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I wanted to vote to close this question which claims to disprove the Riemann Hypothesis, but I realized that, even though we get questions of this kind occasionally, none of the reasons to close is really appropriate. It's not “duplicate”, doesn't need “details or clarity”, doesn't “need more focus”, isn't “opinion-based”, doesn't belong in a different StackExchange network, and it doesn't seem right to add an ad hoc comment (except if we had a clear FAQ to link to, see last paragraph). We could make the case that it's “not about research level mathematics”, but I think this somewhat misses the point (RH is clearly research-level mathematics).

Here and here are other Meta questions about this kind of issue, and while there is clear consensus that such questions need to be closed or deleted, there doesn't seem to be much agreement as to how to do it.

Would it be possible to add another reason for closure that could look something like this: “MathOverflow is not a place to publish claims of proofs or discuss whether such proofs are correct”?

Also (and I realize this is a somewhat different question), is there a standardized FAQ to which to redirect people who claim to have solved this-or-that famous problem, that explains (politely but firmly) why experts can't afford to take the time to read such claims? Because the typical answer of “send it to a journal” really isn't honest: no journal is going to even attempt to referee a one-page paper (or a 1000-page paper, for that matter) coming from J. Random Nobody with claims to prove or disprove RH, it's just going straight to the garbage can, and the note would even be rejected from the arXiv. (We can tell them to post them on viXra, but it would be a lie to say that any expert would ever read them.) A more honest answer would be something like “if you can prove or disprove RH, then you can probably start by making a name for yourself by tackling on some other easier problems”, but probably someone wrote such an explanation down somewhere already and we can just link to it.

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    $\begingroup$ It seems that there can be only three custom close reasons - see: How do moderators make changes to the site-specific closed question reasons? and How do moderators update custom off-topic reasons for their site? Maybe somebody (the moderators?) can check whether this is still true. (However, even if the maximum is three, on MO there is still one free spot.) $\endgroup$
    – Martin Sleziak
    Commented Apr 30, 2022 at 10:30
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    $\begingroup$ @MartinSleziak Yes, there is presently one free slot. If there is agreement on this, I can add the proposed close reason there. (If it turns out that there are more important uses for that slot, it can be changed at any time.) $\endgroup$
    – Stefan Kohl Mod
    Commented Apr 30, 2022 at 11:18
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    $\begingroup$ Re: is there a standardized FAQ to which to redirect people. This isn't exactly what you're asking for, but on Academia there is this post: I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank? $\endgroup$
    – Martin Sleziak
    Commented Apr 30, 2022 at 11:30
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    $\begingroup$ FWIW the style of that deleted question resembles a known "repeat offender", but I don't know if it is appropriate to have a reason for closing that is "we have told you repeatedly why your efforts in this direction are almost certainly doomed" $\endgroup$
    – Yemon Choi
    Commented Apr 30, 2022 at 14:08
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    $\begingroup$ @StefanKohl, how do we express agreement? (I definitely want more close reasons; and, though I don't know if "spending" a close reason on "MO isn't the forum for proposed proofs of open problems" is the best use of it, I don't have any obviously better candidate. I do wish we had the old blunter reasons back ….) $\endgroup$
    – LSpice
    Commented May 1, 2022 at 14:27
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    $\begingroup$ @LSpice Some patience please ... . $\endgroup$
    – Stefan Kohl Mod
    Commented May 1, 2022 at 21:46
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    $\begingroup$ @StefanKohl, my apologies; I did not mean to sound impatient. $\endgroup$
    – LSpice
    Commented May 2, 2022 at 1:14
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    $\begingroup$ @LSpice Re: how do we express agreement? So far, this question has no answers. E.g., you (or somebody else) could post an answer with suggested wording for the new close reason. (And other users could up/downvote to show whether they agree or not.) Similarly, if somebody is against this new close reason, they could post an answer summarizing the arguments why it is not a good idea - and then MO users could show by voting on that answer whether or not they agree. (In the absence of answers, perhaps at last voting on the question says something about the (dis)agreement with the suggestion.) $\endgroup$
    – Martin Sleziak
    Commented May 2, 2022 at 8:38
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    $\begingroup$ Some journals do referee dubious proofs of major open problems - I have been asked to do this for the Annals. I don't think they're actually happy to have such papers sent their way, but the Journal of Number Theory is, since they charge for them (and pay the referee). $\endgroup$
    – Will Sawin
    Commented May 2, 2022 at 12:22
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    $\begingroup$ If a new close reason is added, I think it should be as general as possible to handle many reasons of this type. Maybe "This is a type of question disallowed by the site's rules" and then a link to a page with some examples. $\endgroup$
    – Will Sawin
    Commented May 3, 2022 at 16:36
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    $\begingroup$ Martin points to a useful FAQ. Here's another link that contains a lot of useful and well thought out advice for an "amateur" who thinks they've proven a long-standing conjecture such as the Riemann hypothesis. This is where I tend to direct people who submit a short proof of RH or the Golbach or twin prime conjectures to a journal at which I'm an editor: cohn.mit.edu/advice $\endgroup$
    – Joe Silverman
    Commented May 5, 2022 at 22:07
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    $\begingroup$ @MartinSleziak Just recording that in addition to the useful Meta.SE links you shared, there were important updates to the close system in 2019. $\endgroup$
    – Tim Campion Mod
    Commented May 8, 2022 at 3:57

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A bit of an update, too long for a comment.

