Paul Halmos’s “automathography”, I Want to be a Mathematician, contains plenty of good advice for those in the early stages of a mathematical career — even though the career path it describes has changed since Halmos’s day. Here’s his advice on how to read a theorem:
Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
Actually, this is how a mathematician should read any piece of writing that’s trying to convince them of anything. (This is why mathematicians are so unpopular, and so necessary, on university committees…)