Wikipedia talk:WikiProject Mathematics

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Emmy Noether FA review

It would be much appreciated if people could read the Emmy Noether article and check for statements that are unclear, under-cited, or otherwise unbecoming the encyclopedia project. XOR'easter (talk) 22:06, 12 October 2024 (UTC)

For those more knowledgeable with the subject matter than I am, the two sections that may need some more citations the most are the ones on ascending and descending chain conditions and algebraic invariant theory. Sgubaldo (talk) 23:29, 12 October 2024 (UTC)

My impression from working on the article previously was that everything discussed in it is addressed in the references already present (and for a math topic, having a clickly blue linky number for each sentence doesn't necessarily go further to satisfying WP:V than having one per subsection). But this would be a good opportunity to point readers at references that are particularly good. Anybody have favorite books about either of those? XOR'easter (talk) 18:30, 13 October 2024 (UTC)

The section on algebraic invariant theory doesn't make enough contact with Noether's work in the area, which was eclipsed by that of Hilbert. Both the Rowe and Dick source describe her dissertation done under Gordan, which was devoted to symbolic computation of invariants, and in fact a later source of some embarrassment. The section would benefit by emphasizing this, and summarizing the sources better (and referring to them). Tito Omburo (talk) 19:33, 13 October 2024 (UTC)

Care to tackle that? I could try, but I'm not sure when I'll have an uninterrupted block of time long enough. XOR'easter (talk) 21:00, 13 October 2024 (UTC)

@Sgubaldo, @Tito Omburo, @XOR'easter. The discussion now is into FARC: one delist and one keep. I have found some of the unsourced sections after looking up at its content. Dedhert.Jr (talk) 11:55, 29 October 2024 (UTC)

As an update to this, there's now 13 citation needed tags left to take care of. 5 are specifically in the ascending and descending chain conditions section. Sgubaldo (talk) 15:29, 3 November 2024 (UTC)

Thanks. XOR'easter (talk) 17:21, 4 November 2024 (UTC)

The first epoch of algebraic invariant theory says "an example, if a rigid yardstick is rotated, the coordinates (x₁, y₁, z₁) and (x₂, y₂, z₂) of its endpoints change ...". How is this related to the article but does not explicitly says about that example? Dedhert.Jr (talk) 07:25, 5 November 2024 (UTC)

I think that line was just trying to explain what "invariant" means. I trimmed the notation, since we don't use it later. 10 {{citation needed}} tags remain. XOR'easter (talk) 21:35, 10 November 2024 (UTC)

Needed: a readable introduction to algebraic invariant theory, and likewise for ascending/descending chain conditions. XOR'easter (talk) 20:17, 15 November 2024 (UTC)

I've reached out to an algebraist colleage to ask for assistance. --JBL (talk) 21:03, 16 November 2024 (UTC)

@JayBeeEll, apologies for the ping, just wondering if you were still able to do this. Sgubaldo (talk) 12:21, 6 December 2024 (UTC)

Hi Sgubaldo -- I'm traveling currently and not able to log in or to make time to edit at the moment. I did make a couple changes based on my colleague's advice that dealt with one or two of the cn tags (back in November) -- I think I can probably fix up a couple more of them, but I will not get to it for at least another week. --158.144.178.11 (talk) 17:08, 9 December 2024 (UTC)

Alright, thank you. Sgubaldo (talk) 17:12, 9 December 2024 (UTC)

I've done the cn tag relating to Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern, which was mentioned in the FAR. I have a question about one of the sentences in that paragraph. Full disclosure that I am not familiar with much abstract algebra. The sentence currently reads "...the Dedekind domains: integral domains that are Noetherian, 0- or 1-dimensional, and integrally closed in their quotient fields." and defines Dedekind domains.

This is what Page 13 of Noether, 1983 (collected papers) says (formatted slightly for brevity):

In Abstrakter Aufbau der Idealtheorie ... Noether gave the first characterization of the class of rings now known as Dedekind rings: the commutative rings in which factorization of ideals as products of prime ideals holds. She showed that the following conditions were necessary and sufficient for the validity of the prime ideal factorization theorem:
I – The ascending chain condition for ideals.; II – The descending chain condition modulo every non-zero ideal.; III – Existence of a unit element.; IV – Non-existence of zero divisors.; V –  Integral closure in the field of fractions.

This is what Page 96 of Rowe, 2021 says:

In [Noether 1927a], Emmy Noether was able to give a general proof of Dedekind’s fundamental theorem and its converse on the basis of five axioms for a Dedekind ring. In her earlier paper [Noether 1921b], “Theory of Ideals in Ring Domains,” she introduced a general concept for rings that merely had to satisfy one axiom: the ascending chain condition. This acc now became Axiom 1 in [Noether 1927a] and its counterpart, the descending chain condition (dcc), was formulated as Axiom 2. She had not, however, explicitly stated that the ring R must possess an identity element for multiplication. Pavel Urysohn brought this oversight to her attention in 1923, and so she introduced this as Axiom 3, while pointing out that Urysohn had alerted her to it [Noether 1927a, 494]. Axiom 4 further stipulates that the ring must have no zero divisors. Finally, Axiom 5 introduces the decisive condition that the ring R must be algebraically closed in its associated quotient field (i.e. the smallest field that contains R). These are the five axioms for a Dedekind ring found in textbooks today.

