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This is a freestanding post taking its content from a previous discussion on the modal window for first-time askers. Thanks to Martin Sleziak and Tim Campion for the encouragement to post it separately here, so that the moderators can handle the issue better:

I have a suggestion to improve the help page for "What topics can I ask around here?", which currently emphasizes some rarely-relevant items and lacks some often-relevant items.

First proposed edit: After the title question's bolded answer,

mathematical questions related to current research in mathematics

I would add something like

which you are well-placed to ask if you've had graduate-level training in mathematics or another mathematical discipline. (If you haven't had that training, the question is likely to be off-topic.)"

That parenthetical warning does not appear anywhere on the page now.

Second proposed edit: I would emphasize this content by revising the first two paragraphs on the page, which currently showcase such details as

It’s also OK to ask and answer your own question

and

If no site currently exists that will accept your question, you may commit to or propose a new site at Area 51, the place where new Stack Exchange communities are democratically created.

Those two comments are so rarely relevant that I'd put them much lower on the help page, to let the more relevant comments float to the top.

Should we make these edits to the help page?

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    $\begingroup$ Thanks for posting this. I for one think these are great suggestions. The tricky thing might be figuring out the process for editing that page. $\endgroup$ – Tim Campion Apr 24 at 0:21
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    $\begingroup$ “if you've had graduate-level training in mathematics”: Does not make sense outside of North America and a few other countries. In Europe (e.g., Germany, Russia), this would correspond to a Bachelor's degree in mathematics, i.e., undegraduate-level training. $\endgroup$ – Dmitri Pavlov Apr 24 at 2:19
  • $\begingroup$ @DmitriPavlov, do you have a phrase to suggest? Would "training in mathematics or a mathematical discipline at the level of US graduate school" be substantially better? $\endgroup$ – Matt F. Apr 24 at 2:36
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    $\begingroup$ Ok, good news! It looks like it is quite easy for moderators to edit that help page. So once we reach some consensus on what changes should happen, I think it should be easy to implement. I just checked: for me it is indeed as simple a clicking a little "edit" button on the page and then it's similar to the question / answer editing interface. $\endgroup$ – Tim Campion Apr 24 at 2:43
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    $\begingroup$ @MattF.: Only if one is familiar with the US system. How is one supposed to know what US graduate schools in mathematics are like if one had no interaction with the system? Even if one is familiar with the US system, this still leaves too much ambiguity. For instance, what is the minimum allowed level of questions on category theory? There are relatively few graduate schools in the US where category theory is taught formally, and even then it is unlikely to be mandatory. $\endgroup$ – Dmitri Pavlov Apr 24 at 2:51
  • $\begingroup$ @DmitriPavlov, I think it's helpful to say something. I'm open to other phrasings. $\endgroup$ – Matt F. Apr 24 at 8:52
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    $\begingroup$ @DmitriPavlov Maybe replacing "graduate-level" by "PhD-level" would make that sentence more universally understandable? -- Or would the meaning then still be unclear in Russia (which, as I understand, has a 2-step PhD system -- Kandidat Nauk / Doktor Nauk)? $\endgroup$ – Stefan Kohl Apr 24 at 9:07
  • $\begingroup$ @StefanKohl: Russia does not have a “two-step PhD system”. There is a PhD degree and a Habilitation degree. Your proposal would be unsuitable because MathOverflow does allow questions below the PhD level as it is practiced in countries like Germany and Russia. $\endgroup$ – Dmitri Pavlov Apr 24 at 12:19
  • $\begingroup$ @DmitriPavlov Then maybe I misread the explanations in the Wikipedia article on this. And of course "PhD-level" is not quite a perfect description of what is on-topic here -- but which single word can be such? -- Maybe you have a better suggestion on what to write. $\endgroup$ – Stefan Kohl Apr 24 at 12:51
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    $\begingroup$ @MattF.: We do say something, namely, “current research in mathematics”. Appealing to graduate-level mathematics or PhD degrees is useless, since the users who would understand such an explanation (basically, PhD students and higher) do not cause any noticeable problems in the first place. It is undergrads with low-division mathematics questions that post most of the off-topic questions, and they have no clue what “graduate-level” means. $\endgroup$ – Dmitri Pavlov Apr 24 at 12:56
  • $\begingroup$ @StefanKohl: The article that you cited clearly states “The German Habilitation and, to some extent, the French habilitation à diriger des recherches (HDR) are comparable to it”. Indeed, even the process itself is quite similar to the German process. (As I understand, the Soviet government simply copied the German 2-level system, but gave different names to degrees for political reasons.) $\endgroup$ – Dmitri Pavlov Apr 24 at 12:59
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    $\begingroup$ @StefanKohl: “but which single word can be such?”: I really do not think you can do anything better than “current research in mathematics”. You may have better success with explaining what not to post, e.g., homework in calculus, linear algebra, differential equations, etc. $\endgroup$ – Dmitri Pavlov Apr 24 at 13:04
  • $\begingroup$ @DmitriPavlov If the term "graduate-level" is as problematic as you suggest, perhaps you might weigh in on its use in the current modal window suggestions (unless you are so pessimistic about users reading the modal window that you don't think it matters there :). $\endgroup$ – Tim Campion Apr 24 at 17:10
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    $\begingroup$ I suggest "PhD-student level" as a substitute for "graduate level," which addresses @DmitriPavlov's objections (which I think are overstated), while also suggesting the needed degree of sophistication. $\endgroup$ – Joel David Hamkins Apr 28 at 20:21
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    $\begingroup$ I think most users who post low-level questions know that a PhD-student level question is not what they have, even if they don't know what "graduate-level" means. This is precisely why I suggested "PhD-student level". $\endgroup$ – Joel David Hamkins Apr 28 at 21:29
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The vast majority of people who write the most common low-quality questions are not going to read this page at all.

