"If the proof starts from axioms, distinguishes several……" — George Polya
"If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way."
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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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In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the…
See all 47 quotes by George Polya »
More Axioms Quotes
This quote is filed under Axioms Quotes,
one of 41 quotes in that category. Here are a few more:
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I tell you the solemn truth, that the doctrine of the Trinity is not so difficult to accept for a…
— Henry Adams
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There are and can be only two ways of searching into and discovering truth. The one flies from the senses…
— Francis Bacon
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My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove…
— Isaac Newton
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The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of…
— Kurt Gödel
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I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of…
— David Hilbert
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If there are such things as political axioms, the propriety of the judicial power of a government being co-extensive with…
— Alexander Hamilton
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Yet Gotama's Dhamma is more than just a series of axioms. It is to be lived rather than simply adopted…
— Stephen Batchelor
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Based on the considerations of history, ancient history, and international axioms, the logic of following up a citizen with his…
— Saddam Hussein
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Freedom can be manifested only in the void of beliefs, in the absence of axioms, and only where the laws…
— Emile M. Cioran
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It is not enough merely to memorize and spout vocal axioms good singing is infinitely more than much talk and…
— Jerome Hines
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You can go through your whole life telling yourself that life is logical, life is prosaic, life is sane. Above…
— Stephen King
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Underlying the preaching of the Puritans are three basic axioms: 1. The unique place of preaching is to convert, feed…
— J I Packer
See all 41 Axioms Quotes »