Jean Bourgain and Joram Lindenstrauss.

I was very sad to hear that Jean Bourgain, among the greatest mathematicians of our time, and a dear friend, passed away. I first met Jean about forty years ago and later we became friends and collaborators. In the 80s and 90s Jean used to visit Israel quite often and had close collaboration with the Banach space Israeli community, and with the Ergodic theory community, and with the Harmonic analysis community, and the PDE community, and later also with the combinatorics, probability, algebra, number theory, and theoretical computer science communities. I always admired his immense mathematical powers and his deep devotion to mathematics.

You can read about Jean Bourgain in Terry Tao’s beautiful obituary post. I was also moved by Svetlana Jitomirskaya’s beautiful facebook post. Some of Jean’s contributions to combinatorics (which formed a small portion of his interests) are mentioned in several posts over my blog (and my lecture below). I will try to come back to these mathematical topics at a later post and here I post a few pictures of Jean over the years. Here is the moving IAS obituary notice. See also Ryan O’Donnell’s moving comment. And here is a MathOverflow question Jean Bourgains relatively lesser known significant contributions. (Added later:) Here is a beautiful tribute on GLL for Jean Bourgain and Michael Atiya. Let me also add a link to the moving obituary post of Terry Tao on Elias Stein.

**My 2016 lecture “Questions for Jean Bourgain” about questions that I (and some colleagues) asked Jean Bourgain over the years, mainly in the areas of combinatorics and combinatorial aspects of convexity.**

**Svetlana Jitomirskaya:**

Вечности заложник

У времени в плену

Eternity’s ambassador

held captive by the time…

He was truly a gift from God to humanity and yet unparalleled in his kindness, humbleness, and generosity.

It is an enormous loss

February 28, 1954 – December 22, 2018

Hermann K*ö*nig,Tadeusz Figiel, Jean Bourgain, and Lior Tzafriri (Banach Center Photo Archive)

With Russell Impagliazzo (picture taken from the IAS obituary)

An early picture near the blackboard

Alex Gamburd, Jean Bourgain, and Peter Sarnak.

Crafoord day, Lund 2012 Carlos Kenig, Ben Green, Jean, Terry Tao, me, and Michael Christ.

At IHES, 1989

### Pictures of early version of our first joint work (around 1990) with Izzy Katznelson, Jeff Kahn and Nati Linial.

The initial approach had a 22 page long proof and my copy has a dense (Hebrew) handwritten explanation all the way to page 15.

Part of Page 6

Part of page 19

At the end our team found a shortcut to the problem itself, but both Jean and I have felt over the years that the deeper methods developed initially by Jean may have further important use.

I am not sure when and where the beautiful picture of Jean Bourgain and Joram Lindenstrauss was taken and what is the source. At some point I saw it in google and copied it to my phone, but could not find it again.

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J. B. Cooper send me a picture and wrote: I think that this picture might interest you. It is clearly the same background as on your photo of Bourgain and Lindenstrauss, which I saw on your tribute to Jean Bourgain,and so identifies the occasion of the latter. It is the Conference on Banach Spaces at Strobl, Austria in the summer of 1989 organised by Walter Schachermayer and the Functional Analysis group at Linz. Quite possibly it may have been taken by Tzafriri. Also present at this conference were Pelczyński, Gowers and a host of other prominent analysts.

(Here is the picture)