[EDITED to add:] See followup at Proposed policy on mathematical questions proposing a more specific policy in the light of comments and voting here.
There's strong consensus that straightforward turn-the-handle mathematics questions don't belong here.
But there is another category of mathematics question that's been contentious from time to time: the highly nontrivial advanced-mathematics question. The sort of thing that might be a question in the International Mathematical Olympiad, or a tricky "for enthusiasts" question set to university mathematics students, or even the subject of a short paper in a mathematics journal.
There is (so far as I can tell) no official policy on such questions. On the one hand, they can be a lot of fun for those with the skills to attack them. On the other hand, they're likely completely inaccessible to a large majority of people here, and arguably they would belong better at math.stackexchange.com than here.
The discussion in the meta question I linked above isn't concerned with that sort of mathematics question. Here are some other meta questions that touch on it:
- Should mathematics questions really be on-topic here? -- the questioner's issue in this case wasn't so much that the questions are unsuitable here, as that they attract bad answers. Question has two answers; one (+3-0) doesn't really answer the question; the other (+9-0) says that substantial mathematical content as such isn't a reason to declare something off-topic.
- Should recreational mathematics be on topic? -- closed as duplicate (of the question above), no answers.
- Should we introduce a new off-topic close reason for math problems? -- followup to the question I linked at the start, suggesting a new close reason (which was in fact introduced).
In so far as the community's opinion can be read out of those questions, it seems to be that highly mathematical questions are just fine here. But observe e.g. these questions:
- Polygon wrapping a cube -- closed for being a mathematics question, comment saying "feels more like a math problem" upvoted 10 times. Seems to be pretty tough; it was about 2 weeks between posting and closing, and the only answer submitted is sketchy and doesn't seem to come close to being the actual proof requested.
- https://puzzling.stackexchange.com/questions/52027/the-powerful-groups -- closed for being a mathematics problem. About group theory. No attempts, no objections made to closing it.
- https://puzzling.stackexchange.com/questions/52026/the-impossible-calculation -- closed and even deleted (so, sorry, some readers will be unable to see this one) for being a mathematics problem. About finite fields, kinda. No attempts, no objections made to closing it.
which suggest that at least some of the time, at least some of the community finds these questions inappropriate. Even though all of them are short, seem like they might be fun to attempt for those who enjoy such things, and may for all I know have clever answers that don't require a lot of "grinding".
(One difficulty about questions of this sort is that telling whether they're outrageously too difficult may be a job requiring professional expertise. How many times can any number appear in Pascal's triangle? Open question. Put n runners on a circular track of length n, starting from the same place all running at different constant speeds; must each of them at some time be at least 1 away from all the others? Open question. Is 33 the sum of three integer cubes? Open question.)
So it doesn't seem that we have a clear consensus on the following question:
Are some questions off-topic on Puzzling for being too heavily mathematical, even though they are not routine textbook exercises, and if so what distinguishes them from questions that are OK?
I'll propose some plausible positions in answers. Others should feel free to add more or to improve mine if I haven't made the best possible case for them.