Top 46 Polya Quotes
#1. 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 Polya
#2. 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 Polya
#3. Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.
George Polya
#4. 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 Polya
#5. There is nothing to learn about reasoning and invention if the motive and purpose of the most conspicuous step remain incomprehensible.
George Polya
#6. It is generally useless to carry out details without having seen the main connection, or having made a sort of plan.
George Polya
#7. If you cannot solve the proposed problem try to solve first some related problem.
George Polya
#8. There are many questions which fools can ask that wise men cannot answer.
George Polya
#9. The result of the mathematician's creative work is demonstrative reasoning, a proof, but the proof is discovered by plausible reasoning, by GUESSING.
George Polya
#10. If you can't solve a problem, then there is an easier problem you can solve: find it.
George Polya
#11. Good problems and mushrooms of certain kinds have something in common; they grow in clusters.
George Polya
#12. 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 Polya
#13. It is better to solve one problem five different ways, than to solve five problems one way.
George Polya
#14. When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
George Polya
#16. 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 Polya
#17. Look around when you have got your first mushroom or made your first discovery: they grow in clusters.
George Polya
#18. It may be more important in the mathematics class how you teach than what you teach.
George Polya
#19. 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 Polya
#20. If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.
George Polya
#21. What is the difference between method and device? A method is a device which you use twice.
George Polya
#22. You should be grateful for all new ideas, also for the lesser ones, also for the hazy ones, also for the supplementary ideas adding some precision to a hazy one, or attempting the correction of a less fortunate one.
George Polya
#24. Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.
George Polya
#25. 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 Polya
#26. There exist a lot of questions that the fools can ask, and the intelligent cannot answer.
George Polya
#27. The open secret of real success is to throw your whole personality into your problem.
George Polya
#28. My method to overcome a difficulty is to go round it.
George Polya
#29. John von Neumann was the only student I was ever afraid of.
George Polya
#30. 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 Polya
#31. The principle is so perfectly general that no particular application of it is possible.
George Polya
#32. I am too good for philosophy and not good enough for physics. Mathematics is in between.
George Polya
#33. If there is a problem you can't solve, then there is an easier problem you can't solve: find it.
George Polya
#34. Geometry is the science of correct reasoning on incorrect figures.
George Polya
#35. An idea which can be used once is a trick. If it can be used more than once it becomes a method.
George Polya
#36. Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean [to be] doing mathematics? In the first place, it means to be able to solve mathematical problems.
George Polya
#37. A mathematics teacher is a midwife to ideas.
George Polya
#38. In order to solve this differential equation you look at it till a solution occurs to you.
George Polya
#39. 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 Polya
#40. 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 Polya
#41. Where should I start? Start from the statement of the problem ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.
George Polya
#42. The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
George Polya
#43. 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 Polya
#44. Beauty in mathematics is seeing the truth without effort.
George Polya
#45. Mathematics consists in proving the most obvious thing in the least obvious way.
George Polya
#46. Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.
George Polya
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