Wikipedia talk:WikiProject Mathematics

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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)

Merge Measurable space into Measure space

This seems sensible, doesn't it? IntGrah (talk) 23:45, 26 May 2024 (UTC)

Maybe, maybe not. The benefit of having two separate pages is that it makes it clear that the notions are different. This also allows other pages that reference these concepts to reference specifically the definition they need and thereby to minimize possible confusion. Note also that each of these two pages has "Not to be confused with ..." link at the top, and also shows the contrast with the other notion. But I can see that this could be debated. PatrickR2 (talk) 06:00, 27 May 2024 (UTC)

I think they should not be merged, since they are different concepts. Note that the Springer EoM also has separate articles for the concepts. Tito Omburo (talk) 12:19, 27 May 2024 (UTC)

Fair enough. I was hoping that one concept would just be described in a sentence in another article, like Weighted graph in Graph, but I see otherwise now. IntGrah (talk) 13:17, 27 May 2024 (UTC)

The two concepts are importantly rather different, especially in applications of measure theory (e.g., probability and dynamics). Tito Omburo (talk) 15:05, 27 May 2024 (UTC)

Agree w/Tito, Patrick. 67.198.37.16 (talk) 02:04, 29 May 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)

Advice on dealing with questionable citations in lead

I'd like some advice on how to handle a problem which I encounter quite often in articles covering basic topics that are widely used in other fields.

The typical scenario goes like this: A is a central notion that was introduced a while ago and on which there are plenty of old and recent textbooks. A is now used in many fields outside of mathematics, and maybe in a trendy field such as machine learning. Some people keep adding references to recent textbook or articles on A in the lead.

Sometimes the references are research articles published in obscure journals, and in that case this is not really a problem (even though one might need to remove the same reference several times). But in some cases the references are legit — or at least "legit-looking" — textbooks, and then because Wikipedia does not have very clear guidelines regarding citations in the lead, I am not always sure what to do and end up losing time.

Maybe a concrete example will help: Have a look at the recent [as of 11/06/2024] history of the article Markov chain, more specifically at this diff and this one. Here we have two different IPs located in Romania who are actively monitoring the article and who seem extremely upset that a textbook by a Romanian author is not listed first to back-up:

• the definition of a Markov chain;
• the assertion that "Markov chains have many applications as statistical models of real-world processes";
• the fact that Markovian and Markov can be used to refer to something that has the Markov property.

Of course, that makes me think that the person behind these IPs is either the author of said textbook; or someone who really likes this textbook.

The problem is that, as far as I can tell without reading it, this does indeed seem like a legitimate textbook on Markov chains. In fact, by some metrics it even seems to be a popular textbook: despite being fairly recent, it is already cited 900 times. That is of course impressive...But also not very surprising, considering that it has been the first reference of the Wikipedia article on Markov chains for a while.

(in fact, to try to get an idea of whether most people citing that book actually did so to reference specific properties and theorems, or simply to add a citation after their first use of the phrase "Markov chain". I am not going to copy and copy and paste excerpts, so as not to point fingers; but some authors seem to think that Gagniuc invented Markov chains, others that think that he recently discovered the game-changing fact that the rows of a stochastic matrix sum to 1, etc).

So, on the one hand I think that reference should be removed from the lead (and probably from the article altogether), because there are tons and tons of excellent textbooks on Markov chains, and I have some suspicions of self-promotion with this one (not to mention that I have no idea whether it is any good). On the other hand, this seems to be a legitimate reference (again, I have not read it) and so I can't really base myself on any clear Wikipedia policy to do so.

I would of course appreciate if someone could help me with this specific example (especially since it looks like some IP users are ready to engage in edit-warring). But I am mostly asking for general guidance here, because it is a problem I encounter regularly.

Best, Malparti (talk) 23:49, 10 June 2024 (UTC)

I'm inclined to agree that these fairly innocuous statements shouldn't be cited in the lead (per the guideline WP:LEADCITE) but instead in the body. The Gagniucs citation is particularly silly as it is used because it cites a 200+ page book without giving a page number. I suggest migrating citations out of the lead into the corresponding places in the body, leaving WP:LEADCITE in your edit summary; if you actually do run into any trouble (your idea about this doesn't seem entirely supported by data) then bringing the issue up here (and perhaps in parallel on the article's talk-page) and seeing if the angry IP pretending to be two different people engages. --JBL (talk) 00:28, 11 June 2024 (UTC)

This can also happen more innocently, when some random editor asks for a citation of some claim and then, to clear the citation needed tag, another editor does a search and finds a random citation that matches the claim. Especially in cases where a claim is a basic fact that everyone working in a subject knows but few bother to write down (because it is so basic), or when the terminology has shifted and the texts haven't been updated to match, finding the claim in a standard textbook rather than in a recent research work can sometimes be difficult. —David Eppstein (talk) 00:42, 11 June 2024 (UTC)