I think the people much more likely to read this page are those, especially graduate students, who are very nervous about asking a question on MO. They need some encouragement and some advice on how to present a question to ensure it is well-received on MO.

In particular, if you are not sure if your question will be well-received, some of the best things you can do to improve its chances are to explain how the question came up, and explain what you have tried so far.

I think this advice, and any other helpful advice along similar lines, should be near the top.


Attempt at a new draft of the beginning of this page:


What kind of questions can I ask here?

MathOverflow's primary goal is for users to ask and answer mathematical questions related to current research in mathematics. If, while attempting novel research in mathematics, you came upon a question which you couldn't solve, but suspect other mathematicians can, then we want your question here.

Your question is most likely to be well-received if you:

  1. Begin my stating a precise mathematical problem
  2. Follow up by providing some additional context -- Where did this problem come from? Are similar results already known?

After the main question, you can also put definitions which you expect some, but not all, mathematicians to know, and strategies which you think might work.

What kind of questions shouldn't I ask here?

Mathoverflow is not for homework questions. Mathoverflow is also not for questions that could easily be homework in common undergraduate classes such as calculus, precalculus, differential equations, linear algebra, algebra, or real and complex analysis.

However, Mathoverflow is for questions asked by students preparing to do research while pursuing a PhD, as long as they have thought seriously about them and haven't solved them, just as much as it is for questions from advanced PhD students, postdocs, and mathematics faculty. If you are outside academia or in a different field of academia, you should use your best judgment about where your question fits. If you're not sure where your question falls here, you can explain the context and background in your question.

Mathoverflow is not for questions based entirely on opinion. This is especially true for questions whose answers are likely to hurt or offend someone, and questions with no clear purpose. Asking for interesting applications of a current research area might be a good question, even though it has an element of opinion, because the answers would help motivate mathematicians in their studies, but asking for the best person working in that area would not be. When in doubt, you can wait on asking these questions until you have more experience of Mathoverflow's culture.

