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Please discuss this question here.
http://mathoverflow.net/questions/37172/what-are-some-open-problems-in-geometry-closed
I think I've gone "on record" as saying that I'm not keen on this kind of question, but that this is more of a personal preference than a wish to set any official policy.
The phrasing of the title doesn't help: it has an unfortunate ring of "Tell me stuff", or "Explain something cool and complicated to me", even if the actual question is a little more specific.
This question also fits into this discussion. I don't have strong feelings one way or the other, but I note that the probability question is more detailed, both about the math and the poster's motivation, than the geometry question.
+1 to Charles. I was actually thinking of the probability question that Mark mentioned above, precisely because it did give more detail and motivation - which serves as a kind of certificate that the questioner has thought about the question themselves and will appreciate some of the answers. (I'm still not that keen on such questions, but the probability one seems a much more defensible and less annoying form of such than the question under discussion here.)
I've just realized one purely subjective reason why this question and its ilk rub me up the wrong way - I feel, on a not entirely rationalized basis, that students of mathematics would do better to learn what they are doing (in terms of reading the literature, playing with examples, and gathering a toolkit) rather than to ask about open problems beyond their ken. So I guess I am not keen on questions which give an impression of wanting to hear about Cool Problems Dammit without demonstrating interest or investment in the techniques of their area.
Of course, this might not apply to the present example, because the author might turn out to have a very good grounding in algebraic geometry and a good problem-solving record. But as it stands the question gives no way to discern if this is the case.
The question linked is really bad! Why in the world was it left up?
@Harry Gindi: I agree that the question as written is awful. My impression is that the reason it stayed open early on are that Richard Borcherds and Gil Kalai, who each have a lot of street cred (for example, I have a lot of respect for both of them) voiced support for the question. My opinions on questions like this seem to be close to Yemon's. In particular, I strongly hope that someone (won't be me, though) edits the question into something with content.
The second argument was about the motives and qualification of the person who asked the question. Is this just a question asked off hand? a fishing expedition? how can we adjust the level of answers to the person who asked the question etc. This is a reasonable point of view. However, in this case, once Richard expressed interest in seeing answers to this question, we can aim the answers to Richard and forget about the qualification and motivation of the original person who asked the question. ("sun"?) We can olso assume that Richard is familiar with alternatives that Mathew raised (ICM and Bulletin papers).
It is an endearing aspect of MO that prominent mathematicians and first year students are participating as equals. But this feature can rapidly become much much less endearing if there will be a feeling that it is abused. So while I understand the few people who initially wanted to close the problem I fail to understand why people continued to vote for closing it after Richard supplied a nice answer and endorsed it.
I say only then that if a "street-credible" mathematician decides to endorse the idea behind a poorly-written big-list or soft-question, he or she should be strongly encouraged to rewrite the question as well (and perhaps re-ask it). This is what Andy Putman did in a similar situation, and I thought that it was a terrific idea. If you don't remember this, I posted about it on meta and could post a link (although I'd prefer not to if it's unnecessary).
I doubt it will surprise anyone to learn that I dislike both questions. I don't think that the extra information in the probability question is enough to "rescue" the question. Both are "fishing" and neither satisfies my criteria for a Good MO Question.
But what disturbs me a little more about this discussion is the idea that a question can be "endorsed"! It's all very well for someone to say, "I like this question". Fine, I can disagree and we can discuss it and - at the least - understand each other's points of view. But a system of endorsement makes a mockery of the idea that a questioner asks a question seeking an answer. Now, it's trying to ask a question that will attract the attention of a "high profile" user, but not to get an answer but to get endorsed! Next, there'll be a call to have questions pre-moderated and only posted if they can gain the attention of a supporter.
Maybe we should get the "afternoon tea" site off the ground so that questions like this can have a happy home there. But I want MathOverflow to be for researchers getting help with their research. I can't see how these questions do this. Are these people wanting to start working on one of these Big Questions? The closest I would accept for this type of question is: "I'm starting my work in area X and I find it useful to know about the Big Questions that people in that area work on to help me keep an eye on the goal. Where can I find out about it?"
A very long time ago, we discussed this on meta. Emerton wanted to post an answer to a question, even though it was poorly written and didn't make too much sense (the question, not the answer!). The decision we reached then was that it would be better for him to re-ask the question and answer it himself than reopen the question. This is fair and avoids the "endorsement model", while still allowing people to post answers they would like to post.
@Andy: I think that this is a good compromise. Why don't you think so?
Gil, my initial impression, largely based on your first comment in the thread, was that the reason people wanted the question to remain open was because of Borcherds's interest in the question. This line of reasoning is repeated here, until Andy Putman's most recent post, above.
FYI, the MO FAQ specifically discourages these kinds questions:
The site works best for well-defined questions: math questions that actually have a specific answer. You'll notice that there is the occasional question making a list of something, asking about the workings of the mathematical community, or something else which isn't really a math question. Such questions can be helpful to the community, but it is extremely tricky to ask them in a way that produces a useful response. So if you're new to the site, we suggest you stick to asking precise math questions until you learn about the quirks of the community and the strengths of the medium. If you have a very broad question (like "Please explain topic X"), try searching Google, Wikipedia, nLab, or looking for survey articles on the arXiv.
