Top 35 George Pólya Quotes (2025 Update)

1. “It is better to solve one problem five different ways, than to solve five problems one way.”

— George Pólya

Featured in: Problem-Solving Quotes, Different Quotes

2. “Mathematics is not a spectator sport!”

— George Pólya

Featured in: Encouraging Quotes for Students, Problem-Solving Quotes, Teaching Quotes

3. “If there is a problem you can’t solve, then there is an easier problem you can’t solve: find it.”

— George Pólya

Featured in: Problem-Solving Quotes

4. “If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.”

— George Pólya

5. “Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.”

— George Pólya

6. “If you cannot solve the proposed problem try to solve first some related problem.”

— George Pólya

7. “Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself.”

— George Pólya

8. “In order to solve this differential equation you look at it until a solution occurs to you.”

— George Pólya

9. “Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.”

— George Pólya

10. “Beauty in mathematics is seeing the truth without effort.”

— George Pólya

11. “Mathematics consists in proving the most obvious thing in the least obvious way.”

— George Pólya

12. “An idea which can be used once is a trick. If it can be used more than once it becomes a method.”

— George Pólya

13. “The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.”

— George Pólya

14. “I am too good for philosophy and not good enough for physics. Mathematics is in between.”

— George Pólya

15. “A mathematics teacher is a midwife to ideas.”

— George Pólya

16. “Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.”

— George Pólya

17. “It may be more important in the mathematics class how you teach than what you teach.”

— George Pólya

18. “My method to overcome a difficulty is to go round it.”

— George Pólya

19. “The open secret of real success is to throw your whole personality into your problem.”

— George Pólya

20. “A GREAT discovery solves a great problem but there is a grain of discovery in any problem.”

— George Pólya

21. “Geometry is the science of correct reasoning on incorrect figures.”

— George Pólya

22. “The best of ideas is hurt by uncritical acceptance and thrives on critical examination.”

— George Pólya

23. “There exist a lot of questions that the fools can ask, and the intelligent cannot answer.”

— George Pólya

24. “Look around when you have got your first mushroom or made your first discovery: they grow in clusters.”

— George Pólya

25. “The teacher can seldom afford to miss the questions: What is the unknown? What are the data? What is the condition? The student should consider the principal parts of the problem attentively, repeatedly, and from from various sides.”

— George Pólya

26. “When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.”

— George Pólya

27. “The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.”

— George Pólya

28. “The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.”

— George Pólya

29. “Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off to become a poet. Hilbert is reported to have remarked: ‘I never thought he had enough imagination to be a mathematician.’”

— George Pólya

30. “Euclid ’s manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.”

— George Pólya

31. “I am intentionally avoiding the standard term which, by the way, did not exist in Euler’s time. One of the ugliest outgrowths of the “new math” was the premature introduction of technical terms.”

— George Pólya

32. “Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.”

— George Pólya

33. “The result of the mathematician’s creative work is demonstrative reasoning, a proof, but the proof is discovered by plausible reasoning, by GUESSING.”

— George Pólya

34. “What is the difference between method and device? A method is a device which you use twice.”

— George Pólya

35. “John von Neumann was the only student I was ever afraid of.”

— George Pólya

36. “Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.”

— George Pólya

37. “You should not put too much trust in any unproved conjecture, even if it has been propounded by a great authority, even if it has been propounded by yourself. You should try to prove it or disprove it...”

— George Pólya

38. “The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.”

— George Pólya