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In Recherchés sur la probabilité des jugements en matière criminelle et matière civile, an important work on  probability published in 1837, the Poisson distribution first appears. The Poisson distribution describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. He also introduced the expression "law of large numbers". Although we now rate this work as of great importance, it found little favour at the time, the exception being in Russia where  Chebyshev developed his ideas.

It is interesting that Poisson did not exhibit the chauvinistic attitude of many scientists of his day.  Lagrange and  Laplace recognised  Fermat as the inventor of the differential and integral calculus; he was French after all while neither  Leibniz nor  Newton were! Poisson, however, wrote in 1831:-

This [differential and integral] calculus consists in a collection of rules ... rather than in the use of infinitely small quantities ... and in this regard its creation does not predate  Leibniz, the author of the algorithm and of the notation that has generally prevailed.

He published between 300 and 400 mathematical works in all. Despite this exceptionally large output, he worked on one topic at a time.  Libri writes []:-

Poisson never wished to occupy himself with two things at the same time; when, in the course of his labours, a research project crossed his mind that did not form any immediate connection with what he was doing at the time, he contented himself with writing a few words in his little wallet. The persons to whom he used to communicate his scientific ideas know that as soon as he had finished one memoir, he passed without interruption to another subject, and that he customarily selected from his wallet the questions with which he should occupy himself. To foresee beforehand in this manner the problems that offer some chance of success, and to be able to wait before applying oneself to them, is to show proof of a mind both penetrating and methodical.

Poisson's name is attached to a wide variety of ideas, for example:- Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity. However, he was not highly regarded by other French mathematicians either during his lifetime or after his death. His reputation was guaranteed by the esteem that he was held in by foreign mathematicians who seemed more able than his own colleagues to recognise the importance of his ideas. Poisson himself was completely dedicated to mathematics.  Arago reported that Poisson frequently said:-

Life is good for only two things: to study mathematics and to teach it.

J J O'Connor and E F Robertson

Список литературы

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