Talk:List of unsolved problems in mathematics

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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)[reply]

Change in section title

"Problems solved since 1995" was recently changed to "problems solved in the last 30 years". I think the former title should be used. See Wikipedia:Manual_of_Style/Dates_and_numbers#Statements_likely_to_become_outdated. Bubba73 ^{You talkin' to me?} 01:52, 20 January 2024 (UTC)[reply]

Based on the MoS outline, agreed. GalacticShoe (talk) 02:14, 20 January 2024 (UTC)[reply]

Done Klbrain (talk) 18:51, 22 February 2024 (UTC)[reply]

Semi-protected edit request on 17 June 2024

This edit request has been answered. Set the |answered= or |ans= parameter to no to reactivate your request.

i want to add an unsolved math question which is (12 45 ∏ 61

35)! 2601:603:4C7F:B6D0:68E7:C8AD:7A34:6A7 (talk) 17:07, 17 June 2024 (UTC)[reply]

What does it mean? —Tamfang (talk) 23:49, 17 June 2024 (UTC)[reply]

Not done for now: Critical lack of explanation why this should be included in the list, and no sources. ABG (Talk/Report any mistakes here) 23:55, 17 June 2024 (UTC)[reply]

Removal of solved problems from the unsolved section

Like the Erdős-Heilbronn conjecture. 2405:201:5502:C989:D1F5:2160:CCE8:4F0A (talk) 05:16, 15 July 2024 (UTC)[reply]

Done Any other ones you noticed? GalacticShoe (talk) 06:34, 15 July 2024 (UTC)[reply]

2 new conjectures

1. Carbrickscity conjecture

The conjecture asks, whether Graham's number - 4 is a prime.

Graham's number: a power of 3

Graham's number - 1: even

Graham's number - 2: a multiple of 5

Graham's number - 3: an even multiple of 3

Graham's number - 4: unknown

2. repunit power conjecture

There are infinitely many cubes of the form 3 mod 4.: 27, 343, 1331, 3375, 6859, 12167, 19683, 29791, 42875, 59319, 79507, 103823, 132651, 166375, 205379, ... (A016839)

There are infinitely many fifth powers of the form 3 mod 4.: 243, 16807, 161051, 759375, 2476099, ... (A016841)

This goes on with any odd exponent.

So, the conjecture asks, whether a repunit other than 1 can be equal to aⁿ, where a is an integer and n is odd and greater than 1.

It is sure, that a repunit other than 1 can never be a square, because squares can never be of the form 3 mod 4, while repunits other than 1 are always of the form 3 mod 4. 94.31.89.138 (talk) 19:53, 28 July 2024 (UTC)[reply]

This is not the place to pose new conjectures. All content here, as in all Wikipedia articles, must be based on reliably-published sources. If you have citations for sources for conjectures to be added, they can be listed here. If not, then they need to be published elsewhere before they can be considered here. —David Eppstein (talk) 20:28, 28 July 2024 (UTC)[reply]

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)[reply]