His death was announced last week by Yale University, where he
was a professor of mathematics. Working with James W. Cogdell,
his main collaborator over a quarter-century, starting in the
mid-1970s, Dr. Piatetski-Shapiro shaped a proof of what is known
as the Converse Theorem, which finds some deep relationships
between different fields of mathematics. The mathematical
constructs are "quite mysterious, even to mathematicians," Dr.
Cogdell explained in an interview this week. But the theorem has
wide applications, including playing a small but important role
in the proof of Fermat's Last Theorem that Andrew Wiles, a
Princeton mathematician, completed in 1994. "It's a very
powerful tool," said Peter C. Sarnak, a professor of mathematics
at Princeton. "He made sure it's in a form everyone can use it."
Born in Moscow, Ilya Piatetski-Shapiro became interested in
mathematics when he was 10. In a memoir, he said that when he
learned about negative numbers from his father, a chemical
engineer, he was struck "by the c