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Paul Halmos Quotes about Science

All Paul Halmos Quotes Education Knowledge Math Mathematics Science quotes Students
[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

[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 Halmos
Knowledge, Science, Analysis
"Celebrating 50 Years of Mathematics".

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.

Paul Halmos
Math, Science, Errors
"I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

...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 Halmos
Science, Essence, Special

The most 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 Halmos
Memories, Science, Thinking
"PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics".

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
Science, Government, Half
Paul Richard Halmos, John Ewing, F.W. Gehring (1991). “PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics”, p.14, Springer Science & Business Media

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