Analytic Theory of Probability

work by Laplace

Also known as: “Théorie analytique des probabilités”

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July 14, 2026

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The Analytic Theory of Probability is a seminal work by Pierre-Simon, marquis de Laplace, published in 1812. It introduced mathematical tools for predicting the probabilities of natural events. Laplace applied these theories not only to games of chance but also to understanding phenomena, vital statistics, and future occurrences, highlighting their significance in physics and astronomy. A key contribution was his demonstration of the central limit theorem, showing that large samples of astronomical observation errors approximate a normal distribution. This work built upon earlier developments in probability theory, including Bayes's theorem, and aimed to establish probability as a foundation for the moral sciences.12

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Pierre-Simon, marquis de Laplace
…Théorie analytique des probabilités (Analytic Theory of Probability), first published in 1812, in which he described many of the tools he invented for mathematically predicting the probabilities that particular events will occur in nature. He applied his theory not only to the ordinary problems of chance but also to…
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…Théorie analytique des probabilités (Analytic Theory of Probability), first published in 1812, in which he described many of the tools he invented for mathematically predicting the probabilities that particular events will occur in nature. He applied his theory not only to the ordinary problems of chance but also to…
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normal distribution
Pierre-Simon Laplace, in his Théorie analytique des probabilités (1812; “Analytic Theory of Probability”), into the first central limit theorem, which proved that probabilities for almost all independent and identically distributed random variables converge rapidly (with sample size) to the area under an exponential function—that is, to a normal distribution.…
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Pierre-Simon Laplace, in his Théorie analytique des probabilités (1812; “Analytic Theory of Probability”), into the first central limit theorem, which proved that probabilities for almost all independent and identically distributed random variables converge rapidly (with sample size) to the area under an exponential function—that is, to a normal distribution.…
Read More