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Mathematics consists in proving the most obvious thing in the least obvious way.

George Polya

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George Polya
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Look around when you have got your first mushroom or made your first discovery: they grow in clusters.
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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.
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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.
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A mathematics teacher is a midwife to ideas.
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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.
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There exist a lot of questions that the fools can ask, and the intelligent cannot answer.
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When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
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The result of the mathematician's creative work is demonstrative reasoning, a proof but the proof is discovered by plausible reasoning, by guessing.
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It may be more important in the mathematics class how you teach than what you teach.
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The open secret of real success is to throw your whole personality into your problem.
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The principle is so perfectly general that no particular application of it is possible.
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My method to overcome a difficulty is to go round it.
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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.
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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.
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A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.
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If you cannot solve the proposed problem try to solve first some related problem.
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The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
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Beauty in mathematics is seeing the truth without effort.
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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.
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Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.
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