# Siméon Denis Poisson

Siméon Poisson

Siméon Denis Poisson
Born

June 21, 1781
Pithiviers, France

Died April 25, 1840
Nationality French
Alma mater École Polytechnique
Notable students  Michel Chasles
Religious stance atheism

Siméon-Denis Poisson (June 21, 1781 – April 25, 1840) was a French mathematician, geometer, and physicist whose mathematical skills enabled him to compute the distribution of electrical charges on the surface of conductors. He extended the work of his mentors, Pierre Simon Laplace and Joseph Louis Lagrange, in celestial mechanics by taking their results to a higher order of accuracy. He was also known for his work in probability.

## Biography

### Childhood

Poisson was born in Pithiviers, a village just outside of Paris. His father, Simeon Poisson was a jurist. His mother was listed by his biographer and fellow scientist, Francois Arago, as mademoiselle Franchetere.[1] One story from his early years has it that a caretaker used to hang him from a nail so that she could perform errands without worrying about his straying about. In his later years, Poisson jokingly referred to his interest in pendulums as having begun at that stage of his life.[2]

At age 14, Poisson was placed in the care of an uncle who was a surgeon, in the hope that he would take up medicine as a career.[3] This was not to Poisson's liking, for his interests turned increasingly toward mathematics. He attended the École Centrale in Fontainbleau, where he placed first in the entrance examinations to the École Polytechnique in Paris.

### University years

In 1798, he entered the Polytechnique and immediately began to attract the notice of the school professors, 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 Étienne Bézout's method of elimination, the other on the number of integrals of an equation of finite differences. The second memoir was examined by Sylvestre-François Lacroix and Adrien-Marie Legendre, who recommended that it be published in the Recueil des savants étrangers, an unparalleled honor for a youth of eighteen. This success at once procured for Poisson an entry into scientific circles.

Joseph Louis Lagrange, whose lectures on the theory of functions Poisson attended at the École Polytechnique, recognized his talent early on and became his friend. Pierre-Simon Laplace, in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, until his death in Sceaux near Paris, was almost entirely occupied with the composition and publication of his many works, and in discharging the duties of the numerous educational offices to which he was successively appointed.

### Professional life

Immediately after completing his course at the École Polytechnique, he was appointed repetiteur there. He was well prepared for that office, for even when he was a pupil at the school, his comrades often went to his room after an unusually difficult lecture to hear him repeat and explain it. He was excused from his final exams upon taking up this appointment. He was made deputy professor (professeur suppléant) in 1802, and, in 1806, full professor in succession to Jean Baptiste Joseph Fourier, whom Napoleon had sent to Grenoble.

In 1808, Poisson became astronomer to the Bureau des Longitudes. When the Faculté des Sciences was instituted in 1809, he was appointed professor of rational mechanics (professeur de mécanique rationelle). That same year, he also joined the faculty of the College of France. In 1811, he published the first edition of Treatise on Mechanics, which was later translated into English.

To promote his election to the Institute, a competition was established in which contestants were asked to determine the distribution of electricity on the surface of conductors. Poisson solved some of the important problems in this class using a potential function that was later developed by George Green, thus linking his name with electromagnetic theory. Poisson was elected to the Institute in 1812, before the prize could be awarded, thus making him ineligible, after which it was decided not to present an award.

Poisson became examiner at the military school (École Militaire) at Saint-Cyr in 1815, examiner at the École Polytechnique in 1816, councillor of the university in 1820, and geometer to the Bureau des Longitudes in succession to Laplace in 1827.

### Marriage

In 1817, he married Nancy de Bardi, who was English but of French immigrant parents. They had two sons and two daughters.[4] His father, whose early experiences led him to hate aristocrats, bred him in the stern creed of the first republic. Throughout the Revolution, the Empire, and the following restoration, Poisson was not interested in politics, concentrating on mathematics. He was appointed to the dignity of baron in 1821; but he neither took out the diploma nor used the title.

The revolution of July 1830 threatened him with the loss of all his honors. However, this disgrace to the government of Louis-Philippe was adroitly averted by François Jean Dominique Arago, who, while his "revocation" was being plotted by the council of ministers, procured him an invitation to dine at the Palais Royal. There 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. Like many scientists of his time, he was an atheist.

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 equaled. Notwithstanding his many official duties, he found time to publish more than 300 works—several of them were extensive treatises, and many were memoirs dealing with the most abstruse branches of pure mathematics, applied mathematics, mathematical physics, and rational mechanics.

### Scientific work

It was in the application of mathematics to physical subjects that Poisson's 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, and perhaps of equal significance, stand the memoirs on celestial mechanics, in which he proved himself a worthy successor to Pierre-Simon Laplace. The most important of these are his memoirs, Sur les inégalités séculaires des moyens mouvements des planètes and 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. des temps (1821); and Sur le mouvement de la terre autour de son centre de gravité in Mém. d. l'acad. (1827).

In the first of these memoirs, Poisson discusses the famous question of the stability of 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, thus making an important advance in 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, entitled 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.

