George Polya Quotes

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.

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.

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.

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

Geometry is the science of correct reasoning on incorrect figures.

Mathematics is not a spectator sport!

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

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

John von Neumann was the only student I was ever afraid of.

A mathematics teacher is a midwife to ideas.

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

The open secret of real success is to throw your whole personality into your problem.

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

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

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

What is the difference between method and device? A method is a device which you use twice.

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

There exist a lot of questions that the fools can ask, and the intelligent cannot answer.

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.

Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.

If you cannot solve the proposed problem try to solve first some related problem.

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

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

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

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

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

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.

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.