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Is this question acceptable?: Where is the hole in my proof?

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    This should be asked in the category "is this *class* of question acceptable", as it is a request for clarification of MO's policy inspired by this discussion http://tea.mathoverflow.net/discussion/922/why-do-people-answer-trivial-questions/ itself prompted by this question: http://mathoverflow.net/questions/53386/question-on-the-bounded-inverse-theorem-for-banach-spaces

    My impression was that the most wrong thing about the Banach spaces question was that it was a question of the form "Where is the hole in my proof?". Aren't such questions strongly discouraged on MO, regardless of the level, or did I imagine it? (The FAQ does not seem to address this, so I'm talking about informal policy here.)

    Thanks in advance!
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    Not knowing whether there is a general policy, but rereading the FAQs, it seems to me such a question is acceptable if the 'level' is right.

    Such a question can be reseatch level, is typically well-defined, and should permit a clear answer.

    For example: X does research in subject A, and for some reasons needs/wants to use a tool from distant subject B.
    Something 'strange' happens in the process, and X strongly suspects this is due to limited understanding of subject B.

    Why not ask on MO for clarification?

    In fact, it seems like a perfect usecase to me. As it is quite likely an expert in B can resolve the problem/confusion fairly easily,
    but X might well not know any expert in B.
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    @an_mo_user: my recollection is that people have reacted negatively to this type of question on meta. I think the basic problem is this: if you already have a proof, you should already be capable of checking it yourself. If you can't readily check it yourself because you don't understand concept C well enough, you should ask a question about concept C instead of a question about your proof.

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    @Qiaochu Yuan: thank you for this information on precedents, which I was unaware of.
    It is most likely impossible to describe what I envision abstractly, yet I will give it one more try:

    Say, I believe I can apply BigComplicatedTheorem, of which I have a so-so understanding but no indepth knowledge, in specific situation A.
    I do so, yet what I get seems wrong. It is impossible, after considerable effort, for me to figure out what is the problem.

    For everybody involved it seems more useful to me to ask:

    Why can't one (or how to correctly) apply BigComplicatedTheorem *in specific situation A* ?

    Rather than:

    How to apply BigComplicatedTheorem (in general)?

    As the latter possibly generates lots of answer that are either known or useless to me and my specific problem.

    However, I can see reasons to see this differently.
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    an_mo_user: I think that in an actual situation, what you describe would turn out to be pretty much what Qiaochu is saying. The point is that the question is not about the proof that the questioner is trying to construct, but about the tools that he/she is using to construct it. Of course, the question should contain motivation and so forth that can include the fact that this is part of a proof under construction, but the question itself should be about the tool.

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    Andrew Stacey, agreed, most likely one can phrase what I envision in such a way that it is compatible with this guideline. Although, one could say, if there is no actual difference then why 'forbid' one way of asking. But, I can see why one would rather discourage people from asking about errors in their proofs; certainly I agrree that, say, linking a pdf and just asking 'what did I do wrong?' is highly inapropriate.

    I feel just a bit uneasy about all these rules about asking; frankly, if somebody asked me what type of question are universally agreed to be acceptable on MO, I would have a hard time answering (and it becomes harder and harder the more I know the site).
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    I don't think we are really disagreeing in practice. I mostly just mean exactly what you mention: linking to a pdf and asking "what did I do wrong?" Really this is a corollary of the general rule of thumb "put some effort into your question" as well as "be specific."

    I also don't think it makes sense to aim for universally acceptable questions; the MO userbase is at this point too large, with too many differing viewpoints, for that to be a reasonable goal.

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    In my opinion, the problem with the Banach space question was its triviality, not that there is something intrinsically wrong with asking what part of some purported proof is incorrect. Such a question is often extremely interesting. Consider the case of Vinay Deolalikar's alleged proof of P ≠ NP.

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    @Greg: That thread wasn't very good either.

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    I don't know what you're referring to (was the Deolalikar paper discussed on MO?). I was speaking of the problems identified by various experts shortly after the paper transpired. (Sorry not to provide more specific attributions; the refutation seems to have been a sort of "polymath" effort.)

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    Greg, there was an attempt to discuss the Deolalikar effort on MO, http://mathoverflow.net/questions/35102/p-not-eq-np-news-closed

    Actually, there were other discussions on MO - just type Deolalikar into the MO search box. And there was a discussion on meta, http://tea.mathoverflow.net/discussion/590/whats-wrong-with-this-proof/

    Judge for yourself as to whether they were any good.
    • CommentAuthorGreg Marks
    • CommentTimeMar 4th 2011 edited
     

    I obviously did a horrendous job of making my point.  Let's try again: ... not that there is something intrinsically wrong with asking what part of some purported proof is incorrect.  Such a question is often extremely interesting.  To me, at least.  For example, consider the analysis of V. Deolalikar's P vs. NP paper at the wiki page:

    http://michaelnielsen.org/polymath1/index.php?title=Deolalikar%27s_P!%3DNP_paper

    and certain links therefrom.

    Another example, perhaps, is T. C. Hales's review article "The status of the Kepler conjecture," Math. Intelligencer 16 (1994), no. 3, 47-58.  And another possible example is the unjustified Selmer group bound in Wiles's initial proof of Fermat's Last Theorem.

    The foregoing are merely my thoughts about issues raised here and are not intended as advocacy of one MO policy or another.

    • CommentAuthorBen Webster
    • CommentTimeMar 4th 2011 edited
     

    Thierry- I think you're interpreting that dictate too literally; I think a question of the form "Here are two facts, it seems to me like they contradict each other. Why am I wrong?" is basically acceptable (maybe because I've been annoyed by them so many of them). That's completely different from asking people to vet a preprint (which I think is mostly what people have complained about in the past).

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    @Ben: this makes sense to me now. Thanks!

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