Just go on . . . and faith will soon return. To a friend hesitant with respect to infinitesimals.

Music that paints nothing is only noise.

Algebra is generous; she often gives more than is asked of her.

Just go on . . . and faith will soon return. To a friend hesitant with respect to infinitesimals.

Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this . . . . The imagination in a mathematician who creates makes no less difference than in a poet who invents. . . . Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.

There are only two kinds of certain knowledge: Awareness of our own existence and the truths of mathematics.