I protest against the use of infinite magnitude ..., which is never permissible in mathematics.

I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.

My young friend, I wish that science would intoxicate you as much as our good Göttingen beer! Upon seeing a student staggering down a street.

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.

You have no idea, how much poetry there is in the calculation of a table of logarithms!

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

Theory attracts practice as the magnet attracts iron.