Baron
Baron is a rank of nobility or title of honour, often hereditary, in various European countries, either current or historical. The female equivalent is baroness. Typically, the title denotes an aristocrat who ranks higher than a lord or knig ...
Siméon Denis Poisson
FRS FRSE
Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and letters, judged to be "eminently distinguished in their subject". This soci ...
(; 21 June 1781 – 25 April 1840) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity and magnetism, thermodynamics, elasticity, and fluid mechanics. Moreover, he predicted the Poisson spot in his attempt to disprove the wave theory of Augustin-Jean Fresnel, which was later confirmed.
Biography
Poisson was born in
Pithiviers
Pithiviers () is a communes of France, commune in the Loiret Departments of France, department, north central France. It is one of the Subprefectures in France, subprefectures of Loiret. It is twinned with Ashby-de-la-Zouch in Leicestershire, Eng ...
,
Loiret
Loiret (; ) is a department in the Centre-Val de Loire region of north-central France. It takes its name from the river Loiret, which is contained wholly within the department. In 2019, Loiret had a population of 680,434.[< ...]
district in France, the son of Siméon Poisson, an officer in the French army.
In 1798, he entered the
École Polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
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 decisions as to what he would study. In his final year of study, less than two years after his entry, he published two memoirs, one on
Étienne Bézout
Étienne Bézout (; 31 March 1730 – 27 September 1783) was a French mathematician who was born in Nemours, Seine-et-Marne, France, and died in Avon (near Fontainebleau), France.
Work
In 1758 Bézout was elected an adjoint in mechanics of th ...
's method of elimination, the other on the number of
integral
In mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
s of a
finite difference
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for t ...
equation and this was so impressive that he was allowed to graduate in 1800 without taking the final examination
,. The latter of the memoirs was examined by
Sylvestre-François Lacroix and
Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are name ...
, who recommended that it should be published in the ''Recueil des savants étrangers,'' an unprecedented honor for a youth of eighteen. This success at once procured entry for Poisson into scientific circles.
Joseph Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia[Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...](_blank)
, in whose footsteps Poisson followed, regarded him almost as his son. The rest of his career, until his death in
Sceaux near Paris, was 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
A teaching assistant or teacher's aide (TA) or education assistant (EA) or team teacher (TT) is an individual who assists a teacher with instructional responsibilities. TAs include ''graduate teaching assistants'' (GTAs), who are graduate school ...
) there, a position which he had 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
Jean-Baptiste Joseph Fourier (; ; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and ...
, whom Napoleon
Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who ...
had sent to Grenoble
lat, Gratianopolis
, commune status = Prefecture and commune
, image = Panorama grenoble.png
, image size =
, caption = From upper left: Panorama of the city, Grenoble’s cable cars, place Saint- ...
. In 1808 he became astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
to the Bureau des Longitudes; and when the was instituted in 1809 he was appointed a 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 had four 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
In political science, a revolution (Latin: ''revolutio'', "a turn around") is a fundamental and relatively sudden change in political power and political organization which occurs when the population revolts against the government, typically due ...
, the Empire
An empire is a "political unit" made up of several territories and peoples, "usually created by conquest, and divided between a dominant center and subordinate peripheries". The center of the empire (sometimes referred to as the metropole) ex ...
, and the following restoration, Poisson was not interested in politics, concentrating instead on mathematics. He was appointed to the dignity of baron
Baron is a rank of nobility or title of honour, often hereditary, in various European countries, either current or historical. The female equivalent is baroness. Typically, the title denotes an aristocrat who ranks higher than a lord or knig ...
in 1825,[ but he neither took out the diploma nor used the title. In March 1818, he was elected a ]Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
, in 1822 a Foreign Honorary Member of the American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
, and in 1823 a foreign member of the Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special ...
. The revolution of July 1830 threatened him with the loss of all his honours; but this disgrace to the government of Louis-Philippe
Louis Philippe (6 October 1773 – 26 August 1850) was King of the French from 1830 to 1848, and the penultimate monarch of France.
