The vitality of thought is in adventure. Idea's won't keep. Something must be done about them. When the idea is new, its custodians have fervour, live for it, and, if need be, die for it. Their inheritors receive the idea, perhaps now strong and successful, but without inheriting the fervour; so the idea settles down to a comfortable middle age, turns senile, and dies.

Algebra reverses the relative importance of the factors in ordinary language.

It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profundity, he is talking nonsense.

Philosophy asks the simple question: What is it all about?

For successful education there must always be a certain freshness in the knowledge dealt with. It must be either new in itself or invested with some novelty of application to the new world of new times. Knowledge does not keep any better than fish. You may be dealing with knowledge of the old species, with some old truth; but somehow it must come to the students, as it were, just drawn out of the sea and with the freshness of its immediate importance.

Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.

When success turns a man's head he faces failure