### Last years

In 1837, Poisson published his "law of large numbers," often referred to as the "Poisson distribution." He used this law of probabilities to analyze the composition of juries and their reliability in returning truthful verdicts. For this purpose, he used French court statistics over a long period of time. His conclusion was that jury decisions should be made by a simple majority vote, which, for a jury of 12 persons, would be 7 to 5.

A year before his death, Poisson's health took a turn for the worse. Although practically an invalid, he continued to attend weekly meetings of the French Academy of Sciences, of which he was president. He was also a foreign member of the Royal Society of London.

Poisson died at 5 a.m. on April 25, 1840, surrounded by members of his family. His funeral was attended by the major figures of French science. The youngest son of the King of France, who had studied under Poisson, was also present[5].

## Contributions

Poisson extended the mathematical investigations of Pierre-Simon Laplace into problems of gravitation and electrical attraction and repulsion.

Poisson's well-known correction of Laplace's partial differential equation of the second degree for the potential:

${\displaystyle {\partial ^{2}\Phi \over \partial x^{2}}+{\partial ^{2}\Phi \over \partial y^{2}}+{\partial ^{2}\Phi \over \partial z^{2}}=-4\pi \rho \;}$

today named, after him, the Poisson's equation or the potential theory equation, was first published in the Bulletin de in société philomatique (1813). This equation basically represents the criteria that must be satisfied for a force field generated by the inverse square laws of gravitation, electricity and magnetism. The potential is a function from which the force fields may be derived.

Poisson's two most important memoirs on the subject are Sur l'attraction des sphéroides (1829), and Sur l'attraction d'un ellipsoide homogène (1835). He also wrote a memoir on the theory of waves (1825).

In pure mathematics, his most important works were his series of memoirs on definite integrals, and his discussion of Fourier series, which paved the way for the classical researches of Peter Gustav Lejeune Dirichlet and Bernhard 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. He also studied Fourier integrals. In addition, it is worth mentioning his essay on the calculus of variations (Mem. de l'acad., 1833), and his memoirs on the probability of the mean results of observations (Connaiss. d. temps, 1827 and later). The Poisson distribution in probability theory is named after him.

In his Traité de mécanique (1811, 1833), written in Laplace and Lagrange style and long a standard work, he showed many new mathematical techniques that influenced later investigators such as William Rowan Hamilton and Carl Gustav Jakob Jacobi.

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, the following may be mentioned:

• Nouvelle théorie de l'action capillaire (1831);
• Théorie mathématique de la chaleur (1835);
• Supplement to the same (1837);
• Recherches sur la probabilité des jugements en matières criminelles et matière civile (1837).

All these were published in Paris.

In 1815, Poisson carried out integrations along paths in the complex plane. In 1831, independently of Claude-Louis Navier, he derived the Navier-Stokes equations dealing with fluid flow.

## Legacy

Poisson represents the tail end of the Enlightenment, a period accompanied by a strong belief that scientific study could solve mankind's problems. He was an atheist, as were many (though not all) of the Enlightenment's leaders. His roots can be traced to Laplace, who said "I do not need this hypothesis," when asked why God was not mentioned in his major work, Celestial Mechanics. Poisson was Laplace's student, and carried on his legacy into many fields, especially mechanics.

The world's disenchantment with the Enlightenment approach became evident with its disdain for mere numerical analyses as determinants of public policy. A realization that a strong political component was an important part of decision-making that could not be reduced to logical analysis also led to its decline. Poisson's last work on probability merely proved what had already been decided without its help: that jury decisions should be made by simple majority.

The Enlightenment, however unbalanced its approach, undoubtedly contributed to the progress of human culture, and Poisson played an important role in furthering the scientific advances represented by that period. His style contrasted markedly with that of his contemporary, André-Marie Ampère, Poisson's competitor in the study of electricity and magnetism, who was led more by inspiration and who possessed a strong spiritual component in his approach to life.

## Notes

1. Arago, 1862, p. 593.
2. Cajori, Florian. 1919. A history of mathematics. New York: The Macmillan Company. 466.
3. Royal Society (Great Britain), Philosophical Transactions (London: Richard Taylor).
4. Arago, 1862, p 659-660.
5. Hacking, 1990, p. 94.

## ReferencesISBN links support NWE through referral fees

• Anonymous. 1840. Obituary: M. Poisson. In The Gentleman's Magazine. London: John Bowyer Nichols and Son.
• Arago, F. and J. A. Barral. 1862. Oeuvres complètes de François Arago. Paris: Gide.
• Benaroya, Haym and Seon Mi Han. 2005. Probability Models in Engineering and Science. Boca Raton: Taylor & Francis. 93-99. ISBN 0824723155
• Hacking, Ian. 1990. The Taming of Chance. Ideas in Context. Cambridge, U.K.: Cambridge University Press. 94-104. ISBN 0521380146
• Hofmann, James R. 1996. André-Marie Ampère. Cambridge Science Biographies Series. Cambridge: Cambridge University Press. ISBN 0521562201
• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.

Awards
Preceded by:
George Biddell Airy
Copley Medal
1832