Armand Borel, 80; Researcher Key to Modern Mathematics

Armand Borel, 80, whose study of mathematical symmetries played a key role in the development of modern mathematics, died of cancer Aug. 11 in Princeton, N.J.

A native of Switzerland educated at the Swiss Federal Institute of Technology in Zurich and the University of Paris, Borel joined the Institute for Advanced Study in Princeton in 1957 and took professor emeritus status in 1993. With interests that ranged broadly outside mathematics, he created and directed a musical concert series at the Princeton institute from 1985 through 1992.

Borel was an expert on Lie groups -- mathematical symmetries named for the Norwegian mathematician Sophus Lie -- and in applying insights from his study of them to understanding profound patterns in the theory of numbers.

His far-reaching work in mathematical research was recognized in 1991 by the American Mathematical Society, which awarded him its Steele Prize for lifelong contributions. According to the citation, his work “provided the empirical base for a great swath of modern mathematics, and his observations pointed out the structures and mechanisms that became central concerns of mathematical activity.”