Science Fair Project Encyclopedia
Jules Henri Poincaré (April 29, 1854 – July 17, 1912) was one of France's greatest mathematicians, theoretical scientists and a philosopher of science. Poincaré (pronounced (IPA) BrE: ; AmE: [ˌpwɑːŋ kɑː ˈreɪ] ; Fr: [pwæ̃ ka ʁe]) is often described as the last "universalist" capable of understanding and contributing in virtually all parts of mathematics.
He made many original fundamental contributions to mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system and laid the foundations of modern chaos theory. Poincaré anticipated Albert Einstein's work and sketched a preliminary version of the special theory of relativity. The Poincaré group was named after him.
Poincaré was born on April 29, 1854 in Nancy into an influential family, his father Leon was a professor of medicine at the University of Nancy and his cousin Raymond Poincaré was to be the President of France 1913 to 1920. His adored younger sister Aline married the spiritual philosopher Emile Boutroux.
During his childhood he was seriously ill for a time with diphtheria and received special instruction from his gifted mother, Eugénie. He excelled in written composition.
In 1862 Henri entered the Lycée in Nancy (now renamed the Lycée Henri Poincaré in his honour). 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. 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.
Poincaré entered the Ecole Polytechnique in 1873. There he studied mathematics as a student of Charles Hermite, graduating in 1875. He went on to study at the École 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 the École des Mines he joined the Corps des Mines as an inspector for the Vesoul region in north east 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.
Soon after he was offered a post as junior lecturer in mathematics at Caen University. He never fully abandoned his mining career to mathematics however and became chief engineer of the Corps de Mines in 1893 and inspector general in 1910.
He began work on his doctoral thesis, which was in the field of differential equations. Poincaré devised a new way of studying the properties of these functions. 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.
Beginning in 1881 and for the rest of his career, he taught at the University of Paris, (the Sorbonne). There he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy.
In 1885 Oscar II, King of Sweden sponsored a mathematical competition with a cash prize for a resolution of the question of how stable is the solar system, a variation of the three-body problem. While Poincaré did not succeed in giving a complete solution, his work was so impressive that in 1888 he was awarded the prize anyway. Poincaré found that the evolution of such a system is often chaotic in the sense that a small perturbation in the initial state such as a slight change in one body's initial position might lead to a radically different later state. If the slight change isn't detectable by our measuring instruments, then we won't be able to predict which final state will occur. 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."
In 1893 he joined the French Bureau des Longitudes which engaged him in the synchronisation of time around the world. In 1897 he backed an unsuccessful proposal for the decimalisation of circular measure and hence time and longitude. This work led him to consider how clocks moving at high speed with respect to each other could be synchronised. In 1898 in “ The Measure of Time” he formulated the principle of relativity, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest. In collaboration with the Dutch theorist Hendrik Lorentz he went on to push the physics of the time to the limit to explain the behaviour of fast moving electrons. It was Albert Einstein however, who was prepared to reconstruct the entire edifice of physics, who produced the successful new relativity model.
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 anti-Semitic colleagues.
A contemporary biographer and psychologist E Toulouse who had studied him at work observed that Poincaré kept very precise working hours. He undertook mathematical research for four hours a day, between 10 am and noon then again from 5 pm to 7 pm. He would read articles in journals later in the evening. He had an exceptional memory and could recall the page and line of any item in a text he had read. He was also able to remember verbatim things heard by ear. He retained these abilities all his life. His normal work habit was to solve a problem completely in his head, then commit the completed problem to paper. He was ambidextrous and nearsighted. His ability to visualise what he heard proved particularly useful when he attended lectures since his eyesight was so poor that he could not see properly what his lecturers were writing on the blackboard. He was however physically clumsy and artistically inept. He was always in a rush and disliked going back for changes or corrections.
Among the specific topics he contributed to are the following:
- algebraic topology
- the theory of analytic functions of several complex variables
- the theory of abelian functions
- algebraic geometry
- number theory
- the three-body problem
- the theory of diophantine equations
- the theory of electromagnetism
- the special theory of relativity
He was also a populariser of mathematics and physics and wrote several books for the lay public.
He published two major works that placed celestial mechanics on a rigorous mathematical basis:
- New Methods of Celestial Mechanics ISBN 1563961172 (3 vols., 1892-99; Eng. trans., 1967)
- Lessons of Celestial Mechanics. (1905-10).
In popular writings he helped establish the fundamental popular definitions and perceptions of science by these writings:
- Dernières pensées (Eng., "Last Thoughts"); Edition Ernest Flammarion, Paris, 1913.
- Bell, Eric Temple (1986). Men of Mathematics (reissue edition). Touchstone Books. ISBN 0671628186.
- Peterson, Ivars (1995). Newton's Clock: Chaos in the Solar System (reissue edition). W H Freeman & Co. ISBN 0716727242.
- Galison, Peter Louis (2003). Einstein's Clocks, Poincaré's Maps: Empires of Time. Hodder & Stoughton. ISBN 034079447X.
- E. Toulouse, Henri Poincaré, Paris (1910) - (Source biography in French)
- Poincaré conjecture
- Poincaré recurrence theorem
- Wikiquote - Quotes by Henri Poincaré
- A review of Poincaré's mathematical achievements
- A timeline of Poincaré's life (in French)
- Poincaré's 1897 article "The Relativity of Space", English translation
- Henri Poincaré, His Conjecture, Copacabana and Higher Dimensions
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