Enrico Bombieri To Speak On The Mathematical Infinity

Enrico Bombieri, IBM von Neumann Professor in the School of Mathematics at the Institute for Advanced Study, will present the lecture “The Mathematical Infinity” on Wednesday, January 31, at 4:30 p.m. in Wolfensohn Hall on the campus of the Institute. Professor Bombieri will discuss the many different ways the concept of infinity has been treated during the ages, from rejecting it as an irrational absurdity to accepting it as the ultimate, inaccessible, perfection.

Professor Bombieri will explain that the debate about infinity is not limited to theology, philosophy and the natural sciences, but that infinity has played, and still plays, a shifting role in mathematics: from total avoidance in the Pythagorean school, to the Aristotelian partial acceptance of it as a useful convention (but always avoidable), to the Cantorian point of view related to counting and leading to a notion of different types of infinity, all of them acceptable at the same time in a precise model of mathematics.

Accessible to a wide audience, the lecture will explore how mathematics has arrived at its present pragmatic view of infinity and some of the counterintuitive paradoxes, as well as some of the positive results, deriving from its acceptance. Finally, the lecture will conclude with a view of how computer science is leading today to a new precise concept, namely the impossibly large in the realm of the finite.

One of the world’s leading authorities on number theory and analysis, Professor Bombieri has a broad mathematical focus, ranging from analytic number theory to algebra and algebraic geometry, and the partial differential equations of minimal surfaces. He was awarded the Fields Medal in 1974 for his work on the large sieve and its application to the distribution of prime numbers, in algebraic geometry, in complex analysis and in partial differential equations.

In the past decade, his main contributions have been in the active area of Diophantine approximation and Diophantine geometry, exploring questions on how to solve equations and inequalities in integers and rational numbers. Some of his work, in particular that which is related to prime number theory, has potential practical applications to cryptography and security of data transmission and identification.

Professor Bombieri received his Ph.D. from the University of Milan in 1963. After serving as Professor at the University of Pisa and the Scuola Normale Superiore at Pisa, he joined the Faculty at the Institute for Advanced Study in 1977, following a Membership here in 1973-74. He was named the IBM von Neumann Professor in 1984.

He is a Member of the Accademia Nazionale in Rome, the Accademia Nazionale dei Lincei, the Royal Swedish Academy, the French Académie des Sciences, the Academia Europaea, and the National Academy of Sciences. In addition to the Fields Medal, he is the recipient of numerous awards, including the Feltrinelli Prize in 1976, the Balzan Prize in 1980, the Cavaliere di Gran Croce al Merito della Repubblica, Italy in 2002 and the Premio Internazionale Pitagora from the City of Crotone in Italy in 2006.

For further information about this event, which is free and open to the public, please call (609) 734-8175.