Wikipedia talk:WikiProject Mathematics/Archive/2022/Feb

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". [1] [2] [3] [4] [5] [6].
• 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.wiki.x.io/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: [7] and [8]. 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 [9]? 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.wiki.x.io/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 [10] 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)