Timeline for Results that are widely accepted but no proof has appeared
Current License: CC BY-SA 4.0
55 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2023 at 14:24 | history | edited | ARA | CC BY-SA 4.0 |
fixed grammar
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| Aug 26, 2022 at 10:49 | answer | added | Timothy Chow | timeline score: 5 | |
| Mar 22, 2022 at 16:36 | answer | added | Timothy Chow | timeline score: 10 | |
| May 5, 2020 at 4:08 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
added 90 characters in body
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| May 4, 2020 at 22:42 | answer | added | Timothy Chow | timeline score: 16 | |
| Apr 21, 2020 at 3:07 | review | Close votes | |||
| Apr 21, 2020 at 16:28 | |||||
| Apr 15, 2020 at 13:35 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
added 298 characters in body
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| Apr 15, 2020 at 12:57 | answer | added | Per Alexandersson | timeline score: 2 | |
| Apr 15, 2020 at 4:59 | answer | added | David Roberts♦ | timeline score: 16 | |
| Apr 14, 2020 at 18:18 | comment | added | Praphulla Koushik | @enthdegree I have absolutely no knowledge of information theory so, I can not give any useful response... It would be nice if you can spend some time on your idea and turn it into an answer for this question.. | |
| Apr 14, 2020 at 18:17 | comment | added | Christian Chapman | Can only be a comment, but modern lattice coding techniques are based on intuitions whose proofs are at best obscure. For example what are upper and lower asymptotic bounds on the typical log-amount of points a (sequence of scale-normalized) construction-A lattice(s) puts in a ball with normalized volume $V$? Should be $\sim V$ but you never use this intuition directly. Instead you only talk about the amount of points in a shape of similar volume that covers a proportionally large part of the ball. Fine for many applications but inconvenient. | |
| Apr 14, 2020 at 17:00 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
added 116 characters in body
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| Apr 14, 2020 at 16:30 | answer | added | Sam Hopkins | timeline score: 12 | |
| Apr 14, 2020 at 0:38 | comment | added | Gerry Myerson | I think it is widely accepted that Helfgott has proved the ternary Goldbach conjecture, although the proof has not yet been published. I don't know whether any published paper has relied on Helfgott's work ("relied", in the sense of stating a theorem and citing Helfgott's work as an essential part of the proof). | |
| Apr 14, 2020 at 0:20 | comment | added | Gerry Myerson | @Blue I think the distinction is between someone writing "if the Birch Swinnerton-Dyer conjecture is true, then....", and someone writing "since the Birch Swinnerton-Dyer conjecture is true ...." and citing a paper claiming, without proof, that it's true. | |
| Apr 13, 2020 at 22:53 | comment | added | BlueRaja | I think all the (unsolved) Clay Mathematics Millennial Problems fit this question? The answers are widely believed to be known, and tons of papers rely on one of them, but most have not been proved. | |
| Apr 13, 2020 at 21:01 | answer | added | Alon Amit | timeline score: 22 | |
| Apr 13, 2020 at 20:14 | comment | added | Andrés E. Caicedo | @Noah It may be in the process of being written up (by someone writing a book on AD+). Woodin has lectured on it at a seminar at Harvard, so there may be notes. There is no published account; I don't know the details. | |
| Apr 13, 2020 at 20:08 | comment | added | Noah Schweber | @AndrésE.Caicedo Has the proof of that really not appeared anywhere (by Woodin or others)? I've seen at least "Turing determinacy implies L(R)-determinacy" quoted as well-established fact. | |
| Apr 13, 2020 at 20:06 | answer | added | R.P. | timeline score: 19 | |
| Apr 13, 2020 at 19:47 | comment | added | Andrés E. Caicedo | @Monroe Which ones do you have in mind? There is the fact that Turing determinacy implies Suslin-coSuslin determinacy (in the presence of DC?), which gives L(R)-determinacy. | |
| Apr 13, 2020 at 18:34 | comment | added | user76284 | @MonroeEskew “Personally I do not understand why people do mathematics without understanding fully what they are doing.” Von Neumann would like to have a word with you. | |
| Apr 13, 2020 at 18:22 | comment | added | user76284 | @CarloBeenakker “I might object that a result without a proof cannot be known to be true as a matter of principle. What other method of verification do we have, other than a proof?” PA is consistent. It is known by intuition :) | |
| Apr 13, 2020 at 16:51 | history | edited | Praphulla Koushik |
edited tags
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| Apr 13, 2020 at 16:28 | answer | added | Timothy Chow | timeline score: 38 | |
| Apr 13, 2020 at 14:43 | comment | added | Praphulla Koushik | @MonroeEskew please feel free to make it as an answer.. I know nothing about them :) | |
| Apr 13, 2020 at 14:28 | comment | added | Monroe Eskew | Several famous results of Hugh Woodin fit the bill. | |
| Apr 13, 2020 at 14:07 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Apr 13, 2020 at 14:07 | history | became hot network question | |||
| Apr 13, 2020 at 12:41 | comment | added | Praphulla Koushik | @VladimirDotsenko If there is a result A published by some one which is used by others but there is no published proof of the result A, that will be an example for the question.. I do not see where opinion is coming here.. :) Please let me know if I am missing something.. I do not want anybody to spend time on something that is opinion based.. That is the whole point of this question.. :) Opinions are not appreciated.. evidence is appreciated.. | |
| Apr 13, 2020 at 12:10 | review | Close votes | |||
| Apr 14, 2020 at 20:37 | |||||
| Apr 13, 2020 at 11:56 | comment | added | Vladimir Dotsenko | I feel that questions about things "widely accepted to be true with no detailed proof" will end up being too much opinion-based. I am not sure that it is appropriate for MO. | |
| Apr 13, 2020 at 11:33 | comment | added | Praphulla Koushik | @HJRW Yes, examples can come from anywhere.. I am.in particular interested in examples coming from these tags.. Yes, big list tag is suitable... | |
| Apr 13, 2020 at 11:31 | comment | added | Praphulla Koushik | @arsmath thank you. | |
| Apr 13, 2020 at 11:25 | comment | added | HJRW | What's the relevance of the ag.algebraic-geometry, ct.category theory and dg.differential-geometry tags? Presumably examples can come from any area of mathematics. The big-list tag would certainly be appropriate, and the question should be community wiki. | |
| Apr 13, 2020 at 11:20 | comment | added | arsmath | Happy to do it. I am very interested in the question. I edited it again to clarify the partial proof point. | |
| Apr 13, 2020 at 11:19 | history | edited | arsmath | CC BY-SA 4.0 |
Edited to clarify partial proof point.
