, it would be better to delete the page instead of redirect. However, it would be better still if someone can replace this with a more accurate definition. (Doesn't have to be anything fancy; it's fine if the page remains a stub.) –jacobolus (t) 03:12, 13 June 2024 (UTC)

To me, as defined there, it appears to be an obfuscated definition for the metric space of arc length around a circle. Embedding it as a great circle on a sphere and then using geodesic distance on the sphere doesn't change anything. Also the part about Gromov is described better at filling area conjecture.

Searching Google Scholar for this phrase finds varying definitions:

• This definition, the arc length metric on a closed curve of length $2\pi$
• Arc length metric on any closed curve
• Arc length metric on a closed curve embedded as a rectifiable curve in a Euclidean space
• "A curve in a Riemannian space whose development in a tangent space is a circle"

The first three are not different except for scale, and seem like the majority of uses.

We probably should have an article on the arc-length metric on simple closed curves, and this title seems like a plausible place to put it if it doesn't already exist elsewhere with better content. So my tendency would be to attempt a rewrite along those lines, removing the definition about geodesics on a sphere between points of a great circle except more briefly as the conjectured answer to the filling area conjecture. —David Eppstein (talk) 04:34, 13 June 2024 (UTC)

Rewrite done and moved to metric circle, somewhat more common and less ambiguous. —David Eppstein (talk) 07:50, 13 June 2024 (UTC)

Thanks! –jacobolus (t) 08:52, 13 June 2024 (UTC)

While we're here, is there any place where this topic can be put into context and related to nearby topics? I feel like our collection of circle-related topics are somewhat atomized and not fit together into any particularly coherent narrative, many are incomplete, they don't do all that much interlinking, etc., and we're lacking much high-level overview. We have Circle, Circle group, Angle (but no separate "Angle measure"), Turn (angle), Radian, Arc length § Arcs of circles, Directional statistics, Circular distribution, Circular mean, Periodic function, One-dimensional symmetry group, Trigonometric functions, Fourier series, Root of unity, Cyclic group, Modular arithmetic, .... Some kind of summary should be in a section Circle but that article also has to discuss the way circles fit into other spaces making it a poor fit for substantial expansion in this direction. I'm not sure if the name Metric circle is used widely enough or if that article quite fits as a central place for discussing the use of the circle as a geometric space though.

As a separate aside, should we have an article Periodic interval or the like? We currently don't, but it seems worthwhile (though it overlaps with many of the topics I listed above). –jacobolus (t) 21:11, 17 June 2024 (UTC)

Let's not forget Jordan curve, pseudocircle, and quasicircle as topological forms of circles.

Anyway, in my rewrite I wanted to focus on specifically the one-dimensional compact Riemannian manifolds (a phrase that unfortunately does not turn up much good sourcing). One can find circle-like objects as Euclidean shapes, objects in topological spaces, rings, etc., but I think trying to write a single article about all of them would be too incoherent. —David Eppstein (talk) 21:45, 17 June 2024 (UTC)

A-class

As far as I remember, WP:WPM was no longer to include A-Class. However, the article Stanislaw Ulam has become an A-class in Military History Project. If that's the case, is it possible that WP:WPM (as well as the other WikiProjects) also consider this article as A-class instead of GA? Dedhert.Jr (talk) 03:18, 21 June 2024 (UTC)

Why? Who cares? The little green plus badge seems fine. If someone cares enough someday they can try to put a little gold star on there instead. –jacobolus (t) 06:08, 21 June 2024 (UTC)

A-class is defunct everywhere except milhist. We cannot consider it to be A-class for other projects because being A-class requires a project-specific dedicated review process that no other project has any more. Technically A-class is a higher rating than GA (but below FA). The solution is to list it as GA in all other projects but with an exception as A-class for milhist. —David Eppstein (talk) 07:13, 21 June 2024 (UTC)

Weren't that time many WikiProjects did some review for A-class? I understand that many of them become defunct nowadays, except for the military history, but is there any solution to change the whole assessment system so that the A-class may also be included in different ways? Wasn't there any discussion about this problem? There was actually if I am not mistaken. It's probably gonna awkward for some WikiProjects does not have A-class, except for that one, in my opinion. Dedhert.Jr (talk) 12:24, 21 June 2024 (UTC)

The solution is to eliminate A-class altogether. But you would need to take that up with the milhist people. —David Eppstein (talk) 18:29, 21 June 2024 (UTC)

@Dedhert.Jr, is there a particular reason you want to have an A class? I think if "B" as basically "whoever rated it thinks it has high quality but it never went through an explicit review", then both GA and FA just tell whether a reviewer gave the article a (hopefully careful) review and then agreed with the nominator that a visible corner badge was warranted. @David Eppstein, maybe we should remove all discussion of "A" class from Wikipedia:WikiProject Mathematics/Assessment. –jacobolus (t) 23:06, 21 June 2024 (UTC)

