Explore Quotes by George Polya

Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off to become a poet. Hilbert is reported to have remarked: 'I never thought he had enough imagination to be a mathematician.'

The principle is so perfectly general that no particular application of it is possible.

Epitaph on Newton: Nature and Nature's law lay hid in night: God said, "Let Newton be!," and all was light. [added by Sir John Collings Squire: It did not last: the Devil shouting "Ho. Let Einstein be," restored the status quo] [Aaron Hill's version: O'er Nature's laws God cast the veil of night, Out blaz'd a Newton's soul and all was light.

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 has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

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.

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

I am too good for philosophy and not good enough for physics. Mathematics is in between.

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

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

Mathematics is not a spectator sport!

Mathematics consists in proving the most obvious thing in the least obvious way.

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

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.

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.

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

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.

Beauty in mathematics is seeing the truth without effort.

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.

My method to overcome a difficulty is to go round it.

Geometry is the science of correct reasoning on incorrect figures.