There is not much utility in memorizing proofs. The primary work should be in trying to understand them. The amount of memorization should be small in math.
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.
You 100% dont have to memorize proofs for that. If you put in work to understand to proof, then you have to remember maybe one tricky step or something like that to reproduce it. Again, just because the proof is on exam does not imply you have to memorize it.
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.
If you use flashcards for learning, you are doing rote learning by definition. There is nothing more rote then making cards and then memorizing their content.
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.