Paul Halmos Quotes

19 Sourced Quotes

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 Halmos
A teacher who is not always thinking about solving problems — ones he does not know the answer to — is psychologically simply not prepared to teach problem solving to his students.

Paul Halmos
It saddens me that educated people don't even know that my subject exists.

Paul Halmos
A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.

Paul 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 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 Halmos
Many people think of mathematics itself as a static art — a body of eternal truth that was discovered by a few ancient, shadowy figures, and upon which engineers and scientists can draw as needed.

Paul Halmos
Pure mathematics can be practically useful and applied mathematics can be artistically elegant.

Paul Halmos
It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

Paul Halmos
The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.

Paul Halmos
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.

Paul 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, 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.

Paul Halmos
Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

Paul Halmos
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method,...

Paul Halmos
Don't just read it; fight it! Ask your own question, look for your own examples, dicover 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 Halmos
The best way to learn is to do; the worst way to teach is to talk.

Paul Halmos
The author discusses valueless measures in pointless spaces.

Paul Halmos
André Weil suggested that there is a logarithmic law at work: first-rate people attract other first-rate people, but second-rate people tend to hire third-raters, and third-rate people hire fifth-raters. If a dean or a president is genuinely interested in building and maintaining a high-quality university (and some of them are), then he must not grant complete self-determination to a second-rate department; he must, instead, use his administrative powers to intervene and set things right. That's one of the proper functions of deans and presidents, and pity the poor university in which a large proportion of both the faculty and the administration are second-raters; it is doomed to diverge to minus infinity.

Paul Halmos
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.

Paul Halmos