"A mathematician who can only generalise is like……" — George Polya
"A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise."
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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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