Pierre-Simon Laplace (1749–1827) stands as one of the towering intellects of modern science. A mathematician, astronomer, and physicist of extraordinary range, he made foundational contributions to celestial mechanics, potential theory, and probability. His formulation of inverse probability—arrived at independently of Bayes—was far more general and systematic, and it was Laplace's work, not Bayes', that established probabilistic reasoning as a tool of mainstream science for over a century.
Early Life and Rise
Born in Beaumont-en-Auge, Normandy, to a family of modest means, Laplace's mathematical genius was recognized early. He studied at the University of Caen before traveling to Paris at age nineteen, where he impressed d'Alembert sufficiently to secure a position at the École Militaire. His prodigious output in celestial mechanics and probability theory quickly established him as one of the leading mathematicians in Europe.
Inverse Probability and the Rule of Succession
In his 1774 Mémoire sur la probabilité des causes par les événements, Laplace formulated what we now call Bayes' theorem in a general form, apparently without knowledge of Bayes' essay. He applied uniform prior distributions to unknown parameters and derived posterior distributions using integration—a technique far beyond what Bayes had attempted. His famous Rule of Succession states that if an event has occurred n times in n trials, the probability it occurs next is (n+1)/(n+2), a result that sparked both admiration and controversy.
“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.”— Pierre-Simon Laplace, Théorie analytique des probabilités (1812)
Théorie Analytique des Probabilités
Laplace's magnum opus in probability, Théorie analytique des probabilités (1812), accompanied by the popular Essai philosophique sur les probabilités (1814), was a monumental synthesis. It contained the central limit theorem, generating functions, the method of least squares justified probabilistically, and a comprehensive treatment of inverse probability applied to astronomy, demography, and jurisprudence. For Laplace, probability was the language in which all uncertain reasoning should be conducted.
Laplace famously imagined an intellect vast enough to know the position and momentum of every particle in the universe, for whom “nothing would be uncertain and the future, as the past, would be present to its eyes.” This thought experiment, while illustrating determinism, also underscores why Laplace saw probability as a measure of human ignorance rather than an intrinsic feature of nature.
Applications in Astronomy and Beyond
Laplace applied his probabilistic methods extensively in his astronomical work, particularly in the five-volume Mécanique céleste. He used inverse probability to estimate planetary masses, to analyze the stability of the solar system, and to combine multiple astronomical observations. His approach to combining observations laid groundwork that would later evolve into the method of least squares and, eventually, modern Bayesian estimation.
Political Life and Later Years
Laplace navigated the turbulent politics of revolutionary and Napoleonic France with remarkable skill. He served briefly as Minister of the Interior under Napoleon, was made a Count of the Empire, and later a Marquis under the Restoration. He continued publishing until late in life, dying in Paris in 1827.
Born in Beaumont-en-Auge, Normandy.
Published his memoir on inverse probability, independently deriving Bayes' theorem in general form.
Proved the stability of the solar system using perturbation theory.
Published the five volumes of Mécanique céleste.
Published Théorie analytique des probabilités.
Published Essai philosophique sur les probabilités.
Died in Paris on 5 March.