Jules-Henri Poincaré

1854-1912

French Mathematician, Scientist and Philosopher of Science

Jules-Henri Poincaré was one of the greatest mathematicians of modern times. In an age of increasing specialization, he was among the last to see all mathematics, pure and applied, as his domain. He used mathematics to investigate many scientific problems, including the motion of the tides and planets, and theories of electricity and light. He was particularly skilled at developing general methods superseding whole collections of mathematical "tricks" used in specific situations. His literary abilities also contributed to the influence of his ideas. He published several widely read books on the philosophy of science, and was elected to the Académie Française on the strength of his writing.

Poincaré was born in the town of Nancy, France, on April 29, 1854, into an accomplished family. His father was a distinguished physician, and his mother was a gifted woman who was instrumental in the education of her rather sickly son. His first cousin, Raymond Poincaré, later served as president of the French Republic during World War I.

Between 1872 and 1875, Poincaré attended the Ecole Polytechnique in Paris, and won many prizes in mathematics there. He had a very good memory, could visualize and solve complex equations in his head, and could quickly write papers requiring little revision. In 1879, Poincaré received his doctorate from the Ecole Nationale Supérieure des Mines, an engineering school. In 1881, he accepted an appointment at the Université de Paris, where he was to teach for the rest of his life.

Poincaré developed the theory of the automorphic function, one that doesn't change when put through certain types of transformations. He demonstrated how automorphic functions could be used to integrate linear differential equations and to express the coordinates of any point on an algebraic curve in terms of a single variable. The entire class of elliptic functions, of which the trigonometric functions are a subclass, is included in this theory. Some automorphic functions were associated with transformations that arose in non-Euclidean geometry. Poincaré was elected to the Academie des Sciences in 1887 in recognition of his mathematical achievements.

In 1887, the Swedish King Oscar II offered a prize for a solution to the "n-body problem," that is, the gravitational interactions and movements of a system containing an arbitrary number of masses. This problem is important for the theory of orbits. For example, the interactions of the Sun, Earth, and Moon constitute a three-body problem. Poincaré's solution, although incomplete, included important new work in mathematics, including the behavior of integral curves of differential equations near singularities, points where the derivative of a function ceases to exist. Not only was he awarded the prize, he was made a knight of the French Legion of Honor as well.

Poincaré also contributed to the fields of topology, number theory, and the dynamics of rotating fluid masses, applying the latter to the evolution of the planets and stars. He studied the dynamics of the electron and independently obtained some of the same results as Albert Einstein (1879-1955) did in developing the special theory of relativity. However, Einstein's formulation gained the upper hand because it was based on fundamental considerations, while Poincaré's was predicated on the later-discredited ether theory of light transmission.

Later in his career, Poincaré turned his gifts to explaining the meaning of science and mathematics to the general public. His works, including La Science et l'Hypothèse (Science and Hypothesis, 1903), La Valeur de la Science (The Value of Science, 1905) and Science et Méthode (Science and Method, 1908) were translated into several languages. His view of mathematical creativity was intuitionist. That is, he believed sudden insights to be a product of previous work done in the subconscious mind. He also emphasized the role of convention, the arbitrary choice of concepts or expression based on a group consensus, in the scientific method.

In 1906, Poincaré was elected president of the Académie des Sciences. Two years later, he was elected to membership in the Academie Française, the highest honor in the French literary world. He died suddenly on July 17, 1912, in Paris.

SHERRI CHASIN CALVO