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.

Hi, that was my second vote to close ever. I definitely felt gun-shy after my email correspondence with the last guy who did not believe FLT, wanted to use MO as a machine for producing an elementary proof, etc. I'm beginning to get some sense of your reputation, so this seems to fit you as well:
{{ Mariano, Jun 30th 2010; Wadim, it often happens that very bad questions get very very good answers. I blame Joel for the most part...}}
Now that I have dipped my toes in the water, I have little objection to giving a little more time. That seems to be what Bill DuBuque is asking for in his roughly simultaneous thread. Now, somewhat independently of whether I ever again vote to close a question, I quite definitely judge the person posting as much as I judge the question.

Dear All,

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.

Best wishes,

Matthew

To me the question seems out of line with the point of MO. Moreover, Emerton answered a reinterpretation of the question that the poster likely never intended. This perhaps plays a mathematics-outreach role but still it's not really in line with what MO is about.

The question does not have an answer, because we can't know how many people understand any theorem. Moreover, it will be perceived as acceptable to ask questions on MO like "how many people understand X" for X any published mathematical result. Do we care to fill up the MO space with such mathematical gossip?

If the poster is seeking clarification or guidance on understanding the plot of the proof or some particular technical aspect, refining the question along those lines would make for an appropriate question, IMO.

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.

Best wishes,

Matt

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.

Emerton, I think your answer is quite nice. My preference would be for the question to be changed to something more in the spirit of your response.

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.

Best wishes,

Matt

Oops! My first answer was, I believe, pretty close to a mathematically correct answer to some form of the OP's question. It was also facetious. Since apparently some people have no sense of humor, it seemed best to edit the question, which then caused some confusion in the comments. I think it best at this point just to delete the answer, but it seems I only have the option to "rollback", which probably isn't the best idea.

Thank you for joining the discussion, Powerpuff. Please leave the new answer in place. Scott M. edited it to emphasize that the negative comments were to the first version. I hope I have a sense of humor, but I am very careful either to joke with people I know or to mock something that is handed to me on a platter.

There are some cherished values in this particular site, as they are trying to build something...They wish to maintain strict anonymity for those who desire it, so that includes you as long as you wish it. They wish to avoid unseemly public discourse, and regard MO and this (Meta, or Meat) as public. They want to avoid trashing anyone's professional reputation. They want to avoid head to head competitive ranking of top mathematicians. They want to avoid gossip. I disliked the FLT question from the start, based on email with another user. The danger in your first answer was the possibility that you were serious, knew exactly how many and exactly who those were, people would then speculate on identities, etc. For my own reaction, please see http://mathoverflow.net/questions/29743/ and http://mathoverflow.net/questions/31565/
I don't much like the idea of anonymity, or pseudonymity, but it is deep in the construction and culture of this site. I make my identity public and my email address easy to find.

Meanwhile, I would like you to stick around. Anyone who can give a substantial response to my imponderable quadratic forms question is valuable. If you register on MO (for me it amounted to clicking on a Google icon, insofar as I have a gmail account) people will be able to view your contributions under one icon. There is some value to indicating location, at least to the extent of giving an approximate time zone.