tea.mathoverflow.net - Discussion Feed ("Is the six dimensional sphere a complex manifold?")

Spiro Karigiannis comments on ""Is the six dimensional sphere a complex manifold?"" (12374)

Spiro Karigiannis — Tue, 04 Jan 2011 12:49:47 -0800

@Sean and @Pete: Indeed, I feel like I can take liberties with Pete as well. That's why I can say that, despite the fact that he spent some time in Canada, he failed to learn how to spell "honour" correctly.... :)

Pete L. Clark comments on ""Is the six dimensional sphere a complex manifold?"" (12373)

Pete L. Clark — Tue, 04 Jan 2011 11:55:03 -0800

@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...

sean tilson comments on ""Is the six dimensional sphere a complex manifold?"" (12369)

sean tilson — Mon, 03 Jan 2011 21:49:43 -0800

@Pete: +1 for professor G_2

Spiro Karigiannis comments on ""Is the six dimensional sphere a complex manifold?"" (12360)

Spiro Karigiannis — Mon, 03 Jan 2011 10:23:11 -0800

@Pete: I would love to read through this paper carefully. But with two courses to teach starting tomorrow, and me having not prepared anything for them yet, it's not going to happen until mid-March at the earliest. Somebody may beat me to it before then.

Pete L. Clark comments on ""Is the six dimensional sphere a complex manifold?"" (12356)

Pete L. Clark — Mon, 03 Jan 2011 08:44:52 -0800

@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?

Spiro Karigiannis comments on ""Is the six dimensional sphere a complex manifold?"" (12350)

Spiro Karigiannis — Mon, 03 Jan 2011 05:50:22 -0800

@Pete: I'm not sure that asking the author if he's willing to have his paper discussed in public is the right way to go. We want to avoid hosting arguments between author and critics.

I think the best thing to do is to have the OP (or someone else who has tried to read the paper) to ask specific questions about the details of the paper. By the way- to those who have the power to edit the question- the actual question itself is still quite poorly worded. It would be best to say "A question about a paper concerning complex structures on $S^6$" or something like that. (With, hopefully, an actual question about that paper!)

Pete L. Clark comments on ""Is the six dimensional sphere a complex manifold?"" (12331)

Pete L. Clark — Sun, 02 Jan 2011 11:17:16 -0800

@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?

deane.yang comments on ""Is the six dimensional sphere a complex manifold?"" (12325)

deane.yang — Sun, 02 Jan 2011 10:26:48 -0800

I second Joseph O'Rourke's request but for a slightly different reason. I personally am skeptical of the correctness of the paper in question, but for me the correctness is secondary to understanding the ideas and motivation underlying the proof. Proofs of well-known open problems can be exciting in themselves, but they are much more exciting and interesting when they lead to cool new mathematics. I don't see yet any evidence of this in the paper under discussion but perhaps someone else does?

Ben Webster comments on ""Is the six dimensional sphere a complex manifold?"" (12324)

Ben Webster — Sun, 02 Jan 2011 10:23:57 -0800

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.

Joseph O'Rourke comments on ""Is the six dimensional sphere a complex manifold?"" (12323)

Joseph O'Rourke — Sun, 02 Jan 2011 10:23:02 -0800

Rather than ask if someone can "say, if the proof is right or not," the more respectful question would be, "could someone explain the proof to me at a high level"? The presumption in the current phrasing is that the proof might be wrong; I'd rather the presumption (in this public forum) be that the proof is likely correct.

Pete L. Clark comments on ""Is the six dimensional sphere a complex manifold?"" (12322)

Pete L. Clark — Sun, 02 Jan 2011 09:00:08 -0800

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?

djordan comments on ""Is the six dimensional sphere a complex manifold?"" (12321)

djordan — Sun, 02 Jan 2011 08:44:16 -0800

I voted to close, since I also recall that this was deemed inappropriate.

Spiro Karigiannis comments on ""Is the six dimensional sphere a complex manifold?"" (12320)

Spiro Karigiannis — Sun, 02 Jan 2011 08:18:28 -0800

I agree that speculation about whether or not a preprint is correct is not appropriate for MO. However, I think we've also agreed that specific questions about specific portions of preprints that the OP is having trouble understanding might be appropriate, if asked "appropriately". In this case, however, the question is very vague ("has anyone checked if this preprint is correct?") so I don't think the question, as stated, is acceptable. (It's too bad, because I would love to hear any good answers to this question...)

Qiaochu Yuan comments on ""Is the six dimensional sphere a complex manifold?"" (12314)

Qiaochu Yuan — Sun, 02 Jan 2011 01:39:51 -0800

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?