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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.

George Polya

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George Polya
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Euclid
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More quotes by George Polya

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Beauty in mathematics is seeing the truth without effort.
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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.
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A mathematics teacher is a midwife to ideas.
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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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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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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
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The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
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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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Mathematics consists in proving the most obvious thing in the least obvious way.
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If you cannot solve the proposed problem try to solve first some related problem.
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Geometry is the science of correct reasoning on incorrect figures.
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It may be more important in the mathematics class how you teach than what you teach.
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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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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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My method to overcome a difficulty is to go round it.
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The principle is so perfectly general that no particular application of it is possible.
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The open secret of real success is to throw your whole personality into your problem.
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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.
George Polya
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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.
George Polya
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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.
George Polya