"Dont 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? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?"
Paul Richard Halmos was a Hungarian-born American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operator theory, ergodic theory, and functional analysis. He was also recognized as a great mathematical expositor. He has been described as one of The Martians.
"What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up."
"I read once that the true mark of a pro — at anything — is that he understands, loves, and is good at even the drudgery of his profession."
"The author discusses valueless measures in pointless spaces."
"Mathematics is not a deductive science — thats a cliché. When you try to prove a theorem, you dont just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared."
"I like words more than numbers, and I always did."
"I was too near it then to see how shallow it all was..."