We talked about this a lot on the old meta 1, 2 but I don't see a concise statement of policy that I can link to, so I'm asking a meta question in hope of generating consensus on such a statement.
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$\begingroup$ Both links to tea seem to be down at the moment, but both of them are available in the Wayback Machine - 1059 and 1422. One of them has one more message from a mod in 2017: 1422. $\endgroup$– Martin SleziakCommented Feb 7, 2022 at 5:54
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3 Answers
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As an official policy, I'd like Felipe's answer with the first sentence missing. That is to say:
[W]e should avoid discussing preprints in general terms. If there is a specific question about a specific step in a proof and suitable context is given so that reading the paper is not a prerequisite, then it is on topic.
This avoids getting into discussions about whether or not a result is crackpot, and I suspect will in fact lead to all questions about crackpot preprints being closed.
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I think we can all agree that discussing crackpot preprints should be off topic. My opinion is that we should avoid discussing preprints in general terms. If there is a specific question about a specific step in a proof and suitable context is given so that reading the paper is not a prerequisite, then it is on topic.
BTW: The Sha paper which I believe prompted this post falls clearly within the crackpot category.
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I think the policy should be as follows:
On questions regarding significant portions of a preprint (any part larger than what fits comfortably in a page of a MathOverflow question), the response should be that the question is too broad for this forum, as it "asks about too much at once".
On questions regarding quality, style, and correctness of a preprint, the response should be that the question is again too broad for this forum. In particular, quality should be assessed by experts (or experts in training) in the field, style by editors interested in publishing the work, and correctness by anyone who is interested in vetting the paper, any condition of which excludes almost all the members of MathOverflow. (This is as opposed to specific and brief questions on quality, style, and correctness which may refer to a specific preprint or set of preprints. Such specific questions may be suitable, but should be phrased in a manner independent of any preprint.) Further, MathOverflow is not for referring to preprints of undetermined quality, style, and correctness, but only to work that has received acceptance by some portion of the mathematical community.
On questions regarding a specific step or proof technique, the question should be written as if the question was found in an accepted text, with sufficient background and motivation provided, and with enough specificity that a good answer can be formed. A link to the preprint can be provided, but only as an adjunct to the question, not as an advertisement for the work. Preferably the link should not be needed to answer the question.
On opinions about a preprint, courtesy suggests brief and cool responses from MathOverflow members, such as "I would recommend it", "I would not recommend it", or "Due to the claims on page x line y, I think the argument cannot be repaired (as it contradicts the established result in [A]) and I have no time nor inclination to suggest a repair."
On questions like "Is my work present in the literature already", the response should be that the question is too broad. On questions like "I did X, Y and Z to tackle question Q, which is clearly different from [A], [B], and [C], is this in the literature?", the proper response should be given by one who is familiar with the area and the literature; anything else should be given as a helpful comment suggesting additional literature to pursue or search terms to use that may have not been previously considered by the poster.
Gerhard "Have I Missed Any Variation?" Paseman, 2013.10.01
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5$\begingroup$ Why is "is my work present in the literature already" too broad? At least, questions of the form "is this theorem known" often get a lot of positive attention on MO. Such questions have specific, objective answers. $\endgroup$ Commented Oct 2, 2013 at 0:40
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1$\begingroup$ I think what is meant is that any question where the answerer has to read the preprint to answer the question is too much to expect. I imagine asking for specific theorems or approaches, spelled out in the post, are reasonable MO questions. $\endgroup$ Commented Oct 2, 2013 at 3:36
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$\begingroup$ @SamHopkins I too, like Masked, read that as being in the form "here is a preprint I wrote, are those results already known", since this thread is about preprints. For specific questions of the form "is this result new" or "has this [very specific thing] been studied before", my experience is that they are received quite well (and I have personally had some success with such). $\endgroup$ Commented Oct 2, 2013 at 8:21