Henri Poincaré
Jules Henri Poincaré 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", since he excelled in all fields of the discipline as it existed during his lifetime. He has further been called "the Gauss of modern mathematics". Due to his success in science, along with his influence in philosophy, he has also been called "the philosopher par excellence of modern science".
As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. 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. Poincaré is regarded as the creator of the field of algebraic topology, and is further credited with introducing automorphic forms. He also made important contributions to algebraic geometry, number theory, complex analysis and Lie theory. He famously introduced the concept of the Poincaré recurrence theorem, which states that a state will eventually return arbitrarily close to its initial state after a sufficiently long time, which has far-reaching consequences. Early in the 20th century he formulated the Poincaré conjecture, which became, over time, one of the famous unsolved problems in mathematics. It was eventually solved in 2002–2003 by Grigori Perelman. Poincaré popularized the use of non-Euclidean geometry in mathematics as well.
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, for which he is also credited with laying down the foundations, further writing foundational papers in 1905. He first proposed gravitational waves emanating from a body and propagating at the speed of light as being required by the Lorentz transformations, doing so in 1905. In 1912, he wrote an influential paper which provided a mathematical argument for quantum mechanics. Poincaré also laid the seeds of the discovery of radioactivity through his interest and study of X-rays, which influenced physicist Henri Becquerel, who then discovered the phenomena. The Poincaré group used in physics and mathematics was named after him, after he introduced the notion of the group.
Poincaré was considered the dominant figure in mathematics and theoretical physics during his time, and was the most respected mathematician of his time, being described as "the living brain of the rational sciences" by mathematician Paul Painlevé. Philosopher Karl Popper regarded Poincaré as the greatest philosopher of science of all time, with Poincaré also originating the conventionalist view in science. Poincaré was a public intellectual in his time, and personally, he believed in political equality for all, while wary of the influence of anti-intellectual positions that the Catholic Church held at the time. He served as the president of the French Academy of Sciences, the president of Société astronomique de France, and twice the president of Société mathématique de France.
Life
Poincaré was born on 29 April 1854 in Cité Ducale neighborhood, Nancy, Meurthe-et-Moselle, into an influential French family. His father was a professor of medicine at the University of Nancy. His younger sister Aline married the spiritual philosopher Émile Boutroux. Another notable member of Henri's family was his cousin, Raymond Poincaré, a fellow member of the Académie française, who was President of France from 1913 to 1920, and three-time Prime Minister of France between 1913 and 1929.Education
During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugénie Launois.In 1862, Henri entered the Lycée 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". Poor eyesight and a tendency towards absentmindedness may explain these difficulties. He graduated from the Lycée in 1871 with a baccalauréat in both letters and sciences.
During the Franco-Prussian War of 1870, he served alongside his father in the Ambulance Corps.
Poincaré entered the École Polytechnique as the top qualifier in 1873 and graduated in 1875. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first paper 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.
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.
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. He graduated from the University of Paris in 1879.
First scientific achievements
After receiving his degree, Poincaré began teaching as junior lecturer in mathematics at the University of Caen in Normandy. 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 Poulain d'Andecy, granddaughter of Isidore Geoffroy Saint-Hilaire and great-granddaughter of Étienne Geoffroy Saint-Hilaire and on 20 April 1881, they married. Together they had four children: Jeanne, Yvonne, Henriette, and Léon.
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 1883 to 1897, he taught mathematical analysis in the 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. He successfully used this approach to problems in celestial mechanics and mathematical physics.
Career
He never fully abandoned his career in the mining administration 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 des 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. He was initially appointed as the maître de conférences d'analyse. Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, 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, to honorary membership of the Manchester Literary and Philosophical Society, in 1892, 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.
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. 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.
In 1904, he intervened in the trials of Alfred Dreyfus, attacking the spurious scientific claims regarding evidence brought against Dreyfus.
Poincaré was the President of the Société Astronomique de France, the French astronomical society, from 1901 to 1903.
Students
Poincaré had two notable doctoral students at the University of Paris, Louis Bachelier and Dimitrie Pompeiu.Death
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, in section 16, close to the Rue Émile-Richard.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 of the highest honour.