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

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

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

It is through science that we prove, but through intuition that we discover.

If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.

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?

In the old days when people invented a new function they had something useful in mind.