Jean Louis, baron Bourgain (French: [buʁɡɛ̃]; (1954-02-28)28 February 1954 – (2018-12-22)22 December 2018) was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.^[3]

Bourgain received his PhD from the Vrije Universiteit Brussel in 1977. He was a faculty member at the University of Illinois Urbana-Champaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, at the Institute for Advanced Study in Princeton, New Jersey from 1994 until 2018.^[4] He was an editor for the Annals of Mathematics. From 2012 to 2014, he was a visiting scholar at UC Berkeley.^[5]

His research work included several areas of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, analytic number theory, combinatorics, ergodic theory, partial differential equations and spectral theory, and later also group theory. He proved the uniqueness of the solutions for the initial value problem of the Korteweg–De Vries equation. He formulated what became known as the Bourgain slicing problem in high-dimensional convex geometry. In 1985, he proved Bourgain's embedding theorem in metric dimension reduction, which states that every metric space can be embedded into an ${\displaystyle l_{p}}$ space of dimension ${\displaystyle O(log^{2}(n))}$ with distortion ${\displaystyle O(log(n))}$. Together with Vitali Milman, he contributed to progress on Mahler’s conjecture in 1987. In 2000, Bourgain connected the Kakeya problem to arithmetic combinatorics.^[6][7] As a researcher, he was the author or coauthor of more than 500 articles.^[8]

Together with Ciprian Demeter and Larry Guth, he proved Vinogradov's mean-value theorem in 2015.

Bourgain was diagnosed with pancreatic cancer in late 2014. He died of it on 22 December 2018 at a hospital in Bonheiden, Belgium.^[9]

Bourgain received several awards during his career, the most notable being the Fields Medal in 1994.

In 2009 Bourgain was elected a foreign member of the Royal Swedish Academy of Sciences.^[10]

In 2010, he received the Shaw Prize in Mathematics.^[11]

In 2012, he and Terence Tao received the Crafoord Prize in Mathematics from the Royal Swedish Academy of Sciences.^[12]

In 2015, he was made a baron by king Philippe of Belgium.^[13]

In 2016, he received the 2017 Breakthrough Prize in Mathematics.^[14]

In 2017, he received the 2018 Leroy P. Steele Prizes.^[15]