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We've previously had some discussion about the suitability of pure math questions for this site. Currently, pure math questions - by which I mean those that have no physics content, even if they arise in a physical context - are off topic. We migrate those to Mathematics. Here are some recent examples, mostly taken from the list of recently migrated questions:

(Most of the above examples were typically migrated after 5 off-topic votes from +3k users and moderators via the Math.SE migration path.)

Last time the topic was brought up on meta, the community seemed in favor of changing our scope to make pure math questions on topic. If we decide to go ahead with it, it would be an easy change. So I thought I'd put forth this formal proposal: shall we make pure math questions on topic?

Ideally, answers should offer:

  • a set of criteria (the more precise, the better) for determining which pure math questions should be on topic for us. The extremes of the spectrum are "all math questions are on topic" (essentially absorbing math.SE's scope into our own - they wouldn't like that though) and "only questions which are about physics are on topic" which is what we have now; answers can suggest anything in between. This could form the basis of an meta question in the future, if necessary.
  • an improved wording for the help center scope page that briefly summarizes what sorts of mathematical questions are on topic and which ones aren't

Vote up the answers you think are good, vote down those which you think are bad, and in either case comment to explain why. As always, reasoned arguments will carry more weight than vote counts.

When (or if) a consensus emerges, we will take it into account and act accordingly. (I'm being vague because I can't guarantee that our site scope will change to reflect the consensus here; we'll also have to come to an agreement with the math.SE community and the SE team.)

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Questions devoid of any physics content (or reference to physics), which focus entirely on mathematical details should be migrated to the mathematics SE. If the question is regarding a mathematical method applied to a physics problem, then it is appropriate for the physics SE.

Nevertheless, a question which focuses entirely on mathematical details, whilst perhaps appropriate for the mathematics SE, should be kept on the physics SE if it is motivated by physics, even though it may not necessarily be regarding how it is precisely applied to a physics problem.

An example: there was a question regarding how to compute the normals given a metric, and potentially its embeddings. The question did not feature a particular example from a physics problem, but it was on the physics SE because it was motivated by physics (specifically, because the normals are used to compute the extrinsic curvature which is part of the gravitational action boundary term).

In addition, the requirements and expectations of the OP should be partially kept into consideration. It may be although the question is highly mathematical, the OP desires a physicist's perspective or approach, which may have subtle differences from a mathematics SE answer.

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    $\begingroup$ For completeness, do you have a link from Math.SE to the example? $\endgroup$
    – Qmechanic Mod
    Commented Apr 13, 2014 at 9:08
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    $\begingroup$ @Qmechanic: Unfortunately, I can't find it. I think it was deleted by the OP, simply because it didn't receive any answers. $\endgroup$
    – JamalS
    Commented Apr 13, 2014 at 9:43
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    $\begingroup$ I don't understand this reasoning. If I'm solving a physics problem I may come across the expression 1+1. The fact that my interest in 1+1 is motivated by a physics problem does not make "how do I add integers" a suitable question for this site. $\endgroup$
    – DanielSank
    Commented Sep 24, 2015 at 4:04
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Yes, math questions should be on topic, when they are questions about mathematical concepts that are more used and known by physicists than mathematicians. In my view, the rationale should always be "on which site would a particular question have the best chance to get an answer?" Surely our primarily goal is to help an OP as much as we can?

With that in mind, certain math questions would get more attention on this site than on math SE; the average physicist will know more about vector analysis, tensor analysis, certain aspects of group theory, certain differential equations, special functions, Legendre polynomials, Fourier analysis, integral transforms and calculus of variations than the average mathematician. The well-known textbook Mathematical Methods For Physicists can serve as a rough guide. Moreover, a physicist will often solve these questions in a different way than a mathematician would, which sometimes might be more helpful to the OP.

An example is this question on Laplace's Equation in Spherical Coordinates, which the OP encountered in Griffith's EM. Despite the fact that the question was answered here and my answer was accepted, a mod still decided to migrate it to math SE, where, not surprisingly, it didn't get any attention whatsoever. So what was the point?

In general, I don't like self-imposed arbitrary rules to decide which topics are supposedly on-topic or not. I favour a much more pragmatic approach when dealing with 'borderline' cases: just wait and see if a question gets enough attention, and when it doesn't, then consider a migration.

