Talk:List of unsolved problems in mathematics/Archive 2

Archive 1

Archive 2

Suggestion for improvement

This is an excellent collection of unsolved problems in mathematics, unparalleled by any other list I know of.

But many, many of the problems are listed solely by name without any explanation of what the problem is.

These problems are in almost all cases linked to a description of the problem named.

But that does not work for a long list: A reader cannot be constantly clicking on links and then the back button.

Much more useful are the problem for which at least a rough description is included in the article.

SO: This article will become more and more useful as more and more problem descriptions are added. 2601:200:C000:1A0:144F:3970:779E:D68C (talk) 01:42, 27 April 2022 (UTC)

Good point. I'll be adding short descriptions to the best of my ability soon. GalacticShoe (talk) 02:48, 27 April 2022 (UTC)

It took a long time, but short descriptions have finally been added to most of the listed problems. GalacticShoe (talk) 01:47, 26 June 2022 (UTC)

The Erdős–Faber–Lovász conjecture has been proved

According to the Wikipedia article of the same name, "A proof of the conjecture for all sufficiently large values of k was announced in 2021 by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus."

Accordingly, I will remove the entry from this list. ^-^ Atomic putty? Rien! (talk) (talk) 13:23, 7 July 2022 (UTC)

Unfortunately I'm going to have to revert this, specifically because there is no bound (or at least none that I could find) for the "sufficiently large" $k$. This probably feels like a nitpick, but there are explicit cases where bounds can be astronomically high (for example, we only know for certain that Chen's theorem#Variations holds above $e^{e^{36}}\approx 1.7\cdot 10^{1872344071119343}$) and until we have a bound, we can't say that the conjecture is true in full generality. To justify this, another conjecture known to hold for sufficiently large values but that is still listed as unsolved is Sendov's conjecture; Terence Tao proved the sufficiently-large part in 2020. Thanks for bringing this up though! (P.S. for future reference please move solved problems to the 'Problems solved since 1995' section) GalacticShoe (talk) 18:00, 7 July 2022 (UTC)

Dubner's Conjecture seems to be wrongly stated

The brief description says: "Dubner's conjecture: every number greater than 2408 is the sum of two primes which both have twins." But the linked article describes the conjecture as: "every even number greater than 4208 is the sum of two t-primes". It's trivially apparent that the word "even" is required. And there is an inconsistency about the threshold number - which is it? RMGunton (talk) 09:42, 18 November 2022 (UTC)

Indeed -- I have corrected the minor errors here. JBL (talk) 20:37, 18 November 2022 (UTC)

Whoops, that one's on me. Thanks for catching it! GalacticShoe (talk) 22:49, 18 November 2022 (UTC)

Semi-protected edit request on 13 December 2022

Please change:

Uniform 5-polytopes – find and classify the complete set of these shapes

to start with "convex uniform 5-polytopes." The literature, including the cited source, only discusses convex uniforms. Discussion of uniform 4-polytopes and above without the "convex" qualifier is mostly limited to a small enthusiast community, so I was surprised to see it mentioned on this page. 11wx (talk) 01:20, 13 December 2022 (UTC)

 Done Thank you. Ovinus (talk) 08:35, 13 December 2022 (UTC)

Semi-protected edit request on 21 December 2022

"Днестровская тетрадъ" shall be "Днестровская тетрадь"

"Эрлаголъская тетрадъ" shall be "Эрлагольская тетрадь" VKleban (talk) 18:21, 21 December 2022 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. casualdejekyll 18:37, 24 December 2022 (UTC)

 Done Sources are already present in the text. Thank you. Dintre (talk) 11:14, 4 January 2023 (UTC)

Set theory note

There was a 2021 edit at the start of the set theory section that reads a little odd. It reads

• Note: These conjectures are about models of Zermelo-Frankel set theory with choice, and may not be able to be expressed in models of other set theories such as the various constructive set theories or non-wellfounded set theory.

Given any FOL Set theory (many here List_of_first-order_theories#Set_theories) with the same signature (the bulk just works with \in and not more), a problem expressed in the language is the same for any of them. What's probably meant here is (and that's my proposed replacement)

• The notable conjectures in the subject of set theory were typically formulated in the context of Zermelo-Frankel set theory, and usually with Choice. By the completeness theorem, the problems may be understood as concerning the models thereof. The provability of the conjectures listed below might not be open in other set theories, such as ones over a logic or with axioms that are weaker, stronger or conflicting with it (e.g. a constructive set theory, Tarski-Grothendieck set theory resp. a non-wellfounded set theory.)

In fact the middle sentence mentioning models is probably even redundant also.

--178.115.55.162 (talk) 17:15, 21 November 2023 (UTC)