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Jules Henri Poincare, generally acknowledged to be the outstanding mathematician
of his age, was born in Nancy, France, in 1854. He was a first cousin
of Raymond Poincare, the eminent statesman and president of the French
republic during World War I. After graduating from the Ecole Polytechnique in
1875, Henri took a degree in mining engineering at the Ecole des Mines in 1879,
and in that same year also earned a doctorate in science from the University of
Paris.
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Upon graduating from the Ecole des Mines, he was appointed to a
teaching post at Caen University,
but two years later moved to the University
of Paris, where he held several professorships in mathematics and science until
his death in 1912.
Poincare has been described as the last of the universalists in the field of
mathematics. It is certainly true that he commanded and enriched an astonishing
range of subjects. At the Sorbonne, he brilliantly lectured each year on a
differint topic in pure or applied mathematics, many of these lectures shortly
after appearing in print. He was a prolific writer, producing more than thirty
books and 500 technical papers. He was also one of the ablest popularizers of
mathematics and science. His inexpemsive paperback expositions were avidly
bought and widely read by people in all walks of life; they are masterpieces
that, for lucidity of communication and engaging style, have never beem excelled,
and they have been translated into many foreign languages. In fact, so
great was the literary excellence of Poincare's popular writing that he was
awarded the highest honot that can be conferred on a French writer-he was
clected a member of the literary section of the French Institut.
Poincare never cared to remain in one field for very long, but preferred to
jump nimbly from area to area. He was described by one of his contemporaries
as "a conqueror, not a colonist." His doctoral dissertation on differential equations
concerned itself with existence theorems. This work led him to develop
the theory of automorphic functions, and, in particular, the so-called zeta-
Fuchsian functions, which Poincare showed can be used to solve second-order
linear differential equations with algebraic coefficients. Like Laplace, Poincare
contributed notably to the subject of probability. He also anticipated the twentieth-
century interest in topology, and his name is found today in the Pioncare
groups of combinatorial topology. We have alreadym in Section 13-7 and Problem
Study 13.12, seen Poincare's interest in non-Euclidean geometry. In applied
mathematics, this versatile genius contributed to such diverse subjects as
optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential
theory, quantum theory, theory of relativity, and cosmogony.
All his life, Poincare was physically awkward, nearsighted, and absentminded,
but he possessed almost complete retention and instant recall of anything
he had ever read. He worked his mathematics in his head while restlessly
pacing about, and when it was completely thought through, he committed it to
paper rapidly and with essentially no rewriting or erasures. In contrast to his
hasty and extensive production, one recalls the metisulously prepared productions
of Gauss, and Gauss notto: "Few, but ripe."
There are stories of Poincare's lack of manual dexterity. It was said of him
that he was ambidextrous-that is, he could perform equally badly with either
hand. He had no ability whatever in drawing, and he earned a flat zero in the
subject in school. At the end of the school year, his classmates jokongly organized
a public exhibition of his artistic masterpieces. They carefully labeled
each item in Greek-"This is a house," "This is a horse," and so on.
It may well be that Poincare will be the last person of whom it can in a
reasonable sense be claimed that all of mathematics was his province. Mathematics
has grown at such an incredible rate in modern times that it is believed
quite impossible for anyone ever again to achieve such a distinction.
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