I am a master student in mathematics. For me a large part of doing mathematics is thinking about, reading and verifying the proof of theorems that I find them in my field of study. I can do this action in 3 ways:

- When I see a theorem I get a paper and think to prove it: this action takes time a lot and maybe I couldn't prove it after thinking for a lot of time.
- Finding the proof of the theorem in a book or in the internet and begin reading, going step by step with proof,understanding and verifying all steps: this action may takes time a lot and maybe it is not necessary that I read all steps and it's better that I jump from not important steps (but how I can find that a step is not important?).
- Finding the proof of the theorem and just read it like reading a newspaper for finding the sketch of the proof: this action is good because of its speed but maybe there be some important details in the proof that I couldn't see them in this type of reading.

My questions:

- What is the way that famous mathematicians like Fields medalists take for reading the proofs usually?
- Which way is the the best for which proofs? (For example classifying proofs and saying that the first way is good for the first class and...)

doesn'tread proofs. He simplywritesthem. $\endgroup$ – Fan Zheng Apr 13 '15 at 16:29