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    $\begingroup$ Pulsar wrote (v2): Surely our primarily goal is to help an OP as much as we can? No, not necessarily. E.g. the Phys.SE community has put some restrictions on what homework-type questions can be asked, for starter. It is not up to OP to decide what is on-topic, it is up to the Phys.SE community. $\endgroup$
    – Qmechanic Mod
    Commented Apr 14, 2014 at 14:11
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    $\begingroup$ +1, especially for "In general, I don't like self-imposed arbitrary rules to decide which topics are supposedly on-topic or not. I favour a much more pragmatic approach when dealing with 'borderline' cases: just wait and see if a question gets enough attention, and when it doesn't, then consider a migration." I've never seen the point in closing any kind of question unless there's a specific pragmatic reason not to have that kind of question on the site. $\endgroup$
    – N. Virgo
    Commented Apr 16, 2014 at 7:59
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Math questions relevant to physics should be allowed, even encouraged. To quote Gell-Mann (as related in "The Second Creation"):

"But, you know, the way they teach math is so abstract and peculiar, it's very hard for a student to know what's going on. Mathematicians tend to present things in such a - what is the word? - such a nonconstructive way. They like to prove that there is something, but not actually show you what it is. When they give examples, they are so trivial that you don't learn anything from them."

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    $\begingroup$ Can you expand on how we would define "relevant to physics"? $\endgroup$
    – David Z Mod
    Commented Apr 13, 2014 at 5:51
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    $\begingroup$ @DavidZ: relevant: closely connected or appropriate to the matter at hand. Synonyms: pertinent, applicable, apposite, material, apropos, to the point, germane. $\endgroup$
    – Art Brown
    Commented Apr 13, 2014 at 6:00
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    $\begingroup$ Quoting a dictionary definition isn't useful. I mean, how do you propose to decide whether an individual question is relevant to physics or not? $\endgroup$
    – David Z Mod
    Commented Apr 13, 2014 at 6:06
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    $\begingroup$ @DavidZ: judgment: the ability to make considered decisions or come to sensible conclusions. synonyms: discernment, acumen, shrewdness, astuteness, sense, common sense, perception, perspicacity, percipience, acuity, discrimination, reckoning, wisdom, wit, judiciousness, prudence, canniness, sharpness, sharp-wittedness, powers of reasoning, reason, logic. $\endgroup$
    – Art Brown
    Commented Apr 13, 2014 at 6:25
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    $\begingroup$ Again, not useful. I presume you know why. $\endgroup$
    – David Z Mod
    Commented Apr 13, 2014 at 6:30
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    $\begingroup$ @DavidZ why can we not let the person with the question decide whether he/she would like to ask it on physics SE or maths SE? I don't think it is reasonable to think we can write a policy that captures exactly when a question is on-topic (or off-topic). There must always be some room to wiggle around. $\endgroup$
    – Hunter
    Commented Apr 13, 2014 at 11:53
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    $\begingroup$ @Hunter because the person with the question is not necessarily the best judge of our site's scope. Part of the appeal of SE sites is that people know they will and won't see certain kinds of questions when they come here. If we declare that any question that the poster wants to be on topic here is on topic here, visitors can no longer have that expectation. $\endgroup$
    – David Z Mod
    Commented Apr 13, 2014 at 16:07
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    $\begingroup$ @DavidZ ok, that is a good point. I'm not sure how to solve this problem unfortunately. I do know that it often is not useful/productive to ask maths questions on math SE due to the reasons that Dilaton has given here. Therefore, I hope we can find a way to make this policy less strict. $\endgroup$
    – Hunter
    Commented Apr 13, 2014 at 16:12
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    $\begingroup$ @Hunter the way it should work (late edit: according to the original plan for the Stack Exchange network as envisioned by its creators) is that physicists also participate on Mathematics and answer the physics-themed mathematical questions that arise there. $\endgroup$
    – David Z Mod
    Commented Apr 13, 2014 at 16:16
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    $\begingroup$ @DavidZ yeah, but in practice this is not true. Thus, if we take the theoretical point-of-view, then maths questions should not be allowed on physics SE. However, if we take a pragmatic point-of-view, then these type of questions should be allowed on physics SE. (IMHO) $\endgroup$
    – Hunter
    Commented Apr 13, 2014 at 16:19
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    $\begingroup$ I find it very hard to believe that your picking out a word from a phrase and quoting a dictionary is "the best you can do" here. It is infinitely more believable that you were being intentionally obstinate. $\endgroup$
    – Kyle Kanos
    Commented Apr 13, 2014 at 18:04
  • $\begingroup$ I deleted a nonconstructive comment discussion. Everyone please remember to keep the commentary civil. $\endgroup$
    – David Z Mod
    Commented Apr 15, 2014 at 0:22
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There exists the middle road in this question, and it is similar to the one used for homework, i.e. ask for context. Pure mathematical questions at all levels should be discouraged if they have no physics context.

