Talk:List of unsolved problems in mathematics

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)

References

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)

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

Set Theory vs Model Theory

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)

Solved problem?

Sorry not a regular wikipedia contributor so not sure how things work round here. It seems there are counterexamples for the problem "Is the line graph of a non-word-representable graph always non-word-representable?" https://arxiv.org/abs/2509.03339 ~2026-26641-59 (talk) 13:46, 2 May 2026 (UTC)

Requesting solution audit

using srmech and foundational metric field ontology knowledge to systematically walk through this list. everything can be independently cross validated, all tools are public. --- https://github.com/lemonforest/mlehaptics/pull/677 --- I'm not here to argue, I'm here share knowledge. peace out ganja bear. Steven Kirkland ^(talk) 16:32, 23 May 2026 (UTC)

Wikipedia is officially not interested until the proof appears in publications other than its author's. —Antonissimo (talk) 01:14, 24 May 2026 (UTC)

Too many solved problems on this article specifically about unresolved problems

Why was 1995 chosen as the cutoff year for including solved problmes on this page? As the years go by, more and more conjectures are going to get solved and placed into that section, until eventually most of the material on this article becomes about solved problems after 1995 instead of unsolved problems in mathematics. Instead of having a fixed year, it should be a specific time gap, something like solved within the past 10 years. ~2026-45449-24 (talk) 14:09, 19 August 2026 (UTC)

Per MOS:RELTIME it's discouraged to have cutoffs set to relative times because those can become outdated if not regularly updated, and regular updates are tedious. It might be worth moving up the cutoff to a later year though (perhaps 2005?) GalacticShoe (talk) 14:18, 19 August 2026 (UTC)

That is also fine by me, anything to reduce the number of solved conjectures in this bloated section.

If we're moving up the cutoff to a later date, I'd probably like to see when the original change in the section name was made from "Problems solved recently" to "Problems solved since 1995" and use that original gap as the difference to apply to 2026. ~2026-45449-24 (talk) 14:24, 19 August 2026 (UTC)

In January 2015 the section title was titled Problems solved since 1975 and the content of the section had significantly less material on it than today; there were only 26 conjectures listed in the section. To get that few conjectures in the section today probably requires setting an even later date than 2005, maybe 2010 or 2015. ~2026-45449-24 (talk) 14:34, 19 August 2026 (UTC)

That section on the article was originally called "Problems solved recently" instead of "Problems solved since 1995", see for example this old revision from 3 September 2026. ~2026-45449-24 (talk) 14:18, 19 August 2026 (UTC)

Section date cutoff moved from 1995 to 2010. ~2026-45449-24 (talk) 14:44, 19 August 2026 (UTC)

There are still 56 problems listed in the section with a 2010 cutoff year, over twice the amount that was in the section in the January 2015 revision, so maybe the suggested 2015 cutoff year above might be better. ~2026-45380-64 (talk) 23:40, 19 August 2026 (UTC)

Now down to 38 solved problems with 2015 cutoff which is a more acceptible size for the section in my opinion. ~2026-45380-64 (talk) 23:46, 19 August 2026 (UTC)