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

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.

In order to solve this differential equation you look at it until a solution occurs to you. George Polya

In order to solve this differential equation you look at it until a solution occurs to you.

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

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

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

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.

Beauty in mathematics is seeing the truth without effort. George Polya

Beauty in mathematics is seeing the truth without effort.

Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice. George Polya

Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.

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

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.

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted. George Polya

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

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

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

If there is a problem you can't solve, then there is an easier problem you can't solve: find it. George Polya

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

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

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.

An idea which can be used once is a trick. If it can be used more than once it becomes a method. George Polya

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

Geometry is the science of correct reasoning on incorrect figures. George Polya

Geometry is the science of correct reasoning on incorrect figures.

Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery. George Polya

Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.

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

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.

Mathematics is not a spectator sport! George Polya

Mathematics is not a spectator sport!

Born: December 13, 1887

Died: September 7, 1985

Profession: Mathematician

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