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== Set theory note == |
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== André–Oort conjecture is proved without RH == |
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There was a 2021 edit at the start of the set theory section that reads a little odd. It reads |
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* 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. |
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⚫ | |||
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) |
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== Suggestion for improvement == |
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* The notable conjectures in the subject of set theory were typically formulated in the context of [[Zermelo-Frankel set theory]], and usually with [[axiom of choice|Choice]]. By the [[Gödel's completeness theorem|completeness theorem]], the problems may be understood as concerning the models thereof. The provability of the conjectures listed below might not be open in [[List_of_first-order_theories#Set_theories|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]].) |
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This is an excellent collection of unsolved problems in mathematics, unparalleled by any other list I know of. |
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In fact the middle sentence mentioning models is probably even redundant also. |
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But many, many of the problems are listed '''solely by name''' without any explanation of what the problem is. |
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--[[Special:Contributions/178.115.55.162|178.115.55.162]] ([[User talk:178.115.55.162|talk]]) 17:15, 21 November 2023 (UTC) |
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These problems are in almost all cases '''linked''' to a description of the problem named. |
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== Change in section title == |
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But that does not work for a long list: A reader cannot be constantly clicking on links and then the back button. |
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"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]]. [[User:Bubba73|Bubba73]] <sup>[[User talk:Bubba73|You talkin' to me?]]</sup> 01:52, 20 January 2024 (UTC) |
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Much more useful are the problem for which at least a rough description is included in the article. |
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SO: '''This article will become more and more useful as more and more problem descriptions are added.''' [[Special:Contributions/2601:200:C000:1A0:144F:3970:779E:D68C|2601:200:C000:1A0:144F:3970:779E:D68C]] ([[User talk:2601:200:C000:1A0:144F:3970:779E:D68C|talk]]) 01:42, 27 April 2022 (UTC) |
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== Semi-protected edit request on 17 June 2024 == |
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:It took a long time, but short descriptions have finally been added to most of the listed problems. [[User:GalacticShoe|GalacticShoe]] ([[User talk:GalacticShoe|talk]]) 01:47, 26 June 2022 (UTC) |
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{{edit semi-protected|List of unsolved problems in mathematics|answered=yes}} |
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== The Erdős–Faber–Lovász conjecture has been proved == |
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i want to add an unsolved math question which is (12 |
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45 |
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∏ |
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61 |
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35)! [[Special:Contributions/2601:603:4C7F:B6D0:68E7:C8AD:7A34:6A7|2601:603:4C7F:B6D0:68E7:C8AD:7A34:6A7]] ([[User talk:2601:603:4C7F:B6D0:68E7:C8AD:7A34:6A7|talk]]) 17:07, 17 June 2024 (UTC) |
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:What does it mean? [[User:Tamfang|—Tamfang]] ([[User talk:Tamfang|talk]]) 23:49, 17 June 2024 (UTC) |
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According to the Wikipedia [[Erdős–Faber–Lovász conjecture|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." |
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::[[File:Red information icon with gradient background.svg|20px|link=|alt=]] '''Not done for now:'''<!-- Template:ESp --> Critical lack of explanation why this should be included in the list, and no sources. [[User:AlphaBetaGamma|ABG]] <small> ([[User talk:AlphaBetaGamma|Talk/Report any mistakes here]]) </small> 23:55, 17 June 2024 (UTC) |
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Accordingly, I will remove the entry from this list. ^-^ [[User:Atomic putty? Rien!|Atomic putty? Rien! (talk) ]] ([[User talk:Atomic putty? Rien!|talk]]) 13:23, 7 July 2022 (UTC) |
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: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" <math>k</math>. 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 <math>e^{e^{36}} \approx 1.7\cdot10^{1872344071119343}</math>) 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) [[User:GalacticShoe|GalacticShoe]] ([[User talk:GalacticShoe|talk]]) 18:00, 7 July 2022 (UTC) |
Latest revision as of 23:55, 17 June 2024
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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)
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)
- Based on the MoS outline, agreed. GalacticShoe (talk) 02:14, 20 January 2024 (UTC)
Semi-protected edit request on 17 June 2024
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)
- What does it mean? —Tamfang (talk) 23:49, 17 June 2024 (UTC)
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)