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Henri Poincaré

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Henri Poincaré (1854–1912), a French mathematician, was one of the last mathematicians who made fundamental contributions to several different areas of mathematics. For this reason he was referred to as the "Last Universalist". In this regard he was similar to German mathematician David Hilbert.

He remained a powerhouse in pure mathematics even as the emphasis and locus of mathematics shifted to applied mathematics in Great Britain and Germany. Poincaré was the leading French scientist in 1900, and one of the best in Europe.

Areas of Work

Began his career in wikipedia:Complex Analysis, a field with a distinguished pedigree:

  • Weierstrauss (German)
  • Riemann (German)
  • Cauchy (French)
    • Liouville
    • Hermite
    • Poincaré
    • Hadamard

Automorphic Functions

Originally called "Fuchsian" functions after German mathematician wikipedia:Immanuel Lazarus Fuchs.

Topology

Originally known as "analysis in situ".

See the wikipedia:Poincaré Conjecture (now considered a Theorem); concerns which types of manifold are topologically equivalent (homeomorphic) to a sphere. This was one of the wikipedia:Millenium Prize Problems that was ultimately proved a Muscovite mathematician wikipedia:Grigori Perelman.

Three-Body Problem

Considered planetary systems, e.g. Sun-Jupiter-Saturn and Sun-Earth-Moon. Wrote a paper on the subject that garned a scientific prize offered by the King of Sweden. Built on analysis of special cases done by Lagrange.

As a result, was seen as a pioneer in non-linear analysis and wikipedia:Chaos Theory.

Philosophy of Science

Also contributed to the philosophy of science, and wrote popular works for a lay audience.

Some of his interest lay more particulary in philosophy of physics, beyond the area of relativity as discussed above:

  • Poincaré-Duhem Hypothesis

Also known as wikipedia:Conventionalism, this is the viewpoint that scientific theories have to be viewed holistically, considering background assumptions, social considerations, etc.

See also the work by wikipedia:Willard Van Orman Quine, especially wikipedia:Two Dogmas of Empiricism.

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