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.

You see all the movies where people say, 'Don't fight out of anger'? They say that for a reason.

That quest for something pretty. A cheat. A cliche. Flowers and Christmas lights, it's what we're programmed to love.

I realize I waited too long but please don't move on.

A creed is an ossified metaphor.

The Holy Roman Empire was neither holy nor Roman nor an empire, the United Nations is a disunited collection of regimes, many of which do not represent the nations they govern.

The size of a person is more important than the size of the problem.

This is what happens in prisons I think you're not giving the prisoners the credit for how ingenious they are.

The wheel of a man's life. No mercy. No pity.

True citizens of the heavenly city are the best residents of the earthly city.