The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.

Faith in the possibility of science, generated antecedently to the development of modern scientific theory, is an unconscious derivative from medieval theology.

The vitality of thought is in adventure. Ideas won't keep. Something must be done about them. When the idea is new, its custodians have fervor, live for it, and if need be, die for it.

Without adventure civilization is in full decay.

It is not paradox to say that in our most theoretical moods we may be nearest to our most practical applications.

The point about zero is that we do not need to use it in the operation of daily life. No one goes out to buy zero fish.

Without deductive logic science would be entirely useless. It is merely a barren game to ascend from the particular to the general, unless afterwards we can reverse the process and descend from the general to the particular, ascending and descending like angels on Jacob's ladder.