At the institute, Dr. Weil was considered an intellectual peer of colleagues who were among the century's most influential scholars, Albert Einstein, J. Robert Oppenheimer, the mathematician John von Neumann and the logician Kurt Godel among them.
''I think of him as one of the few people who shaped the mathematics of the 20th century,'' said Dr. Enrico Bombieri, a professor of mathematics at the institute. ''His ideas are still fundamental.''
In 1994, Dr. Weil (pronounced VAY) won the equivalent of the Nobel Prize, which is not awarded in mathematics, when he received the Kyoto Prize in Basic Science from the Inamori Foundation of Kyoto, Japan.
That award honored the part of his work known as the Weil conjectures, which provided the principles for modern algebraic geometry. The patterns of numbers that Dr. Weil discovered are now applied, for example, in writing almost-unbreakable secret codes and in enhancing the accurate transmission of computer data.
Other applications of his work can be found in elementary particle physics.
But such practical applications were far from Dr. Weil's mind, said Dr. Phillip Griffiths, director of the institute and a mathematician. Dr. Weil, he said, provided answers to some of the most subtle questions about ordinary numbers. ''He will certainly be remembered as one of the giants of mathematics of all times,'' Dr. Griffiths said. Beyond that, he was a scholar and historian and was fluent in languages -- ''in Sanskrit, in Persian, you name it,'' Dr. Griffiths said.
He introduced ideas of topology -- the study of geometric figures -- into arithmetic, permanently changing the way scholars study the science of computing by numbers.
Dr. Weil was born in 1906 in Paris, became devoted to mathematics in his early teens and received his doctorate from the University of Paris in 1928. His thesis solved a problem concerning elliptic curves that had been posed by the mathematician and philosopher Henri Poincare.
In the 1930's, he rejected the avant-garde circles of Paris and instead went off to India to study its culture and to teach. ''He was the last person you would think of in a salon,'' Dr. Bombieri said. ''He would have had only acerbic words to say about all that.''
In India, he taught at Aligarh University from 1930 to 1932, then returned to France to teach at Marseille University and Strasbourg University until 1940.
Dr. Weil was one of the founders of the influential Bourbaki, a group of French mathematicians who rebelled against the French establishment and whose original writings from the 1930's unified all of mathematical knowledge for the first time. The Bourbaki remain highly influential in the field to this day.
To avoid the draft, he went to Finland. ''As a soldier,'' he said, ''I would be entirely useless, but as a mathematician I could be of some use.'' The Finns returned him to the French, who imprisoned him for six months.
In prison, he created and proved a hypothesis that is analogous to the Riemann hypothesis -- named for a German mathematician -- which became a basic element of number theory and is regarded as one of his most insightful mathematical achievements, Dr. Phillips said.
He later joined the French Army to earn his release from prison, then came to the United States to teach at Haverford College in Pennsylvania. He taught at the University of Chicago from 1947 to 1958, and at the University of Sao Paulo in Brazil from 1945 to 1947.
He joined the Institute for Advanced Study in 1958. After he retired from there in 1976, he wrote on mathematics and edited works by Jacques Bernoulli and Pierre de Fermat, two giants in mathematics.
His wife, Eveline, died in 1986.
He is survived by two daughters, Nicolette Schwartzman of Princeton and Sylvie Weil Weitzner of Manhattan, and three grandchildren.
His younger sister, the philosopher Simone Weil, died in England in 1943.
Dr. Weil cultivated an image of an ill-tempered, impossible character. Asked for his department's budgetary needs at the institute, he would reply, ''Give us enough chalk.''
Only his close peers knew that his whimsical spirit had helped name the Bourbaki group, after an imaginary Russian general from an invented land of Poldavia.
At his death, the only honor listed in his official biography at the institute simply said, ''Member, Poldavian Academy of Science and Letters.''
By FORD BURKHART, August 10, 1998 © The New York Times Company