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Is there any reason for answers like "Too elementary/trivial", "Not research level" and so forth?

I understand what the level of this site is, but at times it would take 3 minutes to give a proper answer to an elementary question instead of the 30 seconds needed to spit a judgement.

I suffer this even outside this site and in real life: those who know don't answer (in many ways) and those who answer usually don't help much. Something similar happens with books and papers: there is a gap between textbooks and research level mathematics (or just some more elaborate examples, for what I can tell).

How are the ''beginners'' supposed to learn? Working on our own is good but it takes a lot of time and sometimes we may still need something to refine our work.

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    $\begingroup$ Sometimes people do answer such elementary questions, usually in comments. But many users don't want to encourage the asking of such questions by offering quick answers, because of the potential for opening the floodgates and have the site be overrun by elementary questions. This would certainly turn away a large number of valued users who don't want that. There's Mathematics.StackExchange for the more elementary questions. What's wrong with using that? $\endgroup$ – Todd Trimble Jul 31 '14 at 22:32
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    $\begingroup$ Never got a useful answer there. Sometimes it is a wrong answer, sometimes it is just something I already know and sometimes I only get comments of people who would like an answer to my question as well. I understand your point. Maybe it would be good if some MO users would help with MSE as well; I know someone does but still it looks to me there is a considerable gap between the level of the two sites. $\endgroup$ – Wesley Barnard Jul 31 '14 at 22:39
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    $\begingroup$ Sometimes people who don't get a good reception at MSE go ahead and post at MO, linking each question to the other and explaining that no one answered satisfactorily. Of course just because it's not answered there doesn't mean it's appropriate here, but often such an action elicits someone at MO to go there and set things right. Alternatively and maybe better: if there's a question you posted there that's bugging you now (and prompted the writing of this post), link to it now. You can ask whether it would be legitimate to ask at MO, and anyway someone reading this might go there and help. $\endgroup$ – Todd Trimble Jul 31 '14 at 22:58
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    $\begingroup$ You know, Wesley, there's no law guaranteeing everyone an answer to every math question, much less a free answer. Instead of criticizing MO and m.se for not being what you want them to be, be grateful for what the two sites accomplish, and, if you can't get what you want for free, hire a mathematical consultant to answer your questions for you. $\endgroup$ – Gerry Myerson Jul 31 '14 at 23:35
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    $\begingroup$ I, for one, am very sympathetic to the point of view expressed in this question. Even if a question may be off-topic on this site, basic human kindness does suggest that people should provide some help if it would take a minimal amount of effort to do so. Nevertheless, we discourage people from doing so for the reason that Todd mentioned in his first comment: if we always answered off-topic questions, then MO would be flooded with them and it would be substantially harder for MO to serve its actual purpose of answering research-level questions. $\endgroup$ – Eric Wofsey Aug 1 '14 at 0:46
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    $\begingroup$ This is an example of a very general phenomenon in life where it would seem harmless or even beneficial to bend some rule in any individual case, but it is nevertheless important to follow the rule because there would be serious problems if everyone always bent it. $\endgroup$ – Eric Wofsey Aug 1 '14 at 0:47
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    $\begingroup$ Well, I guess I'll go ahead. Wesley has asked two questions at MSE. The most recent is math.stackexchange.com/questions/883801/…, and back in May he asked this: math.stackexchange.com/questions/804083/…. Anyone feel like lending a hand? $\endgroup$ – Todd Trimble Aug 1 '14 at 1:01
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    $\begingroup$ I know there is no law about answering math questions, nor for being kind. I am well aware of this. I was just wondering why people should waste time giving bad comments and voting against a question instead of answering or ignoring it. When a young student asks me something I usually answer and if I have no time (or will) to answer I give them a hint or a reference. This being said, I understand the rules and I appreciate every single word aimed at helping me or showing sympathy. $\endgroup$ – Wesley Barnard Aug 1 '14 at 11:18
