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George Polya Quotes

If there is a problem you can’t solve, then there is an easier problem you can’t solve: find it Picture Quote #1

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 Picture Quote #1

The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time Picture Quote #1

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them Picture Quote #1

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 Picture Quote #1

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 Picture Quote #1

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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 Picture Quote #1

The future mathematician... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line Picture Quote #1

Look around when you have got your first mushroom or made your first discovery: they grow in clusters Picture Quote #1

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 Picture Quote #1

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it Picture Quote #1

Where should I start? Start from the statement of the problem... What can I do? Visualize the problem as a whole as clearly and as vividly as you can... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind Picture Quote #1

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If there is a problem you can’t solve, then there is an easier problem you can’t solve: find it (George Polya Quotes) 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 (George Polya Quotes) The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time (George Polya Quotes) The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them (George Polya Quotes) 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 (George Polya Quotes) 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 Quotes) 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 (George Polya Quotes) The future mathematician... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line (George Polya Quotes) Look around when you have got your first mushroom or made your first discovery: they grow in clusters (George Polya Quotes) 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 (George Polya Quotes) If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it (George Polya Quotes) Where should I start? Start from the statement of the problem... What can I do? Visualize the problem as a whole as clearly and as vividly as you can... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind (George Polya Quotes)

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