I wanted to change it to something like "... Dedekind domains. Noether showed that five conditions were necessary for this to be valid: the rings have to satisfy the ascending and descending chain conditions, they must possess a unit element, but no zero divisors, and they must be integrally closed in their associated quotient fields." but I was worried it was either wrong or redundant. Sgubaldo (talk) 21:25, 18 November 2024 (UTC) Sgubaldo (talk) 21:25, 18 November 2024 (UTC)

The current version is heavy on modern terminology. I suggest "the ideals have unique factorization into prime ideals (now called Dedekind domains). Noether showed that these rings were characterized by five conditions: they must satisfy the ascending and descending chain conditions, they must possess a unit element but no zero divisors, and they must be integrally closed in their associated fields of fractions." + appropriate wikilinks. --JBL (talk) 23:39, 19 November 2024 (UTC)

Done, thanks. Sgubaldo (talk) 00:24, 20 November 2024 (UTC)

Update: citation needed tags are down to 5. Per XOR'easter's message above, two are in the the algebraic invariant theory section and two are under the acc and dcc section. The algebraic invariant theory section, or perhaps both, could do with a better introduction. Sgubaldo (talk) 19:16, 21 November 2024 (UTC)

References

History of representation theory

If anyone here wants to contribute to this new stub, please do! Geometry guy 01:54, 24 November 2024 (UTC)

@Geometry guy: It may make sense to cover invariant theory as well? Since it seems in the past, there wasn’t much a distinction between the two subjects. —- Taku (talk) 05:59, 5 December 2024 (UTC)

I agree - I think a history article like this should be quite broad. Representation theory links to invariant theory, harmonic analysis, the Langlands programme, quantum mechanics and much more, not "just" group theory. We may even decide to change the title at some point, but first there is a lot of material to gather! Geometry guy 13:05, 5 December 2024 (UTC)

Request for opinion on edit to List of Mersenne primes

On 3 November, I made two edits Special:Diff/1255182695 and Special:Diff/1255197206 which were promptly reverted Special:Diff/1255250737 by Szelma W (talk · contribs). On 5 November, I created Talk:List of Mersenne primes and perfect numbers#Recent reversion - is anything salvageable? to discuss the matter, as the revert's edit summary "It was better" didn't really give me a lot to go on.

The problem is, that editor normally edits about once a week with occasional longer gaps, but it's approaching 3 weeks now and they haven't been around to expand on those words. That in itself is not grounds for me to take offence; presumably their Real Life got busy and WP:NOT#Wikipedia is not compulsory.

But I'd like to discuss it with someone before just un-reverting. Is anyone up to having a look at those edits (particularly the larger second one) and their justification on the talk page, and expressing an opinion? Note that this is not the usual after-lengthy-debate request for a 3rd opinion; in this case there has been almost no debate and there are no hurt feelings to worry about. You're free to make your own edit in lieu of any of the available versions, or give me some advice or whatever you like. I just don't trust my own judgment on what's an improvement in this particular case.

Thank you very much!

(I'm sure that re-reading my own edit after three weeks, I'll find something to improve, but I've avoided doing that so far since adding a third version to the discussion is of no use until there's a discussion to add it to.) 97.102.205.224 (talk) 07:02, 24 November 2024 (UTC)

One question from me: why would you break the whole paragraph into several pieces? For example, the first paragraph is meant to be a basic explanation of the background of the Mersenne primes and perfect numbers briefly, with the target started for the audience who did not understand anything about those classes of numbers; the second one is meant to the next step advanced level to understand more about the relationship between those numbers. Breaking them up into several paragraphs, just like you did in your edits, was meant to be each paragraph with overlapping topics between two classes as in the second paragraph you wrote about the perfect numbers and Euler proved the relationship between Mersenne primes and even perfect numbers, with this and that and this and that ... Dedhert.Jr (talk) 04:29, 29 November 2024 (UTC)

@Dedhert.Jr: Thank you for the feedback! I was trying to get "one idea per paragraph". It used to be that the first paragraph talked about Mersenne primes, then started talking about perfect numbers. The second paragraph kept talking about even perfect numbers. I re-broke it so all the prime talk was in the first paragraph, and all the (even) perfect number information was in the second. This seemed (and still seems) better organized to me. (Thus my comment on the talk page "note the paragraph break in place of 'Meanwhile'.")

