Hitler Learns Topology

Memorization is crucial for a subject like math. In a highly technical branch of math like, say, topology, definitions fly at one like bvllets from a m@chine gun. Just to solve a problem you might need immediate access in your head to some 12 definitions, 5 lemmas, 3 theorems, 4 corollaries and 6 prototype/canonical examples meaning you want to keep them all(along with their proofs as proofs carry important techniques and ideas) at the tip of your tongue and top of your head. Just because you "understood" them once in the past doesn't mean much if you cannot recall them immediately right where you need them. Obviously, you can look them up one by one (granted you know what you're looking for). Along the way, you'd have to re-understand them cause understanding is often fleeting in math, but this will make you lose time, momentum and get/keep you stuck in a thick quagmire making the original problem massively more difficult than it is. Many very important results in math (that have become staples) are made up of extremely specific techniques that are very hard to reproduce even after 5 minutes one has read (and presumably understood) them. Even understanding in math comes in waves. To get a deeper understanding of an idea you'd need to have some preliminary grasp on it. I often see the sentiment "in math if you understand something, you don't need to memorize it" on English speaking side of Internet. Contrast that with the old Soviet school (& modern Indian one?) philosophy wh