In the past couple of days one user has asked over 6 questions per day. Is this behavior that we should allow?
I don't have time to write a lot - but please focus on the format of the questions rather than on the user(s). This needs to be a discussion about broad and consistent policy for this site.
EDIT: Consistency is very important to establish. If I copy verbatim a question from my calculus book, and then one from a copy of Hoffman and Kunze, and then one taken from Counterexamples in Analysis, the following sequence of outcomes is sure to occur on this site as it stands now: Closed and berated, answered and accused of posting homework, and finally answered with up votes. This inconsistency is dangerous and is unfair to new and current users of this site. (On MO each would (and should) be closed and mildly berated, along with receiving at least one pointer toward the faq and suggestions for reconsidering the question.)
Now, if I were to be wondering where the heck the Jacobian comes in when transforming coordinates during integration, or questioning my intuition about commutators, or trying to reconcile my understanding of the derivative with the information that there exists a continuous strictly monotonic function with a vanishing derivative almost everywhere - rather than slapping down the question as phrased by the textbook authors - the outcomes above would be much different.
With respect to building a community, the more nuanced, genuine issues in the second paragraph will cultivate mutual respect and provide an interesting place to visit for mathematicians of all levels. A site catering to questions stated as textbook problems will create a repository of homework problems populated by askers only, and I think there are enough sites like this out there already.
The fight here is to save math.stackexchange from becoming an uninteresting place, and grow it into one where genuine, incremental difficulties are explored. At the moment, any newcomer will see verbatim textbook questions being fielded left and right with glee - and will be seduced into submitting their homework question for the doing.
Note: regarding the user whose behavior motivated the question. His most recent questions appear to be quoted verbatim from a problem book, see my comments here. Moreover, said book has complete solutions, so it is not clear what his intent is in posting the questions here.
Update: Alas, it gets even worse. In this answer he has copied without any attribution Zagier's celebrated one sentence proof on primes that are sums of squares. Here's another question (and answer/proof) without proper attribution (followed by his comment to "please vote". Hmm....)
Update 2: He's still posting problems without citing their source, e.g. see his latest problem quoted without citation from the India National Olympiad 2009. This is borderline plagiarism, is it not?
Update 3: Here's another duplicated problem. (Tom)
Update 4: He's at it again. This time he posted a tricky number theory problem whose solution is readily available on other math forums. Later he answered his own question with the precise answer from these other forums. I recognized it immediately since I had posted one of those solutions. When asked for the source of the answer he claims that he devised it. I think that is highly unlikely based on the knowledge level that he's demonstrated in his prior posts (those few that were not quoted verbatim from elsewhere).
UPDATE 5: Once again, in another miraculous coincidence larger than the peak of a Goodstein sequence, he claims to have dreamt up two problems by looking at another thread here. But the truth of the matter - as someone pointed out - is that these two problems are yet again copied without attribution - this time from the 2010 Vojtěch Jarník International Mathematical Competition.
UPDATE 6: After his 2-day suspension he's back to his old tricks, posting yet another problem "from a friend" that was quickly discovered to be from a Chinese Mathematical Olympiad. At this point it seems quite clear that his goal is to amass a huge reputation by posting problems and solutions lifted from collections. Perhaps one way to discourage this behavior is simply to refrain from upvoting his posts till he shows some integrity.
UPDATE 7: Yet again, this time caught red-handed. Here it is quite clear that he didn't spend even a moment thinking about the competition problem because the problem was misstated on the web site that he copied it from - which made the problem trivially solvable with only a moments thought.
I have no issues with someone posting 6 (or more!) well thought out, well written questions a day. I want to echo the sentiment that this isn't about users but about questions.
What bothers me about a large number of questions in a short period of time is that typically the effort put in by the poster is minimal. I'd rather see fewer well thought out, well written questions than many adequate questions.
Here are two (and a half) ways, I think the posts can often be improved.
First, (and there is plenty of wiggle room here) there is generally little or no motiviation. A simple "this theorem would help me to understand X" or "I've been told this theorem is foundational in subject X, so it's crucial that I understand it" would make the question better. The question asker needs to convince potential answerers that their time will not be wasted in answering the question.
Second (and this is by far the most crucial issue), I'd like to see some indication the author thought about the question for an appreciable amount of time. When I see 6 unrelated questions being posted a day, it's hard to imagine the author having spent a few hours a piece or longer on each of them. This is especially bad with questions like "The following fact is true. Prove it." As a general rule of thumb, I think it's very irresponsible to ask someone to do more work for you than you did for yourself.
The half issue (and, admittedly, more of a personal gripe) is the tone. People responding on this site are doing so because they like solving problems, not because they owe anything to the original poster. In this spirit then, I far prefer questions of the form "How can I see this is true" rather than commands of the form "Show this is true", even when the questions contain the same mathematical content. The question asker is getting a favor from everyone else and should act like it.
Finally, I just want to say +1 to Pete's criticism of questions not being appropriately edited by the OPs.
I agree with both Tom and Matt. Especially, I think our responses should:
1) Be applicable to any user fitting a certain pattern of behavior and activity, rather than one particular user;
2) Concentrate at the level of the individual question, not the pattern of posting lots of questions.
