"Mathematics has two faces: it is the rigorous……" — George Polya
"Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself."
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George Polya
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47 Quotes by George Polya
George Polya has 47 quotes on this site.
A few more worth reading:
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Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so…
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The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no…
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The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the…
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The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit…
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Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for…
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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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Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as…
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If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try…
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A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem.…
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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 future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and…
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If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may…
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More Appears Quotes
This quote is filed under Appears Quotes,
one of 1,196 quotes in that category. Here are a few more:
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Power and violence are opposites; where the one rules absolutely, the other is absent. Violence appears where power is in…
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The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes…
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Age appears to be best in four things; old wood best to burn, old wine to drink, old friends to…
— Francis Bacon
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I thought Winston Churchill was a young man of promise, but it appears he is a young man of promises.
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Something very significant appears to be happening in America. There is a dramatic shift in voter affinity toward the GOP,…
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In fact, when care appears, unconditional love often vanishes.
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To a man of pleasure every moment appears to be lost, which partakes not of the vivacity of amusement.
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Isaiah is by far the finest and least objectionable of the seventeen prophets whose supposed productions form the latter part…
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Eloquence, n. The art of orally persuading fools that white is the color that it appears to be. It includes…
— Ambrose Bierce
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The whole world appears to me like a huge vacuum, a vast empty space, whence nothing desirable, or at least…
— David Brainerd
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