*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 1980s. Below, Edward
Witten*...

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General Theory of Relativity

Albert Einstein finished his general theory of relativity in November 1915 and its influence has been profound, dramatically influencing the direction of physics, cosmology, and mathematics. His field equations of gravitation explained how matter curves spacetime, how this curvature tells matter how to move, and it gave scientists the mathematical tools to understand how space would evolve in time, leading to a deeper understanding of the universe’s early conditions and development.

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, articulated...

Why is the expansion of the universe speeding up, instead of being slowed by the gravitational attraction of galaxies and dark matter? What is the history of the Milky Way galaxy and of the chemical elements in its stars? Why are the planetary...

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...

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 evolved...