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    $\begingroup$ I completely agree with the main part of what you say, and I believe it is extremely important to encourage posts by graduate students who might otherwise be hesitant---their contributions are the lifeblood of the site. But I am a little hesitant about the "what have you tried" suggestion, in light of the way this admonishment is often used on math.SE; it is often a kind of harassment there. Although they are quite insistent about the OP stating what has been tried, in my experience, this information is often just not relevant. $\endgroup$ – Joel David Hamkins Apr 27 at 17:27
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    $\begingroup$ @JoelDavidHamkins Thanks! I would like to here you say more about this - in particular, which language do you think should be included early in this page? I am still thinking about how I would formulate my suggestion. Certainly my intention is not to get more people to ask for that. I agree that "what has been tried" is not usually so relevant. My goal is certainly not to change the culture of what people ask for! But it sometimes is relevant. $\endgroup$ – Will Sawin Apr 28 at 1:21
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    $\begingroup$ More fundamentally I think including the information makes a variety of polite responses easier to give and a variety of impolite responses harder to give. (In particular, including the information in a question that is otherwise on the borderline between a good and bad response.) I definitely want to give people advice of some kind, that is somewhat helpful, because I am imagining someone who has heard that MO is a mean place considering whether to write their first question, and I imagine getting some simple, easy-to-follow advice on how to get a good response will make them more confident. $\endgroup$ – Will Sawin Apr 28 at 1:21
  • $\begingroup$ I agree with all that. I am mainly hesitant only about the particular phrase "what have you tried?" because of the manner this particular phrase is abused on math.SE, and I'd hate to see that practice here. How about: ...the best thing you can do to improve its chances are to explain your mathematical question well, with accuracy and precision. Provide the definitions of mathematical terms or notation that you use. Describe the mathematical context in which your question naturally arises. Mention the mathematical techniques that you think might be relevant for a solution. $\endgroup$ – Joel David Hamkins Apr 28 at 7:11
  • $\begingroup$ @JoelDavidHamkins: I think providing appropriate context for the question is by far the most important of these items. (There is always a danger of listing too many requirements.) $\endgroup$ – Dmitri Pavlov Apr 28 at 21:10
  • $\begingroup$ @DmitriPavlov Can you elaborate on that? $\endgroup$ – Will Sawin Apr 28 at 21:13
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    $\begingroup$ @WillSawin: I do not think that saying things like “explain your mathematical question well” can change anything (it's not like anybody is trying to explain it badly, and users typically do try their best). Providing context, on the other hand, is something that can be done easily, but is often omitted, despite its usefulness. $\endgroup$ – Dmitri Pavlov Apr 28 at 21:19
  • $\begingroup$ I also like this suggestion. I agree with @JoelDavidHamkins that "what have you tried" is not needed, though for different reasons: "I tried X and it didn't work" is not very predictive of whether someone else will get a result by trying X (or what they mean by "X"). If they have a good answer to "are similar results already known", that's good enough for me. $\endgroup$ – Matt F. Apr 29 at 15:17
  • $\begingroup$ "real and complex analysis that are commonly required for a Bachelor's degree (B.A. or B.S.).": few universities require complex analysis for a Bachelor's degree in the US. One could simply say "undergraduate real and complex analysis". $\endgroup$ – Dmitri Pavlov Apr 30 at 20:08
  • $\begingroup$ @DmitriPavlov You're saying that "undergraduate" is clear but "graduate" is not? $\endgroup$ – Will Sawin Apr 30 at 20:35
  • $\begingroup$ @WillSawin: Yes, because there are way more undergraduate students than graduate. And both American and European-level undergraduate-level questions about real and complex analysis are likely to be closed on MathOverflow. $\endgroup$ – Dmitri Pavlov Apr 30 at 21:52
  • $\begingroup$ @WillSawin I believe that you are converging on an excellent answer here. $\endgroup$ – Joel David Hamkins May 2 at 14:31
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Concerning the first proposed edit, its modifications are unlikely to make things more clear for users asking low-quality questions.

In particular, such users rarely have any exposure to graduate education, so would have no idea what “graduate-level training” means.

