For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics.

Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

Point set topology is a disease from which the human race will soon recover.

Chance ... must be something more than the name we give to our ignorance.

It is by logic we prove. It is by intuition we discover.

The mind uses its faculty for creativity only when experience forces it to do so.