Paul Halmos

“"Paul Halmos: A Life in Mathematics" at Mathematical Association of America (MAA)”

“{{MacTutor Biography|id=Halmos}}”

“I was too near it then to see how shallow it all was...”

“It takes a long time to learn to live — by the time you learn your time is gone.”

“I like words more than numbers, and I always did.”

“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.”

“Don'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? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?”

“Mathematics is not a deductive science — that's a cliché. When you try to prove a theorem, you don't 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.”

“The author discusses valueless measures in pointless spaces.”

“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.”