I figured from learning proofs back in high school that there are a limited number of approaches one can tackle a Mathematical proof problem, at least for textb

I figured from learning proofs back in high school that there are a limited number of approaches one can tackle a Mathematical proof problem, at least for textbook problems. You just have to be familiar with each of them, that is to work on many problems of the same method, to obtain an intuition. Of course this probably does not help with very tough questions that require out of the box thoughts, but I think it still helps.