The most spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.
Paul HalmosDon't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?
Paul HalmosMathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
Paul HalmosThe beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.
Paul Halmos