Poisson, born the son of a local government administrator at Pithiviers in France, studied at the Ecole Polytechnique, where his teachers included Pierre Simon Laplace and Joseph Lagrange. He himself later held various teaching posts at the Ecole. His important mathematical work was largely in mathematical physics and he also did a considerable amount of experimental work on heat and sound. In thermodynamics he played an important role in making the whole subject amenable to mathematical treatment by showing how to quantify heat precisely. He is also one of the principal founders of the mathematical theory of elasticity.

Poisson is possibly best known for his work on probability, and he was something of a pioneer in applying the techniques of mathematical probability to the social sciences, something that was extremely controversial at the time. The term ‘law of large numbers’ was introduced by Poisson in his seminal work, Recherches sur la probabilité des jugements (1837; Researches on the Probability of Opinions), in which he put forward his discovery of the Poisson distribution. This is the distribution that is a special case of the binomial distribution obtained when the probability of success in a given trial is some constant divided by the number of trials.

Although chiefly an applied mathematician Poisson also made some significant contributions to pure mathematics, in particular to complex analysis. It was Poisson who first thought of integrating complex functions along a path in the complex plane.