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Jules Henri Poincare (1854 –1912) was a French mathematician, theoretical physicist, engineer, and a 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. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincare conjecture, which was one of the most famous unsolved problems in mathematics until it was solved in 2002–2003. In his research on the three-body problem, Poincare 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. Poincare made clear 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. Poincare discovered the remaining relativistic velocity transformations and recorded them in a letter to Dutch physicist Hendrik Lorentz (1853–1928) 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. The Poincare's group used in physics and mathematics was named after him.
Poincare was born on 1854 in Cite Ducale neighborhood, Nancy, Meurthe-et-Moselle into an influential family. His father Leon Poincare (1828–1892) was a professor of medicine at the University of Nancy. His adored younger sister Aline married the spiritual philosopher Emile Boutroux. Another notable member of Jules' family was his cousin, Raymond Poincare, who would become the President of France, 1913 to 1920, and a fellow member of the French Academy. He was raised in the Roman Catholic faith. However, he rejected Christianity in later life and was said to be a deist.
During his childhood he was seriously ill for a time with diphtheria and received special instruction from his mother, Eugenie Launois (1830–1897). In 1862, Henri entered the Lycee in Nancy (now renamed the Lycee Henri Poincare in his honor, along with the University of Nancy). He spent eleven years at the Lycee 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 general, a competition between the top pupils from all the Lycees across France. His poorest subjects were music and physical education, where he was described as "average at best". However, poor eyesight and a tendency towards absentmindedness may explain these difficulties. He graduated from the Lycee 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.
Poincare entered the Polytechnic School in 1873. There he studied mathematics as a student of Charles Hermite, continuing to excel and publishing his first in 1874. He graduated in 1875 or 1876. He went on to study at the Ecole des Mines, continuing to study mathematics in addition to the mining engineering syllabus and received the degree of ordinary engineer in March 1879. As a graduate of theEcole 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, Poincare was preparing for his doctorate in sciences in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. It was named Sur les proprietes des fonctions definies par les equations differences. Poincare 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 realized that they could be used to model the behavior of multiple bodies in free motion within the solar system. Poincare graduated from the University of Paris in 1879.
Soon after, he was offered a post as junior lecturer in mathematics at Caen University, but 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 associate professor of analysis. 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, Poincare was elected to the French Academy of Sciences. He became its president in 1906, and was elected to the French Academy in 1909.
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, Poincare joined the French Bureau des Longitudes, which engaged him in the synchronization of time around the world.
In 1897 Poincare backed an unsuccessful proposal for the decimalization 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 synchronization of time between bodies in relative motion.
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.
In 1912, Poincare 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 Poincare family vault in the Cemetery of Montparnasse, Paris.
A former French Minister of Education, Claude Allegre, has recently (2004) proposed that Poincare be reburied in the Pantheon in Paris, which is reserved for French citizens only of the highest honor. Poincare had two not able doctoral students at the University of Paris, Louis Bachelier (1900) and Dimitrie Pompeiu (1905).
Poincare made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology.
He was also a popularize of mathematics and physics and wrote several books for the lay public.
The problem of finding the general solution to the motion of more than two orbiting bodies in the solar system had eluded mathematicians since Newton's time. This was known originally as the three-body problem and later the n-body problem, where n is any number of more than two orbiting bodies. The n-body solution was considered very important and challenging at the close of the nineteenth century. Indeed in 1887, in honor of his 60th birthday, Oscar II, King of Sweden, advised by Gosta Mittag-Leffler, established a prize for anyone who could find the solution to the problem. The announcement was quite specific: "Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly". In case the problem could not be solved, any other important contribution to classical mechanics would then be considered to be prize worthy. The prize was finally awarded to Poincare, even though he did not solve the original problem. One of the judges, the distinguished Karl Weierstrass, said, "This work cannot indeed be considered as furnishing the complete solution of the question proposed, but that it is nevertheless of such importance that its publication will inaugurate a new era in the history of celestial mechanics". The version finally printed contained many important ideas which led to the theory of chaos. The problem as stated originally was finally solved by Karl F. Sundman for n = 3 in 1912 and was generalized to the case of n > 3 bodies by Qiudong Wang in the 1990s.
Poincare’s work at the Bureau des Longitudes on establishing international time zones led him to consider how clocks at rest on the Earth, which would be moving at different speeds relative to absolute space (or the "luminiferous ether"), could be synchronized. At the same time Dutch theorist Hendrik Lorentz was developing Maxwell's theory into a theory of the motion of charged particles ("electrons" or "ions"), and their interaction with radiation. In 1895 Lorentz had introduced an auxiliary quantity (without physical interpretation) called "local time" and introduced the hypothesis of length contraction to explain the failure of optical and electrical experiments to detect motion relative to the ether (see Michelson–Morley experiment). Poincare was a constant interpreter (and sometimes friendly critic) of Lorentz's theory. Poincare as a philosopher was interested in the "deeper meaning". Thus he interpreted Lorentz's theory and in so doing he came up with many insights that are now associated with special relativity. In The Measure of Time (1898), Poincare said, "A little reflection is sufficient to understand that all these affirmations have by themselves no meaning. They can have one only as the result of a convention". He also argued that scientists have to set the constancy of the speed of light as a postulate to give physical theories the simplest form. Based on these assumptions he discussed in 1900 Lorentz's "wonderful invention" of local time and remarked that it arose when moving clocks are synchronized by exchanging light signals assumed to travel with the same speed in both directions in a moving frame.
