Timeline for Endless controversy about the correctness of significant papers
Current License: CC BY-SA 4.0
59 events
| when toggle format | what | by | license | comment | |
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| May 9 at 14:45 | comment | added | Timothy Chow | @YiftachBarnea I thought that it was now generally agreed that the amenability of the Thompson group is an open problem. There is an old MO question devoted to the amenability of the Thompson group. | |
| May 8 at 20:30 | comment | added | Yiftach Barnea | I don't know enough to write an answer about it, and do not have the knowledge to judge any of it. However, there are a couple of issues in geometric group theory that I am aware of. One is the endless disagreement whether the Thompson group is amenable. The other is the work of Kharlampovich and Myasnikov which was both criticised for ethical issues and correctness. | |
| May 25, 2023 at 13:30 | history | edited | Ievgeni |
edited tags
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| Feb 4, 2023 at 11:42 | review | Close votes | |||
| Feb 4, 2023 at 19:52 | |||||
| Jan 28, 2021 at 14:33 | comment | added | Tom Copeland | Adjunct question: Examples of instances in which authoritarian shortsightness/turf wars impeded progress in a field? E.g., Heaviside's mathematics on transmission of signals in telegraph cables, and the history of the Belousov-Zhabotinsky reaction. | |
| Jun 1, 2020 at 19:07 | comment | added | Ben McKay | Since Abbas Bahri's death, his web site is no longer available, but the paper I mentioned seems to have been published in Advanced Nonlinear Studies, Volume 15: Issue 2. | |
| Jun 1, 2020 at 18:32 | comment | added | YCor | Gromov's famous and great book "Hyperbolic groups" contains a lot of statements with somewhat sketchy proofs (or no proof at all, such as "by an easy argument"), and sometimes statements that are technically false (missing assumptions). This applies to other famous works of Gromov. "What should we do in order to salvage mathematical topics that suffer such tensions?" Simply, subsequent authors prove or correct these in detail. I'm not sure there was any tension in this case, but it's largely thanks of the work of subsequent authors. | |
| Jun 1, 2020 at 18:28 | history | edited | YCor | CC BY-SA 4.0 |
specified title; added tags (journals being synonym of "publishing" which is closest tag to "publication")
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| Jun 26, 2019 at 13:03 | comment | added | Gateau au fromage | @DenisSerre A side question for my own interest: could you please tell us about the example you have about wave stability in PDE models for fluid dynamics? Not that I want to use the example to answer your question. It's more that I am interested in those topics and would like to read about it. | |
| Jan 1, 2019 at 12:40 | comment | added | Ryan Budney | I know of plenty of examples of such controversies in topology -- at least one has been mentioned already. The controversies that stick around the longest often are the ones where it is difficult to state what the problem is. In Freedman's work you see it in complicated iterated induction arguments where one applies subtle topological operations. In other papers you might see a thought-process develop through the paper and if you're not fully into it, you get lost at the latter stages as the argument gets more complicated. I'm fairly agnostic about such controversies -- the truth is stable. | |
| Jan 1, 2019 at 9:58 | comment | added | none | Fermat famously wrote in his copy of Arithmetica that he had a proof too long to fit in the margin... | |
| Dec 31, 2018 at 19:37 | answer | added | Timothy Chow | timeline score: 45 | |
| Jul 9, 2018 at 21:24 | review | Close votes | |||
| Jul 10, 2018 at 17:25 | |||||
| Jun 26, 2018 at 13:59 | answer | added | Mikhail Katz | timeline score: 0 | |
| Oct 10, 2017 at 20:35 | comment | added | Robert Frost | @PhilipOakley I'd not seen that before; it's very interesting. In the unlikely event you're interested my opinion on Q Theory, I think to amplify some miniscule phenomenon to the point we can make a boolean statement about it, we must be triggering our "boolean" decision on some minute switching component. This is the principle of how amplification works. So I suspect there's a continuum going on down there but we can only "see" the switches which we can build out of the waves. Based on the quick video I watched on Bell's theorem this can explain it. youtube.com/watch?v=5JCm5FY-dEY | |
| Oct 10, 2017 at 14:57 | comment | added | Philip Oakley | @RobertFrost, the en.wikipedia.org/wiki/Bertrand_paradox_(probability) is interesting in that it has similarities to the issues in Quantum Mechanics of Bell's Theorem and the way folk get confused about relative polarisation probabilities (which are around a circle). As stated, the mechanism drives the probability, and the misunderstandings. One can be too un-informed about a prior! | |
