Everything about Simeon Poisson totally explained
Siméon-Denis Poisson (
June 21,
1781 –
April 25,
1840), was a
French mathematician,
geometer, and
physicist. The name is in
French.
Biography
Poisson was born in
Pithiviers, south of Paris.
In 1798, he entered the
École Polytechnique in
Paris as first in his year, and immediately began to attract the notice of the professors of the school, who left him free to make his own choices as to what he'd study. 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 a
finite difference equation. The latter was examined by
Sylvestre-François Lacroix and
Adrien-Marie Legendre, who recommended that it should be published in the
Recueil des savants étrangers, an unprecedented honour for a youth of eighteen. This success at once procured entry for Poisson into scientific circles.
Joseph Louis Lagrange, whose lectures on the theory of functions he attended at the École Polytechnique, recognized his talent early on, and became his friend (the
Mathematics Genealogy Project lists Lagrange as his advisor, but this may be an approximation); while
Pierre-Simon Laplace, in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, till his death in
Sceaux near Paris, was almost entirely occupied by the composition and publication of his many works and in fulfilling the duties of the numerous educational positions to which he was successively appointed.
Immediately after finishing his studies at the École Polytechnique, he was appointed
répétiteur (teaching assistant) there, a position which he'd occupied as an amateur while still a pupil in the school; for his schoolmates had made a custom of visiting him in his room after an unusually difficult lecture to hear him repeat and explain it. He was made deputy professor (
professeur suppléant) in 1802, and, in 1806 full professor succeeding
Jean Baptiste Joseph Fourier, whom Napoleon had sent to
Grenoble. In 1808 he became
astronomer to the
Bureau des Longitudes; and when the
Faculté des Sciences was instituted in 1809 he was appointed professor of
rational mechanics (
professeur de mécanique rationelle). He went on to become a member of the Institute in 1812, examiner at the military school (
École Militaire) at
Saint-Cyr in 1815, graduation examiner at the École Polytechnique in 1816, councillor of the university in 1820, and geometer to the Bureau des Longitudes succeeding Pierre-Simon Laplace in 1827.
In 1817, he married Nancy de Bardi and with her he'd [several?] children. His father, whose early experiences had 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 wasn't interested in politics, concentrating on mathematics. He was appointed to the dignity of
baron in 1821; but he neither took out the 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
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, 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.
Like many scientists of his time, he was an
atheist.
As a teacher of mathematics Poisson is said to have been extraordinarily successful, as might have been expected from his early promise as a
répétiteur at the École Polytechnique. As a scientific worker, his productivity 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 mathematics,
applied mathematics,
mathematical physics, and rational mechanics.
A list of Poisson's works, drawn up by himself, is given at the end of Arago's biography. All that's possible is a brief mention of the more important ones. It was in the application of mathematics to physics 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 (or in the opinion of some, first) in importance 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,
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
Connaissances des temps (1821), etc.; and
Sur le mouvement de la terre autour de son centre de gravité, in
Mémoires de l'Académie (1827), etc. 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
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.
Contributions
Poisson's well-known correction of Laplace's second order
partial differential equation for
potential:
»
today named after him
Poisson's equation or the
potential theory equation, was first published in the Bulletin de la société philomatique (1813). If a function of a given point ρ = 0, we get
Laplace's equation:
»
In 1812 Poisson discovered that Laplace's equation is valid only outside of a solid. A rigorous proof for masses with variable density was first given by
Carl Friedrich Gauss in 1839. Both equations have their equivalents in
vector algebra. Poisson's equation for the
divergence of the gradient of a
scalar field, φ in 3-dimensional space is:
»
Consider for instance Poisson's equation for surface
electrical potential, Ψ as a function of the density of
electric charge, ρ
e at a particular point:
»
which influenced the work of
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 didn't live to complete. Among these may be mentioned
- Nouvelle théorie de l'action capillaire (4to, 1831);
- Théorie mathématique de la chaleur (4to, 1835);
- Supplement to the same (4to, 1837);
- Recherches sur la probabilité des jugements en matières criminelles et matière civile (4to, 1837), all published at Paris. A translation of Poisson's Treatise on Mechanics
was published in London in 1842.
In 1815 Poisson studied integrations along paths in the complex plane. In 1831 he derived the
Navier-Stokes equations independently of
Claude-Louis Navier.
Further Information
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