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.

Mathematics is the queen of science, and arithmetic the queen of mathematics.

To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

Theory attracts practice as the magnet attracts iron.

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

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