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I was wondering if a question along the lines of the following would be appropriate for MO:

An open problem that seems to get a lot of attention every once in a while is the amenability of Thompsons group $F$.
The problem seems to generate both proofs and disproofs at a fairly high rate, compared to many other open problems.
What is more, it seems that a big part of these are actually serious attempts by serious mathematicians, rather than the "usual" elementary attempts one sees for the more famous problems.

For examples, see for instance the MO question Is Thompson's Group F amenable? as well as (what as far as I can tell is the newest attempt, but I may have missed some) http://arxiv.org/abs/1408.2188.

Is there something inherent to this problem which causes this, i.e. some aspect that makes so many serious mathematicians convince themselves that they have a solution, and so many other serious mathematicians to take so long to find the errors?

Note that I am specifically not asking about what the errors were in previous attempts, unless there is some general type of error that tends to come up in many of them

I am asking here first, since this would to some extend be a soft question, and one which might not allow for a very definite answer.

Added: Given the positive response I will post the above version in about a day if there are no further comments.

Note: Question has been asked here: What makes the amenability of Thompsons group $F$ such a tricky problem?

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  • $\begingroup$ I would welcome such a question -- though I think you should give examples of the mentioned failed attempts at proving / disproving the amenability of $F$, in order to illustrate what you are asking. $\endgroup$ – Stefan Kohl Nov 10 '14 at 11:38
  • $\begingroup$ @StefanKohl Good suggestion, I added some examples. $\endgroup$ – Tobias Kildetoft Nov 10 '14 at 11:57
  • $\begingroup$ I agree with @StefanKohl, as long as emphasis is put on the last paragraph, so that answers merely of the form "I looked on Google and I have found a claim of a solution" are agreed to be off-topic $\endgroup$ – Yemon Choi Nov 10 '14 at 12:46
  • $\begingroup$ @YemonChoi Good point. Do you have any suggestion on how to make sure that part is emphasized? $\endgroup$ – Tobias Kildetoft Nov 10 '14 at 12:55
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    $\begingroup$ @TobiasKildetoft: I would write that very explicitly. -- People tend to interpret the question in their favorite way otherwise, as it happened e.g. with my question Mathematical research published in the form of poems, where answerers freely assert that e.g. medieval or ancient chinese poems have been published in a similar form as a paper in Math. Z.. $\endgroup$ – Stefan Kohl Nov 10 '14 at 13:50
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    $\begingroup$ What would be considered a good answer to this question? You might suggest some possibilities yourself, or illustrate by saying something like "I get that for the Jacobian conjecture, it is the naturality of the statement, like the Jordan curve theorem, which I don't see here", to give people an idea where the ballpark is or isn't. $\endgroup$ – The Masked Avenger Nov 11 '14 at 2:46
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    $\begingroup$ @TheMaskedAvenger That is a good question that I will probably need to think a bit more about. I was thinking of adding something along the lines of "I am specifically not asking about what the errors were in previous attempts, unless there is some general type of error that tends to come up in many of them" (this might also help the question become more focused and avoid a bunch of answers with links to previous attempts). $\endgroup$ – Tobias Kildetoft Nov 11 '14 at 8:17
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    $\begingroup$ Now that the question is "live" on MathOverflow I suggest you add a link here to it. $\endgroup$ – Yemon Choi Nov 13 '14 at 16:33

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