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)

By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.

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.

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.

Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.

Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.