The Infinite is only a manner of speaking.

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

If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

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.

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

In mathematics there are no true controversies.

Mathematics is the queen of the sciences.