Talk:List of unsolved problems in mathematics

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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 ${\displaystyle C^{3,\alpha }}$. Based on our section on Hölder spaces it appears this means that the surface is ${\displaystyle C^{3}}$ and its third-order partial derivatives all satisfy the Hölder condition of order ${\displaystyle \alpha \in (0,1]}$.

This would confirm the original conjecture in its literal formulation of "sufficiently smooth". Since the Hölder condition is weaker than continuous differentiability, ${\displaystyle C^{4}}$ surfaces all work, but some ${\displaystyle C^{3}}$ 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 ${\displaystyle C^{2}}$ 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 ${\displaystyle C^{2}}$. 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.^[1]

 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)

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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)

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)

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)

No. ~2025-33320-90 (talk) 20:47, 13 November 2025 (UTC)

Currently, the section on Model Theory contains an unordered list of problems in various subfields. Some of them on set theory. The dedicated Set Theory section on the other hand contains some conjectures about implications over ZF, but then also some very broad questions concerning nice big models.

The Model Theory section should certain by sorted - and likewise one could sort the Set theory section into distinct types of problems. Likely one would want to move similar classes of problems to one spot - e.g. some meta-theoretical problems explicitly concerning models into the model theory section.

Possibly a more drastic section moving would be in order - present the Set Theory section first, list proper implications questions in set theory, and then smoothly transition into the Model theory section, which ends in more algebraic questions. Go ahead with ideas and action - I'll check in to this at a later point.. ~2025-33331-30 (talk) 13:29, 9 December 2025 (UTC)