Not to mention that such a description makes no sense for much of Europe, where the undergraduate curriculum contains most of the more standard parts of North American-style graduate curricula.

It may be far more efficient to point out what is not acceptable:

  • Questions about homework of any kind.

  • Questions about non-proof-based mathematics classes, such as calculus, precalculus, differential equations, linear algebra.

  • Questions that can be easily answered after passing elementary proof-based mathematics classes, such as algebra, real and complex analysis, general topology.

In any case, such modifications are unlikely to have any substantial effect, since users that make low-quality posts typically do not read any guidance on what posts are acceptable.

A bigger problem, it seems to me, is that many graduate students are now afraid to ask questions on MathOverflow.

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I believe that it is very important to make the phrasing essentially positive, so as to encourage questions as much as possible from the main population of people that might make valuable contributions to MathOverflow. We need in particular to phrase things so as to encourage questions from graduate students who might otherwise feel inhibited to contribute.

In my comments on Will Sawin's answer, with which I am very largely in agreement, I had suggested something like the following:

In order to achieve a good reception for your question, perhaps the most important thing to do is to explain it well, with mathematical accuracy and precision. Provide explanation for or definitions of the mathematical terms or notation that you use, in light of the fact that people around the world do not always use the same terminology and notation that you may have learned. Describe the mathematical context in which your question naturally arises. Mention the mathematical techniques that you think might be relevant for a solution.

Perhaps one could hint at the idea that this is a site for sophisticated mathematical users by saying also something like:

This is a site for mathematically sophisticated users, mostly at the PhD-student level and above, and so do not be inhibited to explain your mathematical ideas with full technical detail.

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At least from my point of view, it is not clear what "another mathematical discipline" means. Physics? Statistics? That wording is confusing, in my view.

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    $\begingroup$ I think it's worth mentioning this, given that we have high-rep users like Andrej Bauer (PhD in computer science), Carlo Beenaker (PhD in physics), and Iosif Pinelis (PhD in probability and mathematical statistics) -- I think the phrase is clear enough. $\endgroup$ – Matt F. Apr 24 at 21:56
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    $\begingroup$ I'm not debating this; I just find the wording confusing, at least from my background. The concept of 'mathematical disciplines' that are not mathematics is unusual for me. $\endgroup$ – Federico Poloni Apr 24 at 22:08
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Here is a suggestion for a rather different approach (either in the "What topics" page or the modal window):

  • If you can find 10 questions on mathoverflow.net where you are confident that you understand both the question and the accepted answer, then you can assume that you are in the target audience for the site. If you ask questions at the same sort of level, then they will usually be considered on-topic (but you should check more specific criteria on some other page).
  • If you cannot find 10 questions where you are confident that you understand both the question and the accepted answer, then you are probably not in the target audience, and questions that you ask here are likely to be closed without being answered. It may be better for you to ask your question at math.stackexchange.com (but you should read the advice at https://math.stackexchange.com/help/on-topic first).
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    $\begingroup$ Of course, Mathematics is not the only possible alternative for lower-level questions - link to this post which lists several sites is included in the help-center: My question was closed on MO because it is not research level. Where should I ask instead? $\endgroup$ – Martin Sleziak Apr 28 at 7:15
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    $\begingroup$ This is an interesting idea -- although asking somebody to comb through the site and digest 10 questions and answers as a prerequisite for asking a question seems a little steep. I might suggest a lower number like 2-3. Of course, I could imagine somebody cherry-picking 2-3 borderline questions or something, but really if somebody is thoughtful enough to actually go through this exercise, then the chances that they might ask a good question are already much higher than the baseline. $\endgroup$ – Tim Campion Apr 28 at 17:16
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    $\begingroup$ Really the issue is that as soon as somebody knows enough to comprehend what the criteria for good questions are, they are likely ready to ask a good question themselves. So whatever the wording, it shouldn't inspire people to have existential crises and obsess over whether their questions are suitable for the site. $\endgroup$ – Tim Campion Apr 28 at 17:18

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