Timeline for Publishing solution but temporarily holding back solution method
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 15, 2021 at 17:55 | comment | added | Ryan Budney | I found a similar form for the Lawrence-Krammer representation, where the Poincare duality construction (although informative) is far more involved than simply presenting the form algebraically and verifying its properties. People have even suggested to me (after presentations) that the more mysterious methods of presenting the result is probably the approach they would have chosen. | |
| Apr 15, 2021 at 17:51 | comment | added | Ryan Budney | There is Squier's paper where he showed the Burau representation preserves a sesquilinear form. In the paper, the form is given by a formula. I think most readers find the origins of the form mysterious (we even have an MO question about how it was derived). It was created as an intersection form, using a Poincare duality construction. Deriving the form from geometry requires far more work than just writing down the end result and verifying directly the algebraic properties of the form. But there's many more examples like this. | |
| Apr 15, 2021 at 16:15 | comment | added | Timothy Chow | This is probably not quite what you are asking for, but there are many instances of results that are announced but no proof appears for a long time. See this MO question for examples. But in these examples, it's probably because the authors get distracted by other projects, not because they are intentionally trying to keep their methods secret. | |
| Apr 15, 2021 at 15:53 | comment | added | Anthony Quas | @MarkWildon :21? | |
| Apr 15, 2021 at 14:25 | comment | added | Mark Wildon | One possible more recent example is Zagier's proof that every number congruent to 1 modulo 4 (corrected after Gerry's comment) is a sum of two squares. This can be found in 'Proofs from the Book' and was discussed here mathoverflow.net/questions/31113/…; in particular Christian Elshotz has a nice paper explaining how one might discover the proof | |
| Apr 15, 2021 at 12:58 | history | became hot network question | |||
| Apr 15, 2021 at 12:02 | comment | added | Gerry Myerson | @Mark, I would like to see how Zagier proposes to express $3$ as a sum of two squares. | |
| Apr 15, 2021 at 11:45 | comment | added | Mark Wildon | Nowadays my impression is that it is very rare for authors to explicitly hide their methods. In fact, so much of mathematics depends on the application of deep techniques that it would often be hard for them to do so, and still present a rigorous proof. But I'm afraid a lot of methods are implicitly hidden, because they are not amenable to presentation in the usual format of research papers. | |
| Apr 15, 2021 at 11:40 | answer | added | Francesco Polizzi | timeline score: 3 | |
| Apr 15, 2021 at 8:19 | comment | added | Neil Strickland | @RyanBudney can you give examples? I have never heard of anything like this. Of course, people often find counterexamples by a meandering process that cannot easily be summarised. But if some kind of systematic search was used, I would expect people to explain it. | |
| Apr 15, 2021 at 7:35 | comment | added | none | @abx it looks like version 3 of the paper went up more recently, and has more detail. | |
| Apr 15, 2021 at 7:33 | comment | added | abx | The example of Gardam's result is perhaps not a good choice. According to Quanta the talk was on (last) February 22, while Gardam put his preprint on ArXiv on February 23... | |
| Apr 15, 2021 at 5:46 | comment | added | Ryan Budney | Yes, this is reasonably common. As has been mentioned below, sometimes the method of finding the counter-example is less important than the counter-example itself. Sometimes authors enjoy the mystique of presenting something with hidden methods. Perhaps this is a bit meta, but by and large proofs are supposed to hide the worst of the struggles you might have had in the process of discovery -- after all they're meant to be as enlightening as possible. | |
| Apr 15, 2021 at 5:36 | answer | added | Alessandro Della Corte | timeline score: 2 | |
| Apr 15, 2021 at 4:56 | history | asked | none | CC BY-SA 4.0 |