I went ahead and took A class out of Wikipedia:WikiProject Mathematics/Assessment, as well as making the description there of B class sound a bit more polished than previously. My impression is that B class should generally be at least approaching GA quality; we have both "C" and "Start" to describe articles that still need significant work. –jacobolus (t) 01:04, 22 June 2024 (UTC)

@Jacobolus. Well, if anybody wants to have an A-class, then I guess I can give them support, but I have no idea where to start. It reminds me about the discussion of GAN in which someone enticed to nominate the article to higher class FA: Prime number, Reversible cellular automaton, and Prince Rupert's cube. But for nowadays, this is fine. Dedhert.Jr (talk) 09:07, 22 June 2024 (UTC)

OR cleanup at an Archimedean topic

Wikipedia:No_original_research/Noticeboard#The_Method_of_Mechanical_Theorems is of interest to this WikiProject. It concerns The Method of Mechanical Theorems, about a work by Archimedes that was rediscovered in 1906. I am in the process of cleaning up the explanation of the propositions, which has no references and is written like a textbook, and have already completely rewritten the explanation of the lead. My current idea is to summarize each proposition in accordance to the principles of MOS:PLOT, with possible secondary sources about the text; an English translation by the discoverers of the text is in one of the current references. –LaundryPizza03 (dc̄) 21:38, 21 June 2024 (UTC)

I don't think there is any problem explaining a proof. In fact, WP:TECHNICAL explicitly encourages editors to write things in a way that can be understood by a broad audience. In particular, this section blanking removed content that is not only not original research (it is broadly consistent with Heath's summary of the method), but also is extremely useful in understanding the article as a whole (and in fact is a very lucid exposition of Archimedes method of proof). Accordingly, I have reverted the removal of this introductory section, as well as the removal of the section on volumes. I think the substantive problems are mostly over style (phrases like "we see that", common in mathematics exposition). Finally, please don't coopt WP:PLOT. This is a real scientific topic, and there is absolutely no reason not to explain the method in an "in universe" tone, like we would with any other scientific topic. Tito Omburo (talk) 23:43, 21 June 2024 (UTC)

More mathematically literate editors are badly needed there. The article is quite good, given that it is supposedly rampant with "original research". Much clearer than either Heath's summary of The Method or The Method itself. Tito Omburo (talk) 00:12, 22 June 2024 (UTC)

Setting all other issues aside momentarily, I don't see the relevance of MOS:PLOT here. That is about summaries of fictional works; the concerns addressed there are orthogonal to the ones relevant here. XOR'easter (talk) 16:35, 22 June 2024 (UTC)

I'm not sure it's worth carefully following, but much of the concrete advice in MOS:PLOT seems more or less applicable to technical books too. For instance we want to keep a neutral "out of universe" tone, using a "narrative present" tense, it's worth being explicit about the difference between description of the text vs. commentary, it's usually better to write summaries as prose instead of lists or timelines, and it's reasonable enough to cite a work itself as a primary source about its own content. Much of the advice is fiction-specific though. One part that shouldn't be forced on technical-book articles is "Plot summaries cannot engage in interpretation and should only present an obvious recap of the work." We should be clear about which part is summary vs. interpretation, but these could certainly be organized per chapter or per topic instead of rigidly separated into different top-level sections of the article. –jacobolus (t) 17:37, 22 June 2024 (UTC)

I prefer to base descriptions of the content of non-fiction books purely on what published reviews of those books say the books are about. MOS:PLOT is in a guideline whose full title is Manual of Style/Writing about fiction; as that title makes clear, it does not apply to nonfiction. —David Eppstein (talk) 21:09, 22 June 2024 (UTC)

Pythagorean quadruple, Formulas for generating Pythagorean triples

Both recently (well, a few months ago) edited heavily by Tetraso, mostly focused on citing the work of one Robert Amato. This was also true the last time this editor appeared on WP, in 2017 (see User_talk:Tetraso#Your_edit_in_Pythagorean_triple). Could perhaps use some more eyes; I'm particularly skeptical of the fact that it comes with the disappearing of an earlier, obviously reliable, source. --JBL (talk) 20:30, 21 June 2024 (UTC)

Jay Bee Ell‬,

Let's start with the topic 'Formulas for generating Pythagorean triples.' I would just like to contribute by adding some results that improve knowledge and are not focused on citing a scientific article. Several experts in the subject have cited or used the result that I added. In this regard, please see https://www.scopus.com/authid/detail.uri?authorId=57190007076. Regarding the author, please see https://orcid.org/0000-0002-7058-2128. I have only reported the results, trying to be concise. Those who wish to see the proofs of the reported results should have access to the references of the scientific article. The results are innovative and suitable for obtaining new results and applications in fields such as geometry, trigonometry, linear algebra, and number theory, as you can see in 'A Novel Approach for Studying Pythagorean Triples Suitable for Students at all Educational Levels' (https://ejpam.com/index.php/ejpam/article/view/5133). Regarding the topic 'Pythagorean quadruple,' I have just corrected an injustice. Wacław Sierpiński, in the article 'Pythagorean Triangles' pp. 102–103, did not cite that the result is based on the results of the article published in 1981, which you can find at https://zbmath.org/0586.51019. I have reported the 2017 article because it contains comprehensive results and because it is impossible to find the 1981 article, as the journal where it was published no longer exists. The cited journals were indexed (at least in the year of publication) in Scopus and Web of Science. Thanks. Tetraso (talk) 09:17, 22 June 2024 (UTC)

