There are no solved problems; there are only problems that are more or less solved.

Mathematics is the art of giving the same name to different things.

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.

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.

If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living

It may happen that small differences in the initial conditions produce very great ones in the final phenomena.