| Oct 10, 2017 at 6:27 | comment | added | jpmc26 | While this is most certainly a math site, since you mentioned fluid dynamics, it's worth considering that when dealing with physics, experimental results trump mathematical purity to a degree. If the dispute you mention is ever settled, it will probably be settled by whether the theories that arise from it make accurate predictions about our world. If they do, then I expect someone will eventually resolve the mathematical issues. | |
| Oct 10, 2017 at 1:43 | comment | added | Adam Davis | @GerryMyerson You asked why people might be closing. Whether those reasons are valid is a topic for meta. Note that I do not have the ability to close, so I'm only providing a possible explanation. Consider contributing to questions such as meta.mathoverflow.net/questions/1325/… so the community may further refine its requirements. | |
| Oct 9, 2017 at 21:55 | comment | added | Gerry Myerson | @Adam, some of the most informative pages here are the result of list type questions. | |
| Oct 9, 2017 at 14:06 | comment | added | Adam Davis | @GerryMyerson This is a list type question, with no objectively right or wrong answer. As such it could be a list of significant length, and the voting becomes a popularity contest. If the list becomes longer than a page, then you often find better and/or later answers languishing at the bottom while early and/or popular answers sit near the top. See meta.stackexchange.com/questions/124450 and meta.stackexchange.com/questions/238219 and, perhaps most salient, mathoverflow.net/help/dont-ask where this ticks many boxes for questions that shouldn't be asked. | |
| Oct 8, 2017 at 18:00 | comment | added | Joel Adler | @DenisSerre I suppose that there are requirements for a computer program to be used in a proof. Its correctness must be shown somehow. | |
| Oct 7, 2017 at 7:30 | comment | added | Wildcard | @AlexandreEremenko "endless" by exact definition means "without end." Surely you know that. The proposed rephrasal to "unresolved" sounds reasonable. | |
| Oct 6, 2017 at 18:53 | comment | added | Martin Seysen | The controversy about the correctness of the proof of the classification theorem for the finite simple groups lasted from its announcement 1983 until 2004, where the last known gap has been filled. See e.g. en.wikipedia.org/wiki/Classification_of_finite_simple_groups. I don't know if this qualifies, since that classification comprises hundreds of articles. | |
| Oct 6, 2017 at 16:05 | answer | added | Robert Haraway | timeline score: 23 | |
| Oct 6, 2017 at 14:15 | comment | added | Denis Serre | @JoelAdler. I don't have problems with a computer-aided proof if the community (in this case, that of graph theory) is convinced. My concern is more that in some cases, the community might not reach a consensus of whether a proof is reliable or not. And such a proof could be computer-aided, or not. | |
| Oct 6, 2017 at 14:12 | comment | added | Denis Serre | @DanFox. Could be. It turns out that English is not my mother tongue. Sometimes, I employ a word as it was a french one. Feel free to edit the question. Your concern was raised also by Peter Heinig. | |
| Oct 6, 2017 at 14:09 | comment | added | Joel Adler | How would you rate the computer based proof of the four colour theorem? Is it accepted as a proof? Does one still look for a proof that does not rely on the use of a computer? | |
| Oct 6, 2017 at 13:58 | history | reopened |
Leo Alonso Igor Belegradek R.P. Denis Serre Timothy Chow |
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| Oct 6, 2017 at 13:31 | comment | added | Dan Fox | Would the question be more acceptable were "endless" replaced by "unresolved"? It seems that doubts of this sort (with respect to his own work) were in part what motivated Voevodsky's program related to computer assisted proof verification. Additionally, there are some such controversies and those who do not work in an area do not always know what their status is, so the question is potentially useful, if properly channeled. | |
| Oct 6, 2017 at 12:58 | review | Reopen votes | |||
| Oct 6, 2017 at 14:03 | |||||
| Oct 6, 2017 at 12:42 | history | edited | Denis Serre | CC BY-SA 3.0 |
added 168 characters in body
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| Oct 6, 2017 at 10:32 | review | Reopen votes | |||
| Oct 6, 2017 at 11:13 | |||||
| Oct 6, 2017 at 6:02 | comment | added | Peter Heinig | @GerryMyerson: re "Please, speak up!": I for one did not vote to close, yet favorably see its having been closed. This isn't any criticism of the opening poster. The intention was well-meant, but I think that in its present form the question much too broad to be mathematically informative (it is so broad that it invites all sorts of 'opinion-pieces'). Such questions can be informative if technically formulated (with proof-theoretic/epistemological constraints imposed, and without inflammatory English words like 'controversy', 'famous', 'guilty', and another word too strong to cite. | |
| Oct 6, 2017 at 2:44 | history | closed |
