[centimeter]

> It’s much easier to go over something and declare “this makes sense” than it is to come up with that something in the first place.

Obviously, but that’s not what we were talking about. We were comparing memorization to understanding, not inventing to learning.

If you’re good at math, you should be able to re-derive any formula or procedure quickly (up to, say, constant factors) without having to memorize it (after the derivation has been explained to you).

If you run into a problem that you can’t solve because you didn’t drill the steps hard enough, you don’t actually understand the problem. This isn’t necessarily your fault - many math courses teach by symbolic manipulation without the conceptual grounding required to actually re-derive the symbolic procedures yourself. Few students will seek that understanding on their own outside of class, in which case they’re stuck with memorization.

> the reason for Russian/Chinese dominance in certain areas of math was due to how those areas benefitted very much from rote practice.

I think this supports my point - these “certain areas” are small. There is a relative paucity of mathematical/physical innovation from China (especially per capita!). The west still dominates mathematical invention.