Who makes a paper every week,

and every month a new technique,

and founds new branches every year,

and does not know the sense of fear?

And legends—whom d'you hear about?

And if you met him you'd be proud.

Of course...

There are two labyrinths of the human mind: one concerns the composition of the continuum, and the other the nature of freedom, and both spring from the same source—the infinite. —Baron von Leibniz...

Jean Bourgain, IBM von Neumann Professor in the School of Mathematics, was bestowed the title of Baron by the Belgian government in July 2015. In association with the honor, Bourgain designed a coat of arms inscribed “In hope against hope.”...

In 2016, the Institute celebrated the work and impact of Jean Bourgain, IBM Von Neumann Professor in the School of Mathematics and member of the Faculty since 1994. Recipient of the Fields Medal and the Shaw Prize...

Thanks to the rabbit I pulled out of my hat on my returning from the museum the other evening, I’ve been able to get back on track. But today I’m filled with a strange mixture of optimism and dread. . . . the complexity of the mathematical landscape that’s now opened up makes my head spin if I think about it for more than a few moments.

I sometimes like to think about what it might be like inside a black hole. What does that even mean? Is it really “like” anything inside a black hole? Nature keeps us from ever knowing. (Well, what we know for sure is that nature keeps us from...

The study of expander graphs has been a rapidly developing subject in discrete mathematics and computer science. Expander graphs are sparse graphs, meaning they have few edges, with strong connectivity properties. They have many applications,...

This lecture, presented by Jean Bourgain, IBM von Neumann Professor in the School of Mathematics, was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the...

**Computational Intractability and Pseudorandomness**

The areas of computational intractability and pseudorandomness have been among the most exciting scientific disciplines in the past decades, with...

Although the concept of randomness is ubiquitous, it turns out to be difficult to generate a truly random sequence of events. The need for "pseudorandomness" in various parts of modern science, ranging from numerical simulation to cryptography,...

During the first term of 2007–08, School of Mathematics Professor Jean Bourgain and Member Van Vu of Rutgers, The State University of New Jersey, ran a program on arithmetic combinatorics. The Members in residence for the program ranged from...