# Poisson, Siméon-Denis

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[pwasõ] (1781–1840) French mathematician: contributed to electrostatics, magnetostatics, probability theory and complex analysis.

Poisson’s talent in creative mathematics was recognized by while he was at the École Polytechnique. He had begun training as a surgeon, but found he had neither taste nor talent for the work. In 1800 he was appointed to a post at the École. Poisson’s mathematical contributions were to mathematical physics, and he added to this by conducting experiments in sound and heat. He developed the theory of heat and elasticity (Poisson’s ratio is the ratio between the lateral and longitudinal strain in a wire).

In 1812 Poisson adopted an early ‘two-fluid’ theory of electricity which was later superseded. He used potential function, originally applied in gravitation, and showed that it could be used for electrostatic problems. Using a suggestion by he used the technique to prove the formula for the force at the surface of a charged conductor, and to solve for the first time the charge distribution on two spherical conductors a given distance apart experimental results were in close accord with Poisson’s formula.

His paper of 1824 constructed a ‘two-fluid’ theory of magnetism, and expressed the magnetic potential at any point as a sum of volume and surface integrals of magnetic contributions (magnetostatics).

Poisson built upon Laplace’s work in probability theory. Poisson’s formula gives the probability of a given number of events if its probability is low, and it has wide applicability. The Poisson distribution, which is related to this, was later shown to be a special case of the general binomial distribution. Poisson also wrote an important memoir in 1833 on the Moon’s motion.

In pure mathematics he advanced complex analysis, being the first person to integrate complex functions along paths or contours in the complex plane (now called contour integration).

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