the problem with "I'm reading X and don't understand Lemma A.B.C" is not the level but the amount of thought that's gone into the question before asking on MO ... MO is not a place of first resort, it's a place of middle resort

Too often it has seemed to me that these questions have been asked instead of trying another text, asking one's advisor or even just taking some time to think about it. I realise that this has been my main objection to these questions, more than the level at which they are asked. That said, I lean towards Todd's interpretation number 2.

Secondly, I want to emphasise that, in my comment above, I never endorsed rudeness on MO. This is a serious problem, particularly when levelled at first-time visitors.

Thirdly and finally, in response to quid, I feel like I need to explain further why it's useful to be able to ask questions in one's own field on MO. The example that he cites, my question Is there a non-Hopfian lacunary hyperbolic group?, is a good one. He's correct that I could have e-mailed Mark Sapir, and indeed I considered doing so. Here are three reasons why I'm glad I didn't.

1. Mark might have felt some obligation to reply, even if he is busy. By asking on MO, I don't intrude on his time.

2. I would only have got Mark's point of view. In the end, I received three excellent answers, all of which contributed something positive.

3. I might have e-mailed Mark directly if I was about to write a paper on the subject. But this question occurred to me at an earlier stage in my thought process, when I'm trying to get a feel for a problem and work out what might reasonably be true. As such, my question, though important to me, didn't feel urgent enough to warrant an e-mail.

In fact, the ideal setting to ask the question would have been in person at a seminar or conference. But sometimes logistics make that impossible, and in this instance MO made a great alternative.

I cannot speak for anyone else, but for me the occasional outbreaks of needless unfriendliness (to other people, not to me) are much more off-putting than relatively elementary questions from graduate students.

Neil, you speak for me too.

Also, too much is made of this criterion "graduate-level". It's entirely changeable: do you really know what graduate mathematicians learn in India or Indonesia or Iceland or Ireland? One of the graduate courses I took included some highly obscure corners of universal algebra, which perhaps no one else on the whole of MO knows about. If someone did happen to ask about one of those obscure corners, and I criticized their question as being "something I learned about in a first course on universal algebra", that would be ridiculous. (Yet, I perceive that that kind of criticism is increasingly common.) Graduate education also changes over time; the age range of MO users probably covers over 50 years. The concept of a "standard" graduate education is a non-starter.

Kevin Walker wrote:

In the early days of MO I remember people often saying that the ideal MO question is one which you (an expert in field X but a newcomer to field Y) would have difficulty with but could be answered quickly and easily by an expert (in field Y).

I fully support that.

My work takes me to many foreign areas of mathematics, and I'd be really sad if it wasn't possible to use MO to enlist the help of willing experts.

That doesn't mean I don't my homework - I do. I don't ask questions on MO lightly. But it needs to be appreciated that when you're an outsider to a field, you don't have an insider's instinct for what's routine and what's difficult. You may have no idea whether you're asking an elementary question or something unsolved. And looking stuff up can be hard when you don't have an insider's vocabulary. (Who could guess, for instance, that a particular property of rings is called "Cohen-Macaulay"?) Of course, you can acquire an insider's vocabulary by going away and reading an entire book. But isn't the purpose of MO that we help each other?

If you get stuck on a lemma, I think you should try several steps before asking on MO

Of course. MO is for when you're honestly stuck, after giving it the good old college try.

However, if you are reading a graduate text in a field for which there are several such texts, then there's no reason to ask on MO every time you get stuck. In particular, I don't like questions that can be read as "Please write me an exposition of this standard fact for which lots of expositions have been written, since I got stuck on one of them and don't want to go find another."

Agree with that too, very strongly. There is no lack of observable laziness on MO; so many cases where it almost seems asking on MO is a reflex, whereas if the OP would just think for a minute or so, the answer would be clear.

I think that questions of the form "I'm having trouble with this detail in the proof of Lemma 3.32 in research paper P" are typically (but of course not necessarily) on topic. [EDIT: but in light of Henry Cohn's comment above I now realize that other people had in mind lemmas in standard graduate texts, which is a little different.]

Quid's suggestion that we drop "advanced undergraduate" from the FAQ is (in my opinion) a good one. I think many, perhaps most, people would interpret this to mean "fourth year undergraduate, not first year undergraduate". The undergraduates who are advanced in the sense that we intend know who they are and can figure out that "graduate student" includes them too.

