The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time.

Probability theory is nothing but common sense reduced to calculation.

Nature laughs at the difficulties of integration.

What we know here is very little, but what we are ignorant of is immense.

It is interesting thus to follow the intellectual truths of analysis in the phenomena of nature. This correspondence, of which the system of the world will offer us numerous examples, makes one of the greatest charms attached to mathematical speculations.

Je n'avais pas besoin de cette hypothèse-là.

All the effects of Nature are only the mathematical consequences of a small number of immutable laws.