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    $\begingroup$ I opened this discussion here just to say I see a problem: there is a huge gap between textbooks and research papers and between M.SE and MO. Those who swim in between get sometimes lost. Since the community behind the sites is really great and showed devotion and care, I would think that some feedback about the user's need may be interesting. Maybe I represent many others and maybe not... Again, thank you for your time and for everything you do for other people looking for help. $\endgroup$ – Wesley Barnard Aug 1 '14 at 11:24
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    $\begingroup$ Wesley, my impression is that the level of MSE is generally sufficient for handling questions at the level of your projection question. There are plenty of reasonably high-powered mathematicians who visit the site; someone like Matt Emerton would surely have been capable of answering your question -- you had some bad luck getting the appropriate attention. My guess is that the real problem is that the volume of questions there is just too high, and many questions wind up slipping through the cracks. $\endgroup$ – Todd Trimble Aug 1 '14 at 14:37
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    $\begingroup$ I had the impression that beginning graduate level questions were OK for MO, and it seems to me that projection question meets that standard. Have things changed? (Regarding MSE, I have nothing against it, but I personally don't want to spread myself any thinner.) $\endgroup$ – Donu Arapura Aug 1 '14 at 15:41
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    $\begingroup$ @FelipeVoloch while I agree overall with your comment and those above, I am a little uncomfortable: wasn't one of the original roles of MO to be a place where researchers could ask questions that they suspected would be well-known or straightforward to specialists in other areas? We don't all have "grad school" backgrounds and we don't all have people on our corridors who know about character theory, structure of semisimple Lie groups, etc. Functional analysts may not know "basic" results of geometric group theory, and vice versa $\endgroup$ – Yemon Choi Aug 2 '14 at 13:20
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    $\begingroup$ @Tobias I'm regularly amazed (and dismayed) by the over-precise meaning some people attach to the phrase "graduate level". The level of knowledge of graduate students is wildly variable within individual departments, let alone countries, let alone the world. And, of course, it depends enormously on the student's interests (as Yemon says). To go even further and talk about "advanced" graduate level... I don't see how it could begin to be meaningful. The cynical side of me suspects that some people (not necessarily you!) simply use "graduate level" to mean "what I knew as a grad student". $\endgroup$ – Tom Leinster Aug 3 '14 at 19:50
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    $\begingroup$ @TobiasKildetoft What do you mean by "graduate level", and why do you think "first graduate course" makes universal sense? I recall an MO question where everyone was incredulous at a poster who did not know of Smith normal form, yet the poster knows more (I'll wager) about nuclear Cstar algebras than all the people who piled on to close. $\endgroup$ – Yemon Choi Aug 5 '14 at 2:37
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    $\begingroup$ My unease with "graduate level" is that it shunts emphasis onto the level of the jargon in the question, rather than how much thought and initiative has been displayed in asking the question. A question on the lines of "I'm an additive number theorist wondering if there is some form of Plancherel theorem for compact groups" is better in my eyes than "please help me understand the proof of Lemma 3.41 in this book on strawberry-flavoured Chow groups of vibranium stacks over Wakandan tori" $\endgroup$ – Yemon Choi Aug 5 '14 at 2:52
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The reason for answers like "Too elementary/trivial", "Not research level" and so forth have been given in comment: they are meant to keep MO focused on its goal of connecting professional mathematicians together in order for them to help each other.

Concerning your other question, "How are the ''beginners'' supposed to learn?", I would answer that beginners are supposed to take classes if they want to learn. MO is certainly not meant to replace higher education in mathematics, which is an unreasonable goal in any case. It is sure difficult to learn by oneself, and that is one of the reason why there is so much money spent in higher education.

To end on a personal note, I am willing to participate to MO because it is a fruitful trade between the things I learn here and the time I spend answering; I am not ready to spend much time to help everyone on the Internet that wants to understand some mathematics: this is a job and, however happy I am to see people interested in math, I just have already more than enough to do with my own students and research.

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