when you take a math contest, you know that 90% of the time, you know all the theorems necessary to solve the problems. The answer is not some obscure fact that you need to have memorized, but instead you know that the solution is right in front of you if you look at it right.

Mathematics is a form of play and self-expression:
https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
#insiderswords