One of Andrew Stacey's question http://mathoverflow.net/questions/24437/is-compact-implies-sequentially-compact-consistent-with-zf might be a good example of a research-level question under interpretation number 2. My own take on MO is that largely it's for "research-level questions" under that interpretation. It can also be used for interpretation number 1, but that's not the primary mission. And I would say that graduate-student questions about lemma 3.1.1 certainly fit that bill. They could try asking on m.se, but more and more I see people who do that and don't get an answer, and then come to MO (hat in hand, practically). I think they should feel not at all ashamed to ask on MO in the first place.

I agree that the level of "acceptable question" has risen noticeably since the early days.

Afterall the site was founded by a (then) advanced graduate student (AFAIK). And, while I was not around at that time, reading older questions and what some people around since a longer while tell in the start of MO standards were lower and supposedly people were happier. No matter what is written in the FAQs 'we' will never get rid of a (in my opinion more or less constant) number of 'strange' or clearly too elementary questions. The question is what ratio of all questions this is.

HJWR says:

To continue to attract world-class users, the level of questions has to be remain high.

Various people around since more or less the start say that the standards got higher. Thus, I do not think any particular action is needed so that just the standards remain high. IMO the perceived quality gets lower because some intersting content starts to be lacking. Also cf. Andreas Blass statement above (emphasize mine):

One reason I like MO is that I can often learn something about areas distant from my own interests by reading questions (even ones that are too elementary for the specialists and therefore get closed), answers, and comments.

So, one could also say by ever raising the standards one takes (everything) away what Andreas Blass gets in return for his 250+ answers.

To continue on the topic of world-class users let me also quote Bill Thurston (from his profile):

I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication.

Judging from some of the (detailed!) answers he gave to certain questions this is not just some empty phrase. So, yes some world-class users might not get attracted to MO for one reason or another but perhaps some go more or less inactive because of a growing (pseudo-)sophistication. Could also happen. In general, from what they often answer and sometimes also ask it seems that in general various world-class users that are actually around are not that worried about enforcing most exact standards of research level. And some other world class mathematicians will never use the site whatever is done regarding standards.

And also:

It's truly remarkable that I can ask a question in a public forum and get an answer from Ian Agol or Mark Sapir.

It might be remarkable, but is it really useful. Couldn't you have written an email to Mark Sapir to inquier about non-Hopfian lacunary hyperbolic groups?

While I never asked anything so far if ever I would ask something it would be somehow graduate level, I guess, because it would be rather outside my field. I have absolutely no need for a public place to ask experts in my field. If I want to ask them something I ask them (privately). But I could find it useful to ask experts outside my field something. But then chances are this won't be really research level.

In brief, IMO the model of MO is really useful for asking experts outside ones own field and/or for people that do not (yet) really have 'their' field (viz. graduate students). By contrast, to run some ten expert-to-expert sites on one site seems not so useful.

ADDED: It occured to me that this could be misunderstood as me advocating that the expert-to-expert questions should not be asked at all. This was not my intention. What I mean is it would not be useful to have only those, and indeed for getting those answered the existence of the site is not so important as there would be other viable ways.

+1 to Alexander Woo. That sentence would be a great addition to the FAQ (continuing under the assumption that anyone actually reads it).

It seems to me that recently, in gr.group-theory at least, there have been quite a lot of questions of the form 'I'm a graduate student reading book X, and I don't understand the proof of Lemma 3.14'. As far as I'm concerned, math.SE should be the first port of call for those questions. They're not my interpretation of 'research level'.

Let me just mention that I'm aware that these proposed modifications to the FAQ run the risk of exacerbating the internet-wide perception of MO as an unfriendly place for visitors. But, for me, the value of MO lies not in the number of mathematicians who use it regularly, but in their quality. It's truly remarkable that I can ask a question in a public forum and get an answer from Ian Agol or Mark Sapir. To continue to attract world-class users, the level of questions has to be remain high. I know of at least one first-rate mathematician who I believe left MO because the level of questions wasn't high enough.

I agree on the 'topic' and 'substance' part. But my impression is that depending on the topic the meaning of 'too elementary' changes quite a bit. Meanwhile in view of the comments, in particular BR's (and before the crosspost one) I voted to close 'your' question. Since however one interprets things I think a certain level of prior work is in order before asking a question. (In the original question of this thread my impression was eventually that this criterion was met; others had perhaps a different impression; but to decide this is always hard.)

