*In the twentieth century, mathematicians developed a deep theory of knots, which was revolutionized by the discovery of the Jones polynomial—a way to calculate a number for every knot—by Vaughan F. R. Jones in the early*...

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.”

When Friedrich Hirzebruch was a Member in the School of Mathematics in 1954, his paper, "Some problems on differentiable and complex manifolds", was published in the *Annals of Mathematics*. In it he asked whether Chern numbers in...

Physicists have used Feynman diagrams as a tool for calculating scattering amplitudes that describe particle interactions for more than six decades. Their broad utility was due initially in large part to the seminal work of Freeman Dyson,...

*“Scientific research in many domains of knowledge has time after time proved the necessity of abandoning or remoulding viewpoints which, due to their fruitfulness and apparently unrestricted applicability, were regarded as indispensable for*...

One of the remarkable discoveries in astrophysics has been the recognition that the material we see and are familiar with, which makes up the earth, the sun, the stars, and everyday objects, such as a table, is only a small fraction of all of the...

“Everything here is fraught with danger and excitement,” says Nima Arkani-Hamed, Professor in the School of Natural Sciences. With a broad sweep of his hand, he motions to the diagram he has drawn on the chalkboard in his office of the range of...

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...

On the occasion of the 1993 dedication of Simonyi Hall, Phillip Griffiths, then-Director of the Institute, spoke on “Mathematics—From Servant to Partner” in which he described how the relationship between mathematics and other disciplines had...

“The critics feel passionately that they are right, and that their viewpoints have been unfairly neglected by the establishment. They strike a populist note. They bring into the public arena technical claims that few can properly evaluate. They...