Siméon-Denis Poisson (1781–1840)

French mathematician, born at Pithiviers in the department of Loiret, on the 21st of June 1781. His father, Siméon Poisson, served as a common soldier in the Hanoverian wars; but, disgusted by the ill-treatment he received from his patrician officers, he deserted. About the time of the birth of his son, Siméon Denis, he occupied a small administrative post at Pithiviers, and seems to have been at the head of the local government of the place during the revolutionary period. Poisson was first sent to an uncle, a surgeon at Fontainebleau, and began to take lessons in bleeding and blistering, but made little progress. Having given promise of mathematical talent he was sent to the École Centrale of Fontainebleau, and was fortunate in having a kind and sympathetic teacher, M. Billy, who, when he speedily found that his pupil was becoming his master, devoted himself to the study of higher mathematics in order to follow and appreciate him, and predicted his future fame by the punning quotation from La Fontaine:— 1

	“Petit Poisson deviendra grand
	Pourvu que Dieu lui prête vie.”

In 1798 he entered the École Polytechnique at Paris as first in his year, and immediately began to attract the notice of the professors of the school, who left him free to follow the studies of his predilection. In 1800, less than two years after his entry, he published two memoirs, one on É. Bezout’s method of elimination, the other on the number of integrals of an equation of finite differences. The latter of these memoirs was examined by S. F. Lacroix and A. M. Legendre, who recommended that it should be published in the Recueil des savants étrangers, an unparalleled honour for a youth of eighteen. This success at once procured for Poisson an entry into scientific circles. J. L. Lagrange, whose lectures on the theory of functions he attended at the École Polytechnique, early recognized his talent, and became his friend; while P.-S. Laplace, in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, till his death on the 25th of April 1840, was almost entirely occupied in the composition and publication of his many works, and in discharging the duties of the numerous educational offices to which he was successively appointed. Immediately after finishing his course at the École Polytechnique he was appointed repetiteur there, an office which he had discharged as an amateur while still a pupil in the school; for it had been the custom of his comrades often to resort to his room after an unusually difficult lecture to hear him repeat and explain it. He was made professeur suppléant in 1802, and full professor in succession to J. Fourier in 1806. In 1808 he became astronomer to the Bureau des Longitudes; and when the Faculté des Sciences was instituted in 1809 he was appointed professeur de la mécanique rationelle. He further became member of the Institute in 1812, examiner at the military school at St. Cyr in 1815, leaving examiner at the École Polytechnique in 1816, councillor of the university in 1820, and geometer to the Bureau des Longitudes in succession to P.-S. Laplace in 1827. His father, whose early experiences led him to hate aristocrats, bred him in the stern creed of the first republic. Throughout the empire Poisson faithfully adhered to the family principles, and refused to worship Napoleon. When the Bourbons were restored, his hatred against Napoleon led him to become a Legitimist—a conclusion which says more for the simplicity of his character than for the strength or logic of his political creed. He was faithful to the Bourbons during the Hundred Days; in fact, was with difficulty dissuaded from volunteering to fight in their cause. After the second restoration his fidelity was recognized by his elevation to the dignity of baron in 1825; but he never either took out his diploma or used the title. The revolution of July 1830 threatened him with the loss of all his honours; but this disgrace to the government of Louis Philippe was adroitly averted by F. Arago, who, while his “revocation” was being plotted by the council of ministers, procured him an invitation to dine at the Palais Royale, where he was openly and effusively received by the citizen king, who “remembered” him. After this, of course, his degradation was impossible, and seven years later he was made a peer of France, not for political reasons, but as a representative of French science.

  As a teacher of mathematics Poisson is said to have been more than ordinarily successful, as might have been expected from his early promise as a repetiteur at the École Polytechnique. As a scientific worker his activity has rarely if ever been equalled. Notwithstanding his many official duties, he found time to publish more than three hundred works, several of them extensive treatises, and many of them memoirs dealing with the most abstruse branches of pure and applied mathematics. There are two remarks of his, or perhaps two versions of the same remark, that explain how he accomplished so much: one, “La vie n’est bonne qu’à deux choses—à faire des mathématiques et à les professeur”; the other, “La vie c’est le travail.”

  A list of Poisson’s works, drawn up by himself, is given at the end of Arago’s biography. A lengthened analysis of them would be out of place here, and all that is possible is a brief mention of the more important. There are few branches of mathematics to which he did not contribute something, but it was in the application of mathematics to physical subjects that his greatest services to science were performed. Perhaps the most original, and certainly the most permanent in their influence, were his memoirs on the theory of electricity and magnetism, which virtually created a new branch of mathematical physics. Next (perhaps in the opinion of some first) in importance stand the memoirs on celestial mechanics, in which he proved himself a worthy successor to P.-S. Laplace. The most important of these are his memoirs “Sur les inégalités séculaires des moyens mouvements des planètes,” “Sur la variation des constantes arbitraires dans les questions de mécanique,” both published in the Journal of the École Polytechnique (1809); “Sur la libration de la lune,” in Connaiss. d. temps (1821), &c.; and “Sur la mouvement de la terre autour de son centre de gravité,” in Mém. d. l’acad. (1827), &c. In the first of these memoirs Poisson discusses the famous question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces. Poisson showed that the result could be extended to a second approximation, and thus made an important advance in the planetary theory. The memoir is remarkable inasmuch as it roused Lagrange, after an interval of inactivity, to compose in his old age one of the greatest of his memoirs, viz., that Sur la théorie des variations des éléments des planètes, et en particulier des variations des grands axes de leurs orbites. So highly did he think of Poisson’s memoir that he made a copy of it with his own hand, which was found among his papers after his death. Poisson made important contributions to the theory of attraction. His well-known correction of Laplace’s partial differential equation for the potential was first published in the Bulletin de la société philomatique (1813). His two most important memoirs on the subject are “Sur l’attraction des sphéroides” (Connaiss. d. temps, 1829), and “Sur l’attraction d’un ellipsoide homogène” (Mém. d. l’acad., 1835). In concluding our selection from his physical memoirs we may mention his memoir on the theory of waves (Mém. d. l’acad., 1825).

  In pure mathematics, his most important works were his series of memoirs on definite integrals, and his discussion of Fourier’s series, which paved the way for the classical researches of L. Dirichlet and B. Riemann on the same subject; these are to be found in the Journal of the École Polytechnique from 1813 to 1823, and in the Memoirs de l’académie for 1823. In addition we may also mention his essay on the calculus of variations (Mém. d. l’acad., 1833), and his memoirs on the probability of the mean results of observations (Connaiss. d. temps, 1827, &c.).

  Besides his many memoirs Poisson published a number of treatises, most of which were intended to form part of a great work on mathematical physics, which he did not live to complete. Among these may be mentioned his Traité de mécanique (2 vols. 8vo, 1811 and 1833), which was long a standard work; Théorie nouvelle de l’action cappillaire (4to, 1831); Théorie mathématique de la chaleur (4to, 1835); Supplément to the same (4to, 1837); Recherches sur la probabilité des jugements en matières criminelles, &c. (4to, 1837), all published at Paris.

  See F. Arago, Biographie de Poisson, read before the Académie des Sciences on the 16th of December 1850.