In general I think it is really hard to formulate the FAQs regarding this. In some sense I think it might be better to drop 'advanced undergraduate' and add the 'advanced' to 'graduate' for the description of the 'standard audience' or 'default audience'. Of course not to exclude undergraduates but perhaps more harm is done by instances were people are somehow mislead to ask too simple questions and then get 'in trouble'. Not sure though. But recently some very regular user (I believe Andy Putman but did not recheck) argued that the default assumption for users not providing background should be a PhD in maths. But this is then a quite different intended audience. And some standard argument is 'should be of interest to professional research math.', which I hardly use myself, but I would also interpret as more or less post PhD. But perhaps this is also a cultural difference, and those using professional research math actually consider graduate students as such. (Not that I would disagree that much but I would not use it like this myself.)

"Ideally, an appropriate question is one for which a useful answer would help with work leading to a paper suitable for publication in a mathematics research journal."

Though there are no hard and fast rules about who may post here, the intended audience is professional mathematicians, mathematics graduate students, and advanced undergraduates. If your question is closed as "off topic," it might be because it was too elementary. This doesn't mean that your question is "bad," just that MathOverflow isn't the right place for it.

Now my understanding was this was meant to discourage questions which are in some sense "too elementary", or "in undergraduate student mode" - that's not a question of topic, but a question of substance or depth. However, I may well have misremembered; and I am in fact ambivalent about the question I linked to (note that "many of us" sometimes includes "me", but not always). My point was more that the OP's reaction in the question I linked to seemed similar to that of EMS, as in "what did I do? what is your problem, man?"

(While I type, it seems from the comments to the new question that this may be a case of the questioner not being sufficiently diligent in reading the papers.)

I am not quite sure what you mean with I 'should not' vote to reopen?

24h ago I said I have no real opinion; quite a bit of things happened in between, now I have one, what's wrong with that?

Added: Shortly thereafter final vote occured. Question open.

If we were to tend to a place where questions are written so that non-experts can't even tell what the subject is, I would get bored rather fast!

There are currently two votes to reopen. While I have my misgivings about the question, and am not entirely happy with the attitude/assumptions of the OP as shown in comments, I am casting a third vote to reopen so that (a) the question might be improved (b) an answer that Suvrit appears to have sketched in the comments can be added as an actual answer, CW if necessary.

That was a rather strange and incoherent email you forwarded to me. The writer does not seem to be connected to the discussion in a substantial way, and I am reasonably certain it is not the person asking the question. If this progresses to harassment, you should probably contact authorities with legal power instead of MathOverflow moderators.

That being said, for me typing svm into Google the third item after two obvioulsy unrelated things is the wikipedia page of 'support vector machines' and there are a couple of other relevant hits. So, at least with some moderate effort one could find this out.

IMO the first comment is the most 'toally inappropriate' thing in this entire exchange. [ADDED: the comment in question was delted by a moderator; so the curretnly first is not meant.]

For the question itself I have no real opinion; but apparently at least Suvrit (not to say others don't but he documented it somehow) has an informed critical opinion on it.

As a general question which I have raised before, are mathematical modelling questions within the scope of MO?

Let me rehash from earlier debates which never reached any conclusion. There is a large continuum in applied mathematics, ranging from people whose goal is to prove theorems that happen to be on questions close to applications to people who have no interest in proving theorems but rather are interested in combining known theorems and algorithms to model systems coming from other disciplines and calculate features of these systems. The issue is whether questions about applied mathematics far away from the theorem proving end are within scope.

Frequently mathematical modellers are considered mathematicians, either because the disciplines to which they apply their work has only experimentalists and no significant tradition of theoretical modellers, or because they are interested in models from many different disciplines, or both.

For an example of the latter, if you have a large integer programming problem you want to solve, there are experts in integer programming who may have never proven a new theorem in their life but who are very familiar with existing techniques and are capable of combining them in creative ways in order to find a solution (or sufficiently good approximate solution) to your problem with a feasible amount of computational resources (i.e. decades rather than millenia of processor time).

In the department where I work, everyone from number theorists to harmonic analysts knows what an SVM is. It's as basic as knowing what an integrating factor is for ODEs. If this is true across an entire math department, it should surely be true of a sizable number of specifically functional analysis experts of a math website. If others don't know it, that's fine. But again, they should just ignore the question rather than calling for it to be closed.