[anon_tor_12345]

i read polya's book as an undergrad to my detriment. 10 years later and having "solved" several problems, i can authoritatively say that it is not how difficult problems are solved. the real "how to solve it" for problems that aren't exercises is closer to what feynman said in one of his books: a good physicist [or mathematician] has 5-10 problems on their mind at all times and when they learn of a new technique they apply it to their problem. such learning happens by reading monographs, papers, and going to conferences. that is to say that math (or theoretical physics) is socially produced/developed.