TITLE: How to study a math text
QUESTION [6 upvotes]: Hello,
recently I've been trying various attempts regarding how to approach a math book to learn in the best way. Should one memorize the theorems and proofs so that one can recite them? I tend to sometimes forget proofs and such after some time, so my question is the following.
When you're trying to learn from a book and it's a new subject, how do you usually do? Do you learn all theorems and proofs? Do you write it down? Or do you just read? This is a general question, I'm aware of that, I do however hope that this question will fit the community.

REPLY [2 votes]: I am a big believer in learning by exploration: It builds independence and confidence... something you need if you plan to pursue further your math journey. That means when you find an interesting result or theorem in a book, explore it's consequences, see the details of the proof, etc. It helps your understanding.
Most important when learning math: do a lot of exercises. If possible, do a lot of difficult ones. Really, do them, there is no learning if don't get your hands dirty! Don't expect to solve every single difficult problem you try, but seriously, trying them will help you tremendously. As a rule of thumb, I never spend more that half an hour on a problem, unless it's really something very motivating. 
And last: Life is sequence of choices, and exploration takes time, a lot of it!
Which means: you learn much faster by reading (and paying attention to what you read, they call it focus), but you don't master something unless you get your hands dirty, as I said.