Paul R. Halmos
(3 Mar 1916  2 Oct 2006)

Science Quotes by Paul R. Halmos (12 quotes)
...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
— Paul R. Halmos
I remember one occasion when I tried to add a little seasoning to a review, but I wasn’t allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: “The author discusses valueless measures in pointless spaces.”
— Paul R. Halmos
If the NSF had never existed, if the government had never funded American mathematics, we would have half as many mathematicians as we now have, and I don't see anything wrong with that.
— Paul R. Halmos
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, experiment and guesswork.
— Paul R. Halmos
Study actively. 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?
— Paul R. Halmos
The computer is important, but not to mathematics.
— Paul R. Halmos
The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me—both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.
— Paul R. Halmos
The 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 R. Halmos
The student skit at Christmas contained a plaintive line: “Give us Master’s exams that our faculty can pass, or give us a faculty that can pass our Master’s exams.”
— Paul R. Halmos
To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.
— Paul R. Halmos
What’s the best part of being a mathematician? I'm not a religious man, but it’s almost like being in touch with God when you’re thinking about mathematics. God is keeping secrets from us, and it’s fun to try to learn some of the secrets.
— Paul R. Halmos
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. … They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That’s what mathematics is to me.
— Paul R. Halmos
Quotes by others about Paul R. Halmos (1)
We [Irving Kaplansky and Paul Halmos] share a philosophy about linear algebra: we think basisfree, we write basisfree , but when the chips are down we close the office door and compute with matrices like fury.