Paul Halmos Quotes

On this page you can find the TOP of Paul Halmos's best quotes! We hope you will find some sayings from Mathematician Paul Halmos's in our collection, which will inspire you to new achievements! There are currently 34 quotes on this page collected since March 3, 1916! Share our collection of quotes with your friends on social media so that they can find something to inspire them!
  • The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.

  • 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.

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

  • 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.

    Math  
    "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.
  • 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 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 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 Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics".
  • The heart of mathematics is its problems.

  • 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 Richard Halmos (1983). “Selecta: expository writing”, Springer Verlag
  • The computer is important, but not to 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
  • [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.

    "Celebrating 50 Years of Mathematics".
  • Mathematics - this may surprise or shock some - is never deductive in creation.

  • 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.

  • 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?

    "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.
  • 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 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
  • The only way to learn mathematics is to do mathematics.

    Math  
  • Feller was an ebullient man, who would rather be wrong than undecided.

  • 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.

    Math  
  • 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 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.

    P.R. Halmos, Paul Richard Halmos (1982). “A Hilbert Space Problem Book”, p.7, Springer Science & Business Media
  • To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

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

  • 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.

    "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.
  • Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

    Math  
    "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.
  • A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.

  • ... 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."

    Math  
  • The library is the mathematician's laboratory.

  • You are allowed to lie a little, but you must never mislead.

  • ...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.

  • 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."

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

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  • We hope you have found the saying you were looking for in our collection! At the moment, we have collected 34 quotes from the Mathematician Paul Halmos, starting from March 3, 1916! We periodically replenish our collection so that visitors of our website can always find inspirational quotes by authors from all over the world! Come back to us again!

    Paul Halmos

    • Born: March 3, 1916
    • Died: October 2, 2006
    • Occupation: Mathematician