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

Mathematics is concerned only with the enumeration and comparison of relations.

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)

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

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.

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.