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Top 20 Paul Halmos Quotes (2025 Update)

Paul Halmos Quote: “The only way to learn mathematics is to do mathematics.”

1. “The only way to learn mathematics is to do mathematics.”

— Paul Halmos

Featured in: Study Quotes, Practice Quotes, Teaching Quotes, Math Quotes

Paul Halmos Quote: “The best way to learn is to do; the worst way to teach is to talk.”

2. “The best way to learn is to do; the worst way to teach is to talk.”

— Paul Halmos

Paul Halmos Quote: “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?”

3. “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

Paul Halmos Quote: “The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.”

4. “The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.”

— Paul Halmos

Paul Halmos Quote: “The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method,...”

5. “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

Paul Halmos Quote: “To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.”

6. “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

Paul Halmos Quote: “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.”

7. “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

Paul Halmos Quote: “Applied mathematics will always need pure mathematics just as anteaters will always need ants.”

8. “Applied mathematics will always need pure mathematics just as anteaters will always need ants.”

— Paul Halmos

Paul Halmos Quote: “The library is the mathematician’s laboratory.”

9. “The library is the mathematician’s laboratory.”

— Paul Halmos

Paul Halmos Quote: “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.”

10. “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

Paul Halmos Quote: “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.”

11. “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

Paul Halmos Quote: “You are allowed to lie a little, but you must never mislead.”

12. “You are allowed to lie a little, but you must never mislead.”

— Paul Halmos

Paul Halmos Quote: “Mathematics – this may surprise or shock some – is never deductive in creation.”

13. “Mathematics – this may surprise or shock some – is never deductive in creation.”

— Paul Halmos

Paul Halmos Quote: “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.”

14. “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

Paul Halmos Quote: “The author discusses valueless measures in pointless spaces.”

15. “The author discusses valueless measures in pointless spaces.”

— Paul Halmos

Paul Halmos Quote: “In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some and here it is; read it, absorb it, and forget it.”

16. “In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some and here it is; read it, absorb it, and forget it.”

— Paul Halmos

Paul Halmos Quote: “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.”

17. “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

Paul Halmos Quote: “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.”

18. “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

Paul Halmos Quote: “The computer is important, but not to mathematics.”

19. “The computer is important, but not to mathematics.”

— Paul Halmos

Paul Halmos Quote: “Feller was an ebullient man, who would rather be wrong than undecided.”

20. “Feller was an ebullient man, who would rather be wrong than undecided.”

— Paul Halmos

Paul Halmos Quote: “It saddens me that educated people don’t even know that my subject exists.”

21. “It saddens me that educated people don’t even know that my subject exists.”

— Paul Halmos

Paul Halmos Quote: “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.”

22. “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

Paul Halmos Quote: “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.”

23. “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

Paul Halmos Quote: “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.”

24. “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

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