(I am aware that some people might frown on this question, but I had no place to ask; this will definitely be voted to be closed in SE. I apologize in advance.)
I am currently a 1st year grad student and I would like to ask for your advice on how to study math. I am wondering to what extent do I have to understand proofs in the lecture. I understand what is going on in the lecture, but if someone asks me to regenerate proof, then I cannot do it. To be more specific, if the proof solely consists of a bunch of inequalities, it is unlikely that I can regenerate proof; on the other hand, if the proof relies on one good idea, then I can provide key insight behind the proof even though I cannot provide a complete proof. I keep practicing until I can redo the proof by myself, but this has been too exhaustive and time-consuming.
Also, I forgot a lot of proofs in undergraduate math; for example, I don’t remember how to prove L’hospital’s rule (even though I recall that it uses mean value theorem), and it feels bad to be using the theorem without remembering the proof. Ideally, I would like to remember every proof I do, but I am not smart enough for it. Can anyone provide a tip and share your experience how you handled this?