Is there a clear rule against "check this proof" type questions?

Question

I discovered that the meta question "Questions" of the type "I have written something, please give me feedback" from more than three years ago still does not have any answer, while What is our policy on asking about correctness of preprints?, although having several answers and links to some tea discussions, does not seem to contain any decisive conclusion.

So I decided to raise this again. For a specific recent extreme example: what to do with Riemann Hypothesis which asks whether a proof of RH is correct? My immediate reaction is off-topic, but is there a commonly shared explanation for the OP on why is this an inappropriate question?

Answer 1

Since I was one of the "delete" votes for "Riemann Hypothesis", I'll present my standpoint here.

In that particular instance you do not need to know pretty much anything beyond elementary algebra and a little bit of undergraduate complex analysis to evaluate that "proof of Riemann Hypothesis" by yourself or to ask your friend or colleague next door to do it if you are too lazy. Dragging such obvious nonsense to MO is more or less equivalent to spamming, IMHO.

Reuns responded in a very precise manner to it, leaving no uncertainty about the issue whatsoever. I was way more harsh (to the extent that my comment was, apparently, deleted by moderators). But no matter which way you look at it and what you say (or agree not to say) about it, a piece of junk remains a piece of junk.

This much said, I see nothing wrong about discussing the correctness of some proofs that can be classified as "correct" or "flawed" in principle and for which figuring out the answer requires some expertise in the field. Ideally, in such cases the OP should pinpoint a particular place that bothers him in the argument, but this assumes that he has sufficient qualifications for that, and that is, obviously, not always true. So, I would decide such issues on a case-to-case basis without trying to make any general rule at all. If there is somebody who is qualified to answer and is willing to spend his time on the investigation, I see no reason (and no moral right) for anyone else to interfere with such attempt. If nobody answers, than it is fine too: no one is obliged to think of any particular question no matter how well it is posed.

In general, my main premise is that MO is about mathematics and not about the formal rules for the posters and respondents. If somebody asks a meaningful and non-trivial question about mathematics and somebody else answers it in a meaningful way, why should anybody else care what exactly that exchange was about?

Answer 2

The real reason, I suspect, is that it is a common request which we (the past, current, and with high probability future MathOverflow community) are tired of hearing, like checking on proofs of 1 not equal to 0.9999999.... . History is rife with examples of failed attempts which actually made some contribution to the literature, as well as successful attempts which solved a variant. Trying to answer the question properly with explanation and full understanding by the questioner is often much like trying to teach a pig to sing: it is rather unproductive, and it annoys the pig (thanks to Mark Twain; I leave the assignment of the role of pig in the above scenario as an exercise for the reader).

I don't think there are good close reasons in the standard set for this situation. I think the general comment "This is the wrong forum for your question." should be used, with perhaps a link to one of the more appropriate meta posts. If you link to this one, then a more acceptable reason would be that the task of verifying proofs and reporting on them is outside the scope of this forum, as it would detract from the goals of providing useful answers to research questions and closely related matters.

Gerhard "Did That; Got The Tshirt" Paseman, 2017.12.13.