Armand Borel ( 1923 – 2003 )

The Swiss mathematician Armand Borel died August 11, 2003, in Princeton from a rapidly evolving cancer. Few foreign mathematicians had as many connections with France. He was a student of Leray, he took part in the Cartan seminar, and he published more than twenty papers in collaboration with our colleagues Lichnerowicz and Tits, as well as with me. He was a member of Bourbaki for more than twenty years, and he became a foreign member of the Académie des Sciences in 1981. French mathematicians feel that it is one of their own who has died. He was born in La Chaux-de-Fonds in 1923 and was an undergraduate at Eidgenössische Technische Hochschule of Zürich (the “Poly”). There he met H. Hopf, who gave him a taste for topology, and E. Stiefel, who introduced him to Lie groups and their root systems. He spent the year 1949–50 in Paris, with a grant from the CNRS1. A good choice (for us, as well as for him), Paris being the very spot where what Americans have called “French Topology” was being created, with the courses from Leray at the Collège de France and the Cartan seminar at the École Normale Supérieure. Borel was an active participant in the Cartan seminar while closely following Leray’s courses. He managed to understand the famous “spectral sequence”, not an easy task, and he explained it to me so well that I have not stopped using it since. He began to apply it to Lie groups, and to the determination of their cohomology with integer coefficients. That work would make a thesis, defended at the Sorbonne (with Leray as president) in 1952, and published immediately in the Annals of Mathematics. Meanwhile Borel returned to Switzerland. He did not stay long. He went for two years (1952–54) to the Institute for Advanced Study in Princeton and spent the year 1954–55 in Chicago, where he benefited from the presence of André Weil by learning algebraic geometry and number theory. He returned to Switzerland, this time to Zürich, and in 1957 the Institute for Advanced Study offered him a position as permanent professor, a post he occupied until his death (he became a professor emeritus in 1993). Jean-Pierre Serre is professor emeritus of the Collège de France. His email address is [email protected]. This part of the article is a translation of the presentation made by him to the Académie des Sciences in Paris on September 30, 2003 (© Académie des Sciences and printed with permission). Anthony W. Knapp assisted with the translation. Citations within this article. Borel’s Collected Papers are [Œ], and his 17 books are referred to as [1] through [17]. These are all listed in a sidebar on page 501. An item like [Œ 23] is Borel paper number 23 in [Œ]. Citations of work by people other than Borel are by letter combinations such as [Che], and the details appear at the end of the article.