As Louis Philippe, Duke of Chartres, he distinguished himself commanding troops during the Revolutionary Wa ...
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
The Palais-Royal () is a former royal palace located in the 1st arrondissement of Paris, France. The screened entrance court faces the Place du Palais-Royal, opposite the Louvre. Originally called the Palais-Cardinal, it was built for Cardinal ...
, 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
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence for ...
.[
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 equaled. 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
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
, mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
, and rational mechanics. ( Arago attributed to him the quote, "Life is good for only two things: doing mathematics and teaching it.")
A list of Poisson's works, drawn up by himself, is given at the end of Arago's biography. All that is 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
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
and magnetism
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
, 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
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, 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 ''Connaissance des temps
The ''Connaissance des temps'' (English: Knowledge of the Times) is an official yearly publication of astronomical ephemerides in France. Until just after the French Revolution, the title appeared as ''Connoissance des temps'', and for several ye ...
'' (1821), etc.; an
''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 orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
s, 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.[
As a tribute to Poisson's scientific work, which stretched to more than 300 publications, he was awarded a French ]peerage
A peerage is a legal system historically comprising various hereditary titles (and sometimes non-hereditary titles) in a number of countries, and composed of assorted noble ranks.
Peerages include:
Australia
* Australian peers
Belgium
* Belgi ...
in 1837.
His is one of the 72 names inscribed on the Eiffel Tower.
Contributions
Potential theory
Poisson's equation
Poisson's well-known generalization of Laplace's second order partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
for potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
:
is known as Poisson's equation after him, was first published in the ''Bulletin de la société philomatique'' (1813).[ If , we retrieve Laplace's equation
:
If is a ]continuous function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value ...
and if for (or if a point 'moves' to infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions amo ...
) a function goes to 0 fast enough, a solution of Poisson's equation is the Newtonian potential In mathematics, the Newtonian potential or Newton potential is an operator in vector calculus that acts as the inverse to the negative Laplacian, on functions that are smooth and decay rapidly enough at infinity. As such, it is a fundamental object ...
of a function
:
where is a distance between a volume element and a point . The integration runs over the whole space.
Poisson's two most important memoirs on the subject are ''Sur l'attraction des sphéroides'' (Connaiss. ft. temps, 1829), and ''Sur l'attraction d'un ellipsoide homogène'' (Mim. ft. l'acad., 1835).
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
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
in 1839. Poisson's equation is applicable in not just gravitation, but also electricity and magnetism.
Electricity and magnetism
As the eighteenth century came to a close, human understanding of electrostatics approached maturity. Benjamin Franklin
Benjamin Franklin ( April 17, 1790) was an American polymath who was active as a writer, scientist, inventor, statesman, diplomat, printer, publisher, and political philosopher. Encyclopædia Britannica, Wood, 2021 Among the leading inte ...
had already established the notion of electric charge and the conservation of charge
In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is alwa ...
; Charles-Augustin de Coulomb
Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attrac ...
had enunciated his inverse-square law of electrostatics. In 1777, Joseph-Louis Lagrange introduced the concept of a potential function that can be used to compute the gravitational force of an extended body. In 1812, Poisson adopted this idea and obtained the appropriate expression for electricity, which relates the potential function to the electric charge density . Poisson's work on potential theory inspired George Green's 1828 paper, '' An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism''.
In 1820, Hans Christian Ørsted demonstrated that it was possible to deflect a magnetic needle by closing or opening an electric circuit nearby, resulting in a deluge of published papers attempting to explain the phenomenon. Ampère's law and the Biot-Savart law were quickly deduced. The science of electromagnetism was born. Poisson was also investigating the phenomenon of magnetism at this time, though he insisted on treating electricity and magnetism as separate phenomena. He published two memoirs on magnetism in 1826. By the 1830s, a major research question in the study of electricity was whether or not electricity was a fluid or fluids distinct from matter, or something that simply acts on matter like gravity. Coulomb, Ampère, and Poisson thought that electricity was a fluid distinct from matter. In his experimental research, starting with electrolysis, Michael Faraday sought to show this was not the case. Electricity, Faraday believed, was a part of matter.
