Borel, who was a professor emeritus at the Institute for Advanced Study in Princeton, New Jersey, was a highly influential figure in two groups of mathematicians that at different times and in different places had a profound influence on the evolution of mathematics after World War II.
In the years just after the war, Borel, who was born in a French-speaking area of Switzerland, was close to a number of French mathematicians, including Jean Leray, Andre Weil, Henri Cartan and Jean-Pierre Serre, who self-deprecatingly referred to themselves as the Bourbaki Group, after a spectacularly unsuccessful French general in the Franco-Prussian War of 1870.
These mathematicians set themselves the lofty goal of reconceptualizing the whole of mathematics to give it a new degree of unity and abstraction in what Borel referred to as the second French Revolution.
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, Borel's work became a major influence on some of the most important developments in contemporary mathematical research.
Borel became a leading figure in a second group of mathematicians that was formed during the 1960's and 1970's at the institute, where he was a professor from 1957 to 1993. Besides Weil, this group included Robert Langland and Pierre Deligne.
Borel and the others sought to use their insights into Lie group theory to understand profound patterns in the theory of numbers.
© International Herald Tribune, August 16, 2003 p4