He discussed the "principle of relative motion" in two papers in 1900 and named it the principle of relativity in 1904, according to which no physical experiment can discriminate between a state of uniform motion and a state of rest. In 1905 Poincare wrote to Lorentz about Lorentz's paper of 1904, which Poincare described as a "paper of supreme importance". In this letter he pointed out an error Lorentz had made when he had applied his transformation to one of Maxwell's equations, that for charge-occupied space, and also questioned the time dilation factor given by Lorentz. In a second letter to Lorentz, Poincare gave his own reason why Lorentz's time dilation factor was indeed correct after all: it was necessary to make the Lorentz transformation form a group and gave what is now known as the relativistic velocity-addition law. Poincare later delivered a paper at the meeting of the Academy of Sciences in Paris on 5 June 1905 in which these issues were addressed.
Poincare expressed a disinterest in a four-dimensional reformulation of his new mechanics in 1907, because in his opinion the translation of physics into the language of four-dimensional geometry would entail too much effort for limited profit. So it was Hermann Minkowski who worked out the consequences of this notion in 1907.
Like others before, Poincare (1900) discovered a relation between mass and electromagnetic energy. While studying the conflict between the action/reaction principle and Lorentz ether theory, he tried to determine whether the center of gravity still moves with a uniform velocity when electromagnetic fields are included. He noticed that the action/reaction principle does not hold for matter alone, but that the electromagnetic field has its own momentum. Poincare concluded that the electromagnetic field energy of an electromagnetic wave behaves like a fictitious fluid ("fictive fluid") with a mass density of E/c2. If the center of mass frame is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible—it's neither created nor destroyed—then the motion of the center of mass frame remains uniform. But electromagnetic energy can be converted into other forms of energy. So Poincare assumed that there exists a non-electric energy fluid at each point of space, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the center of mass remains uniform. Poincare said that one should not be too surprised by these assumptions, since they are only mathematical fictions. However, Poincare’s resolution led to a paradox when changing frames: if a Hertzian oscillator radiates in a certain direction, it will suffer a recoil from the inertia of the fictitious fluid. Poincare performed a Lorentz boost (to order v/c) to the frame of the moving source. He noted that energy conservation holds in both frames, but that the law of conservation of momentum is violated. This would allow perpetual motion, a notion which he abhorred. The laws of nature would have to be different in the frames of reference, and the relativity principle would not hold. Therefore he argued that also in this case there has to be another compensating mechanism in the ether.
Poincare himself came back to this topic in his St. Louis lecture (1904). This time (and later also in 1908) he rejected the possibility that energy carries mass and criticized the ether solution to compensate the above mentioned problems: The apparatus will recoil as if it were a cannon and the projected energy a ball, and that contradicts the principle of Newton, since our present projectile has no mass; it is not matter, it is energy. [..] Shall we say that the space which separates the oscillator from the receiver and which the disturbance must traverse in passing from one to the other, is not empty, but is filled not only with ether, but with air, or even in inter-planetary space with some sub tile, yet ponder able fluid; that this matter receives the shock, as does the receiver, at the moment the energy reaches it, and recoils, when the disturbance leaves it? That would save Newton's principle, but it is not true. If the energy during its propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown, at least for the air, that there is nothing of the kind. Michelson and Morley have since confirmed this. We might also suppose that the motions of matter proper were exactly compensated by those of the ether; but that would lead us to the same considerations as those made a moment ago. The principle, if thus interpreted, could explain anything, since whatever the visible motions we could imagine hypothetical motions to compensate them. But if it can explain anything, it will allow us to foretell nothing; it will not allow us to choose between the various possible hypotheses, since it explains everything in advance. It therefore becomes useless.
Poincare’s work habits have been compared to a bee flying from flower to flower. Poincare was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.
The mathematician Darboux claimed he was intuitive, arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic. He believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.
Paul Painleve (the visible French mathematician and the politician twice, was the prime minister of France) has estimated Poincare's value for a science so: «He has comprehended all, all has deepened. Possessing extraordinary an innovative mind, he did not know limits to the inspiration, tirelessly laying new ways, and in the abstract world of mathematics repeatedly opened novel areas. Everywhere, where the human mind however it is difficult and thorny only got there was its way - whether it be problems of wireless telegraphy, Rontgen’s rays radiation or a geogenesis - Henri Poincare went beside … Together with the great French mathematician from us the unique person which reason could capture everything that is created by reason of other people has gone, to get into the essence of everything that the human idea has comprehended for today, and to see in it something new».

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