Wikipedia talk:WikiProject Mathematics

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Dynamical system

The article dynamical system has, in the past six months, more than doubled in size from the earlier version. The older version was not ideal either, but I am concerned that the current article has become difficult to use as a reference article. It for one thing needs a stylistic cleanup. But the current article also has no clear spine, whole early sections are written like personal reflections, complete with far too many images. There are duplications of content, some of which is a little dubious. I would like to solicit opinions about what to do with this, including any tags for content that violates content policies (WP:V, WP:DUE, etc), which content should be trimmed or cut, how it should be reorganized, etc. Sławomir Biały (talk) 11:15, 2 July 2026 (UTC)

Sphere packing in a cube

Worth it to merge Sphere packing in a cube to Cube, despite this stub article has many citations? Dedhert.Jr (talk) 03:11, 7 July 2026 (UTC)

No, these are completely different topics. However, feel free to mention or summarize the packing problem in Cube, e.g. in § Related topics. –jacobolus (t) 04:20, 7 July 2026 (UTC)

No, but there's also Sphere packing in a sphere and those two could reference each other. I wonder if anything strange happens to how densely they are filled for higher dimensions. NadVolum (talk) 14:23, 7 July 2026 (UTC)

Pascal's triangle

The history section of the article is a bit nuanced, as it doesn't describe who first formulated the first description of the Pascal triangle.Myuoh kaka roi (talk) 14:24, 14 July 2026 (UTC)

Section § History mention Karaji and says that Piṅgala discoveered Pascal's triangle around 1,000 years before Karaji. What else is lacking in the section? By the way, al-Karaji was not Arab, contrarily to wht you suggested in your edit D.Lazard (talk) 14:54, 14 July 2026 (UTC)

I was confused about the statement that Persian mathematician Al-Karaji (953–1029) wrote a now-lost book which contained the first description of Pascal's triangle from Arabs I thought that "from Arabs" means that it was discovered by arabs and al karaji is an arab even though Persian mathematician is mentioned . Myuoh kaka roi (talk) 14:59, 14 July 2026 (UTC)

Because this discussion is specific to the article Pascal's triangle, it might be more productive to hold the discussion at Talk:Pascal's triangle. Mgnbar (talk) 15:24, 14 July 2026 (UTC)

Draft:2763 (number)

Hello! Is it possible if you could tell me the notable properties or if there are any notable properties in the draft? Just asking so that I can improve the draft. Budew1234 (talk) 04:50, 16 July 2026 (UTC)

The submission of this draft has been declined 3 times. It is clear tha we do not need an article with this title. D.Lazard (talk) 09:00, 16 July 2026 (UTC)

Jacobian conjecture counterexample

Flagging this update for attention. I think it satisfies WP:BASICMATH and - given the author's background - WP:RSSELF (also, a number of academic research mathematicians have already reacted approvingly), but it might be helpful for other experienced editors to join the discussion at Talk:Jacobian_conjecture#Apparently_disproved. Regards, HaeB (talk) 05:35, 20 July 2026 (UTC)

This is the rare case, I think, where we probably should leave the statement in the article with a {{better source needed}} tag rather than deletion. It seems to me that this is indeed a counterexample to the conjecture, so if we leave it in for a few weeks better sources will be forthcoming, and this is a good service to likely readers when they come here looking to read up on the conjecture. I think it does not strictly fall within WP:CALC, but I think we should make a small exception here bearing in mind the recent Hannah Cairo debacle. Sławomir Biały (talk) 07:31, 20 July 2026 (UTC)

I agree. Yes, this is original research that has not been regularly published. But we have to consider the reasons of Wikipedia policies.

The main reason for WP: No original research is that reliable sources are needed to judge the importance of a result. Here, there is no doubt on the importance of the result.

Another reason of the requirement of reliable sources is WP:Verifiability. Here, the verification falls under WP:CALC, since the verification that the counterexample is correct is a simple calculation.

