The cause was heart failure, M.I.T. officials said.
Dr. Rota dealt with abstract matters like probability, phenomenology and combinatorial theory, or combinatorics. His interest in philosophy centered on the existential thoughts of two 19th- and 20th-century German philosophers, Edmund Husserl and Martin Heidegger.
At M.I.T., Dr. Rota was the only professor of applied mathematics and philosophy, a dual position to which he was appointed in 1974.
Combinatorics in higher mathematics is the study of permutations and combinations of elements in finite sets. In an interview with M.I.T. News last year, he gave this definition of his field of study:
''Combinatorics is putting different-colored marbles in different-colored boxes, seeing how many ways you can divide them. I could rephrase it in Wall Street terms, but it's really just about marbles and boxes, putting things in sets.''
Indeed, Dr. Rota added, some of his best students go to Wall Street. ''It turns out that the best financial analysts are either mathematicians or theoretical physicists,'' he said.
Dr. Rota wrote several books and contributed to many more. His latest, ''Indiscrete Thoughts'' (Birkhauser, 1997), was a collection of essays that limned the lives of notable mathematicians. His purpose was to debunk ''the myth of monolithic personality'' in his profession, although not all of his subjects were pleased with their portraits.
He was co-author of ''Discrete Thoughts'' (Birkhauser, 1986) as well as books on combinatorial geometrics, computer science and ordinary differential equations.
Gian-Carlo Rota was born in Vigevano, a town in northern Italy about 20 miles southwest of Milan. He came to the United States in 1950 and graduated summa cum laude from Princeton University in 1953. He received an M.A. in 1954 and a Ph.D. in mathematics in 1956 from Yale University.
He taught at New York University, Harvard University, M.I.T. and Rockefeller University before rejoining M.I.T. in 1962 as a full professor of mathematics. He was a fellow of the American Academy of Arts and Sciences and of the American Association for the Advancement of Science, and a member of the National Academy of Sciences.
Dr. Rota's survivors include his sister, Ester Rota Gasperoni of Paris. His marriage to Teresa Rondon-Tarchetti ended in divorce.
By WOLFGANG SAXON, May 1, 1999 © The New York Times Company