So I don't think the people that voted to close were doing much other than trying to keep the site consistent with its mandate.
The problem I have with the statement "The site works nicely for good well defined questions, and it also works nicely for good "big list" questions, and it also works nicely for good "please explain topic X" questions." is the underlying assumption that the site can do these three at the same time. My view is that the second two drive out the first, and that whilst the first is of direct use to me in my job, the other two are just "of casual interest", and can be found elsewhere. So to keep this site of active use to me in my job, I stomp on the other two types of question.
If Ryan asked a question on "big problems in knot theory", I would vote to close it really quickly:
Also, you missed the point of my reformulation of the question (and note that I still don't like this question). It wasn't the start of the reformulation that was important, but the end: "Where can I find out about it?". Namely, don't tell me vast swathes of information, but tell me where I can get hold of that information.
To grossly twist a popular saying: If someone comes here on a fishing expedition, the worst thing to do is give them a fish. The best thing to do is point them to a book in the library (or website or whatever) where they can read up about how to find the best rivers in which to fish.
"Stomp" was perhaps not a great choice of word - it was meant slightly humorously. I do try to not be aggressive in my behaviour on MO and I hope I don't come across that way. I am more outspoken here precisely because it is a little out of sight and because here I'm trying to persuade and explain. In particular, when I vote to close I try to ensure that there's a comment explaining my action.
Your argument comes across as: "Here's an example of a big-list question that I've found useful so we should allow all big-list questions.". There've been big-list questions that I've found useful. The problem is, that there's no end to the ones that have just been sheer noise. I'm not too happy about the overwhelming number of algebraic geometry questions either, since I consider those to just get in the way and have no useful content whatsoever. The difference between big-list and algebraic-geometry is that it's really hard to ask a question about algebraic-geometry so there's a limit to the number of questions on that that MO will get. However, it's really easy to ask big-list questions so without some discouragement, the site will get swamped by them.
I can tolerate a few, but the ones that are easiest to tolerate are the ones where it's clear how the information is directly going to help the person asking. But that's a rule I apply to all questions: it should be clear how the information is going to help the person who asked.
Dear Gil (and any anyone still reading),
My concern is that we're not being clear to people who use MO (or are considering using MO) what MO is. To be rather hyperbolic about this, the new byline for MO could be "MO - a place where you can go to talk about the things high-status mathematicians want you to be talking about".
I have not witnessed even-handedness when it comes to deciding which borderline (or policy-violating) MO questions remain open -- for example how many borderline MO threads have been kept open only for [insert name of active undergrad student on MO]'s interest?
By and large my opinion on rules is if they can't be enforced fairly, then the rule should be changed to something that can be enforced.
Dear Ryan,
First of all, note that Gil says that he believes it was a mistake to close your question, so his position is consistent.
As you know, I tend to side with Gil on these matters, in that I generally dislike seeing questions closed. If you had asked for your question to be reopened, I would have voted for this. Since you acquiesced in its closing, it's not been clear (until now) that this is what you wanted.
In general, I don't think that this is an issue of favouring high-status mathematicians; rather, if a member of the MO community (and reputations serves as a reasonable surrogate for measuring the extent to which a user is a true member of the community) says that they find a question interesting/valuable/worthwhile, I think it is a low-cost courtesy to not close the question. (I think that the math-at-dinner post, or whatever it was, gives an example of this.)
If you go all the way back to the meta thread on VA, you will see that I expressed a similar opinion there. You will also see, from my language there, that I don't think that this courtesy is completely divorced from a consideration of peoples non-MO reputations. However, I don't think (perhaps naively) that there is a serious danger of abuse. After all, we are only talking about courtesy and conventional behaviour here. Any abuse of this courtesy can easily be checked by using the tools available (e.g. withholding courtesy and exercising closing powers).
If you feel that you weren't extended this courtesy, and were (so to speak) coerced into closing your question, that is regrettable, and I think that the solution is to reopen your question.
Finally, I don't think that kind of courtesy that Gil and I are discussing is a loophole in the rules, or some secret knowledge that allows some to game the system. Rather, we are just suggesting that people here exercise the same courtesy they would exercise in any other aspect of their professional life (which is, I agree, probably much more courtesy than one typically sees exercised on an internate forum; thankfully, MO is not a typical such forum.)
Dear Ryan,
Sorry; the "VA thread" is here. In finding this thread I also saw some of the comments surrounding mine, including those of Noah Snyder, which reminded me that he made good arguments akin to yours that my suggestion of "courtesy" is a little naive, and that a policy solution is preferable.
I would certainly prefer it if we could resolve these issues simply through applications of professional courtesy, but I also appreciate your point of view that such issues should be handled by policy, rather than by some implicit assumptions on people's behaviour. Unfortunately, I'm not sure that I have much more to say, since I always feel somewhat in the minority in these discussions in any case.
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