Without any doubt, the regularity which astronomy shows us in the movements of the comets takes place in all phenomena. The trajectory of a simple molecule of air or vapour is regulated in a manner as certain as that of the planetary orbits; the only difference between them is that which is contributed by our ignorance. Probability is relative in part to this ignorance, and in part to our knowledge.

I see with much pleasure that you are working on a large work on the integral Calculus ... The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.

The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.

If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.

Probability theory is nothing but common sense reduced to calculation.

Nature laughs at the difficulties of integration.

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