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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.

George Polya

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George Polya
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More quotes by George Polya

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There exist a lot of questions that the fools can ask, and the intelligent cannot answer.
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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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Mathematics consists in proving the most obvious thing in the least obvious way.
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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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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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One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.
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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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The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
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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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My method to overcome a difficulty is to go round it.
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If you cannot solve the proposed problem try to solve first some related problem.
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A mathematics teacher is a midwife to ideas.
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The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.
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It may be more important in the mathematics class how you teach than what you teach.
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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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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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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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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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Beauty in mathematics is seeing the truth without effort.
George Polya