The question Tate conjecture (Proved?) was asked yesterday, and quite quickly closed; it was then re-opened, and then closed (by, I think, a different set of 5). Questions about proofs of correctness have been discussed at length before, but given that it seems there is plenty of interest in both upvoting, closing, and reopening the question, it might be good to have a proper discussion about this question here to make things seem a bit less contentious and edit-bellicose to other users.

What are the opinions of the community on this issue? (My own appears in a comment to the question, but I am open to changing my mind!)

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    $\begingroup$ You might be interested to learn (as I was) that Kontsevich thinks the Tate Conjecture (and the Hodge Conjecture) are actually false!. $\endgroup$
    – David Roberts Mod
    Commented Apr 27, 2023 at 7:13
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    $\begingroup$ This seems to be mainly about this particular question (rather than closing/reopening in general) - so I guess that the tag (specific-question) seems a suitable tag for this question. Tangentially - just as a curiosity - questions that were closed and reopened several times. $\endgroup$ Commented Apr 27, 2023 at 8:05
  • $\begingroup$ @MartinSleziak Good point! I'll add that tag. $\endgroup$ Commented Apr 27, 2023 at 11:22
  • $\begingroup$ @Carl-FredrikNybergBrodda Hi! I voted to reopen too because I agree with your reasoning in the comments there. That said, Jan stated that they now plan to delete the question, see here, so I think reopening/closing it might not be an issue anymore. $\endgroup$
    – Emily
    Commented Apr 27, 2023 at 20:06
  • $\begingroup$ @Emily Even if the question is deleted, a new question could be crafted. Perhaps something along the lines of What were the main ideas and gaps in Yoichi Miyaoka's attempted proof (1988) of Fermat's Last Theorem? $\endgroup$ Commented Apr 27, 2023 at 20:42
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    $\begingroup$ If I understand correctly, you cannot vote to close a question twice, so it must have necessarily been a different set of 5. $\endgroup$ Commented Apr 27, 2023 at 21:43
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    $\begingroup$ The OP has now deleted the question. $\endgroup$
    – David Roberts Mod
    Commented Apr 28, 2023 at 5:27
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    $\begingroup$ We need a possibility to cast a clopen vote. $\endgroup$ Commented May 2, 2023 at 16:19

1 Answer 1


As of this writing, the question concludes with the following paragraph:

I'd like to conclude by respectfully reiterating that, on one hand, the author seems to be reliable, and on the other, even in the case there's a fatal mistake somewhere, I'm sure it will be found agreeable that we are only human and it happens to everyone, so no harm done for him as long as it is caught and acknowledged quickly (I wouldn't want to put undue pressure on him with my question).

In a comment, the OP also says this:

I'd prefer to not expose the author of the preprint to too much pressure in the early stages of his career. As long as he rectifies the situation (e.g. by withdrawing the preprint in a timely manner), he should move on and be given every opportunity to prove himself in the future.

In my mind, the fact that the OP feels the need for such disclaimers is a bad sign. It suggests that social factors are playing a heavy role, to the point where they may be interfering with free and open discussion of the actual math. Longtime MO users will recall the decision made in the case of Atiyah and the Riemann Hypothesis. While the situation with the current question is not quite the same, I think that it's generally a sign of an inappropriate question if people feel the need to issue heavy disclaimers. Indeed, the OP seems to feel similarly, and plans to delete the question.

Now, initially, the question did not have these disclaimers. The first version pretty much just asked, "Is this paper correct?" and as such seems like a clear candidate for closure, per MO's usual policy. Later versions added some specific mathematical content, and it looked like it might be headed toward an acceptable MO question, but in every revision, the main question was still "Is this paper correct?" and not the actual math. I think I would have voted to close every revision.

Having said all that, I think it's still possible that this question could be turned into an acceptable one, if the "Is this paper correct?" part is deleted and the focus is on a specific mathematical claim in the paper that turns out to be subtly wrong. I can imagine something along those lines that would not require disclaimers of the form, "No offense; I know you're smart and all, but..."

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    $\begingroup$ The question has now been self-deleted $\endgroup$
    – David Roberts Mod
    Commented Apr 28, 2023 at 8:49
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    $\begingroup$ I'm not sure you avoid the social implications by just not mentioning them. Whether or not a proposed solution to a conjecture is correct seems like the kind of thing that should be discussed by the mathematical community and (unf imo) MO may be the best place to do that online. I don't think asking about specific conjectures is a good substitute if it's a long manuscript. $\endgroup$ Commented Apr 28, 2023 at 20:06

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