Talk:List of unsolved problems in mathematics

Possible equivalents of the axiom of choice

Add the open problems from here, including whether PP implies AC, whether WPP implies AC, and whether the Schröder–Bernstein theorem for surjections implies AC. These are some of the oldest open problems in set theory. 50.221.225.231 (talk) 16:02, 26 November 2024 (UTC)

Semi-protected edit request on 3 February 2025

Request:

I want to request for “Neumann-Reid Conjecture” to be added to the list of unsolved problems in “Topology”.

The statement of the conjecture:

“The only hyperbolic knots in the 3-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots.”

Background and resources:

1. In 1992 Neumann and Reid established that hyperbolic knot complements have hidden symmetries if and only if they cover rigid-cusped orbifolds, in the same paper they further questioned whether any examples exist beyond the three known: the complements of the figure-eight knot and the two dodecahedral knots (cf. Section 9, Question 1)[1].
2. This conjecture is recorded as Problem 3.64(a) in the Kirby problem List [2].
3. The conjecture remains unresolved despite of decades of research, for instance:
   1. The 2015 paper by Michel Boileau, Steven Boyer, Radu Cebanu, Genevieve S. Walsh (cf. Conjecture 1.1). [3]
   2. The 2020 paper by Eric Chesebro, Jason DeBlois, Neil R Hoffman, Christian Millichap, Priyadip Mondal, William Worden (cf. Conjecture 1.1). [4]

ArshiGh (talk) 01:29, 3 February 2025 (UTC)

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Your request is valid and well written. However, it may not be added because of the xy policy.(3OpenEyes' communication receptacle) | (PS: Have a good day) (acer was here) 09:40, 4 February 2025 (UTC)

Semi-protected edit request on 23 February 2025

Remove the Carathéodory conjecture from this list as it has been solved in 2024 by Guilfoyle and Klingenberg (full citations contained in Carathéodory conjecture). Boundary Condition (talk) 18:20, 23 February 2025 (UTC)

I'm not an expert on this topic, but reading the article it seems that the solution was for a specific case, not a fully general solution. Can you elaborate a bit? PianoDan (talk) 00:27, 25 February 2025 (UTC)

So our article on the Carathéodory conjecture has the following formulation:

"The conjecture claims that any convex, closed and sufficiently smooth surface in three dimensional Euclidean space needs to admit at least two umbilic points."

The way I interpreted the result is that they apparently showed this to be true when "sufficiently smooth" is $C^{3,\alpha }$. Based on our section on Hölder spaces it appears this means that the surface is $C^{3}$ and its third-order partial derivatives all satisfy the Hölder condition of order $\alpha \in (0,1]$.

This would confirm the original conjecture in its literal formulation of "sufficiently smooth". Since the Hölder condition is weaker than continuous differentiability, $C^{4}$ surfaces all work, but some $C^{3}$ surfaces may not. There still does seem to be the question of if it's possible to lower the smoothness class required to the lowest possible $C^{2}$ though. I will also need someone else to confirm whether my interpretation is correct. GalacticShoe (talk) 16:18, 25 February 2025 (UTC)

This is correct - the original Conjecture, first reported in 1924, made no mention of the exact degree of smoothness of the surface. The phrase "sufficiently smooth" has been inserted later - the minimal smoothness required for the Conjecture to make sense is $C^{2}$. The 1940's proof for real analytic surfaces depended very heavily on real analyticity and, as such, was a special case of the Conjecture. The big jump is from real analytic to smooth, and proving it for any degree of smoothness is sufficient to confirm the original Conjecture. Boundary Condition (talk) 08:40, 26 February 2025 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. | Please send the exact links and reopen this request! Valorrr (talk) 14:57, 23 March 2025 (UTC)

The following published paper contains a description of the complete proof .

 Not done: The page's protection level has changed since this request was placed. You should now be able to edit the page yourself. If you still seem to be unable to, please reopen the request with further details. Day Creature (talk) 16:41, 5 September 2025 (UTC)

Semi-protected edit request on 9 July 2025

Please move the lonely runner conjecture section from combinatorics to number theory. Russqb (talk) 14:56, 9 July 2025 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. Dahawk04 (talk) 13:21, 10 July 2025 (UTC)

https://en.wikipedia.org/wiki/Lonely_runner_conjecture

The wikipedia article for the lonely runner conjecture clearly states that it is a "number theory problem", speicifcally it is a type of Diophantine approximation.

Here is an article on the lonely runner conjecutre, as published in the Electronic Journal of of Combinatorial Number Theory https://www.sfu.ca/~goddyn/Papers/063tight_lonely_runner.pdf Russqb (talk) 18:14, 10 July 2025 (UTC)

Korouvka or Korouvska?

The Russian has a c that is not represented in the English 2607:FEA8:FF01:4FA6:4DC1:5F3B:801A:1AFE (talk) 03:27, 16 August 2025 (UTC)

Apparently Kourovka is the name of the town and Kourovskaja its adjective; the English uses the naked town name, as is usual (we don't say e.g. "the Osloish agreement"). —Tamfang (talk) 19:12, 17 August 2025 (UTC)

In MathSciNet the work in question appears to be primarily called (in English) the Kourovka Notebook or less often Kourov Notebook, despite not matching the transliteration of the Russian title Коуровская тетрадь. —David Eppstein (talk) 20:05, 17 August 2025 (UTC)