For background, see:
- Should mathematics questions really be on-topic here? (about "routine" mathematics questions)
- What tricky mathematical questions are on topic here? (about "heavy" mathematics questions)
- Revisiting the 'math question or math puzzle' policy (mostly about "heavy" questions)
We have been less than perfectly consistent in our treatment of mathematics questions here. There's pretty good agreement that we should close questions that just ask for routine calculations, and indeed they generally get closed promptly with helpful explanations for the questioners; but at the other end of the spectrum, when a question turns up that looks as if it requires heavy-duty mathematical machinery it sometimes gets closed and sometimes not, and the justifications aren't perfectly clear either way around.
The purpose of this question is to propose a specific, explicit policy. I'd like to give it a couple of days for refinement and then see whether it meets with general approval. So:
Until 2017-07-15: Please comment, edit, etc., in order to help turn this into a policy that will serve us well.
From 2017-07-16 on: Please upvote if you think the proposal here, or something almost identical, is good; downvote if you think we should have a substantially different policy or no policy; and comment if your opinion is not perfectly and completely expressed by your vote if any.
Proposed policy on mathematical questions
There are at least two ways in which a mathematical question can be problematic.
- It can be routine, simply asking the solver to turn the handle on some standard procedure.
- It can be inaccessible, not realistically approachable by any but a small fraction of PSE participants.
Questions that are routine are simply not on-topic here. The only thing this really has to do with mathematics is that a large fraction of the routine questions asked here are mathematical. If your question can be answered by following a standard procedure, it almost certainly doesn't belong here.
(What about questions that can in principle be solved by brute force, but where solving them less stupidly is a good puzzle? Best to make it explicit in the question that a non-brute-force solution is required.)
Questions that are inaccessible are harder to judge, but:
- The mere fact that a question involves high-level mathematics doesn't disqualify it.
- A question that is incomprehensible to the large majority of PSE readers is (I hereby declare) off-topic and almost certainly a bad question in any case. Such questions are likely to get closed, and even if they escape they are not likely to be well received.
- Some perfectly good questions (typically tagged enigmatic-puzzle) are incomprehensible at first, but usually you can see how one might come to understand them, and when the solution is seen everything makes (at least some) sense. I'm talking here about questions that are incomprehensible because you can't understand them without knowledge of something that takes days to years of hard intellectual work to get into a human brain.
- A question whose solution consists of standard manoeuvres is really a routine question, even if those manoeuvres are difficult for anyone other than a professional mathematician. These questions, too, are liable to be closed as off-topic and/or downvoted.
- If a question requires heavy mathematical machinery, there had better be a Puzzling-friendly payoff for it: perhaps the solution, despite the machinery, is surprisingly short and elegant, with some beautiful central idea that simplifies it; or perhaps the question itself is obviously attractive even though the solution is tough. Preferably both.
One difficulty facing abstruse questions is that it may be hard to tell whether they have such a Puzzling-friendly payoff, and readers cannot reasonably be expected to tell the difference between a question redeemed by a startlingly elegant answer and a question that's just painful. If you ask an intimidating-looking question, you might consider offering explicit reassurance that despite appearances it has Puzzha-nature.
Puzzle-setters, please feel free to post mathematical puzzles -- but make sure they really are puzzles and not mere problems: they should be fun to solve, and preferably fun to read the solutions of. Please make sure your question makes at least some sense to readers with only amateur mathematical knowledge. If your question is liable to look to readers as if it's no fun, consider providing some sort of evidence that it is. And if the fun consists only of an elegant solution, please consider posting your elegant solution if after a couple of weeks have elapsed no one else has found it.
Others, please vote to close routine questions and questions that are downright incomprehensible. When in doubt, consider seeking advice in The Sphinx's Lair and/or discussing things with the questioner to understand whether there's more to the question than handle-cranking. Please don't try to close questions merely because there is mathematics in them. And, whether closing or querying or whatever, please be polite and welcoming.
Edited 2017-07-14 to clarify what I said about incomprehensibility a bit.