The hardest science has the softest forms. Mathematics is often seen as a growing body of definitions, axioms, formulas, and theorems, all fitted together with the greatest precision. Each new proof adds extra cross-bars and...

The Institute hosted the Beyond Endoscopy conference, led by Professor Emeritus Robert P. Langlands, on September 30 and October 1, 2016. View talks from the conference below.

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Explore a collection of Robert Langlands’s papers, as well as some of his lectures and correspondence, on topics ranging from functoriality, representation theory, and base change to endoscopy, Shimura varieties, percolation, and geometric theory...

We felt like we were in uncharted territory: no mathematicians we knew had ever received grants of this magnitude before. Normally, mathematicians receive relatively small individual grants from the National Science Foundation. This sounded a bit scary . . . We turned to the Institute for Advanced Study as the place to foster innovation. As they say, the rest is history.

Modular arithmetic has been a major concern of mathematicians for at least 250 years, and is still a very active topic of current research. In this article, I will explain what modular arithmetic is, illustrate why it is of importance for...

The fundamental lemma has been described as a gross understatement. Says Andrew Wiles, a Visitor in the School of Mathematics and an Institute Trustee, “At first, it was thought to be a minor irritant, but it subsequently became clear that it was not a lemma but rather a central problem in the field.”

It has been said that the goals of modern mathematics are reconstruction and development.^{1} The unifying conjectures between number theory and representation theory that Robert Langlands, Professor Emeritus in the School of Mathematics...

Born on October 6, 1936, in British Columbia, Robert Langlands grew up in a small town where his father owned a building supply store. “When I was a child I liked to add and subtract,” says Langlands. “In our store, my mother worked. And I...

The Langlands program is incredibly vast and far-reaching. The deepest aspect of it, as far as we know, involves the number theory setting where Langlands started close to forty years ago. However, the...

In the 1999–2000 academic year, Robert Langlands, Professor Emeritus in the School of Mathematics, presented a series of Institute talks, “The Practice of Mathematics,” aimed at explaining several central mathematical problems to a general...