Once I started down this path, I tried to have topic-focused paragraphs, with a paragraph break where there was a change of focus:

1. Mersenne primes
2. (Even) Perfect numbers and the Euclid–Euler theorem
3. Odd perfect numbers (open problem)
4. Infinitiude (open problem)
5. Source of values in the table
6. Tentative numbering of 49–52

As I wrote in the edit summary, "Seriously rework lead to keep each paragraph focused on one idea. "

I'm trying to open a topic, say something about it, and then close the topic for the benefit of a lay reader who can't keep too many new (to them) ideas in their head at once. There are links between paragraphs, but they're weaker than the links within paragraphs. I also tried to order things so links between paragraphs were short but in logical order. Thus, I moved discussion of odd perfect numbers to immediately after the paragraph about even perfect numbers, pushing the infinitude issue down a little. The latter is more coupled to the list itself and the mechanics of search efforts, while new paragraphs 2 and 3 answer the question implied by the article title: "why is the list of Mersenne primes and the list of perfect numbers the same list?"

I feel that's an important question to give a clear answer to, and that clarity is served by separating the odd perfect number discussion from the infinitude question.

I'm quite interested in this discussion. To me, the reorganization is Obviously Better, and the point of the edit comment was mostly to draw other editors' attention to that over bikeshedding potential minor wording issues that could be fixed easily enough.

If it's not obvious to you, I have something to learn. 97.102.205.224 (talk) 02:39, 1 December 2024 (UTC)

The article List of Mersenne primes and perfect numbers has featured-list status, following the criteria of WP:FLCR. Per WP:TECHNICAL, they are quick summaries to make the (non-mathematics) readers understand, so you don't have to write an over-detailed explanation. Dedhert.Jr (talk) 10:01, 1 December 2024 (UTC)

@Dedhert.Jr: And I'm not trying to add details. I added no information, just reordered and regrouped what was already there. A second worry I had was that without a clear focus, the more open-ended style of the article before I edited it it would tempt an editor to add more detail. One of my goals in having discussion of a point end after its paragraph is to reduce the temptation to elaborate. The two critical points I think the article must cover are:

• how the list was made, and the prospects for its extension, and
• why the two lists are the same list.

If you see extraneous fluff that doesn't contribute to those points, I'm happy to delete it.

Would you mind if I copied & migrated this discussion to the article talk page? I think we will eventually want it archived there. (One way to agree is to do it yourself, of course.) 97.102.205.224 (talk) 13:20, 1 December 2024 (UTC)

I don't think changes should be added. The article is already in good shape. You can ask the nominator of the FL, but I am worried that one declared its issue in real life. So, you just have to wait for other responses in this project. But if you keep insisting on creating a draft in this place, I don't mind it; or you can create a sandbox: Talk:List of Mersenne primes and perfect numbers/sandbox Dedhert.Jr (talk) 01:29, 2 December 2024 (UTC)

As for why the two lists are the same list: we have a separate Good Article on that, Euclid–Euler theorem. —David Eppstein (talk) 02:56, 2 December 2024 (UTC)

@David Eppstein: Yes, and the text in the List article should be mostly a pointer to that, but I think the List article needs to say at least "there is a 1-1 correspondence between Mersenne primes and even perfect numbers due to the Euclid-Euler theorem, and it is unknown whether any odd perfect numbers exist, so the list below is all known perfect numbers." Maybe a few more words about the fact that the known constraints on odd perfect numbers are so tight most people suspect there are none, but that's negotiable.

The current text does explain the separate contributions of Euclid and Euler, which is also negotiable if abbreviation is desired.

It's just the fact that there is a theorem about even perfect numbers and an open question about odd perfect numbers (there are no known. nor a non-constructive existence proof, nor a disproof) that needs to be (IMHO) stated explicitly in the List article. I'd be opposed to e.g. merely mentioning Euclid-Euler and expecting the reader to know what it says.

(I'm happy to assume it's obvious to even a lay reader that all natural numbers are either even or odd. Going all Russell & Whitehead would not help clarity.)

---

(Deep breath.)

Circling back, while I don't mind also discussing what material should be in the List article, I'd like to not lose sight of my proposed reorganization which has no substantial additions or deletions of material.

It's particularly discouraging that the tangential discussion about what should or shouldn't be included has never gotten close to a specific proposal for an addition or deletion. If nobody's proposing such a thing, why are we wasting electrons discussing it? Are we in violent agreement that the List article should not be expanded?

I've been expounding at length on why I think the reorganization is an improvement, and my perception of the responses so far has been vague skepticism, neither agreeing nor explicitly disagreeing. If I'm wrong about it being an improvement, I'd urgently like to understand why, because the ability to judge good and bad writing is important to my ability to edit Wikipedia at all.

