How do you choose what exercises & proofs to do?

Question

How do you choose what exercises and proofs to see through? There's so much math to learn that if you proved everything you came across, you might not reach your learning goals. Also, some problems seem more interesting than others, some are too elementary and some would take days.

Answer 1

I try to either prove or find a proof for any theorems used in a subject I am trying to learn. This way, I understand why a theorem is true and I can remember the theorem far more easily than just memorizing the theorem.

Answer 2

I agree with Sujaan Kunalan. Learning and understanding the proof (not memorizing the proof but understanding the idea behind it) helps you remember a theorem because then you really understand it on a deeper level and when you don't remember the theorem it is always good practice to quickly derive it (which is not hard if you remember the idea behind the proof). Deriving it yourself also helps you remember it even better than the first time.