It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.

The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.

Mathematicians stand on each other's shoulders.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

Does the pursuit of truth give you as much pleasure as before? Surely it is not the knowing but the learning, not the possessing but the acquiring, not the being-there but the getting there that afford the greatest satisfaction. If I have exhausted something, I leave it in order to go again into the dark. Thus is that insatiable man so strange: when he has completed a structure it is not in order to dwell in it comfortably, but to start another.

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.