Thank you for your comments. 97.102.205.224 (talk) 09:04, 2 December 2024 (UTC)

Portals

User:Nerd271 is edit-warring to add the mathematics portal (which I consider to be totally useless noise; for instance its "did you know" entries have not been updated for many years) to articles including Noam Elkies, Hilbert's fifth problem, and Green–Tao theorem. I note that the portal is also linked from hundreds of other articles; I think it should be removed en masse, or at best kept only on the articles on major subfields of mathematics. Additional opinions welcome. —David Eppstein (talk) 01:52, 1 December 2024 (UTC)

User:David Eppstein - Hmmm. So we have another portal enthusiast. Hmmm. Robert McClenon (talk) 01:59, 1 December 2024 (UTC)

We do, and I see that development as positive. Wikipedians are divided on the merits of portals: several discussions have closed with substantial arguments for and against them but no consensus to remove them. A 2019 exercise in which you played a substantial role deleted most of our portals, hopefully keeping the better ones. Much of this portal's content rotates automatically. It would be useful for an expert to update its pools of source material. However, mathematics is not a particularly fast-moving field. It is not obvious that omitting recent developments (which would appear only occasionally) justifies unlinking the whole portal to prevent its discovery. Certes (talk) 18:15, 1 December 2024 (UTC)

Accusing me "edit-warring" is a bit of a stretch. I merely disagreed with David Eppstein and left it as that. There was no hostility on my part. But looking into the histories of those pages, you could see that Eppstein was rather hostile. Navigational panes and portals help our readers. Please see Wikipedia:Portal. Nerd271 (talk) 01:59, 1 December 2024 (UTC)

You disagreed and restored your edit two more times, failing to follow WP:BRD. That is edit-warring.

Portals are a decrepit and unmaintained relic of the earliest years of Wikipedia. They should go. —David Eppstein (talk) 02:05, 1 December 2024 (UTC)

That's an opinion of yours. I happen to disagree. I was just editing as normal. You boldly reverted me. But I was not convinced by your reasoning, so I reverted back. No hard feelings. You reverted me with comments in all caps. In response, I reverted you in return only on one page to avoid escalation. I don't think you can sensibly accuse me of edit-warring here. Besides, there is such a thing as BRD Misuse. You have the right to be bold and to disagree with other editors. But this behavior is not suitable for Wikipedia.

Anyway, there is no need to be so hostile to the point of dropping a threat on someone else's talk page. Consider using one of the relevant talk pages. We can bring in other opinions. Nerd271 (talk) 02:15, 1 December 2024 (UTC)

Perhaps you haven't noticed that this very discussion is one that I started, on this topic, on a relevant talk page? —David Eppstein (talk) 02:23, 1 December 2024 (UTC)

I was referring to the pages where you reverted me. They seem more relevant. One of them is sufficient. We can request a third opinion on there, too. Nerd271 (talk) 02:29, 1 December 2024 (UTC)

The issue is broader than individual pages. That's why I started a discussion here instead. —David Eppstein (talk) 02:43, 1 December 2024 (UTC)

Is anyone maintaining Portal:Mathematics? It does average about 300 daily page views, so at least some readers are winding up there, though it's not clear to me what those readers are looking for or what they need. Do people visit that page multiple times or are these one-off events? Are readers arriving there from Wikipedia:Contents/Portals (linked from the main page), from the portal links in various article see also sections, from the portal links in {{WikiProject Mathematics}} which appears on many talk pages, from Wikipedia:WikiProject Mathematics, or from somewhere else?

It seems like a mistake to me to link this portal from every mathematics article. Looking at Special:WhatLinksHere/Portal:Mathematics, I think such links should be removed from at least the vast majority of the articles there. The link in the WPM template is already quite enough marketing for this page IMO.

I can't see the relevance to Noam Elkies, to take the example here. David Eppstein's idea of linking it from a handful of articles (perhaps Mathematics, Geometry, Calculus, or the like) seems like a plausible compromise. –jacobolus (t) 05:51, 1 December 2024 (UTC)

The Portal:mathematics is linked by {{Math_topics_sidebar}}, so simply removing any explicit page links to the portal would cause only the major articles to have the portal link, per the suggestion of David Eppstein and Jacobolus. On the other hand I looked at how Portal:physics is linked in a few articles. It is erratic to be sure, but other than sidebars the links tend to be See Also. In this way the portal link is acting like a small tag that the topic of the article is in the field of physics. This does not seem bad. Perhaps the problem here is the lack of maintenance, which to be honest would hardly be special to Portals.

The claim that the Portal:mathematics needs maintenance is unclear because the page has no content of its own. There must be more to that story. Johnjbarton (talk) 18:44, 1 December 2024 (UTC)

Re maintenance: It has lists of "do you know" hooks, not updated for years, etc. They are all in cobwebby subpages. —David Eppstein (talk) 18:42, 2 December 2024 (UTC)

Well for example the Wikipedia main page has a bunch of people and a whole process involved in rotating the news items, obituaries, featured pictures and articles, and "did you know" entries, so that that visitors to the page will always see something fresh and will have some reason to return repeatedly. I'm not really the person to ask, as I don't spend much time looking at the Wikipedia main page, but others make a habit of browsing it every day.

I think the original concept for "portal" pages was that they would be similar, but since nobody does those tasks for other portals, they end up with a small stale collection of rotating info. I don't have a good sense of what kind of material would be interesting / enticing / ... to readers of a math portal page. I don't understand how/why people click through to there or what they are looking for, so I'm not sure how much effort it's worth putting in to improving it. –jacobolus (t) 17:29, 3 December 2024 (UTC)

Are we sure that the Portal is a problem? Do people who read it complain? As far as I can tell the rotation is automated. I did not see any rotating news items or obituaries. The content seems include a random selection of "Featured articles" for example. If there are parts that are human selected, we could simply remove those parts.

