Henri Poincaré

Henri Poincaré
PSM V82 D416 Henri Poincare.png
Henri Poincaré
(photograph published in 1913)
Born(1854-04-29)29 April 1854
Died17 July 1912(1912-07-17) (aged 58)
Other namesJules Henri Poincaré
EducationLycée Nancy (now Lycée Henri-Poincaré [fr])
Alma mater
Known for
Scientific career
FieldsMathematics and physics
Sur les propriétés des fonctions définies par les équations différences (1879)
Doctoral advisorCharles Hermite
Doctoral students
Other notable students
Henri Poincaré Signature.svg
He was an uncle of Pierre Boutroux.

Jules Henri Poincaré (/;[2] French: [ɑ̃ʁi pwɛ̃kaʁe] (About this soundlisten);[3][4] 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist,"[5] since he excelled in all fields of the discipline as it existed during his lifetime.

As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics.[6] He was responsible for formulating the Poincaré conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003 by Grigori Perelman. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.

Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Hendrik Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformations.

The Poincaré group used in physics and mathematics was named after him.


Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle into an influential family.[7] His father Leon Poincaré (1828–1892) was a professor of medicine at the University of Nancy.[8] His younger sister Aline married the spiritual philosopher Emile Boutroux. Another notable member of Henri's family was his cousin, Raymond Poincaré, a fellow member of the Académie française, who would serve as President of France from 1913 to 1920.[9]


Plaque on the birthplace of Henri Poincaré at house number 117 on the Grande Rue in the city of Nancy.

During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois (1830–1897).

In 1862, Henri entered the Lycée in Nancy (now renamed the Lycée Henri-Poincaré [fr] in his honour, along with Henri Poincaré University, also in Nancy). He spent eleven years at the Lycée and during this time he proved to be one of the top students in every topic he studied. He excelled in written composition. His mathematics teacher described him as a "monster of mathematics" and he won first prizes in the concours général, a competition between the top pupils from all the Lycées across France. His poorest subjects were music and physical education, where he was described as "average at best".[10] However, poor eyesight and a tendency towards absentmindedness may explain these difficulties.[11] He graduated from the Lycée in 1871 with a bachelor's degree in letters and sciences.

During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps.

Poincaré entered the École Polytechnique in 1873 and graduated in 1875. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper (Démonstration nouvelle des propriétés de l'indicatrice d'une surface) in 1874. From November 1875 to June 1878 he studied at the École des Mines, while continuing the study of mathematics in addition to the mining engineering syllabus, and received the degree of ordinary mining engineer in March 1879.[12]

As a graduate of the École des Mines, he joined the Corps des Mines as an inspector for the Vesoul region in northeast France. He was on the scene of a mining disaster at Magny in August 1879 in which 18 miners died. He carried out the official investigation into the accident in a characteristically thorough and humane way.

At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les propriétés des fonctions définies par les équations aux différences partielles. Poincaré devised a new way of studying the properties of these equations. He not only faced the question of determining the integral of such equations, but also was the first person to study their general geometric properties. He realised that they could be used to model the behaviour of multiple bodies in free motion within the solar system. Poincaré graduated from the University of Paris in 1879.

The young Henri Poincaré

First scientific achievements

After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy (in December 1879). At the same time he published his first major article concerning the treatment of a class of automorphic functions.

There, in Caen, he met his future wife, Louise Poulin d'Andesi (Louise Poulain d'Andecy) and on 20 April 1881, they married. Together they had four children: Jeanne (born 1887), Yvonne (born 1889), Henriette (born 1891), and Léon (born 1893).

Poincaré immediately established himself among the greatest mathematicians of Europe, attracting the attention of many prominent mathematicians. In 1881 Poincaré was invited to take a teaching position at the Faculty of Sciences of the University of Paris; he accepted the invitation. During the years of 1883 to 1897, he taught mathematical analysis in École Polytechnique.

In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics.


He never fully abandoned his mining career to mathematics. He worked at the Ministry of Public Services as an engineer in charge of northern railway development from 1881 to 1885. He eventually became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.

Beginning in 1881 and for the rest of his career, he taught at the University of Paris (the Sorbonne). He was initially appointed as the maître de conférences d'analyse (associate professor of analysis).[13] Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability[14], and Celestial Mechanics and Astronomy.

In 1887, at the young age of 32, Poincaré was elected to the French Academy of Sciences. He became its president in 1906, and was elected to the Académie française on 5 March 1908.

In 1887, he won Oscar II, King of Sweden's mathematical competition for a resolution of the three-body problem concerning the free motion of multiple orbiting bodies. (See three-body problem section below.)

The Poincaré family grave at the Cimetière du Montparnasse

In 1893, Poincaré joined the French Bureau des Longitudes, which engaged him in the synchronisation of time around the world. In 1897 Poincaré backed an unsuccessful proposal for the decimalisation of circular measure, and hence time and longitude.[15] It was this post which led him to consider the question of establishing international time zones and the synchronisation of time between bodies in relative motion. (See work on relativity section below.)

In 1899, and again more successfully in 1904, he intervened in the trials of Alfred Dreyfus. He attacked the spurious scientific claims of some of the evidence brought against Dreyfus, who was a Jewish officer in the French army charged with treason by colleagues.

Poincaré was the President of the Société Astronomique de France (SAF), the French astronomical society, from 1901 to 1903.[16]


Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905).[17]


In 1912, Poincaré underwent surgery for a prostate problem and subsequently died from an embolism on 17 July 1912, in Paris. He was 58 years of age. He is buried in the Poincaré family vault in the Cemetery of Montparnasse, Paris.

A former French Minister of Education, Claude Allègre, proposed in 2004 that Poincaré be reburied in the Panthéon in Paris, which is reserved for French citizens only of the highest honour.[18]

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