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.

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

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

To the distracting occupations belong especially my lecture courses which I am holding this winter for the first time, and which now cost much more of my time than I like. Meanwhile I hope that the second time this expenditure of time will be much less, otherwise I would never be able to reconcile myself to it, even practical (astronomical) work must give far more satisfaction than if one brings up to B a couple more mediocre heads which otherwise would have stopped at A.

Ask her to wait a moment - I am almost done.

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

Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.