If we don't understand why people use it, I don't see how it follows that we should delete it or eliminate references. Johnjbarton (talk) 17:56, 3 December 2024 (UTC)

I'm not saying we should delete it. I just don't think it's relevant to put in the "see also" section of every mathematics article; those links seem like promotional spam to me, one more distraction for readers to tune out. –jacobolus (t) 18:05, 3 December 2024 (UTC)

balance puzzle

may someone be so kind to look at my comments in the talk page? thanks. 151.29.39.54 (talk) 17:36, 1 December 2024 (UTC)

What are you talking about? ‹hamster717🐉› ^{(discuss anything!🐹✈️ • my contribs🌌🌠)} 17:59, 1 December 2024 (UTC)

Talk:Balance_puzzle. --JBL (talk) 19:47, 1 December 2024 (UTC)

Partial trace

Hello. I came across Partial trace as part of the soon-to-be-ending WP:NOV24 unreferenced articles drive. It has been completely unsourced for some 15 years, and looks mathematics-y, but it is beyond me to try and sort out. I was hoping that a kind soul in WP:WPMATHS might be able to take it on. Or recommend a better project to ask for help. Thank you! SunloungerFrog (talk) 22:18, 1 December 2024 (UTC)

Thanks for the reminder. Partial traces are commonly found in Google Books and Scholars. Just wait for it, although I am not an expert in this field. Dedhert.Jr (talk) 01:34, 2 December 2024 (UTC)

Thank you very much Dedhert.Jr and Michael Hardy for your help with the article. Hugely appreciated! SunloungerFrog (talk) 09:18, 2 December 2024 (UTC)

Project page section on list of publications in mathematics

The project page includes a section referring (as a particularly good role-model...) to the recently deleted List of important publication in computer science. Should we rephrase the section, or should we simply remove it? I am not sure whether it adds much to our guidance to single out those articles in particular. Felix QW (talk) 17:33, 2 December 2024 (UTC)

It does not seem to add much useful information. I would say remove it. PatrickR2 (talk) 20:04, 2 December 2024 (UTC)

I have rewritten and renamed that section to focus on things we actually do now instead of abandoned/deleted cruft. The counterpart lists for computer science and for cryptography were both deleted this year. Apparently, List of important publications in mathematics survived a deletion debate back in 2011 because sources on that general theme do exist... but the article as it stands seems to be a big pile of OR. After a few years of outstanding complaints and no action, I refactored the corresponding list in physics to be policy-compliant instead of opinionating. XOR'easter (talk) 22:04, 7 December 2024 (UTC)

Thank you very much! Felix QW (talk) 09:08, 8 December 2024 (UTC)

Russian journal and pentagonal pyramid

I am having trouble reading the Russian language in this journal [1] after having so many improvements of the article Pentagonal pyramid from the user in Talk:Pentagonal pyramid/GA1. Can someone elaborate? Dedhert.Jr (talk) 05:20, 3 December 2024 (UTC)

Did you try translate.google.com? "... It was found that cathode activation allows growing pentagonal pyramids with high growth steps in large quantities. The paper presents experimental results on the relaxation of internal elastic stress fields associated with disclination-type defects in such pentagonal pyramids...." –jacobolus (t) 18:56, 3 December 2024 (UTC)

I have tried to use Google Translate, but this untrustworthy engine reminds me of the possibility that the translation may be inaccurate. Dedhert.Jr (talk) 01:53, 5 December 2024 (UTC)

Is "pentagonal pyramidal-shaped copper" just a block of copper in the shape of a pentagonal pyramid? XOR'easter (talk) 02:33, 8 December 2024 (UTC)

"In the work, copper pentagonal pyramids with high growth steps were grown by the method of electrodeposition on microgrids", as Google Translate said. Again, I am skeptical about the translation; an interesting topic, but sadly have to remove it later. Dedhert.Jr (talk) 09:04, 8 December 2024 (UTC)

Navigation templates for mathematical operations

There's a template, {{Mathematical expressions}}, which tries to summarize all the operations that can make up, well, a mathematical expression. I'm not sure where else it's used, but someone has placed an instance of it at the bottom of the Exponentiation article, in the manner of a navigation template.

I was surprised to see it there, and I don't think it really works as a navigation template. So I took a stab at creating a proper, Navbox-based navigation template, now at {{Mathematical operations}}.

The result is indeed a decent-looking navigation template, and it would work much better at the bottom of Exponentiation or any of the other articles it indexes, but: I really don't know if we need a navigation template like this at all. Also I'm no mathematician, so the categorization scheme I've created within {{Mathematical operations}} may be hopelessly naive.

So: I toss the ball to this WikiProject. If you have comments or suggestions I'm happy to listen, but if you care enough to comment, feel free to just go ahead and make changes to the template — I take no ownership over it. Or if you think the effort is worthless, please say so — I won't be offended.

