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Paul R. Halmos
(3 Mar 1916 - 2 Oct 2006)
Hungarian-American mathematician who coined the terms mathologist and mathophysicist to distinguish between pure and applied mathematicians. He wrote several books on mathematics, and his love of communicating it to others won him several awards for his mathematical exposition.
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Science Quotes by Paul R. Halmos (18 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 Want to be a Mathematician: an Automathography in Three Parts (1985), 324.
[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
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 13.
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 R. Halmos
In I Want to be a Mathematician: an Automathography (1985), 123.
I love to do research, I want to do research, I have to do research, and I hate to sit down and begin to do research—I always try to put it off just as long as I can.
— Paul R. Halmos
In I Want to be a Mathematician: an Automathography (1985), 321.
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 R. Halmos
In I Want to be a Mathematician: an Automathography (1985), 37.
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
In I Want to be a Mathematician: An Automathography (1985), 120.
I spent most of a lifetime trying to be a mathematician—and what did I learn. What does it take to be one? 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 R. Halmos
In I Want to be a Mathematician: an Automathography (1985), 400.
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
From interview (1981) with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 3.
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
In I Want to be a Mathematician: an Automathography in Three Parts (1985), 321.
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
In I Want to be a Mathematician: An Automathography (1985), 69.
The computer is important, but not to mathematics.
— Paul R. Halmos
From interview (1981) with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 3.
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
In I Want to be a Mathematician: An Automathography (1985), 3.
The only way to learn mathematics is to do mathematics.
— Paul R. Halmos
In 'Preface', A Hilbert Space Problem Book (1974, 1982), vii.
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
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 9.
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
In I Want to be a Mathematician: An Automathography (1985), 146.
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
In I Want to be a Mathematician: An Automathography (1985), 400.
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
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 21.
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 R. Halmos
In I Want to be a Mathematician: an Automathography (1985), 321.
Quotes by others about Paul R. Halmos (1)
We [Irving Kaplansky and Paul Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free , but when the chips are down we close the office door and compute with matrices like fury.
In Paul Halmos: Celebrating 50 Years of Mathematics (1991), 88.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
