This is a question I have been thinking about for a while, which seems especially important as I hope to transition from undergraduate to graduate study in the next year, where studying for an exam becomes less important and studying for actual learning becomes more important.
I have always been required as part of my degree to learn proofs. Seemingly, basically, just memorising them line-by-line - there might be other methods for answering "prove [random proposition in the lecture notes]" questions, but memorisation is most effective and effectively forced by a tight time limit.
I always thought there had to be a good reason these kind of questions were put - in fact, apparently required by guidelines to be put - in the examinations. Therefore, even when teaching myself maths, I put in the effort to memorise as many proofs of theorems and propositions as I could. This especially seemed useful for maintaining understanding over long periods of time.
Now, I wonder if this was all just a bit of a waste of time. I have read many people commenting here that doing problems is far more useful - "you learn maths by doing it".
Am I wrong? Is there value in memorising proofs (after having read and understood them, not as opposed to skipping them entirely)? Or is this just a waste of time? What about when reading research papers?