Academic journal article Proceedings of the American Philosophical Society

Armand Borel

Academic journal article Proceedings of the American Philosophical Society

Armand Borel

Article excerpt

21 MAY 1923 * 11 AUGUST 2003

ARMAND BOREL, professor emeritus in the School of Mathematics at the Institute for Advanced Study since 1993, died at home in Princeton on 11 August 2003, only two months after the first symptoms of a terminal illness appeared. He had celebrated his eightieth birthday on 21 May.

Borel was born in 1923 in the French-speaking city of La Chaux-deFonds in Switzerland. He soon distinguished himself as an exceptional student and graduated in 1947 from the Swiss Federal Institute of Technology (Eidgenössische Technische Hochschule) in Zürich, where he was introduced to the study of topology and Lie groups by the famous mathematicians Heinz Hopf and Eduard Stiefel. He immediately obtained a position as assistant at the same institution, which he held for two years, and then, with a research grant from the French CNRS (Centre National de la Recherche Scientifique), he moved to Paris for the 1949-50 year. This was a turning point in his mathematical development. There he quickly got acquainted with senior members of the Bourbaki group - namely Henri Cartan, Jean Dieudonné, Laurent Schwartz - and with the younger members - notably Roger Godement, Pierre Samuel, Jacques Dixmier, and most importantly Jean-Pierre Serre, who became a close friend and collaborator of Borel's. The discussions with these mathematicians had a lasting influence on Borei and completed his preparation. He joined the Bourbaki group in the same year.

Borei returned to Switzerland with a position as adjunct professor of algebra at the University of Geneva from 1950 to 1952. In these years he completed the write-up of his thesis for a Doctorat d'État and defended it at the Sorbonne in Paris. His thesis, of fundamental importance in the theory of Lie groups, was published without delay in the prestigious journal Annals of Mathematics.

The same year, with his thesis as his entry card, Borei arrived with his young bride, Gaby, at the Institute as a member of the School of Mathematics. His membership in the School was renewed for a second year (at that time renewal of membership was done almost automatically, Borei told me, adding that he thought it was a very good thing). Then he spent a year in Chicago, where he profited highly from the presence of André Weil, thus adding algebraic geometry and number theory to his already vast knowledge of algebra and topology.

In 1957 he joined the School of Mathematics at the Institute as a professor, remaining until his retirement in 1993. At the time of his death he had authored or edited 16 books and more than 180 papers and was working on a major monograph in collaboration with Lizhen Ji of the University of Michigan at Ann Arbor on the subject of compactifications of homogeneous spaces. He became a U.S. citizen on 18 February 1986.

He was a member of the National Academy of Sciences of the USA and of the American Academy of Arts and Sciences; a foreign member of the Finnish Academy of Sciences and Letters, of the American Philosophical Society, and of the Academia Europea; a foreign associate of the French Academy of Sciences; an honorary fellow of the Tata Institute in Bombay, India; and the laureate of an honorary doctorate from the University of Geneva. He was a recipient of the Brouwer Medal of the Dutch Mathematical Society, of the Steele Prize of the American Mathematical Society, and of the Balzan Prize of the Italian-Swiss International Balzan Foundation.

His scientific activities, besides research, involved participation in the Consultative Committees of the International Congresses of Mathematicians in 1966 and 1978, participation in the editorial boards of the most prestigious mathematical journals in a span of more than thirty years, and also teaching (I can mention various summer schools on mathematical topics at a high level and a three-year program in Hong Kong in his last years).

Less obvious, but not less important, was his presence in the Bourbaki group. …

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