Paul Halmos Quotes

26 quotes in 441 categories

• To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.
• 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…
• [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,…
• 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…
• ...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…
• The computer is important, but not to mathematics.
• 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.
• The only way to learn mathematics is to do mathematics.
• The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both…
• 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,…
• Mathematics - this may surprise or shock some - is never deductive in creation.
• The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method, ...
• 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…
• The best way to learn is to do; the worst way to teach is to talk.
• Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the…
• It saddens me that educated people don't even know that my subject exists.
• Mathematics is not a deductive science, that's a cliché ... What you do is trial and error, experimentation, guesswork.
• The heart of mathematics is its problems.
• 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 author discusses valueless measures in pointless spaces.

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