Andrew Critch has asked me to start a thread here, in response to some comments I made about a question of his on MO. Ultimately, he changed his question around a bit and my comments became inapplicable, so I deleted them, but I think Andrew still wants a record of them (even though I suspect he disagrees with them) so I'll make them here.
A couple of weeks ago when I started looking at MO, I could see several interesting examples of maths questions. I love little maths puzzles was often tempted to try and answer them. I just want to make the remark that at the minute there are loads of questions on MO and I think it's reasonable to say that many of them and perhaps even most of them are not maths questions. They are questions about mathematics, sure, but they are not questions in the traditional "example sheet" sense. They are questions of the form "can anyone say anything about X" or "where's a good place to learn about X" or (my pet hate) "can anyone give me necessary and sufficient conditions for when X is true". The reason this last one is my pet hate is that the answer is trivially "yes: X is true iff X is true".
My discussion with Andrew on this point (which actually seemed to coerce him into asking a more precise question) seemed to quickly focus on the following issue: when someone says "give me necessary and sufficient conditions for X to be true", clearly "X is true iff it's true" is an inappropriate answer (even though it's logically correct), which seems to indicate that the real question is something else. My belief is that the real question is often "can someone give me non-trivial examples either of the form "X implies Y" or of the form "Y implies X" or, preferably, of the form "X iff Y" ".
This post isn't a question. It's really just a talking point. It's a pet peeve of mine when someone asks a question which admits a trivial answer because to me it indicates that they haven't really formalised what question they really wanted to ask. On the other hand in my opinion MO is sort-of deluged with this sort of question at the minute. That may or may not be a good or bad thing. The only reason I'm posting here is that Andrew asked me to. I suspect that Andrew will have comments to make on this issue, and clearly the remarks on his MO question were not the place to make them, but now he has a chance to make them here :-)
"Obnoxious" covers a wide area, including "logically correct but unhelpful". The problem is that a good criterion for an answer to a *mathematical question* to be "the right one" is "is it logically correct"!
<i>When someone says "give me necessary and sufficient conditions for X to be true", clearly "X is true iff it's true" is an inappropriate answer (even though it's logically correct), which seems to indicate that the real question is something else. My belief is that the real question is often "can someone give me non-trivial examples either of the form "X implies Y" or of the form "Y implies X" or, preferably, of the form "X iff Y""</i>
I think you raise some good points in your post (although on balance I disagree with the implication that imprecise questions are bad), but this is just silliness. When humans do mathematics with other humans, and they say "are there necessary and sufficient conditions for a graph to be Eulerian?" then clearly they don't want an answer like "A graph is Eulerian iff it's Eulerian." Presumably if someone habitually answered questions like that, he would have his math license revoked. Generally speaking, they also don't want something totally trivial like "A graph is Eulerian only if it has at least one vertex." If someone were to ask me that question, I'd say that a graph is Eulerian iff it's connected and every vertex has even degree. If for some reason I didn't know that this was sufficient, I might say, "Well, I don't know a full answer, but it's not too hard to see that it's necessary for the graph to have even degrees, and be connected." Certainly I <i>wouldn't</i> say something along the lines of "Well, do you want nontrivial properties that imply that a graph is Eulerian? that every Eulerian graph satisfies? preferably both?" Unless I'm having lunch with an automated proof system, this is pretty much all assumed as part of the question.
I guess I am trying to represent the other point of view, which is: if the OP doesn't really know what they want, and just ask for necc and suff conditions for a graph to be Eulerian, it means they haven't worked hard enough on their own problem. If they worked harder on it and came up with the conjecture that even degree was a good point, they could then ask a maths question: "is it true that Eulerian iff even degree?". I guess I'm saying that I am seeing a lot of "lazy" questions on MO at the minute.
I agree that there's certainly a lot of temptation to use MO to be lazy. But sometimes you're asking about a class of objects for which there's no such easy characterization ("What are necc. and suff. conditions for a finite group to be simple?") or you're asking about something outside your usual comfort zone, where perhaps you could come up with a conjectural characterization but only after a lot of time spent pursuing wrong lines of argument and looking at ultimately-irrelevant literature. (Yeah, I have experience in this area.) In these cases, better to find someone who actually knows the area and can point you in the right direction, whether it's to a paper or to a sketch of an argument. And sometimes you just have a blind spot! Lazy questions are absolutely a Bad Thing if there are too many of them, but in moderation they're just an instance of comparative advantage.
Maybe there should be some forum (technically, something like this one) attached to MO, for those math-related non-math questions. Some place for _opinions_. If such a place already exists (and I don't know that), MO could prominently link to that place. For the many questions related to "how do I learn X" or "what is a reference for Y" I think a wiki would be even better, since those questions will always come up again. At the Tricki, someone suggested a forum/wiki to discuss errata of papers. That is another thing I would love to see somewhere on the web, but definitively not on MO.
Oh my god, I think I did this before. Thanks for the Milne suggestion (I read it). (btw, changed into "attached to MO") above.
Now on-topic: I don't think the meta-forum is a good place to discuss non-meta questions. At least, the name and the layout are not inviting to do so. I would prefer 2 (or more) different forums.