To be sure we're all on the same page, here's the current setup. If you have sufficient rep, you can click the "close" button on a question, and you get a popup which looks like this:

General Close Reasons

These are some general close reasons common to the entire Stack Exchange network as I understand, and which, if we wanted to change them, would at the very least require some discussion with Stack Exchange (and they might tell us no).

What we do have control over is the options you get if you choose the second option on this list -- the community-specific reasons. If you do that, you get the following options:

Site-Specific Close Reasons

We currently have two options here, and we can have up to three. As a technical point, it appears to be possible for moderators to delete a close reason or to create a new one, but not to edit the description in an existing close reason. We can also tinker with the order they appear in.

As mentioned here, we've just updated the help page to which that first, generic site-specific close reason links:

This question does not appear to be about research mathematics within the scope defined in the help center.

We've now included language there which for the first time explicitly says that these sorts of "check my work" or "result announcement" questions are off-topic. With these updates, the first, generic site-specific close reason technically plays exactly the role suggested by Will Sawin in a comment, because the help page being linked to there now says something about these sorts of close reasons among others. So in some sense this means the answer to the question is "no, we already have a close reason which covers these cases."

However, the close reason in question ("This question does not appear to be about research mathematics within the scope defined in the help center.") leaves something to be desired, because it doesn't summarize what list of reasons it actually covers directly -- you have to follow some link and hunt around a bit to get a list of things this close reason might mean. This is not very helpful either to close-voters or to close-votees.

Therefore, I agree that the close reasons could probably use some kind of update, with a few goals:

  1. The close reasons should be more specific, so that everybody is clear on why exactly a question is being closed.

  2. The specificity of the close reasons should be spelled out in the actual text of the close reason, in addition to containing links to somewhere these reasons are discussed in more detail.

With this in mind, I think it's worth opening up the discussion a bit more broadly. If we have 3 slots for close reasons, I think we can reserve one to be a "catch-all" containing a laundry list of reasons and a link to the help page in case we think to add something later, but we have the opportunity to use the other two in a more specific way. Most likely it's worth keeping the second site-specific close reason (directing the user to Math Stack Exchange) in some form at least, which would leave one more slot. If we have one slot for a more specific close reason, what is the best reason for it to be covering?

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    $\begingroup$ I feel that the two most common reasons for which I vote to close a question are ① “this is homework” (in which case I click the “not research level math” because homework, from people who didn't even bother to try, isn't appropriate for MSE either; but anyway, “not research level math” is clear enough, so I'm happy with it), and ② some variation around “this is not a place to get your proof of <famous conjecture> checked” (in which case I also click “not research level”, but for reasons explained in the present question, I'm not super happy with it). $\endgroup$
    – Gro-Tsen
    Commented May 6, 2022 at 18:37
  • $\begingroup$ You write that it is not possible for the moderators to edit the description in an existing close reason, but then you suggest it's worth keeping the second site-specific close reason in some form. How can we keep it in any form other than its current form, if it can't be edited? $\endgroup$
    – Gerry Myerson
    Commented May 7, 2022 at 2:26
  • $\begingroup$ I find the reason "This question does not appear to be about research mathematics within the scope defined in the help center." to be not so much site-specific, as an instance of "This question does not appear to be about [site topic] within the scope defined in the help center.". I agree that editing the reason to not just use such boilerplate language would be a good move, if only to specify that a very narrow class of research-level questions are off-topic, namely checking claimed proofs of famous conjectures $\endgroup$
    – David Roberts Mod
    Commented May 7, 2022 at 2:42
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    $\begingroup$ @GerryMyerson I'm willing to contemplate the idea of deleting a close reason, and then creating a new, similar but better close reason to replace it. $\endgroup$
    – Tim Campion Mod
    Commented May 7, 2022 at 13:58
  • $\begingroup$ @DavidRoberts Agreed -- it's really only "site-specific" in the technical sense that we have the control to directly delete it if we like (and replace it with something similar but new if we like.) $\endgroup$
    – Tim Campion Mod
    Commented May 7, 2022 at 14:00
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    $\begingroup$ Partly to get my own thoughts straightened out on this broader question, I've opened up a broader meta question. $\endgroup$
    – Tim Campion Mod
    Commented May 9, 2022 at 23:30

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