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I think I remember a discussion to the effect that we shouldn't speculate about whether preprints are correct or not on MO. Does that discussion apply to this case?
I'm with Spiro on this. The current specific form of the question is not ideal, but the question itself is very compelling. So how do we fix it?
Pete & Spiro- Did you guys read this thread? That is response to much more thoughtful and well-written question, though one which was a bit more aggressively stated. I believe the consensus was best put by Matt Emerton that "one should always be very polite and cautious in pointing out possible mistakes in other peoples work, and a widely read professional forum does not lend itself to such politeness and caution."
That said, this always going to be a bit case by case; in this case, I'm actually tempted to close as a duplicate.
@Ben: yes, I read the thread you referred to. You have already pointed out what I felt was a key difference: the question was quite aggressively stated, indeed in a way which seemed likely to lead to a rift between the young mathematician who asked it and the veteran mathematician whose work was being discussed.
Again, if the question is changed from "Is this particular claimed proof that S^6 admits a complex structure correct?" to something like "What are the key ideas of this particular paper [that claims that S^6 admits a complex structure]?" then the combative aspect is lost. I do think that some kind of analysis of one's work is exactly what you want when you put papers on the arxiv. It is possible that the outcome of this will be pointing out a mistake, which should then be done in a very polite and cautious manner. But I don't see that it's impossible to have a constructive discussion of the paper. In this case, I am biased in that I cannot participate in such a discussion but I would be very interested to follow it.
About closing the question as a duplicate: sure, that's reasonable. If one does do that, I think it might be reasonable to modify the earlier question to make explicit mention to this preprint, for otherwise everything moves a level down: the "Hey, what about this paper?" becomes an answer and then responses to that become comments, which would be very tedious.
It strikes me just now that a reasonable idea would be to contact the author of the paper and gauge his opinion on public discussion of the paper. If it's okay with him, it seems like it has to be okay, and probably the converse is also true, no?
@Spiro: well, if we shouldn't discuss the author's paper in public with his permission, we certainly shouldn't do it without his permission.
I think you're probably right that asking a specific (technical) question about the paper would be for the best...Care to take a crack at it, Professor G_2?
@Sean: thanks. Just so you know, Spiro and I were in grad school together, so I feel like I can take a few liberties with him. Which is not to say that the epithet "Professor G_2" is meant to be anything else than a badge of honor...
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