Jean Bourgain, problem solver

Abstract

Jean Bourgain, a truly exceptional and prolific problem solver who transformed multiple areas of mathematics, died on December 22, 2018, aged 64, after a prolonged battle with cancer. Jean Bourgain, 1954–2018. Image courtesy of Institute for Advanced Study/Andrea Kane. Jean received almost every award in the field of mathematics, ranging from the Fields Medal in 1994 (widely regarded as the premier award for mathematicians under the age of 40) to a baronetcy by the Belgian government in 2015. He was elected to the National Academy in 2011, but as a colleague of his noted after his death, “Even considering this, it is hard not to think that in some ways the weight of his contributions has still somehow gone underappreciated within the larger mathematical and scientific community.” Jean’s early work was in the geometry of high-dimensional (or infinite-dimensional) spaces, as well as closely related objects such as large (or infinite) matrices. For instance, he showed how to efficiently approximate a high-dimensional convex body using randomly selected points in that body, and (with Tzafriri) showed that starting from an arbitrary large matrix (obeying some mild conditions), one could select a large number of columns to create a submatrix that … [↵][1]1Email: tao{at}math.ucla.edu. [1]: #xref-corresp-1-1