I think 1) is self-explanatory. As for 2), this issue has come up at MO and I have expressed the opinion that if N questions are each appropriate individually and not related to each other in some problematic way (e.g. duplication), then it should be appropriate to post the set of N questions. This was not universally agreed upon: IIRC, someone said something like "What if all the questions on the front page were by a single user?" But I don't see what is inherently problematic about that. Indeed, if a single user is asking lots of good questions in an irredundant way, I say kudos!
I would push for 2) even more strongly on this site, since to my mind one of the biggest shortcomings in math.SE so far is that there are simply not enough questions to make browsing the site a suitably rewarding and addictive experience.
I do think that with these provisos, some criticism / advice should be given, but I do not have the time just now to do so in a suitable way. So right now I'll just say one thing relatively briefly: to my mind, one of the biggest problems on this site is with OP's not editing and clarifying their questions in response to the comments and answers they receive. This applies in particular to the questions, um, in question, and I think this may be a good place to focus a discussion.
Thanks to all for the thoughtful replies. I should emphasize that my intent was to pose the problem in the abstract - motivated partly by one user's recent behavior. I thought it would be interesting for all to see different opinions throughout the community - from students to professors.
Almost surely it is the case that if one poses questions too rapidly then the quality of the Q&A experience will deteriorate - simply because the questioner and answerer will have less time to chew on the problem. The user at hand may be so caught up in the novelty of having access to so many experts that he has not spent the time to introspect on the whole process. If he did he might realize that spacing out the questions temporally will likely lead to higher-quality replies and, moreover, will provide more time for him to engage with the repliers.
We should strive not only to give solutions to problems but also to teach how to solve problems. One of the important things to stress in that regard is that to succeed in mathematics requires sustained effort attacking problems. If students don't spend enough time chewing on problems before they post them here then they will not learn essential problem solving skills that are crucial to succeed as a mathematican.
Perhaps an analogy is appropriate. Since students now have easy access to calculators many of them no longer know how to calculate. Hopefully the analogous thing will not happen here. It would be a shame if some student never learned how to solve problems because he gave up too soon before posting them here. That was never a problem in the old days. But now it may well be with such easy online access to a large community of diverse experts who can quickly tackle almost any question posed by an undergraduate. We should do all that we can to discourage that from happening. Otherwise we may be robbing the student of valuable learning experiences.
How about a tag to indicate that the Questioner knows his answer (and/or that his is a published "Challenge" problem), and an explicit policy that the Questioner should use that tag?
I see my role, as an Answerer, as providing insights (when I have them) about the question at hand. Ideally, the Questioner would provide enough context for me to know just how much insight is sought.
When a Questioner asks for "intuitive" descriptions of topics or asks for alternative approaches to a solution, it's reasonably clear that I have an opportunity to help that person, and this is my primary motivation for participating in this site.
When a Questioner posts yet another Olympiad problem, I'd like to know that before I invest time on attempting a solution and typing it up in LaTeX, especially when the Questioner already has access to a perfectly good answer (and plans to post it after a few days). After all, if I wanted to work through dozens of Olympiad-style problems, I'd get my own compilation books or visit ArtOfProblemSolving.
All I'm asking for is warning about the nature of a question, so that I can set my Answering priorities appropriately. A tag would help me filter questions better, and adding a tag should be dead-simple for a Questioner. (If he still doesn't bother, someone else can add the tag later. Of course, it shouldn't be the job of others to police questions like that, which is why excessive negligence on the part of the Questioner constitute some kind of policy violation.)
Relatedly, I'd appreciate having the Questioner's name in the "Top Questions" list, since this is the primary face of M.SE (and what I check most often). Not only would this sometimes tip me off about questions I might want to ignore, it would likely also clue me in on questions I might really enjoy.
Here's something else that might be worth considering, provided it's technically feasible:
Allow moderators to void the reputation points assigned to a question that comes verbatim from a textbook, Olympiad, or other published source.
(Up-votes and down-votes should still be recorded, to provide feedback about the value of the question itself. These votes simply don't contribute to the Questioner's reputation total.)
Granted, there's a fuzzy line here. After all, I think it's perfectly legitimate --and quite common-- to post an exasperating textbook exercise and ask for help with its solution. That said, the casual visitor who drops in for emergency homework assistance probably doesn't care one way or another about any of this "reputation" stuff.
If there's some concern over having reputation points voided, the Questioner might be more inclined to provide appropriate context: "This is what I've tried", "Here's the answer from the solution manual, and I just don't understand Step 5", "The standard approach would seem to be algebraic, but I suspect there's a geometric truth here somewhere", etc. Context is key.
And, hey ... If you've decided to pass along a question from an Olympiad that you thought was interesting, that's great! (I do hope it's tagged appropriately, though. :) Just don't expect to take credit for someone else's thought-provocation if you have nothing to add. That's simply dishonest.
So, you should earn reputation for your question. It's perfectly okay that yours be a question about Author/Teacher/Contest X's question, but just asking X's question doesn't make it yours.
Of course, with this all being highly subjective, any reputation-voidance should allow for appeal, as with closing questions.
Just a thought.