Paul Halmos Quotes

#1. The library is the mathematician's laboratory.

Paul Halmos

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

Paul Halmos

#3. 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

#4. 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

#5. 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

#6. 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

#7. 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

#8. 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

#9. Feller was an ebullient man, who would rather be wrong than undecided.

Paul Halmos

#10. The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.

Paul Halmos

#11. 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 converse true? Where does the proof use the hypothesis?

Paul Halmos

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

Paul Halmos

#13. 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

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

Paul Halmos

#15. The only way to learn mathematics is to do mathematics.

Paul Halmos

#16. The heart of mathematics is its problems.

Paul Halmos

#17. The computer is important, but not to mathematics.

Paul Halmos

#18. 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

#19. 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

#20. A clever graduate student could teach Fourier something new, but
surely no one claims that he could teach Archimedes to reason
better.

Paul Halmos

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

Paul Halmos

#22. A smooth lecture ... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.

Paul Halmos

#23. Applied mathematics will always need pure mathematics just as anteaters will always need ants.

Paul Halmos

#24. 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

#25. 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

#26. 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

#27. 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