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General: Discussing work in progress in answers

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    There is a question that's been asked for which I can give an answer to a related question (but not the same question). The problem is that the answer relates to work in progress which won't be out for a few months, and this work is of the type that a fairly significant number of experts could also figure out the answer (or how to derive the answer), so there is a reasonable possibility of getting scooped.

    Now it is fairly established that putting a preprint on the arXiv establishes priority (or at least independence), but would answering a question on MathOverflow do the same? Would it be better in this situation to give more details or fewer? (The answer is one line, a reasonable sketch of the proof fits in the answer box, and the paper (which will include a generalization) probably won't go over 10 pages.)
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    Any authentic timestamp establishes priority. One can always question the authenticity of timestamps. The arXiv timestamps are perhaps better recognized than MO timestamps. MO timestamps offer the same type of support as arXiv timestamps since MO provides full revision history to everyone and access to the actual database is controlled. (Only one moderator has enough access to potentially alter timestamps.) Both are not fully tamper proof, but the arXiv has a much longer history of such usage. If anyone has thoughts on how to make MO timestamps more trustworthy or reliable, we would be happy to look into implementation possibilities.

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    Francois, I'm afraid you've mistaken a social question for a technical one. This could be my fault for not making that clear in the first place.
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    How is this a social question?

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    In my opinion, yes, an MO answer (or any other public online posting) can establish priority. If it were me I would sketch the proof and say explicitly that the paper/preprint will appear soon.

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    I still tend to think you're more likely to get scooped by being secretive than by being open. If this is something that many people have the tools to work out, the longer you wait to announce, the more likely that someone else will do it.

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    Actually, I would take the opposite view that a statement or indication of proof on Mathoverflow would not, and should not, be sufficient to establish priority.
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    I agree strongly with Donu. I do not think anything less than a complete and freely accessible proof establishes priority.
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    @Chris Godsil (and Donu Arapura): I am very puzzled by your opinion. Suppose I give a seminar talk wherein I sketch the proof of new Theorem A. I include enough of the key details so that dozens of experts in the relevant field would be able to easily fill in the gaps. Word of this result gets around and two months later, before I've gotten around to finishing my paper, Mathematician X publishes a detailed proof of Theorem A along exactly the lines that I described in my seminar talk. Surely you are not saying Mathematician X (who perhaps was in the audience of the talk) has priority for Theorem A?

    If we replace the seminar talk with an MO answer in the above hypothetical situation, I don't think that very much changes.

    Maybe you were imagining a slightly different situation, where the sketch in my seminar talk or MO answer fell well short of including all the key ideas. There is a continuum of possibilities interpolating between offering no proof at all and providing an extremely detailed sketch, and I agree that somewhere within that continuum is a grey area where it's not clear that I should get credit for Theorem A. But I think it is common, in situations like this, for it to be possible to give all important details of a proof in a few sentences. In rare cases, the mere statement of Theorem A would be sufficient for experts to easily figure out the proof.

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    @Kevin: I suspect that basically we agree. For a given topic, it may be possible in a seminar to give sketch of the proof that any expert could complete. Provided this is widely accessible, this should establish priority. The grey areas arise when there is significant gaps and or errors, or no clear record. There is no need for a proof to be written down to establish priority, I think.
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    Kevin,

    To clarify my earlier comment, while I don't disagree with your opinion about who ought to get the credit in the above scenario, in general, priority questions can be subtle and sometimes messy, especially in cases where the claimant has not provided full details initially. It seems like a bad idea to use Mathoverflow for this purpose.
    • CommentAuthorfedja
    • CommentTimeDec 24th 2012
     
    I wouldn't rely on citing an MO post in priority disputes. On the other hand, I guess I posted some stuff here that either was work in progress at the time of posting, or could be easily turned into a decent article and so far nobody has "scooped" me; on the contrary, I had to spent some time declining co-authorships. In general math. community is, perhaps, less reasonable than it should be but far more reasonable than most people think in terms of "stealing" other people's work. During all 20 years of my career, I shared all my ideas, old and new alike, with anyone who was willing to listen and still no kind soul spared me and my co-authors the trouble of writing and proofreading the papers despite I'm quite a procrastinator and it is not unusual for me to publish the result 1-2 years after I get it or not to publish it at all. So, I would just post what I know. After all, our main task is still to share the knowledge and advance the craft; getting salary increases and grants is only a secondary purpose....

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