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The question How many people fully understand the proof of Fermat's Last Theorem? was closed seemingly within less than an hour of it first being asked, and then reopened ten hours after being closed. As far as I can tell, the reason it was reopened was that I posted a series of comments giving an answer to the question (which are now reworked as an actual answer).
I didn't vote to reopen this question, since (given that no TeX was required to answer it) it was easy enough to answer in comments.
But I'm not sure that it needed to be closed so rapidly. As Noah Snyder noted in a comment, it was a reasonably precise question,
and there are several people posting on MO who work in algebraic number theory/automorphic forms who were in a position to give a reasonable answer to it. Also, I don't think that there is any reason to think it would lead to long discussions or arguments; as far as I know, the proof of FLT is not a topic of controversy (except among cranks, but there was absolutely nothing crankish about the phrasing of the question).
Anyway, the point of the present post is for me to make the following request (a variation on several such requests made from those
"on the left"):
Perhaps we can be slightly less hasty to close politely and succinctly posed questions like this, so as to at least give a chance for someone to answer it. I think it projects a better image of the mathematical community, and does no harm.
+1. I agree with Emerton. There are some questions which should clearly be closed fast, but that was not one of them.
Thanks for your response. I understand that you are circumspect about questions from possible non-experts/professionals about FLT;
this particular question didn't seem to give of those vibes, which is why I was happy to engage with it.
I just looked again at the OP's user page, and saw that he has been suspended, possibly because of posting large numbers of low quality questions in rapid succession. I hadn't realized this when posting my answer to his FLT question, or when I began this thread.
If this is correct (that the FLT question was one of a string of dubious questions) then I understand better peoples' motivation for rapid closing.
Matt, I agree with you on most issues related to closing of questions, but to me, this was a very clear case of:
(a) Argumentative question: "how many people" implies some judgment on how difficult proof is, and it does not admit a precise answer unless you are willing to speculate about various people's mental processes;
(b) Potential disruption, as you have already noticed.
On the point (a), the vibes I got were rather similar to questions about potential Fields medalists (some deleted, some closed).
Dear Ryan and VP,
Thanks for your responses. Regarding "how many people understand X", I suspect that FLT will be a more likely choice of
specialization for X than most other results, for basic historical/cultural reasons.
Also, while we can't know everyone's thought processes, I suspect that there are very few people who would have studied and understood in a serious way the proof of FLT who are not grad students in math or practicing mathematicians, certainly not enough to affect the order of magnitude (which is what the question asked for). If you grant that, I don't think that my substitute metric (people attending conferences in the area) is so unreliable.
Finally, I think that there is some merit to answering this question: our subject (pure mathematics) is fairly esoteric, and so in particular the proof of FLT and all it involves is certainly so. On the other hand, FLT as a statement is much less so; it has a cultural status which, while marginal compared to many other topics, is much less so than modern pure mathematics. Because of this, it's easy to see why amateurs might be unhappy with, or skeptical of, the proof of FLT, and I think it's worthwhile to explain that, yes, while there aren't legions of people who have carefully studied the proof and analyzed it, there are a reasonable number, that the proof techniques continue to be reworked, and that they are part of a topic of serious and ongoing research. (In short, that it's not just Wiles, Taylor, and two or three other friends pulling the wool over everyone's eyes.) MO may not be the best forum for this, but I don't think it's the worst.
P.S. I understand that I am in the minority in my views with regard to closing questions, so take this as an explanation as to why I answered the question if you prefer, rather than as an attempt to sway your (and others') opinions.
I just upvoted Emerton's answer which I very much enjoyed, and also voted to (re)close the question. I doubt that a more precise and helpful answer exists, so perhaps the question has served its purpose. Also, looking at all the questions the OP asked, it does not feel like he/she is serious about any of them, so drawing more attention to the question would play into that.
I share Hailong's and Ryan's sentiments expressed in comments 10 and 11.
Matt: I doubt that many professional mathematicians feel that Wiles and a few other people are pulling the wool over everyone's eyes, but I'd not be thrilled by arguing with Fermatists on this topic. If anything, I think that counting people attending conferences leads to an underestimate (I am going to offer myself as an anecdotal example of someone who never attended such a conference - the closest it ever came to was a special lecture of Wiles, but I worked through large parts of the proof).
Dear Long, Ryan, and VP,
Thank you to all three of you for the kind words regarding my answer.
With regard to VP's response to my remark about wool being pulled over people's eyes,
I agree that professional mathematicians are surely completely happy with the situation regarding FLT, and I wouldn't want to argue with cranks either. But I can imagine that there are many people with an interest in FLT who are neither cranks nor professionals, and I don't think that it hurts to try to give them some sense of the scope of the field, even it is only rough. (I agree that this is not the stated mission of MO, but as you probably know, I've never felt that it's particularly important to follow that mission in a rigid fashion.)
I certainly understand your reasons for voting to close/reclose, given the OP's (short but somewhat sorry) history. If I'd educated myself about it first (as I should have done), I probably wouldn't have started this thread.
One last thing: Ryan, I doubt that anyone would object if you changed the title of the question (I wouldn't, for one), although it may not be worth bumping it the top again to do this.
Since this question is becoming a little contentious, please upvote my comment (currently the last one on the original question) linking to this meta thread so readers can view the debate here.
Edit: never mind, as Will has now included the link in the original question.