This is sort of a general question but how does a mathematician do his/her work? Specifically, does he try to memorize every theorem he comes across or just the important ones? (If the latter, how does he say which are more important?) If he uses a reference book of some sort daily to do his work, then what exactly does he learn by going to school to learn all of this for, if he can just as easily look it up (I've gotten the idea that he learns some kind of "mathematical maturity" but what exactly is this)? Well, I've got a lot more questions but my biggest one is whether a mathematician tries to memorize all the (important) theorems he comes across and how he decides which are important.