Earlier quoted context omitted.
The great grandparent to your post (the one who initially brought up the necessity of rote learning) is a quant at a market maker. Anecdotally, my favorite professor from undergrad (born in China, PhD from the best department in his field [my personal opinion]) said he thought the reason for Russian/Chinese dominance in certain areas of math was due to how those areas benefitted very much from rote practice. He advis…
+1 on the drilling specific techniques. Any skill is reinforced by consistent targeted practice, and to think that math is an exception where you can break through with pure genius is just deluding yourself. The only way I got through my undergrad math was by doing problem set after problem set until the concepts were second nature, and the courses that didn't have a sufficient breadth of exercises to drive home fund…
Applying derivations that someone else invented doesn’t require “pure genius”; it only requires you to be able to follow the person who discovered it, which is a lot easier than finding it yourself.
> The only way I got through my undergrad math was by doing problem set after problem set
It sounds like you didn’t really understand what you were doing then. It’s hard to phrase this without just sounding like I’m bragging, but I never had to practice doing anything I actually understood. If I felt like I needed practice, that was a sure sign I didn’t get it, which I always tried to fix with careful thinking instead of repetitive memorization