Timeline for Which mathematician sampled published proofs and found one third of them to have errors?
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2021 at 18:52 | vote | accept | msouth | ||
| Aug 22, 2019 at 4:46 | comment | added | Manfred Weis | maybe also interesting in that context: academia.stackexchange.com/a/54247 | |
| Aug 22, 2019 at 3:27 | comment | added | GH from MO | @TimothyChow: Yes, I remember these stories now. I agree that years are more significant than hours :-) | |
| Aug 22, 2019 at 3:22 | comment | added | Timothy Chow | @GHfromMO : Experts certainly found that Perelman's arguments were "incomplete" in the sense that it took years to flesh them out. Even today, S.-T. Yau has gone on record (e.g., in his memoir "The Shape of a Life") as saying that he's worried about whether Perelman's argument is really complete. For a different kind of example, did the original (pre-Flyspeck) Hales-Ferguson proof of the Kepler conjecture contain "significant errors"? See Part 2 of arxiv.org/abs/0902.0350 | |
| Aug 22, 2019 at 3:19 | comment | added | GH from MO | @TimothyChow: Wait, do Perelman's preprints contain significant errors? | |
| Aug 22, 2019 at 3:11 | comment | added | Timothy Chow | @GHfromMO : Okay. Many people are even more generous than you are. For example, I think that the standard view is that Perelman's preprints on the Poincare conjecture do not contain significant errors. | |
| Aug 22, 2019 at 3:09 | comment | added | msouth | @TimothyChow In the answer that I eventually posted you can see the character of things he found wrong in his own work--in some cases, the theorem was still correct but the proof had minor errors, in others, it was worse. The problem that first drove him to create a structured proof was particularly difficult to get right (something about an algorithm having to do with concurrency), and it may be that his interest in that kind of thing meant he was in an area of study that was more prone to that kind of error, giving him a higher number of "hits" for wrong prose proofs in his search. | |
| Aug 22, 2019 at 3:08 | comment | added | GH from MO | @TimothyChow: By "significant error" I mean that the expert reader finds the argument wrong or incomplete, and even with thinking about it for a couple of errors, the reader cannot fix it. These are the only errors I really care about (although let me say that, in my youth, I would prepare lengthy lists of errata for every book I read, and this included typos as well). | |
| Aug 22, 2019 at 3:00 | comment | added | Timothy Chow | Depending on the definition of the adjective "significant" in the phrase "significant error," I'm sure one could get almost any error rate in the range $[\epsilon,1-\epsilon]$. To get $1-\epsilon$, define an error to be significant if a computer proof assistant would notice something imperfect. To get $\epsilon$, define an error to be significant if the whole idea of the proof is completely wrong. | |
| Aug 22, 2019 at 2:57 | history | edited | msouth | CC BY-SA 4.0 |
bell labs reference was erroneous and can't contribute positively to the discussion, should not be prominent in the question
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| Aug 22, 2019 at 1:22 | comment | added | Richard | The 1% estimate is very close to the official 0% figure, put forward by math hardliners, and which is something toxic. From my own experience (I'm a professional mathematician too) around 70% papers are in need of at least a small fix. This is of course not a problem, math is wonderful as it is, and it always goes forward, one way or another. | |
| Aug 22, 2019 at 0:33 | comment | added | msouth | Thanks @ToddTrimble! Do you know if anyone has tried to independently check his one-third claim? When I got that hit on google, I only read to that sentence about the one-third and was disappionted to find it was not footnoted. Once I'd unwittingly made an ass of myself by posting a question with the answer linked in it, I thought, 'hmmm, I should read the rest of that", and, yes, there it was, staring me in the face 20+ years later :). Cool that you've heard Lamport say that in person! | |
| Aug 22, 2019 at 0:26 | answer | added | msouth | timeline score: 6 | |
| Aug 22, 2019 at 0:25 | comment | added | Todd Trimble | By the way, Lamport calls them "structured proofs". | |
| Aug 22, 2019 at 0:16 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
added 34 characters in body; edited tags
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| Aug 22, 2019 at 0:02 | comment | added | Todd Trimble | I've heard Leslie Lamport put forth that estimate as well. It might even be right, but if his example of Kelley's oversight in proving the Cantor-Schroeder-Bernstein is at all representative, it's not necessarily cause for alarm. | |
| Aug 21, 2019 at 23:34 | history | edited | msouth | CC BY-SA 4.0 |
Edit to point out that I might have included the answer in my question accidentally.
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| Aug 21, 2019 at 23:25 | comment | added | GH from MO | My own experience. I have read (refereed, reviewed etc.) a lot of papers. I also talk to my colleagues regularly, and I have not heard about any serious anomaly. The published literature (in decent journals) is very trustworthy. Are you a research mathematician? I am. | |
| Aug 21, 2019 at 23:24 | comment | added | user142929 | I have studied in two universities (but not a PhD) and I tell you on the part that I have known as a student those professors that I am very difficult to even imagine, that they make mistakes in their work writting his/her papers. And also, and now I talk from the ignorance that I have the perception that the editors also are very very rigorous and serious. | |
| Aug 21, 2019 at 23:16 | comment | added | msouth | @GHfromMO What are you basing those numbers on? | |
| S Aug 21, 2019 at 23:13 | history | suggested | Ali Taghavi |
I add a tag.
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| Aug 21, 2019 at 23:10 | comment | added | GH from MO | My estimate is that less than 1% of mathematical papers (in decent journals) contain incorrect theorems, and less than 5% of mathematical papers has any significant error. | |
| Aug 21, 2019 at 22:44 | review | Suggested edits | |||
| S Aug 21, 2019 at 23:13 | |||||
| Aug 21, 2019 at 22:30 | review | First posts | |||
| Aug 21, 2019 at 23:35 | |||||
| Aug 21, 2019 at 22:25 | history | asked | msouth | CC BY-SA 4.0 |