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| Apr 13, 2020 at 11:11 | comment | added | Praphulla Koushik | I wanted to include partial proofs as example but that is fine.. :) The question looks more clearer now.. thank you arsmath | |
| Apr 13, 2020 at 11:08 | comment | added | arsmath | I was unclear on one thing myself. Do you want to include partial proofs as an example, or exclude? It now reads like you want to exclude them. | |
| Apr 13, 2020 at 11:03 | history | edited | arsmath | CC BY-SA 4.0 |
Tried to clarify wording
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| Apr 13, 2020 at 10:34 | comment | added | Wojowu | I think the intent of the question would've been clearer if it asked (explicitly, especially in the title) for results which were announced to be true, but for which but whose proof has never appeared (yet). Anyway, clarifications considered, interesting question and +1 from me. | |
| Apr 13, 2020 at 10:03 | comment | added | Praphulla Koushik | @GerryMyerson thank you. Edited :) | |
| Apr 13, 2020 at 10:01 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
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| Apr 13, 2020 at 9:06 | comment | added | Gerry Myerson | OK, so it looks like you are asking for situations where A has asserted in print that he/she has a proof of X, but hasn't published a proof of X, and then B publishes a proof of Y, where the proof depends on the validity of X. Is that it? | |
| Apr 13, 2020 at 9:03 | comment | added | Monroe Eskew | Personally I do not understand why people do mathematics without understanding fully what they are doing. | |
| Apr 13, 2020 at 8:16 | comment | added | arsmath | Maybe reword it as "accepted to be true" but "no publicly available proof"? | |
| Apr 13, 2020 at 7:58 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
added 168 characters in body
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| Apr 13, 2020 at 7:51 | comment | added | Praphulla Koushik | I am looking for statements which people use to create new mathematics, assuming that statement is true, but there is no proof written.. For example as in page 20,21,22.. @GerryMyerson Does it makes it any clearer? | |
| Apr 13, 2020 at 7:41 | comment | added | Gerry Myerson | Everybody knows that Goldbach's Conjecture is true, that the Twin Prime Conjecture is true, that there are infinitely many primes of the form $n^2+1$, and so on, and so forth, even though there are no (credible) proofs. Is that the kind of result you are asking for, Praphulla? Or do you mean results which do have a proof, it's just that no one has bothered to write a proof out? Probably no one has written out a proof that $9876543\times9638527=95195326372161$, but I trust that it's true because my calculator says so. Is that the kind of result you mean? | |
| Apr 13, 2020 at 7:30 | review | Close votes | |||
| Apr 13, 2020 at 10:10 | |||||
| Apr 13, 2020 at 7:25 | comment | added | Praphulla Koushik | @CarloBeenakker Is the question in its present form looks ok for you? “I might object that a result without a proof cannot be known to be true as a matter of principle. What other method of verification do we have, other than a proof? Divine revelation?” Please have a look at the slides in the question for the relevance of this question... | |
| Apr 13, 2020 at 7:18 | comment | added | Carlo Beenakker | I might object that a result without a proof cannot be known to be true as a matter of principle. What other method of verification do we have, other than a proof? Divine revelation? (A previous version of the question asked for results that were "believed" to be true, rather than "known" to be true, then I could generate a vast list from all theorems that assume the Riemann hypothesis.) | |
| Apr 13, 2020 at 7:15 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
deleted 3 characters in body; edited title
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| Apr 13, 2020 at 6:09 | comment | added | Praphulla Koushik | This question is not intended to be a debate on whether some result is true or not :) I am only looking for results whose proofs are not published.. | |
| Apr 13, 2020 at 6:06 | history | asked | Praphulla Koushik | CC BY-SA 4.0 |