Optics
Poisson was a member of the academic "old guard" at the Académie royale des sciences de l'Institut de France, who were staunch believers in the particle theory of light
In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass.
They vary greatly in size or quantity, from s ...
and were skeptical of its alternative, the wave theory. In 1818, the Académie set the topic of their prize as diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
. One of the participants, civil engineer and opticist Augustin-Jean Fresnel
Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular th ...
submitted a thesis explaining diffraction derived from analysis of both the Huygens–Fresnel principle
The Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating ...
and Young's double slit experiment.
Poisson studied Fresnel's theory in detail and looked for a way to prove it wrong. Poisson thought that he had found a flaw when he demonstrated that Fresnel's theory predicts an on-axis bright spot in the shadow of a circular obstacle blocking a point source
A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can ...
of light, where the particle-theory of light predicts complete darkness. Poisson argued this was absurd and Fresnel's model was wrong. (Such a spot is not easily observed in everyday situations, because most everyday sources of light are not good point sources.)
The head of the committee, Dominique-François-Jean Arago, performed the experiment. He molded a 2 mm metallic disk to a glass plate with wax. To everyone's surprise he observed the predicted bright spot, which vindicated the wave model. Fresnel won the competition.
After that, the corpuscular theory of light was dead, but was revived in the twentieth century in a different form, wave-particle duality. Arago later noted that the diffraction bright spot (which later became known as both the Arago spot Arago may refer to:
People
* Aragó, a family name of the kings of the Aragonese Crown
* Étienne Arago (1802–1892), French journalist, theater director, and politician; brother of Juan, François, and Jacques
* François Arago (1786–1853), F ...
and the Poisson spot) had already been observed by Joseph-Nicolas Delisle
Joseph-Nicolas Delisle (; 4 April 1688 – 11 September 1768) was a French astronomer and cartographer.
Life
Joseph was born in Paris, one of the 11 sons of Claude Delisle (1644–1720). Like many of his brothers, among them Guillaume Delisle, ...
and Giacomo F. Maraldi a century earlier.
Pure mathematics and statistics
In pure mathematics
Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, ...
, Poisson's most important works were his series of memoirs on definite integrals and his discussion of Fourier series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''p ...
, the latter paving the way for the classic researches of Peter Gustav Lejeune Dirichlet
Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and ...
and Bernhard Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...
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 integral
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
s.
Poisson wrote an essay on the calculus of variations (''Mem. de l'acad.,'' 1833), and memoirs on the probability of the mean results of observations (''Connaiss. d. temps,'' 1827, &c). The Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...
in probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
is named after him.
In 1820 Poisson studied integrations along paths in the complex plane, becoming the first person to do so.
In 1829, Poisson published a paper on elastic bodies that contained a statement and proof of a special case of what became known as the divergence theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the vol ...
.
Mechanics
Analytical mechanics and the calculus of variations
Founded mainly by Leonhard Euler and Joseph-Louis Lagrange in the eighteenth century, the calculus of variations saw further development and applications in the nineteenth.
Letwhere . Then is extremized if it satisfies the Euler–Lagrange equationsBut if depends on higher-order derivatives of , that is, if then must satisfy the Euler–Poisson equation,Poisson'
''Traité de mécanique''
(2 vols. 8vo, 1811 and 1833) was written in the style of Laplace and Lagrange and was long a standard work.
Let be the position, be the kinetic energy, the potential energy, both independent of time . Lagrange's equation of motion readsHere, the dot notation for the time derivative is used, . Poisson set . He argued that if is independent of , he could writegiving He introduced an explicit formula for momenta,Thus, from the equation of motion, he gotPoisson's text influenced the work of William Rowan Hamilton
Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Irela ...
and Carl Gustav Jacob Jacobi
Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasiona ...
. A translation of Poisson'
Treatise on Mechanics
was published in London in 1842. Let and be functions of the canonical variables of motion and . Then their Poisson bracket
In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. Th ...
is given by
Evidently, the operation anti-commutes. More precisely,