Hello all, I'm still a math newbie. I'm just about finished with part 1 of Spivak's calculus; this is my first experience with more advanced math / deeper understanding (in high school and college I did well in calculus because I could memorize to perform operations, but I never had to understand why the formulas were the way they were; no proofs were mentioned). Anyway, in doing some of Spivak's proofs, I am 1) Understanding and memorizing the results...for instance, I am rembering if g is continuous at a, and f is continuous at g of a, then f(g(a)) is continuous 2) Most of the results are intuitive to me 3) I am understanding the proofs as I go through them...I am able to logically understand all that he is saying. What I am not able to do, however, is memorize or recreate all the proofs. Some of them are very long and complicated and frankly I dont know how anybody came up with them in the first place. Especially the proof of why a function can't have to limits; the lemma he provides + the proof derived from the lemma are 2 pages of incredibly confusing work arounds to get to the results. And this is only part 1 of spivaks calculus....im sure this stuff is a cake walk for most math majors and it will only get harder from here on out. So my question is, do you math guys all remember/can recreate most proofs? Im not talking about proving something like the triangle inequality, I'm talking about the really complex ones. Is having an intuitive understanding, remembering the outcomes, and following the proofs when I go through them enough?