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 which was "understand -> drill -> memorize". IMO, the former philosophy produces weaker, barely able mathematicians.
This vid below about Hitler learning topology echoes some of what's typed above.
I remember a math grad student friend who said "math is a young man's game". He compared it to cycling; nothing you do in your old age would compare to what you could do earlier.
In fact according to him math is worse than cycling, if I'm correct that cyclists peak in their early 40s. Contrast that to economics, which specifically offers the Clark Medal for the best work performed by someone under forty, because old-timers would otherwise snaffle up every prize.
People repeat that quote a lot, but I don't think there's much evidence for it. The main thing is people have kids, and kids take time. Boom 10 years gone from high-performance productive individual-contributor work. It was uncommon for people to go back to school at a later age, but maybe not anymore?
That's fair. I didn't relate that my friend went on to say that the reason math is a young man's game is that it's only the young who can read and memorize results fast enough, and keep enough of that information in their head at one time, to do important work at the frontiers of math. The brain has physical limits, just as the rest of the body does.
I am revolted by that idea. And I'm certainly a better coder than I was in my thirties, and I was better then than I was in my twenties. (Not that I'm under the illusion that my work compares to PhD-level math.)
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 which was "understand -> drill -> memorize". IMO, the former philosophy produces weaker, barely able mathematicians.
This vid below about Hitler learning topology echoes some of what's typed above.
https://www.youtube.com/watch?v=SyD4p8_y8Kw