%0 Journal Article %1 tao2020exploring %A Tao, Terence %D 2020 %K mathematics readings theory %T Exploring the toolkit of Jean Bourgain %U http://arxiv.org/abs/2009.06736 %X 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.

@article{tao2020exploring, 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.}, added-at = {2020-09-21T15:30:14.000+0200}, author = {Tao, Terence}, biburl = {https://www.bibsonomy.org/bibtex/2ecae88e12a527d55c1ea5b706a015c53/kirk86}, description = {[2009.06736] Exploring the toolkit of Jean Bourgain}, interhash = {a60723736d381cec491fd75f9f7c00cc}, intrahash = {ecae88e12a527d55c1ea5b706a015c53}, keywords = {mathematics readings theory}, note = {cite arxiv:2009.06736Comment: 17 pages. To appear, Bulletin of the American Mathematical Society}, timestamp = {2020-09-21T15:30:14.000+0200}, title = {Exploring the toolkit of Jean Bourgain}, url = {http://arxiv.org/abs/2009.06736}, year = 2020 }