Quotes from George Polya

There are many questions which fools can ask that wise men cannot answer.

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

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.

Geometry is the science of correct reasoning on incorrect figures.

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

Mathematics is not a spectator sport!

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

A mathematics teacher is a midwife to ideas.

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

I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.

Beauty in mathematics is seeing the truth without effort.

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

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

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 any problem.

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