Naive example from an experimentalist : I am thinking of using "this mathematical tool" in the context of string theories but I cannot find the set of its symmetry groups. Instead of "what are the symmetry groups of "this".

It may be that a physicist has a hunch that a certain mathematical tool will be useful in a specific physical context and does not want to reveal it before it has matured into a full preprint ( for obvious reasons). Then mathematics.se and its conceptual difficulties should be faced.

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Mathematics : Physics = Grammar : Literature

While many writers may be very good at grammar, one would not ask a pure grammar question to a writer, but to a linguist.

There is a big difference between a question of mathematics as applied to physics and a question of pure mathematics. While many physicists are good at applying mathematics, only a few of them have the breadth or depth of knowledge that a mathematician has.

My fear is that pure mathematical questions would not receive as good answers here ans on math.se or mathoverflow and my very strong suspicion is that they would not receive a good peer review because of course pure mathematics is a larger set of concepts and skills as compared to the subset used in physics.

We want to maximize usefulness of the network and minimize effort of the communities:

Where would someone likely go to look for an answer to this question? Differential equations are very useful in physics, but most DE questions probably live in our maths sites. We don't want to have the same question in two places, or worse, questions randomly spread between the two sites.

Finally, remember that if you can answer a question here, you can also do so on the maths sites!

In short:

  • migrate pure maths questions to the appropriate level mathematics site
  • criterion to define "pure maths": if answering the question requires physics knowledge, then keep the question; if answering the question does not require any physics knowledge, migrate away.
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    $\begingroup$ Maybe a comment is better than a mere downvote, no? $\endgroup$
    – Sklivvz Mod
    Commented Apr 14, 2014 at 22:31
  • $\begingroup$ Please use the comments only to talk about this particular answer. You can talk about your diatribe in Physics Chat. $\endgroup$
    – Sklivvz Mod
    Commented Apr 15, 2014 at 7:59
  • $\begingroup$ I didn't vote (up or down) but I'm not clear what your intention is. In my mind your analogy could also be Math.SE : Physics.SE = English.SE : Writers.SE which seems to support the "no math here" approach. But then your second paragraph seems to say that math is okay here if it's about physics. So I guess I'm just unclear exactly on where you fall -- plus your answer doesn't meet the two things DavidZ asked for an "ideal" answer: a set of criteria and wording for the help page. $\endgroup$
    – tpg2114
    Commented Apr 15, 2014 at 14:20
  • $\begingroup$ @tpg2114 Thanks, see if my edit addresses your comment! $\endgroup$
    – Sklivvz Mod
    Commented Apr 15, 2014 at 14:26
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    $\begingroup$ It does but I'm not sure I agree with how you define pure math :) Where do we draw the line on "required" physical knowledge? One could argue any conservation law requires physics to understand while another could argue it's just an X order (O|P)DE which could be handled as "pure math" also. Just some things to think on. $\endgroup$
    – tpg2114
    Commented Apr 15, 2014 at 14:48
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    $\begingroup$ Just for clarification on your last comment: if someone has a question about differential geometry which is absolutely vital to understand the Einstein equations, then it should be migrated anyway? For instance, the majority of questions related to chapter 2 & 3 (i.e. introductory chapters) of Sean Carroll's General Relativity (a physics subject) book should be migrated? $\endgroup$
    – Hunter
    Commented Apr 15, 2014 at 15:20
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    $\begingroup$ To be even more clear: one can talk about DE without talking about conservation laws. That would make those pure maths. If one is trying to understand how DE apply to conservation laws, it's not pure math. If someone has a question (say) on a purely mathematical notation of tensor calculus, it should go, but if the question touches physics, or anything which is better explained by a physicist, which includes questions about passages of physics textbooks, then they should stay. The principle: if a mathematician who doesn't know physics can do the job equally or better, then migrate away. $\endgroup$
    – Sklivvz Mod
    Commented Apr 15, 2014 at 15:27
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    $\begingroup$ Smart physicists ask math questions to mathematicians all the time -- this is no different. $\endgroup$
    – Sklivvz Mod
    Commented Apr 15, 2014 at 15:28
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    $\begingroup$ Ok, thanks. I couldn't disagree more with your point of view, but everybody has the right to their opinion. $\endgroup$
    – Hunter
    Commented Apr 15, 2014 at 15:42
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    $\begingroup$ Smart physicists ask math questions to mathematicians all the time, but for some types of math question you're just better off asking a physicist. "If a mathematician who doesn't know physics can do the job equally or better" would be a very difficult criterion to apply in practice. $\endgroup$
    – N. Virgo
    Commented Apr 16, 2014 at 7:56
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    $\begingroup$ "Smart physicists ask math questions to mathematicians all the time -- this is no different." Are you saying that smart physicists would ask a math question at Math.SE, hence if someone asks a math question here he is not a smart physicist? Also where is it more likely for a physicist to ask his math question at the physics department or walk over to the math department, find someone who is willing to answer and then possibly explain to him that this was not what he was asking and so on? $\endgroup$
    – MBN
    Commented Apr 17, 2014 at 15:09
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TL;DR: This site is about Physics. Questions posted here should also be about physics.

