The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

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.

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)

Theory attracts practice as the magnet attracts iron.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.