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Bad rules. My suggestions ask yourself the following all the time 1) Do I ~really~ understand what the definition / theorem is supposed to tell me. 2) A proof is just a reason why something is true in maths. Do you understand ~why~ a statement is true? 3) Exercise all the time. You won't learn math by memorizing definitions, theorems and proofs.

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How is this disagreeing with the OP? It specifically says that memorizing e.g. theorems is bad.

If you're in grad school taking qualifying exams, memorizing theorems is required. There's just too much stuff to digest. Undergrads and younger students have ample time to learn mathematics with serious depth. This is not true for the average math grad student. The comfort you had in learning mathematics as a youngling just instantly disappears when you get to grad school. This is painful, but you have to learn to accept that you won't be competent at all the mathematics you are exposed to. Some very fine mathematicians experience this.

Rote memorization is of course not enough but you need to remember relevant theorems. It's necessary but not sufficient for deeper understanding.

What would it even mean to "understand" a theorem but to be unable to state it (and prove it)?

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