The long section in Formulas for generating Pythagorean triples looks undue, particularly given that it is only supported by a single primary source that has mostly been cited by its own author. XOR'easter (talk) 16:32, 22 June 2024 (UTC)

I had the same impression. The added citations seem good otherwise, though I haven't checked them carefully. Tito Omburo (talk) 17:10, 22 June 2024 (UTC)

The long section is the concise statement of two theorems that allow, given a predetermined integer, to find all the Pythagorean triples that contain it or only the primitive triples. The primary sources are two and distinct. Tetraso (talk) 18:04, 22 June 2024 (UTC)

@Tetraso I think the concern is that your only contributions to Wikipedia consist of promoting your own publications, and your published articles seem to be in journals with lax editorial standards. In general Wikipedia is not intended to be a venue for self promotion, and articles should try to be neutral with weight given to various aspects of the topic / particular sources in proportion to their importance as recognized in the literature broadly. Sometimes expert Wikipedians cite their own papers or cite papers by people they have directly worked with when they think it is necessary for the article (e.g. the first or an important source about an essential claim), but most are modest about this, giving credit where due to other sources, minimizing self aggrandizement, and trying to keep the articles balanced as best they can; citing themself is typically a tiny proportion of a Wikipedia author's effort. When a Wikipedian has a clear conflict of interest others treat those contributions with necessary skepticism, and when a Wikipedian focuses on self promotion and makes no other contributions it's often abusive or disruptive, and those contributions are commonly reverted. –jacobolus (t) 18:37, 22 June 2024 (UTC)

Dear Jacobolus, I don't understand how you can say that the articles are published in journals with lax editorial standards. These journals are indexed in Scopus or Web of Science. This is simply offensive. I don't see any self aggrandizement in wanting to contribute results that can be useful for the topic. Is including references self aggrandizement? You are discouraging participation in the community and the free exchange of information. I have no personal advantage in adding results to Wikipedia. Tetraso (talk) 19:02, 22 June 2024 (UTC)

I didn't investigate closely, but in User talk:Tetraso#Your edit in Pythagorean triple D.Lazard mentioned a predatory journal.

In general, we should aim to cover aspects of a topic that are mentioned in highly cited and well respected secondary sources such as textbooks or survey papers. Sometimes newer sources are are worth citing in regard to some new details about existing topics, but typically as one source among many.

Novel work about new aspects of a subject that is published in somewhat obscure journals and hasn't yet had time to garner community feedback and respect is often best to just wait on. If it proves to be important, then over the following years that will be made clear as it is discussed and built upon by other authors, summarized in survey papers, etc.

As with most other decisions in Wikipedia, there are no black and white rules for these editorial decisions, and ultimately what sticks around in articles depends on Wikipedians' consensus.

If you are an expert about Pythagorean triples, presumably you know some things that are not yet in the article but discussed in the literature (not specifically your own published paper), which would be worth adding with a clear summary and the appropriate citations. After all this is a topic which is centuries old and which has been written about by hundreds of authors. But from what I can tell you haven't tried to do that.

It's hard to imagine that the only thing any expert can think of that is missing from some article(s) but is essential to include is their own personal work. So if all a Wikipedian does is cite themself, that raises red flags: it seems more like an effort to use Wikipedia to direct readers to the author's own work, and less like an attempt to make the article the best it can be. It shortcuts the work of doing serious literature survey and the hard decisions involved in writing the encyclopedia, instead forcing that work on other volunteers who must rush to evaluate the cited source and its impact and rewrite the appropriate sections to weigh it against other sources and put in in proper context. –jacobolus (t) 20:54, 22 June 2024 (UTC)

JP Journal of Algebra, Number Theory, and Applications (which published the 2017 paper [2]) was de-listed from MathSciNet; it is published by Pushpa, which was on Beall's List. Also it is beyond bizarre to complain that Wacław Sierpiński (who died in 1969) didn't cite (in his publication from 1962) a paper written in 1981. (I also do not understand how this would be a justification for citing your own work from the past decade but not any of these prior works.)

Based on the discussion here I am inclined to revert both additions, the next time I have 30 minutes free. --JBL (talk) 21:29, 22 June 2024 (UTC)

Regarding Pythagorean Quadruples, I made a mistake because the year 2003 confused me. I am sorry. I have already provided the reference before. For Formulas for generating Pythagorean triples, do as you see fit. Tetraso (talk) 22:42, 22 June 2024 (UTC)