About
Jean Bourgain was one of the greatest problem solvers of his time, but his papers are notoriously terse. They were often written in one sitting, and the reader is left to fill in many of the details. The first goal of this project is to understand all of his works completely and to present them in a way that early-career mathematicians can follow. We hope to obtain a complete digestion of each of his papers, including a short summary of what the paper proves and the impact it has had. A digestion does not have to be in the form of a traditional paper: it may include animations, a toggle between levels of detail, video lectures, or more. It may also include a dependency tree of how Bourgain's result builds on previously known mathematics, or record how more recent results rely on Bourgain's work.
We hope that in the process of collecting and digesting all of these papers we will also more clearly see the work of Bourgain as a whole. In Bourgain's toolkit we intend to explore the ideas and techniques that recur across his papers. In Bourgain's collaborators we have recorded the people he has worked with and in Impact of Bourgain's work we are beginning to document the amazing breadth and influence of his work. Together as a community, we hope that this project will more clearly map out the fields he worked in, the connections between them, and his influence on other mathematicians.
This project is also an experiment in how mathematics is presented. We want to try formats beyond the standard PDF, such as animations and recorded talks, and to build a community of mathematicians who team up to digest the most influential papers in their fields. In particular, multiple digestions and group digestions are highly encouraged.
Aside from digesting the papers, we also encourage formalizations in Lean or other proof assistants. How to optimally present and digest formalizations is an interesting question, which we hope will also be elucidated during the course of this project. All maintainers are comfortable with using Lean and are happy to discuss questions regarding how to best present the Lean formalizations of Bourgain's results.
Maintainers
The Bourgain Project is run and maintained by
- Mitchell A. Taylor, University of Oxford and University of Toronto
- João Pedro Ramos, Instituto de Matemática Pura e Aplicada (IMPA)
- Lukas Liehr, Bar-Ilan University
To reach them, write to [email protected]. If you would like to digest a paper yourself, or find a group to digest it with you, the Contribute page explains how. You may also join the Zulip chat “temporaryname”.
Bibliography
The bibliography is merged from three open sources: zbMATH Open, OpenAlex and arXiv.
Citation counts come from OpenAlex and are refreshed about once a week. They were last refreshed on 2026-08-24.
Policies
We ask everyone who contributes to the project to follow a few basic rules.
- Credit. We will follow the usual academic policies towards credit. A digestion that builds on another digestion, a set of lecture notes, or a later paper should say so, and every result or tool that was used – including AI – should be cited with a precise reference. In particular, we acknowledge the use of Claude Opus 5.5 in helping create this website.
- Accuracy. To within good faith, a digestion should be correct and complete. If a step in Bourgain's paper could not be verified, the digestion should say so plainly rather than passing over it, and errors found in the original paper should be tactfully recorded and/or fixed.
- Use of AI. We have no policy on AI tools other than disclosure. We leave it to the contributor to decide whether they want to use AI.
- Copyright. The summaries, digestions, toolkit entries and collaborator biographies are written by this project. The bibliographic records, the citation counts, and the papers themselves are not ours. Links point to the publisher, arXiv, or a repository, and no copyrighted full text is redistributed here.
- Corrections. Anyone who finds an error is encouraged to write to the maintainers. Corrections are made openly and acknowledged.
- Conduct. Discussion on the project, whether about the mathematics or about how it is presented, should be courteous and generous to others, especially to those who are early in their careers.