Impact of Bourgain's work

This section records the influence of Bourgain's work on the rest of mathematics. The citation tree shows every one of his papers, arranged by field, together with the works that cite them, so that one can see how far each result has travelled and in which directions. Below it, the open problems collect the questions his papers left open, what was known when they were posed, and the progress made on them since.

This section is under development and we encourage input from the community. We welcome blog posts explaining the impact Bourgain has had on them as well as personal anecdotes. As the papers are digested, we will also look for unexpected connections between papers/fields and further analyze how his papers influenced the development of various parts of mathematics.

Citation tree

Below is an interactive graph which includes every paper of Bourgain, arranged by subject. Bourgain is at the centre, his fields are on the inner ring and their subject classes on the next, and his papers form the outer shell, rising from 1976 at the bottom to the present at the top. Click a paper to see, in gold, every work that cites it, placed further out the later it appeared. The citations come from OpenAlex.

Impact and followup work

Here, we will add discussions on and organizations of the research directions influenced by Bourgain. We will record and organize followups to his papers, impacts on the community, ingenious methods, generalizations of his results, and more. What we include here will be largely guided by the community, so please join the Zulip chat “temporaryname”.

This section will also record consequences of The Bourgain Project, whether that be new collaborations, solutions to open problems, better organization of the fields affected by Bourgain, a deeper appreciation of his work, or a collection of historical anecdotes.