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I am a bit confused by the close reason for https://mathoverflow.net/questions/154235/minimum-l1-norm-may-not-obtain-the-sparsest-solution?noredirect=1#comment395410_154235.

It is an easy question that the reader could have solved by reading carefully the statements of the theorems, I agree, but it is nevertheless a question encountered while reading a research paper in mathematics. Hence I am unsure about the factual correctness of the statement "This question does not appear to be about research level mathematics within the scope defined in the help center."

"Help center" here links to a page stating:

What kind of questions can I ask here?

MathOverflow's primary goal is for users to ask and answer research level math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books. Of course, individual questions don't have to be worthy of an article, and they don't have to be about new mathematics. A typical example is, "Can this hypothesis in that theorem be relaxed in this way?"

I think the main source of confusion here is that the closure reason "this question is not research-level maths" is used for two different reasons:

  • this question is off-topic because it's not about maths --- for instance, it's about physics, or about vacuum cleaners.

  • this question is a reasonable math question, but it's too easy for a professional mathematician.

Maybe we need a closure reason that is a nice way to tell "too easy, sorry". Something like "this question could be readily answered using standard material for an undergraduate student in mathematics, and so it is not of interest here". Or something better.

There is also an additional reason of confusion in this policy: what is an easy question for a graduate student in, say, algebraic topology, could be a challenging one for a professional researcher in, say, PDEs. A professional mathematician studying topic X could come up with a perfectly reasonable question about topic Y which is "standard" for someone using it, but yet not so easy that it is "undergraduate material". This is material that would be considered "too easy" at a conference on topic Y, but not if you ask another mathematician.

Are these kind of questions on-topic?

I see many questions of this kind on MO. I suspect that even more of them are so, for an expert in the suitable field, and it's just that I cannot recognize them as such. In my point of view, this is often the kind of questions that I want to use MO for. It saves me the hassle of locating in person an expert on topic Y (which my university could not have) and going to his room to ask.

On the other hand, I could see an argument also for banning this kind of "reference-request" questions. If it's something that you could have answered simply by locating a researcher in algebraic topology, any researcher, why are you bothering an entire online forum which includes several Fields medalists?

What would be left? Questions that are really "research-level", as in: they would not be trivial even for an audience comprised entirely of experts in the field. This would reduce a lot the traffic here, and also sectorialize it a lot. Everyone would understand only a very small subset of the questions. Many more questions would be closed. Actually, this criterion would sound very close to "if I you answer it, then close it instead of answering it".

There are two overlapping questions maybe, one about the closing reasons, and one on MO's policies on what is to close. I am sorry, but I find it difficult to split this up into two separate arguments.

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    $\begingroup$ Incidentally, the person asking the question requested (about 1 hour ago) that I migrate it to math.stackexchange.com, so I did. $\endgroup$ – S. Carnahan Jan 12 '14 at 2:18
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    $\begingroup$ It would be interesting to track what happens to it there. What if there is a gap between MO and MSE creating a limbo for otherwise reasonable questions! $\endgroup$ – François G. Dorais Jan 12 '14 at 2:58
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    $\begingroup$ No guarantee is given that just because a mathematical question is reasonable, there is a website where it is suitable (much less a website where it is guaranteed to get a good answer, or even a serious perusal). $\endgroup$ – Gerry Myerson Jan 12 '14 at 4:19
  • $\begingroup$ Just to be clear, there's nothing specific or outrageous in that question, it's just a recent example that helped me in formulating these doubts. $\endgroup$ – Federico Poloni Jan 12 '14 at 5:37
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    $\begingroup$ @FrançoisG.Dorais After two weeks, the question sits at MSE with no other answers or comments and one upvote (are those preserved in the migration?), . So it seems that your concern is well-founded. $\endgroup$ – Federico Poloni Jan 23 '14 at 5:41
  • $\begingroup$ Thanks for keeping track Frederico! Yes, upvotes are preserved during migration, so the question got basically zero attention on MSE... $\endgroup$ – François G. Dorais Jan 23 '14 at 5:43
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    $\begingroup$ By the way, I can move the post back to MO if you think that's the best course of action. $\endgroup$ – François G. Dorais Jan 23 '14 at 5:45
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There has always been a lot of debate regarding what "research-level" actually means. It's changed a lot over time and it's inconsistent across various fields. (There is a plentiful supply of old discussions on tea.mathoverflow.net.) Here are my two cents...

