I'd like to have a thread to discuss how people approach writing proofs. In short, the reason why I'd like to ask about this is I get repeatedly stuck on exercise proofs, let alone proving existing theorems, so it would be nice to know how others "think" to find their solutions. I'd like to know where and if I could post such a thing. Would it be on meta, on math, or none of the two? And how should I tag it apart from "discussion"?
There already are some posts on the main which might be what you are after. I will list here several which I was able to find in a quick search. (I am making this answer CW - if someone finds other useful posts, feel free to add them.)
Related posts, ordered by id:
I would rather you post the particular problem you're stuck in, since there is a very large variety of exercises and theorems one can prove, and each of them requires a different set of abilities, approaches and ideas. I find it very hard to condense them in one post. As Polya and Szego put it:
General rules which could prescribe in detail the most useful discipline of thought are not known to us. Even if such rules could be formulated, they would not be very useful. Rather than knowing the correct rules of thought theoretically, one must have them assimilated into on'e flesh and blood ready for instant and instinctive use. Therefore, for the schooling of one's powers of thought only the practice of thinking is really useful. The independent solving of challenging problems will aid the reader far more than the aphorisms which follow, although as a start these can do him no harm.