Félix Edouard Justin Emile Borel

1871-1956

French Mathematician

Though he is noted for his work on complex numbers and functions, Emile Borel in fact wrote, researched, and taught on a variety of subjects. His Space and Time (1922), for instance, helped make Albert Einstein's theory of relativity comprehensible to non-technically educated readers, and his work extended far beyond the world of mathematics. As an influential figure in French politics, he helped direct that country's policy toward scientific and mathematical research and education.

Borel was born the son of Honoré, a pastor, and Emilie Teissié-Solier Borel, in the French town of Saint-Affrique on January 7, 1871. His was a world heavily influenced by the recent humiliation of the Franco-Prussian War, and on a personal level, Borel, as the younger brother of two sisters, had to fight to distinguish himself.

Distinction came early, however, with an invitation to study at several prestigious preparatory schools in Paris. Borel went on to the Ecole Normale Supériere, a preeminent school in science and mathematics with which he would remain connected for most of his life. After earning his doctorate in 1894, he returned to the Ecole Normale to teach. In 1901, when he was 30, he married Marguerite, the daughter of mathematician Paul Appell. The couple never had children, but adopted one of Borel's nephews, who was later killed during the First World War.

Borel in 1899 became the first mathematician to develop a systematic theory for a divergent series. His work with complex functions, or functions involving complex numbers such as the square roots of negative numbers, led him to prove Picard's theorem, which concerns the number of possible values for a complex function. He also provided an increased understanding of how to measure complicated two-dimensional surfaces, which are said to be "Borel-measurable." In his development of a general notion of area, Borel laid the foundations for what became known as measure theory.

In the realm of topology, Borel articulated a theorem of compactness, concerning the ways in which an infinite set mimics the simpler qualities of a finite set. His theorem became known by the rather inaccurate name of the Heine-Borel theorem—inaccurate because German mathematician Heinrich Heine (1812-1881) actually never formulated a theorem of compactness.

A prolific writer, Borel produced some 300 papers and books, among them Lessons in the Theory of Functions (1898), a classic in measure theory that he published when he was only 27 years old. In 1906, after winning the Petit Prix d'Ormoy, Borel used the prize money to start La revue du mois (Monthly Review), a journal of general interest which he edited with his wife.

During World War I, Borel conducted important investigations into probability theory that helped lay the groundwork for what later became game theory. He also earned the distinguished Croix de Guerre in 1918 for his work during the war. In the interwar period, he served in France's Chamber of Deputies (1924-36) as a representative of Saint-Affrique, and as minister of the navy in 1925. He also became instrumental in directing a number of efforts in scientific and mathematical research and education, for instance by helping establish the Institut Henri Poincaré in 1928 and serving as its president until his death.

During World War II, Borel was briefly imprisoned by the pro-Nazi Vichy regime, and afterward received the Resistance Medal for his efforts. In 1950, he earned the Grand Croix de la Légion d'honneur, among the most coveted prizes available to a French citizen. By then he had retired from the Sorbonne in Paris, where he had taken a position earlier, but he remained active in the world of mathematics up to the time of his death, on February 3, 1956.

JUDSON KNIGHT