I've often heard "MathOverflow is like a colleague down the hall" and I've used that phrase to explain MathOverflow to colleagues who hadn't used it yet. It's often the case that your colleague down the hall can answer your question right away but sometimes your colleague has to think about it for a day or two. Sometimes that doesn't work and your colleague needs to ask a more specialized colleague in another department. Sometimes even that doesn't work and your seemingly innocent question might even reach the great guru...

MathOverflow is a lot like that, except that there is no layering: your question is seen by your colleague down the hall at the same time as it's seen by the great guru. Does that mean that you can't ask the same questions on MathOverflow as you would ask your colleague down the hall?

I like to think that whatever you would ask your colleague down the hall you could also ask on MathOverflow. That's a bit of an idealist attitude but I think it's fair. After all, MathOverflow is also about answering questions. If all questions are for the gurus then there's little interest here for mere mortals!

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    $\begingroup$ +1 for "MathOverflow is like a colleague down the hall" --- I like both the image and the perceived level for questions that it conveys. $\endgroup$ – Federico Poloni Jan 12 '14 at 5:40
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    $\begingroup$ While I like the metaphor too, it's worth remembering many valuable participants at MO don't have the same pool of "colleagues down the hall", as those of us at large research institutions. It's a great start, but not necessarily a complete explanation. $\endgroup$ – Scott Morrison Jan 12 '14 at 7:08
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    $\begingroup$ @ScottMorrison: Isn't it great that MO is the same size for everyone? Another phrase I heard is "MathOverflow is the biggest/best/etc. math department in the world." I don't use this one as often but I do like to think of MO as a playing an equalizing role in the math world. (PS: I can't make sense of your last sentence. I can't figure out what is meant to be the "great start"/"(in)complete explanation".) $\endgroup$ – François G. Dorais Jan 12 '14 at 15:37
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    $\begingroup$ I meant that I don't want us to implicitly exclude someone who has no colleagues down the hall. $\endgroup$ – Scott Morrison Jan 12 '14 at 18:57
  • $\begingroup$ Ah, yes, I didn't mean to imply that. This is just "my two cents." The last paragraph is, at best, a rule of thumb and more likely less since, personally, I would ask to a colleague down the hall in a manner very different than I would ask on MO. The basic idea still makes sense though. $\endgroup$ – François G. Dorais Jan 12 '14 at 19:08
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    $\begingroup$ Maybe a better metaphor is "MO is like that colleague you wish were down the hall". $\endgroup$ – Tobias Kildetoft Jan 13 '14 at 8:22
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It seems to me that many borderline questions can plausibly be asked to itself by a professional mathematician, but look like no effort was put in it. I feel like I can ask a colleague possibly trivial questions around a cup of tea, but I would think about the question more before asking it on MO. Often, I vote to close a question that might have been perfectly reasonable if context, motivation, unsuccessful tries where explained. Writing down these precisions should lead, in some circumstances, the OP to answer itself the question (this did happen to me more than once). In conclusion, I would say that we lack a kind of "Sorry, your question is not well thought out" reason to close.

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  • $\begingroup$ There is an excellent metaphor to explain this process, rubber duck problem solving. $\endgroup$ – Federico Poloni Jan 13 '14 at 7:42
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    $\begingroup$ In the question we are discussing a lot of effort was made by the person who asked it. $\endgroup$ – Gil Kalai Jan 13 '14 at 7:47
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    $\begingroup$ @Gil Kalai: you are quite true, my answer is probably answering a less focused question and is not very relevant to the question mainly discussed. $\endgroup$ – Benoît Kloeckner Jan 14 '14 at 21:14
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I regard the question as more suitable to MathOverflow. (It was largely answered in the comments of Federico Poloni.) The "colleague down the wall" metaphor is useful here, and we can ask ourselves a related criteria: Is this question is going to be of interest to a colleague down the hall. In this case Donoho's result is an example of something I would be interested to learn about even if the question itself reflects some easy (while research-level) misunderstanding. (And it is of less interest to the readership of the sister site.)

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