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Poincaré, Jules Henri

theory functions relativity linear

[pwikaray] (1854–1912) French mathematician: discovered automorphic functions and contributed independently to relativity theory.

Poincaré was the son of a physician and was educated at the École Polytechnique and École des Mines. After teaching at the University of Caen he spent his life from 1881 as a professor at the University of Paris. He became a member of the Académie des Sciences (1887) and also of the Académie Française (1909). Poincaré earned a reputation as ‘the last universalist’, producing about 500 papers and 30 books, which contributed to a wide variety of branches of mathematics and allied subjects. In contrast, he was clumsy, absentminded and inept with simple arithmetic.

In pure mathematics Poincaré discovered auto-morphic functions, which are a generalization of periodic functions in being invariant under an infinite group of linear fractional transformations. This led to work on parameterization of curves, the solution of linear differential equations with rational algebraic coefficients and topology. He also did significant work on the theory of numbers, on probability theory and ergodicity.

In mathematical physics Poincaré published a paper on the dynamics of the electron (1906) which independently obtained within electromagnetic theory several of the results of theory of special relativity (1905). In celestial mechanics he made important contributions to the theory of orbits, the shape of rotating fluids, the gravitational three- and n -body problems and the origination of topological dynamics. In the course of this work Poincaré developed powerful new techniques such as asymptotic expansions and integral invariants.

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