Neil Strickland Andrés E. Caicedo user6976 Alexandre Eremenko Joseph Van Name |
Not suitable for this site | |
| Oct 5, 2017 at 23:07 | comment | added | Alexandre Eremenko | @Gerry Myerson: I voted to close because on my opinion it is poorly stated (what does it mean "ensless"? There were long controversies. How long is "endless"? ) and not within the scope of this site. | |
| Oct 5, 2017 at 21:34 | comment | added | Gerry Myerson | I see three votes to close, and no comments explaining why one should want to close. Please, speak up! | |
| Oct 5, 2017 at 21:30 | answer | added | Gerry Myerson | timeline score: 10 | |
| Oct 5, 2017 at 17:15 | comment | added | Kimball | Depending on interpretation of the question, foundational mathematics may be rife with examples (sets, axiom of choice, consistency, ...). | |
| Oct 5, 2017 at 16:12 | answer | added | Timothy Chow | timeline score: 32 | |
| Oct 5, 2017 at 15:18 | comment | added | Gerhard Paseman | I take it controversy over notation and representation are also not considered here? Otherwise, how to write (in this forum format particularly) composition of functional relations and whether the algebra with empty sub universe should be included in a class have been ongoing items of contention. Gerhard "Maybe More Endless Than Endless" Paseman, 2017.10.05. | |
| Oct 5, 2017 at 14:52 | comment | added | Denis Serre | If I judge from the votes in favour of closing it, the question itself is controversial :) | |
| Oct 5, 2017 at 14:35 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Oct 5, 2017 at 14:07 | answer | added | coudy | timeline score: 62 | |
| S Oct 5, 2017 at 13:53 | history | suggested | David Richerby | CC BY-SA 3.0 |
Typos and light copy-edit
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| Oct 5, 2017 at 13:46 | review | Suggested edits | |||
| S Oct 5, 2017 at 13:53 | |||||
| Oct 5, 2017 at 13:23 | comment | added | Steve Huntsman | Relevant: mathoverflow.net/questions/13896 | |
| Oct 5, 2017 at 13:19 | answer | added | Steve Huntsman | timeline score: 79 | |
| Oct 5, 2017 at 13:13 | comment | added | Stanley Yao Xiao | Would Shinichi Mochizuki's purported proof of the $abc$-conjecture qualify? | |
| Oct 5, 2017 at 12:24 | answer | added | Francesco Polizzi | timeline score: 32 | |
| Oct 5, 2017 at 12:16 | answer | added | Peter Heinig | timeline score: 45 | |
| Oct 5, 2017 at 12:09 | comment | added | Oliver Nash | Though my understanding is based largely on just this article for the layperson, I believe there was apparently controversy around Kuranishi structures and a proof of (a version of) the Arnold conjecture for a time. Not endless but apparently non-trivial. | |
| Oct 5, 2017 at 11:46 | comment | added | Peter Heinig | [Technical subcomment to Robert Frost's very interesting comment: roughly speaking, 'objectivist' is to 'subjectivist' as 'frequentist' is to 'Bayesian'. That is, roughly, 'objectivist'='frequentist' and 'subjectivist'='Bayesian'.] | |
| Oct 5, 2017 at 11:36 | comment | added | Robert Frost | There is also the objectivist vs the subjectivist views of probability and as such no paper which permits the choice of something "at random" is rigorously correct, since there is no such thing as "at random" as demonstrated by Bertrand's paradox en.wikipedia.org/wiki/Bertrand_paradox_(probability) which mathematicans routinely ignore; e.g. when saying that the probability of choosing a $1$ at random from the natural numbers is zero. | |
| Oct 5, 2017 at 11:34 | comment | added | Robert Frost | It was not an endless controversy but Wiles' proof of Fermat's last theorem contained a hole which was raised and he was allowed the privilege of filling it himself. | |
| Oct 5, 2017 at 11:30 | comment | added | Peter Heinig | If the contributions remain respectful and considered, this is an important and useful question. The following is meant as a constructive suggestion of improvement: it would be better if you thought of some way to impose conditions which rule out the 'usual' examples like Almgren's 900+pages regularity paper, or Hales' proof of Kepler's conjecture. (Please note: I am not disputing these papers; I am mentioning them since on the superficial verbal level it is a fact that the latter two are controversial.) Sorry not to have a good suggestion of what additional conditions you could impose. | |
| Oct 5, 2017 at 11:25 | review | Close votes | |||
| Oct 5, 2017 at 12:48 | |||||
| Oct 5, 2017 at 11:21 | comment | added | Ben McKay | Freedman's work on 4-manifolds has also been strongly criticized, and might be what you are looking for: mathoverflow.net/questions/87674/… | |
| Oct 5, 2017 at 11:18 | comment | added | Ben McKay | Abbas Bahri wrote a famous paper criticizing the rigour of various papers. I don't give his paper as an answer, since it is not really an endless controversy, but his concerns seem to have been very serious. sites.math.rutgers.edu/~abahri/papers/five%20gaps.pdf | |
| Oct 5, 2017 at 11:10 | history | asked | Denis Serre | CC BY-SA 3.0 |