George Polya Quotes

• It is better to solve one problem five different ways, than to solve five problems one way.

  George Polya

  Education, Math, Different

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• Resolver problemas es un arte práctico, como nadar, esquiar o tocar el piano: sólo se aprende imitando y practicando.

  George Polya

  Art, Swimming, Practice

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

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• Las matemáticas son la ciencia más barata. A diferencia de la física o la química, no requiere ningún equipo caro. Todo lo que uno necesita para las matemáticas es un lápiz y un papel.

  George Polya

  Science, Doe, Needs

  "Speaking of Science: Notable Quotes on Science, Engineering, and the Environment" by Jon Fripp, Michael Fripp, Deborah Fripp, Newnes (p. 45), 2000.

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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

  Educación, Conocimiento, Matemáticas

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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.

  George Polya

  Mean, Science, Discovery

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• An idea which can be used only once is a trick. If one can use it more than once it becomes a method.

  George Polya

  Math, Ideas, Method

  "Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions".

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• It may be more important in the mathematics class how you teach than what you teach.

  George Polya

  Class, Important, May

  George Polya (1981). “Mathematical Discovery”, John Wiley & Sons Incorporated

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• Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate what other people do with their hands and feet to keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems, and, finally, you learn to do problems by doing them.

  George Polya

  Education, Math, Swimming

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• Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.

  George Polya

  Sides, Problem, Aspect

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

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• 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

  Science, Understanding, Mind

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

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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.

  George Polya

  Swimming, Water, Wish

  George Polya (1981). “Mathematical Discovery”, John Wiley & Sons Incorporated

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• Beauty in mathematics is seeing the truth without effort.

  George Polya

  Education, Math, Effort

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• To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.

  George Polya

  Teacher, Teaching, Math

  George Pólya, Leon Bowden (1977). “Mathematical Methods in Science”, p.1, Cambridge University Press

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• Mathematics is not a spectator sport!

  George Polya

  Sports, Math, Mathematics

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• Incluso los estudiantes bastante buenos, cuando han obtenido la solución del problema y escrito pulcramente el argumento, cierran sus libros y buscan otra cosa. Al hacerlo, se pierden una fase importante e instructiva del trabajo. ... Un buen profesor debe comprender e inculcar a sus alumnos la idea de que ningún problema está completamente agotado.

  George Polya

  Teacher, Book, Hard Work

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• 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

  Truth, Mean, Math

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• When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

  George Polya

  Enseñanza, Matemáticas, Ciencias

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• Soy demasiado bueno para la filosofía y no lo suficiente para la física. Las matemáticas están en medio.

  George Polya

  Philosophy, Math, Not Good Enough

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• The best of ideas is hurt by uncritical acceptance and thrives on critical examination.

  George Polya

  Hurt, Acceptance, Ideas

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

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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

  George Polya

  Hard Work, Science, Lazy

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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.

  George Polya

  Science, Creative, Guessing

  "Induction and Analogy in Mathematics". Book by George Polya, 1954.

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• 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

  Two, Style, Firsts

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

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• Las matemáticas consisten en demostrar lo más obvio de la forma menos obvia.

  George Polya

  Knowledge, Math, Obvious Things

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

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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.

  George Polya

  Educación, Profesor, Enseñanza

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• 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

  Mean, Science, Discovery

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