This site's About page states,

Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics and astronomy. It's built and run by you as part of the Stack Exchange network of Q&A sites. With your help, we're working together to build a library of detailed answers to every question about physics, astronomy and astrophysics.

Emphasis my own (neglect of link also mine). Similarly, the Math.StackExchange's About page states,

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's built and run by you as part of the Stack Exchange network of Q&A sites. With your help, we're working together to build a library of detailed answers to every question about math.

Emphasis again my own.

DavidZ comments in the original post,

Currently, pure math questions - by which I mean those that have no physics content, even if they arise in a physical context - are off topic.

The issue here is that of pure math questions. Obviously questions that contain physical contexts are on topic, no one is disputing that. It should be patently obvious that questions devoid of physics should be off-topic, whether it is about mathematics or not.

(Disclaimer: The following is indicative of the American University system as a whole. I can make no statements regarding University systems elsewhere in the wordl)

Every physicist I have ever met must have taken the following courses in University:

  • Chemistry
    • Further, many solid state physicists must take advanced courses in chemistry so as to make better solid state devices
    • Therefore, any question about Chemistry should be on topic on Physics
  • English Literature
    • Therefore, any question about Literature should be on topic on Physics
  • Computational Science
    • Further, many physicists require computers to do their research on computational physics
    • Therefore, any question about Programming should be on topic on Physics
  • History
    • Some physicists even pride themselves on knowing a lot of historical facts (a professor of mine made it a point to memorize every physicists full names)
    • Therefore, any question about History should be on topic on Physics
  • Foreign Langauges (such as German, Italian, Spanish, or French)
    • In some cases, becoming fluent in a foreign language is a necessity to communicate to collaborators
    • Therefore, any question about Foreign languages should be on topic on Physics

And the list goes on once you get into the elective portion of the general requirements. If you jump into the electives within physics, we diversify even more (e.g. electronics, the now-closed Theoretical Physics site, and the astronomy site).

We have a great site that is dedicated to questions and answers that are about physics and its subfields. Mathematics is not a subfield of physics (surely Mathematical Physics is a subfield of physics, but these are high-level maths that are full of physics concepts that are decidedly on topic.)

We do not need to muddy our waters with questions about algebra & trigonometry or geometry that have nothing to do with physics. Which is the point here, we're not talking about questions about group theory and tensor calculus that have deep physical meaning in advanced topics, we're talking about questions that are rudimentary mathematical questions that have no basis on physics.

