Armand Borel

Armand Borel, a Swiss-born mathematician who became a towering figure in the development of modern mathematics, died Monday in Princeton, N.J. He was 80.

The cause was cancer, said his daughter Dominique Odette Susan Borel.

Dr. Borel, who was a professor emeritus at the Institute for Advanced Study in Princeton, N.J., was an influential figure in two groups of mathematicians that at different times and in different places influenced the evolution of mathematics after World War II.

In the years just after the war, Dr. Borel was close to many French mathematicians, including Jean Leray, Andre Weil, Henri Cartan and Jean-Pierre Serre, who self-deprecatingly referred to themselves as the Bourbaki Group, after an unsuccessful French general in the Franco-Prussian War of 1870.

These mathematicians set themselves the goal of reconceptualizing the whole of mathematics to give it a new degree of unity and abstraction in what Dr. Borel used to refer to, laughingly, as the second French Revolution.

Dr. Borel ' s contribution came through his lifelong study of certain continuous collections of mathematical symmetries, known as Lie groups after the Norwegian mathematician Sophus Lie, and through his efforts to use what he had learned from this work to illuminate other fields of mathematical inquiry.

Because of the increasing importance the theory of Lie groups plays in modern mathematics, Dr. Borel ' s work became a major influence on some of the most important developments in contemporary mathematical research.

Dr. Borel became a leading figure in a second group of mathematicians, formed during the 1960s and 1970s at the institute, where he was a professor from 1957 to 1993. Besides Andre Weil, this group included the American Robert Langland and Pierre Deligne of Belgium.

Dr. Borel and the others sought to use their insights into Lie group theory to understand profound patterns in the theory of numbers.

When Dr. Borel was awarded the American Mathematical Society ' s Steele Prize in 1991 for his lifelong contribution to mathematics, the citation noted that he had " provided the empirical base for a great swath of modern mathematics, and his observations pointed out the structure and mechanisms that became central concerns of mathematical activity. "

In 1973, Dr. Borel led a group of scholars at the institute in a highly publicized clash with its director, Dr. Carl Kaysen, over plans to appoint a sociologist, Robert N. Bellah, to a professorship there. The challengers questioned both his scholarly credentials and the need for a sociology department. In the end, Bellah did not join the institute.

Dr. Borel was born on May 21, 1923, in the small French-speaking Swiss town of La Chaux-de-Fonds. He graduated from the Swiss Federal Institute of Technology in Zurich in 1949 and received a doctorate from the University of Paris in 1952. In 1952 he married Gabrielle Aline Pittet.

A lover of music, Dr. Borel directed a concert program at the Institute for Advanced Study from 1985 to 1992.

He is survived by his wife and his daughters, Dominique and Anne Christine Borel, both of New York.