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

Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.

Geometry is the art of correct reasoning from incorrectly drawn figures.

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

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know

A small error in the former will produce an enormous error in the latter.