See also Talk:Exponentiation#funny table at end, where there are already some good suggestions for improving the new template. —scs (talk) 14:08, 7 December 2024 (UTC)

I have started a discussion at Template talk:Mathematical expressions#Existence of this template. Mgnbar (talk) 15:56, 7 December 2024 (UTC)

Purposeless complication in our article about the gamma distibution

Could people look at this? Michael Hardy (talk) 18:39, 7 December 2024 (UTC)

Pascal's simplex and Pascal's pyramid

In trying to clean up a ... thing, I noticed the article Pascal's simplex. It doesn't look like a topic that can sustain a whole encyclopedia article. Pascal's pyramid is not in great shape, either. I feel like some de-OR-ing, merging, and redirecting is warranted here, but maybe others have a better sense of what is going on. XOR'easter (talk) 02:01, 8 December 2024 (UTC)

I have looked at Pascal's pyramid from time to time, and it always induced a deep sigh. I agree that there's only one article's-worth of content here; I'm sure there must be some other adequate sources out there, but I don't know where. --158.144.178.11 (talk) 17:12, 9 December 2024 (UTC)

I haven't found much. There's more than nothing (e.g., [2] and [3]), but it seems like pretty slim pickings. Maybe the first step is to redirect both Pascal's pyramid and Pascal's simplex to Pascal's triangle § To higher dimensions. XOR'easter (talk) 03:19, 12 December 2024 (UTC)

Google scholar: "pascal pyramid" has 342 results and "pascal tetrahedron" has a further 123 results. pascal trinomial has 1,510 results, at least many of which seem relevant. –jacobolus (t) 03:50, 12 December 2024 (UTC)

I did some searching but was disappointed by how quickly the results trailed off into unpublished preprints and weird stuff. I could well have been pessimistic. XOR'easter (talk) 04:51, 12 December 2024 (UTC)

It's a kind of "let's explore the patterns" topic which can be examined without much prerequisite knowledge, so plenty of the sources are aimed at a student audience. I'm not sure there's all that much to say, but I think it's at least enough to make an article about. –jacobolus (t) 06:22, 12 December 2024 (UTC)

Broken overlines

I just noticed that ${\overline {x}}$ (\overline x) shows up as an underline instead of an overline. What’s going on?—Emil J. 11:39, 12 December 2024 (UTC)

It shows up as an overline on my end... Sgubaldo (talk) 12:21, 12 December 2024 (UTC)

On further investigation, it is broken when math rendering preferences are set to “MathML” or “Client side MathJax rendering”, but it shows correctly when set to “SVG”.—Emil J. 20:06, 12 December 2024 (UTC)

Help resolving disputes about history at Binomial theorem

Hi everyone. Can anyone pop by talk:Binomial theorem to help resolve a dispute about whether or not and how to discuss the history of binomial coefficients and Pascal's triangle in the history section there? user:Wikaviani has been repeatedly blanking material they don't like about these topics, based on in my opinion completely unjustified and inappropriate complaints about the quality of previous sources used there, so I added a pile of additional sources, but for each one they have some kind of complaint: close secondary analysis by subject expert Indian historians of mathematics are rejected because they are a few decades old, but more recent sources are rejected because they are by historians specializing in other regions or by people whose job title is "mathematician" (but writing peer-reviewed papers in math history journals or reputably published history books), with these rejections expressed using language I find to be quite insulting. The content dispute basically boils down to whether the following 10th century passage (here in translation) describes the same thing as Pascal's triangle, which a wide variety of authors claim it does:

"After drawing a square on the top, two squares are drawn below (side by side) so that half of each is extended on either side. Below it three squares, below it (again) four squares are drawn and the process is repeated till the desired pyramid is attained. In the (topmost) first square the symbol for one is to be marked.. Then in each of the two squares of the second line figure one is to be placed. Then in the third line figure one is to be placed on each of the two extreme squares. In the middle square (of the third line) the sum of the figures in the two squares immediately above is to be placed; this is the meaning of the term pūrṇa. In the fourth line one is to be placed in each of the two extreme squares. In each of the two middle squares, the sum of the figures in the two squares immediately above, that is, three, is placed. Subsequent squares are filled in this way."

user:Wikaviani insists it couldn't possibly, because a couple of sources about the history of medieval Islamic mathematics instead claim that the first table of binomial coefficients appeared in works from Persia which means the same numbers couldn't possibly have appeared elsewhere before. Thus they insist on removing any mention of the above from the history section at binomial theorem. –jacobolus (t) 13:29, 12 December 2024 (UTC)

Hi, I just want to represent fairly what the views of sources are, in a way like "some sources claim X" (cite sources) "while others say Y" (cite sources), not removed anything, I even expanded Pascal's triangle with the addition of Indian contributions to it. Besides, could someone explain Jacobolus that mathematicians and physicians are not historians of science please ? They insist to keep a CITEOVERKILL number of sources with many of them having no expertise in the field of history of maths and accuse me of throwing insults around when I say that (see sources number 11 at Binomial theorem please). Also, the so-called "couple of sources" mentioned by Jacobolus are an Oxford publication, an encyclopaedia from Helaine Selin, a book from Roshdi Rashed and and another from Glen Van Brummelen and Nathan Sidoli. Thanks very much. Best.---Wikaviani ^{(talk) (contribs)} 14:03, 12 December 2024 (UTC)

