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

In a living civilization there is always an element of unrest, for sensitiveness to ideas means curiosity, adventure, change. Civilized order survives on its merits and is transformed by its power of recognizing its imperfections.

When you're average, you're just as close to the bottom as you are the top.

Art flourishes where there is a sense of adventure, a sense of nothing having been done before, of complete freedom to experiment.

...the self-satisfied dogmatism with which mankind at each period of its history cherishes the delusion of the finality of existing modes of knowledge.

The learned tradition is not concerned with truth, but with the learned adjustment of learned statements of antecedent learned people.

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