Article,
Exploring the toolkit of Jean Bourgain
(2020)cite arxiv:2009.06736Comment: 17 pages. To appear, Bulletin of the American Mathematical Society.
Abstract
Gian-Carlo Rota once asserted that "every mathematician only has a few
tricks". The sheer breadth and ingenuity in the work of Jean Bourgain may at
first glance appear to be a counterexample to this maxim. However, as we hope
to illustrate in this article, even Bourgain relied frequently on a core set of
tools, which formed the base from which problems in many disparate mathematical
fields could then be attacked. We discuss a selected number of these tools
here, and then perform a case study of how an argument in one of Bourgain's
papers can be interpreted as a sequential application of several of these
tools.
