The Universe is vast. Nothing is more curious than the self-satisfied dogmatism with which mankind at each period of its history cherishes the delusion of the finality of existing modes of knowledge. Skeptics and believers are alike. At this moment scientists and skeptics are the leading dogmatists. Advance in detail is admitted; fundamental novelty is barred. This dogmatic common sense is the death of philosophic adventure.

Civilization advances by extending the number of important operations which we can perform without thinking of them.

Religion is what a person does in his solitariness.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

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

We think of the number "five" as applying to appropriate groups of any entities whatsoever - to five fishes, five children, five apples, five days... We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it

The worship of God is not a rule of safety - it is an adventure of the spirit, a flight after the unattainable.