Jacques Hadamard quotes:

Logic merely sanctions the conquests of the intuition.

Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle.

The shortest path between two truths in the real domain passes through the complex domain.

The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it.

To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.

Can the existence of a mathematical entity be proved without defining it ?