In papers there are often sketchy arguments in proofs that I find hard to understand. Filling in the gaps is laborious and time-consuming. According to the post www.mathoverflow.net/questions/40729/does-a-referee-have-to-check-carefully-the-proof, referees seem to be faced with this problem as well.
Presently I'm preparing my first paper for submission to a journal. Of course I approve the usual conventions and write more or less sketchy proofs myself in order to keep the paper short (around 15 pages). On the other hand, I checked the proofs carefully. So I could support the publishing process by this idea:
Submit two versions of the paper:
- a short one, designated for publishing
- a long one, assigned for the referee with proofs given in full detail
Is this a good idea that simplifies the referee's life (and, maybe, helps getting the paper accepted) or is it, in contrast, maybe even a no-go ?
I appreciate your opinions very, very much. Thanks in advance.
N.b. I intentionally ask the question on MO (and not on academia.stackexchange.com) because I think checking proofs is particular to mathematics and doesn't occur this way in most other fields of science.
Best Answer
You should submit only one version of the paper. Think of the referee as a typical reader, not a judge providing a certificate of correctness. If the referee needs additional information, then other readers will need it too.
Regarding putting a proof in an appendix: There are exceptional cases when this is necessary, but most often it is not, and it can even be annoying to the reader (or seen as a warning sign of a bogus paper!) when important arguments are removed from their context.
Reading a math paper will always be time consuming, but I don't think there is a general convention that proofs should be sketchy. As an inexperienced writer, it is sometimes hard to know when something should be left out, and when leaving it out will be regarded as a gap. Feedback from teachers and supervisors on this matter can be contradictory and confusing. If you feel you still haven't got the knack for it, bear in mind that it is much easier for a referee to ask you to remove details than to figure out when they are missing. I would not endorse any general advice to write sketchy proofs in order to keep the paper short.