@David Eppstein I agree; but I think that it is usually possible to distinguish the situations I am referring to and the more innocent situations that you describe. For instance, Gagniuc's book is repeatedly cited to back-up statements that do not really need a reference, such as "Markov chains can be used to model many games of chance". So to me it really looks like someone — not saying it is Gagniuc; it could be, e.g, a student that worships him — tried to promote his book. Malparti (talk) 23:48, 11 June 2024 (UTC)

Oh, I agree in this case, but "Markov chains can be used to model many games of chance" is exactly the sort of obvious statement that you're likely to see editors demand citations for. For this sort of thing, expository articles rather than research articles or monographs might be a better fit; I found for instance "How long is a game of snakes and ladders?" Math. Gaz 1993 and "Snakes and Ladders and Intransitivity, or what mathematicians do in their time off" Intelligencer 2023. Also those editors may well argue that "many" is WP:PEACOCK and that we should provide specific examples (of which snakes and ladders is one). —David Eppstein (talk) 00:07, 12 June 2024 (UTC)

@David Eppstein Arf, yes you are right; I've actually taken part in unproductive debates on this topic on Wikipedia in another language, and would rather avoid this on en.wiki (all the more so since I tend to be a bit more on the WP:BLUE end of the spectrum than most editors). But thanks a lot for the references, they are indeed much better suited than the current ones so I'll add them to the article over the weekend; ideally, I should take the time to do the same thing for all other such citations... Malparti (talk) 00:19, 12 June 2024 (UTC)

@JBL Thanks, that is useful advice. In fact I don't think that migrating citations out of the lead is needed: in my opinion the body of the article already contains quite a lot of unnecessary citations... Malparti (talk) 23:56, 11 June 2024 (UTC)

Uncontroversial statements discussed later in the article don't need any citation in the lead section, and it can be more legible for readers to defer those footnotes until later. (Of course, it can also be fine to include footnotes in the lead, e.g. when linking to the original source where something was first described.) More generally, when trying to support uncontroversial widely known claims, there are often hundreds+ of sources that could be cited. If you have one easily available, I would recommend leaning on popular and widely cited textbooks or survey papers rather than more obscure sources. People shouldn't be trying to use Wikipedia for self promotion via citation spam. –jacobolus (t) 01:55, 11 June 2024 (UTC)

I generally support moving citations out of the lead into the body or into {{refideas}}, with a comment to the effect that the citation should be deferred to the body. Is there a template with the semantics this is the wrong place for a citation?

I'm a bit hesitant to complain about citation spam, because there are often articles whose contents are garbage but that contain useful citations. In fact, sometimes I use wiki as a search engine and go straight to the references -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:43, 11 June 2024 (UTC)

@Jacobolus "when trying to support uncontroversial widely known claims, there are often hundreds+ of sources that could be cited. If you have one easily available, I would recommend leaning on popular and widely cited textbooks or survey papers rather than more obscure sources." → Yes of course. But my problem is specifically in cases where there is already a source, and it looks like a legit textbook (here: Gagniuc's book is published by a reputable publisher, and very cited) but it still looks like there is something fishy going on. I see it quite frequently. Less frequently than the situation where someone adds an irrelevant paper published in an obscure journal (but, as I said this is not a problem because in that case it takes me very little time to see what is going on and to remove the citation); but still frequently enough that I am starting to feel like this is making me waste my time. Malparti (talk) 00:04, 12 June 2024 (UTC)

If the source clearly supports the claim and is in a highly cited legit textbook, then I wouldn't worry too much about including it in the article somewhere. The lead of Markov chain is currently absurdly overstuffed^[1][2] with gratuitous footnotes.^{[3][4][5][6][7]} In my opinion these should be either removed to the body of the article or consolidated into no more than a couple per paragraph, for legibility. If Gagniuc's book is clear and well written, I think it would be fine enough to include book among a list (inside a single footnote) of relevant survey sources supporting some particular claims in the lead, but it would also be fine to entirely defer those references to the body. Gagniuc's book should be moved down to the "References" section, and a specific page mentioned for each time it is used as a reference. A 20 page research paper is fair enough to cite as a whole unit for a list of claims, but vaguely waving at a 200+ page textbook is too much. –jacobolus (t) 00:30, 12 June 2024 (UTC)

I concur with the sentiment expressed above that uncontroversial statements in the intro that are adequately elaborated upon in the main text don't need footnotes. In this particular case, that block of four citations in a row is just silly. Actually, that whole sentence has problems. The main text of the article doesn't say anything more about "cruise control systems in motor vehicles" (which sounds like a weirdly niche application to advertise up top), or queuing at an airport specifically, or currency exchanges. I'd cut that line after "of real-world processes" and replace the rest with a better summary. XOR'easter (talk) 16:07, 11 June 2024 (UTC)

@XOR'easter I agree that the article has many problems... In fact I think this is one of these articles on a popular topics that suffers a bit from "constant-growth" and needs to be trimmed on a regular basis; but that's a somewhat different issue. I might try to rewrite the lead over the weekend (but I'm pretty sure that if I remove oddly specific examples, they are going to be replaced by other ones in no time). Malparti (talk) 00:06, 12 June 2024 (UTC)

I tried tidying it up, but you're definitely welcome to do a more thorough job! XOR'easter (talk) 21:11, 12 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)