Henri Cartan

Henri Paul Cartan (8 July 1904 – 13 August 2008) was a French mathematician known for his major work in algebraic topology. He was born into a family of mathematicians—his father was Élie Cartan, his aunt Anna Cartan, and his sister Hélène Cartan—but he later said he developed an interest in mathematics on his own, without family pressure. After moving to Paris in 1909 when his father joined the Sorbonne, he attended Lycée Hoche in Versailles. He studied at the École Normale Supérieure from 1923, earning his agrégation in 1926 and a doctorate in 1928 under Paul Montel. His teaching career took him to Lycée Malherbe in Caen, the University of Lille, and the University of Strasbourg. During the German invasion of France, the Strasbourg staff relocated to Clermont Ferrand, where Cartan recommended that mathematicians Marie-Hélène Schwartz and Laurent Schwartz move there for both their research and safety. In 1940 he returned to Paris, teaching at the Université de Paris and École Normale Supérieure, and later at Paris-Sud University from 1969 until his retirement in 1975. He died at age 104, with his funeral held in Die, Drôme.

Cartan was a founding member of the Bourbaki group in 1934 and remained highly active in it. After 1945 he launched his own Paris seminar, which strongly influenced younger mathematicians such as Jean-Pierre Serre, Armand Borel, Alexander Grothendieck, and Frank Adams. Although he had few official doctoral students, they included Joséphine Guidy Wandja, Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre, and René Thom. His early research, through the 1940s, focused on functions of several complex variables, leading to work on complex varieties and analytic geometry. Building on the Cousin problems, he studied sheaf cohomology and coherent sheaves, proving Cartan’s theorems A and B. From the 1950s he turned to algebraic topology, contributing to cohomology operations, homology of Eilenberg–MacLane spaces, and introducing the Steenrod algebra, among other results.

He received many honors: the Cours Peccot in 1932, presidency of the Société mathématique de France in 1950, and leadership of the International Mathematics Union from 1967 to 1970. He was awarded the Émile Picard Medal (1959), CNRS Gold Medal (1976), and Wolf Prize (1980). He spoke at several International Congresses of Mathematicians—as an invited speaker in 1932 and as a plenary speaker in 1950 and 1958. He became a member of the French Academy of Sciences in 1974 and was elected to numerous foreign academies, including the American Academy of Arts and Sciences, the Royal Society of London, and the U.S. National Academy of Sciences. He received honorary doctorates from universities including Münster, ETH Zürich, Oxford, and Cambridge. The French government named him Commandeur des Palmes Académiques (1964), Officier de la Légion d’honneur (1965), and Commandeur de l’Ordre du Mérite (1971).

Politically and socially, Cartan used his influence in the 1970s and 1980s to help free dissident mathematicians, such as Leonid Plyushch from the Soviet Union, Jose Luis Massera from Uruguay, and Sion Assidon from Morocco. For this work he received the Heinz R. Pagels Human Rights of Scientists Award in 1989. Since the 1930s he had close collaborations with German mathematicians like Heinrich Behnke and Peter Thullen, and after World War II he worked to rebuild cooperation between French and German mathematicians. A supporter of European federalism, he led the French section of the Union of European Federalists from 1974 to 1985 and headed the Liste pour les États-Unis d’Europe in the 1984 European elections, which won 0.4% of the vote. In 1992 he spoke at the first European Congress of Mathematics, highlighting Europe’s shared heritage and the reunion of mathematicians from its previously divided parts.