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Here is a solid criterion:

Mathematical questions may be asked, but only in the context of predicting some physical phenomena.

This is the use of mathematics in physics, and what separates it from mathematics for good'ole mathematics sake.

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No, purely-maths topics should not be on topic here.

We currently have a very clear scope: questions which ask about physics concepts.

If we start blurring that by saying some maths questions are on topic, and some are not, then we lose the clarity of the present scope

If we extend the scope to be "any maths or physics question", then we've effectively absorbed maths.se, and both physics.se and maths.se lose out.

Clarity of scope is enormously important. It helps new and established contributors have an unambiguous rule about what is on topic, and what is off-topic.

This would be muddied if the scope is no longer simply "physics concepts", but includes some or all maths.

And so I'm proposing that the present wording on the Help Center Scope Page is sufficient.

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  • $\begingroup$ I largely agree but a colleague recently noted that he'd read a study alleging that mathematicians could identify those problems that physicists declared had been reduce to pure math pretty reliably from among problems using similar concepts that arose in a purely mathematical context. I'll see if I can get a reference. $\endgroup$
    – dmckee --- ex-moderator kitten Mod
    Commented Apr 12, 2014 at 22:00
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    $\begingroup$ "If we extend the scope to be "any maths or physics question", then we've effectively absorbed maths.se, and both physics.se and maths.se lose out." This seems to be a very dramatic statement. Mathematicians study maths for the sake of art, whereas physicists will study maths as a means to an end. Surely mathematician will keep asking their questions on Math SE (it's in the name) and physicists will ask their maths questions on Physics SE. I can speak from personal experience that it is more beneficial to ask maths questions to a physicist (who speaks the same language as me), than to ask $\endgroup$
    – Hunter
    Commented Apr 12, 2014 at 23:02
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    $\begingroup$ it to a mathematician (who will often have a different interest than me). Surely, this is something you cannot deny? $\endgroup$
    – Hunter
    Commented Apr 12, 2014 at 23:02
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    $\begingroup$ Also, please see this post for all the pros to allow for mathematics questions. $\endgroup$
    – Hunter
    Commented Apr 12, 2014 at 23:13
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    $\begingroup$ @Hunter I think I may have said this somewhere else too, but my understanding is that Mathematics is not a site for mathematicians, it is a site for math questions. So the intended audience over there is not limited to mathematicians, and it's not expected that all questions must be answered in mathematicians' language. From their about page: "...a question and answer site for people studying math at any level and professionals in related fields." $\endgroup$
    – David Z Mod
    Commented Apr 14, 2014 at 20:31
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    $\begingroup$ @DavidZ we can go back and forth about this, and discuss how things should work. But the way it actually works right now means that there is an area of questions (related to mathematics) that will most likely not be answered; on physics SE they are considered off-topic, and on maths SE they are not well received (and thus they often don't receive answers) or the answers provided are not useful for physicists. This implies that people have to go outside of the stackexchange community to find answers. $\endgroup$
    – Hunter
    Commented Apr 14, 2014 at 20:50
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    $\begingroup$ It is up to us (i.e. the community) to decide whether this is acceptable or not; and if this is not acceptable, then we need to decide how do we fix this problem. As I have mentioned elsewhere, I hope some of the policies can be made less strict. $\endgroup$
    – Hunter
    Commented Apr 14, 2014 at 20:50
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    $\begingroup$ @DavidZ may I ask you about your opinion of my previous two comments? It appears that the moderators of physics SE do not want to allow for maths questions to be asked on this forum. But it is still not clear to me what the objection is you have (in relation with the previous two comments). $\endgroup$
    – Hunter
    Commented Apr 15, 2014 at 14:02
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    $\begingroup$ Part of the problem is that this supposedly "very clear scope" of restricting questions to "physics concepts" is in fact inherently subjective. What's the definition of a physics concept? We always tell people it's in the help centre, but if you actually go there you won't find one. We get a lot of disagreements about whether questions are on topic, and virtually all of them come down to one person's subjective definition of "physics" differing from another's. $\endgroup$
    – N. Virgo
    Commented Apr 16, 2014 at 8:03

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