The Mathematician Who Conquered Problems Across Analysis

Jean Bourgain changed the landscape of mathematical analysis through an extraordinary range of discoveries. Beginning in Banach-space geometry, he produced major advances in harmonic analysis, ergodic theory and nonlinear partial differential equations, then extended his methods into number theory, combinatorics and theoretical computer science. This documentary follows his career from Brussels and IHES to the Institute for Advanced Study, where he joined the faculty in 1994, the year he received the Fields Medal.

Most mathematicians become identified with one narrow specialty, but Bourgain repeatedly entered new fields and solved problems using combinations of analysis, probability, geometry and arithmetic. His techniques influenced nonlinear evolution equations, exponential sums, expanders and computational complexity. The breadth makes his career an ideal story about unity in mathematics. This documentary shows how one researcher's methods crossed boundaries and why colleagues regarded him as a once-in-a-generation analyst.