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Home > Dictionary of Science Quotations > Scientist Names Index H > Paul R. Halmos Quotes

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.

Science Quotes by Paul R. Halmos (7 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.
Science quotes on:  |  Case (64)  |  Concept (102)  |  Concrete (21)  |  Essence (42)  |  Example (57)  |  Frequent (10)  |  Generality (22)  |  Great (300)  |  Instance (18)  |  Mathematics (587)  |  Seeming (9)  |  Small (97)  |  Source (71)  |  Special (51)

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.
Science quotes on:  |  Funding (12)  |  Government (85)  |  Mathematician (177)

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
I Want to be a Mathematician: an Automathography in Three Parts (1985), 321.
Science quotes on:  |  Cliche (6)  |  Deduction (49)  |  Experiment (543)  |  Guesswork (4)  |  Hypothesis (227)  |  List (5)  |  Mathematics (587)  |  Proof (192)  |  Reason (330)  |  Science (1699)  |  Start (68)  |  Theorem (46)  |  Trial And Error (5)

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.
Science quotes on:  |  Computer (84)  |  Mathematics (587)

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.
Science quotes on:  |  Answer (201)  |  Compute (10)  |  Computer (84)  |  Logarithm (4)  |  Mathematician (177)  |  Memory (81)  |  Question (315)  |  Remember (53)  |  Thinking (222)  |  John von Neumann (7)

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.
Science quotes on:  |  God (454)  |  Learn (160)  |  Mathematician (177)  |  Mathematics (587)  |  Secret (98)

[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.
Science quotes on:  |  Architecture (35)  |  Beauty (171)  |  Certainty (97)  |  Glorious (17)  |  Insight (57)  |  Knowledge (1128)  |  Mathematics (587)  |  Security (27)  |  Structure (191)  |  Truth (750)


Carl Sagan Thumbnail 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) -- Carl Sagan
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