The secret trick is proving theorems. Prove the Pythagoras theorem or prove that quick sort is indeed a NlogN algorithm (the latter needs some real math skills)

The secret trick is proving theorems. Prove the Pythagoras theorem or prove that quick sort is indeed a NlogN algorithm (the latter needs some real math skills). A proof counts only when you can explain even the most boring detail in the proof. Books on math only tell what proofs and in what order you need to learn. I'd compare math proofs to functions, and understanding of math is a lot like understanding how complex functions work down to assembly level.