One of the main things I enjoy about MO and MSE is the chance to solve somewhat difficult problems. On a couple of occasions, I've found proofs of results (posed as questions mostly on MSE) which seem original and not entirely trivial. The examples I'm most fond of are short but tricky, not in any way revolutionary, but have a satisfying "aha!" at a crucial point.
Disappointingly, these questions seem to always disappear into the mists of time. While my answers to "soft questions" often get enormously upvoted and see lots of views, those answers to serious questions which actually have some original intellectual content often go largely unnoticed. Once they fall off the top of the question list, they essentially are never seen again.
Perhaps this fate is inevitable, but it seems a shame to let a cool trick die. This has got me wondering whether to try to publish any of these. I'm not a professional mathematician, so this likely would not materially benefit me in any way. The only goal would be to put the results out in a place where they might be of use. The options I know of are:
- Drop it on arxiv.
- Publish in the usual way, in a topical journal.
- Publish a note in an expository journal like American Mathematical Monthly.
- Submit as a problem to a journal that publishes problems.
I've published in the Monthly before, and it seems a good place for small results of broad interest. However, it's not without cost (submitting takes work), it's not totally clear that results published in the Monthly "do any more good" than those rotting in the bowels of MSE, and moreover not all minor results are of sufficiently broad interest for an expository journal to be a viable option anyway.
So my questions are:
- What's the best way(s) (in the sense of "being maximally useful to those who may find them interesting") to disseminate minor mathematical results?
- Is it worth the effort? Or are all minor discoveries bound to languish in obscurity until such time that they are rediscovered and applied to a major result?
- Are there any good rules of thumb to determine what minor results are worthy of dissemination (if any)?
A couple afterthoughts:
- I've noticed stackoverflow doesn't have the same problem with questions not having any later use, presumably because programming questions are more likely to be shared by many people.
- I can give examples of the minor results that inspired this question if requested.
- I think this question should be community wiki, but apparently I'm not allowed to designate it as such myself.