So, this is a rare case for which the reasons behind the policies are satisfied, even if the policies are not formally satisfied. I think that this is for such rare cases that WP:IAR has been introduced.

Nevertheless, I agree that further sources are needed for understanding why the conjecture is false and which consequences has the existence of a counterexample. Also reliable sources would be useful to simplify the counterexample (for example, the exchange of x and z would make the counterexample clearer, by writing it as ⁠$x\to x+\cdots ,\quad y\to y+\cdots ,\quad z\to z+\cdots$⁠, where the dots are sums of terms of degree at least 2). D.Lazard (talk) 10:38, 20 July 2026 (UTC)

I'm not convinced this falls under WP:CALC. I'm not convinced it doesn't, either, but it is out of the regime where that is normally applied, which is stuff like converting Fahrenheit to Celsius. Stepwise Continuous Dysfunction (talk) 23:13, 20 July 2026 (UTC)

I mean, it basically consists of a small number of calculations such as this one (to pick a concrete example from ):

Evaluate

$(1+xy)^{3}z+y^{2}(1+xy)(4+3xy)$

for

$x=0,y=0,z=-1/4$

and check that the result is $-1/4$.

Personally I almost find that easier than converting Fahrenheit to Celsius ;-)

Regards, HaeB (talk) 00:43, 21 July 2026 (UTC)

In this type of example, it's also just fine to take the claim out from Wikipedia pending the inevitable follow-on sources a few days later. Wikipedia does not need to be the venue for breaking this kind of research before it has been discussed by reliable sources. –jacobolus (t) 07:26, 21 July 2026 (UTC)

It needs a bit more than that. We need to calculate the Jacobean determinant, in particular that the Jacobian determinant is a non-zero constant, and, of course, we also need to evaluate the formula for ${\textstyle {\bigl (}1,-{\tfrac {3}{2}},{\tfrac {13}{2}}{\bigr )}}$. Do Jacobean determinants fall under WP:CALC? I always need to check that I have added or subtracted 32 and multiplied or divided by 5/9 in the right order when converting temperatures by using the freezing and boiling points of water. Phil Bridger (talk) 08:32, 21 July 2026 (UTC)

What falls under WP:CALC is a matter of local consensus, and depends on the context; the more niche and advanced the topic, the more difficult a "routine" calculation might be. In general I'd say "newly discovered counterexample to a relatively famous conjecture" isn't a "routine calculation" irrespective of how difficult it is to verify. We should have sources which put such a thing in context, and we don't want to encourage anyone who thinks they disproved a conjecture to publish it on Wikipedia first, even if the verification seems simple. –jacobolus (t) 09:56, 21 July 2026 (UTC)

I agree with you. Especially about waiting for the inevitable reliable sources. It's better to be right than quick. Phil Bridger (talk) 10:08, 21 July 2026 (UTC)

I agree as well. Stepwise Continuous Dysfunction (talk) 21:51, 22 July 2026 (UTC)

References OK now

Has this question been overtaken by the references now available for the counter example? (https://www.newscientist.com/article/2580374-ais-solution-to-87-year-old-riddle-takes-mathematicians-by-surprise/) — Preceding unsigned comment added by Naraht (talk • contribs) 01:13, 21 July 2026 (UTC)

Yes, we have more sources now - apart from that New Scientist article, MathWorld (generally regarded here as a "mediocre but usable source" for mathematical facts) has updated their article, and Mashable also reports the conjecture as disproven (citing an expert). Regards, HaeB (talk) 06:03, 21 July 2026 (UTC)

This edit could use some scrutiny. The editor is already at 3RR with this. Sławomir Biały (talk) 15:53, 22 July 2026 (UTC)

Review on Draft:Doob's h-transform

I am planning to accept WP:AFC for Draft:Doob's h-transform but I am not able to validate the content matches the references. Any stochastics folks want to take a peek before I approve? HundredVisionsAndRevisions (talk) 19:53, 23 July 2026 (UTC)