Quotes by Paul Halmos - Page 1

The heart of mathematics is its problems.
Paul Halmos / Mathematician
Heart
Mathematics
Problem
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The library is the mathematician's laboratory.
Paul Halmos / Mathematician
Laboratory
Library
Mathematician
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The computer is important, but not to mathematics.
Paul Halmos / Mathematician
Computer
Important
Mathematics
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The only way to learn mathematics is to do mathematics.
Paul Halmos / Mathematician
Learning
Algebra
Math
Way
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You are allowed to lie a little, but you must never mislead.
Paul Halmos / Mathematician
Littles
Lying
Mislead
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The author discusses valueless measures in pointless spaces.
Paul Halmos / Mathematician
Space
Algebra
Seasoning
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The best way to learn is to do; the worst way to teach is to talk.
Paul Halmos / Mathematician
Mathematics
Way
Worst
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Feller was an ebullient man, who would rather be wrong than undecided.
Paul Halmos / Mathematician
Men
Undecided
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It saddens me that educated people don't even know that my subject exists.
Paul Halmos / Mathematician
Educated
Mathematics
People
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Mathematics - this may surprise or shock some - is never deductive in creation.
Paul Halmos / Mathematician
Education
Knowledge
Math
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Applied mathematics will always need pure mathematics just as anteaters will always need ants.
Paul Halmos / Mathematician
Ants
Mathematics
Needs
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The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.
Paul Halmos / Mathematician
Beginners
Doe
Reading
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Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
Paul Halmos / Mathematician
Errors
Math
Trial And Error
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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 / Mathematician
Education
Knowledge
Math
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When a student comes and asks, "Should I become a mathematician?" the answer should be no. If you have to ask, you shouldn't even ask.
Paul Halmos / Mathematician
Answers
Math
Students
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A clever graduate student could teach Fourier something new, but surely no one claims that he could teach Archimedes to reason better.
Paul Halmos / Mathematician
Clever
Graduates
Students
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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 / Mathematician
Drudgery
Mark
Profession
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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 / Mathematician
Knowledge
Teacher
Teaching
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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 Halmos / Mathematician
Luck
Math
Taste
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A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.
Paul Halmos / Mathematician
Teacher
Challenges
Teaching
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... 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 Halmos / Mathematician
Giving
Lines
Math
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A good stack 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 / Mathematician
Education
Jobs
Math
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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 / Mathematician
Government
Science
Half
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The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.
Paul Halmos / Mathematician
Littles
Self
Today
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Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?
Paul Halmos / Mathematician
Doe
Example
Fighting
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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 / Mathematician
Science
Errors
Math
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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 / Mathematician
Heart
Profound
Special
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...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 / Mathematician
Science
Essence
Special
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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 / Mathematician
God
Fun
Religious
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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 / Mathematician
Learning
Truth
Joy
Math
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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 / Mathematician
Education
Teacher
Math
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[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 / Mathematician
Knowledge
Science
Analysis
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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 Halmos / Mathematician
Class
Math
Numbers
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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 / Mathematician
Science
Memories
Thinking
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