Paul Halmos Quotes About Mathematics

Quotes about: Mathematics

• The only way to learn mathematics is to do mathematics.

  Paul Halmos

  Learning, Math, Way

• The best way to learn is to do; the worst way to teach is to talk.

  Paul Halmos

  Way, Mathematics, Worst

• 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

  God, Religious, Fun

  Paul Richard Halmos, John Ewing, F.W. Gehring (1991). “PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics”, p.21, Springer Science & Business Media

• Mathematics - this may surprise or shock some - is never deductive in creation.

  Paul Halmos

  Education, Knowledge, Math

• 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

• ...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

• 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.

• 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

  Math, Luck, Taste

• 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

  Heart, Profound, Special

  Paul Richard Halmos (1983). “Selecta: expository writing”, Springer Verlag

• 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

  Truth, Learning, Math

• 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

  Teacher, Teaching, Knowledge

  Paul Richard Halmos (1983). “Selecta: expository writing”, Springer Verlag

• 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

  Education, Knowledge, Math

  P.R. Halmos, Paul Richard Halmos (1982). “A Hilbert Space Problem Book”, p.7, Springer Science & Business Media

• ... 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

  Math, Giving, Lines

• 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

  Education, Teacher, Math

• 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

  Fighting, Example, Doe

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

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

  Paul Halmos

  People, Mathematics, Educated

• Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

  Paul Halmos

  Math, Errors, Trial And Error

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

• The heart of mathematics is its problems.

  Paul Halmos

  Heart, Problem, Mathematics

• 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

  Math, Class, Numbers

• [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".

• The computer is important, but not to mathematics.

  Paul Halmos

  Important, Computer, Mathematics

  Paul Richard Halmos, John Ewing, F.W. Gehring (1991). “PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics”, p.19, Springer Science & Business Media

• Applied mathematics will always need pure mathematics just as anteaters will always need ants.

  Paul Halmos

  Ants, Needs, Mathematics

• 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

  Education, Jobs, Math

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