I am not a specialist of the history of mathematics, but this is not required to see who is right here. Indeed Wikaviani provides sources saying rougly "As far as we know, the first description of <something> occurred during the 12th century in the Islamic world". On the other hand Jacobolus provides a source containing the translation of a text of the 8th century, in which everyone can recognize easily as a fully correct description of Pascal's triangle, in a very modern style. It is clear that the latter is really reliable, while the former is reliable only if it is not contradicted by data that are ignored by its author. Wikipedia is about facts, not about opinions.

Also, all Wikaviani arguments are based only on its opinion on the sources and their authors, without anything tangible for supporting them, while Jacobolus discusses content and provides verifiable arguments supporting his views.

The discussion at talk:Binomial theorem suggests that Wikaviani is not there for improving the article, but for pushing his point of view. D.Lazard (talk) 15:39, 12 December 2024 (UTC)

Hi, thank you for you response, even if I guess that our past disagreements may influence your quite harsh feedback here about me. You say that you are not a specialist of the history of maths while, interestingly, you are a mathematician, this illustrates what I'm saying about some of the sources provided by Jacobolus. I'm not trying to push anything, I'm trying to improve this topic, both at Binomial theorem and Pascal's triangle, maybe clumsily, but I'm trying. I expanded the Pascal's triangle article this morning, adding what Jacobolus added to Binomial theorem about the triangle. If that translation of that work was enough to settle the subject, I'm wondering why so many prominent sources like the above mentioned by me and that were published well after the said translation are contradicting it ? Also "Also, all Wikaviani arguments are based only on its opinion on the sources and their authors, without anything tangible for supporting them" is not correct, I am not willing to remove the content added by Jacobolus anymore, i want to balance it with what other more recent sources say. Wikipedia is also about WP:NPOV. I would like more feedback from uninvolved editors. Thanks.---Wikaviani ^{(talk) (contribs)} 16:56, 12 December 2024 (UTC)

mathematicians and physicians are not historians of science – This kind of binary classification is oversimplified to the point of being wrong. Many excellent works (both close analysis of primary sources and higher level surveys) in the history of mathematics are done by people whose nominal job title is "mathematician" and who teach pure mathematics courses in a mathematics department. If a scholar has a passion for the history of mathematics and science, reads widely and deeply in the subject, publishes their careful work in peer-reviewed history journals or in books from major scholarly publishers with high editorial standards, and that work is widely cited in the field, then such material clearly meets Wikipedia's "reliable sources" standard, and I would call these scholars "mathematical historians" even if that's not their job title at a university. For example, the best recent source about the specific topic of the combinatorics appearing in ancient Indian works about prosody is Jayant Shah (2013) "A History of Piṅgala's Combinatorics" (preprint) – Shah is a mathematics professor at Northeastern, here writing in Gaṇita Bhāratī, a respected peer-reviewed journal of mathematical history. Ranjan Roy (2021) Series and Products in the Development of Mathematics, published by Cambridge University Press, is a fabulous broad survey by a scholar who did extensive historical research, even if he was also nominally a mathematician. Both of these have been widely cited by historians and in my opinion clearly meet Wikipedia's standards.

insist to keep a CITEOVERKILL number of sources – Just to be clear: I think it's entirely enough to validate this claim with one or two sources, and of diminishing use to readers to add each extra one (though they're all in a single footnote, so not cluttering up the text too much). I would have left a few close sources which discuss the topic in great detail, but given continuing removal of the claims justified by complaints that the career professionals who wrote them were "unreliable", not "expert" enough, "outdated", not "serious" scholars, and so on, I kept trying to find sources which would be acceptable to validate the claim, including recent sources, sources by authors from a range of countries and backgrounds, sources in survey books, etc. My speculation continues to be that the sources aren't really a problem per se; Wikaviani just doesn't want to include the claim (for reasons I can't figure out from their statements alone) and isn't going to change their mind no matter which sources are found.

an Oxford publication, an encyclopaedia from Helaine Selin, a book from Roshdi Rashed and and another from Glen Van Brummelen and Nathan Sidoli. – let's please remain accurate. The original source here is Rashed (1972) "L'induction mathématique: al-Karajī, al-Samawʾal", Archive for History of Exact Sciences 9: 1–21. Then Berggren (1985) is a survey paper about recent work in the history of Islamic mathematics mentioning Rashed's work; later Berggren's paper was republished in a book edited by Sidoli and Van Brummelen. Jacques Sesiano's encyclopedia entry about al-Karajī (in a book edited by Selin) also drew on Rashed's paper. Finally Rashed himself turned the paper into a chapter of his 1994 book. The sourcing here (a single close secondary source from a half-century ago whose claims have been repeated a few times by survey sources) is not substantially different in character than the sourcing I provided for claims about Indian contributions. In any event, I have no problem with Rashed, who did valuable work worth citing in discussing al-Samawʾal and al-Karajī in relevant Wikipedia articles, or with Berggren or Sesiano. Even though Berggren's job title was "mathematician" he did excellent work in the history of mathematics, and his 1985 paper is a fine survey.

