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

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