AKA use spaced repetition software like Anki or SuperMemo
Also, SRS is no panacea, e.g. you can use it to learn a mathematical formula, but not to learn how to apply it. For this, you need actual practice.
It takes some imagination and experimentation to figure out how to break down subject matters into something you can study with cards.
That mathematician is hardly doing this by rote.
It is also absurd way to learn stuff that has relationships in it.
This was a misconception I, too, had.
When I was taking grad analysis, we had to memorize the proofs, as the professor was guaranteed to ask for the proof of one textbook theorem in each exam. I was incensed, but when I memorized the proofs for the final exam, I noticed more "proof patterns" than I had during the whole semester, and got a lot better at the subject.
Memorizing without understanding is useless. Memorizing with understanding is much better than merely understanding.
Also, way better way to test is to put similar made up theorem on exam. Which means you cant just reproduce what you memorized without understanding.