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

I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.

Sin² φ is odious to me, even though Laplace made use of it; should it be feared that sin² φ might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin(φ²), well then, let us write (sin φ)², but not sin² φ, which by analogy should signify sin (sin φ)

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.

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