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

Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eye.

Probability theory is nothing but common sense reduced to calculation.

Ce que nous connaissons est peu de chose; ce que nous ignorons est immense. What we know is not much. What we do not know is immense.

To Napoleon on why his works on celestial mechanics make no mention of God: Your Highness, I have no need of this hypothesis.

Truth and justice are the immutable laws of social order.

His last words, according to De Morgan: Man follows only phantoms.

What we know is not much. What we don't know is enormous.

The most important questions of life are indeed, for the most part, really only problems of probability.

Nature laughs at the difficulties of integration.

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.

The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account.

Napoleon: You have written this huge book on the system of the world without once mentioning the author of the universe. Laplace: Sire, I had no need of that hypothesis. Later when told by Napoleon about the incident, Lagrange commented: Ah, but that is a fine hypothesis. It explains so many things.

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 weight of evidence for an extraordinary claim must be proportioned to its strangeness.

Do you believe in god? I have no need for that hypothesis, he may be around though.

The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simple only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws.

The telescope sweeps the sky without finding God.

The word 'chance' then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.

I have lived long enough to know what I did not at one time believe--that no society can be upheld in happiness and honor without the sentiment of religion.

Your Highness, I have no need of this hypothesis.

"Read Euler: he is our master in everything."

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

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.

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

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