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The causes which destroyed the ancient republics were numerous; but in Rome, one principal cause was the vast inequality of fortunes.

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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.

Teacher, Book, Hard Work, Shut, Argument
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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.

Doe, Mathematics, Needs, Paper, Physics, Science

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

Different, Education, Math, Problems, Way, Ways

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.

Mean, Science, Discovery, Challenges, Grain

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

Art, Swimming, Practice, Learn, Piano

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.

Education, Imitate, Imitation, Math, Solve, Swimming
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