Most importantly, the claims involved here are not in conflict. Rashed's 1972 paper was about looking for evidence of mathematical induction in the work of 12th century scholar al-Samawʾal, specifically in his work on the binomial theorem which was credited by him to a now-lost work by al-Karajī (c. 1000). There was no discussion whatsoever of combinatorial work done in India, nor would we expect there to be – it's irrelevant to Rashed's argument and not something Rashed was an expert about. It's also unsurprising that a survey paper about work on Islamic mathematics or an encyclopedia entry about al-Karajī wouldn't go out of their way to discuss topics irrelevant to their purpose.

Using sources about one topic as a reason to reject claims about another topic does not seem at all justifiable to me. –jacobolus (t) 17:34, 12 December 2024 (UTC)

Of course, a mathematician can also be a historian of maths, but this is not mandatory. Rashed himself is a mathematician and a historian of sciences.---Wikaviani ^{(talk) (contribs)} 18:29, 12 December 2024 (UTC)

Any editor who has spent any time at DYK should know that "first" claims from published sources are often wrong, and when they are wrong can be falsified by other published sources that document earlier occurrences. Here, we have multiple published sources that document early occurrences of binomial coefficients in India, clearly falsifying the "first" claim for Persia. That does not mean India was first, nor that we should omit the material on Persia, but we should not claim Persia as first. Incidentally, the history of the history of Indian study of binomial coefficients goes quite far back; Plofker's book cites Burrow, Reuben (1790), "A Proof that the Hindoos had the Binomial Theorem", Asiatick Researches: 487–497. —David Eppstein (talk) 18:40, 12 December 2024 (UTC)

I don't think the article should take any stance on "priority", since this to me violates the spirit of NPOV. Also, the article shouldn't suggest (as it currently does) that there is some controversy over priority. One paragraph should describe scholarship on the Indian contributions, and the next on that of Persia and the near east. We don't need to say anything about who did what before whom, except to establish basic chronology within each paragraph. Tito Omburo (talk) 21:24, 12 December 2024 (UTC)

You can see my preferred version at special:permalink/1262136996#History, which does roughly this. –jacobolus (t) 00:22, 13 December 2024 (UTC)

That seems fine. The treatment of the history at Pascal's triangle should be improved with similar content. Tito Omburo (talk) 16:37, 13 December 2024 (UTC)

Does anyone use the WP:LIBRARY?

Just curious, does anyone here use the WP:LIBRARY? I'm working my way towards 500 edits so that I can more easily contribute to articles which require more academic citations, but I'm unsure of how good of a resource the library really is. How much mathematics research is available through it? Are there any hoops you have to jump through to gain access to more specialized information (beyond being extended confirmed)? Thanks in advance, /home/gracen/ (they/them) 18:56, 16 December 2024 (UTC)

I use the Wikipedia library frequently, at least every couple weeks I'm looking something up. Bear in mind that the library is not a library of Wikipedia specific resources, but provides access to resources from a wide range of academic publishers in many fields. I primarily use it for legal writing, but I'm sure you can find mathematics content. BD2412 T 19:23, 16 December 2024 (UTC)

I don't know about the mathematics research, but for physics the Library is awesome. The access levels depend dramatically upon the publisher. For some publishers you can read almost any of their content. Some publishers are not even available.

The biggest hoop after you have a login is search. The publisher's search is rocks-and-stones level for the most part. So I do my searches via Google Scholar, then use the title or an unusual author's name to search on the publisher's "advanced search" page which supports exact match.

At least in physics, the decades long shift to open access is starting to have effects. I have found that the document links on Google Scholar (when they exist) now mostly point to published papers on the publishers site. Johnjbarton (talk) 19:24, 16 December 2024 (UTC)

It is more or less comparable to browsing online scholastic resources from a university library. In the era of Sci-Hub and #ICanHazPDF most scholars around the world who are motivated can find access to most recent published papers, but in theory reading academic papers without authorization is some kind of mild copyright infringement, and "Wikipedia Library" is all above board. –jacobolus (t) 19:33, 16 December 2024 (UTC)

I use it. I get access to many of the same sources through my employer but for some of them I don't and sometimes The Wikipedia Library provides a more convenient access path. Quite a few mathematical references are available on JSTOR, in particular, which is available through it, and many mathematical theses are online through Proquest. I don't know of any extra hoops beyond just getting access at all. —David Eppstein (talk) 19:53, 16 December 2024 (UTC)

Unfortunately most of the theses on Proquest that I have ever tried to look at are not available via Wikipedia Library. –jacobolus (t) 21:29, 16 December 2024 (UTC)