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In 1909 he was appointed to a chair of Theory of Functions created specially for him at the Sorbonne and he went on to hold this professorship until 1941. The year 1910 saw him attain the prestigious position of Director of the École Normale Supérieure which he held for ten years. In 1918 he received the Croix de Guerre for his efforts during World War I. In 1921 he was elected to the Académie des Sciences , becoming its president in 1934.

Borel created the first effective theory of the measure of sets of points. This work, along with that of two other French mathematicians, Rene Baire and Henri Lebesgue , marked the beginning of the modern theory of functions of a real variable. Borel, although not the first to define the sum of a divergent series, was the first to develop a systematic theory for a divergent series which he did in 1899.

In addition, he published (1921-27) a series of papers on game theory and became the first to define games of strategy. During this period, however, he had already embarked on a political career. He wrote an important political work in 1924 La politique républicaine :

... and began the struggle for a united Europe, and with unbending optimism continued it for the rest of his life.
...
In the meantime he joined the Republican-Socialist Party, the group to which Briand and Painlevé belonged, and was elected deputy for Aveyron in 1924, for St Affrique in 1928.

After 1924, Borel became active in the French government serving in the French Chamber of Deputies (1924-36) and as Minister of the Navy (1925-40). After his arrest in 1941 and brief imprisonment under the Vichy regime he worked for the Resistance. He was awarded The Resistance Medal (1945), and the Grand Croix Légion d'Honneur (1950). For his scientific work he received the first gold medal of the Centre National de la Recherche Scientifique in 1955.

Borel's most important mathematical works are Le Hasard (1913), L'éspace et le temps (1921), and Traité du calcul de probabilité et ses applications (1924-34). In 1946, when he was 75 years old, Borel published the fascinating book Les paradoxes de l'infini. He also made :

... a number of valuable contributions to the knowledge of Einstein 's theory of relativity.

Source:School of Mathematics and Statistics University of St Andrews, Scotland