Videos

The history of digital computing can be divided into an Old Testament whose prophets, led by Gottfried Wilhelm Leibniz, supplied the logic, and a New Testament whose prophets, led by John von Neumann, built the machines. Alan Turing, whose “On...

One of the oldest subjects in mathematics is the study of Diophantine equations, i.e., the study of whole number (or fractional) solutions to polynomial equations. It remains one of the most active areas of mathematics today. Perhaps the most basic...

In Greek religion, the encounter between mortals and gods was dominated by fear. The belief in the power of gods was based on experience and enhanced through rituals. Cult regulations, narratives of punitive miracles, confession inscriptions, and...

This lecture, presented by Vladimir Voevodsky, 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 events related to the Schools of Mathematics...

John Milnor commented on D’Arcy Thompson’s On Growth and Form, first published in 1917, which studied how the shape of an organism changes as it grows and the way that shape changes in the course of evolution. Milnor discussed the hypothesis that...

In this lecture, John Milnor, Co-Director of the Institute for Mathematical Sciences at Stony Brook University and a former member of the Faculty of the School of Mathematics at the Institute for Advanced Study (1970-90), offers commentary on the...

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...

Quantum theory radically transforms our fundamental understanding of physical reality. It reveals that the world contains a hidden richness of structure that we have barely begun to control and exploit. According to quantum theory, what we perceive...

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 events related to the Schools and...

In this talk, Nima Arkani-Hamed, Professor in the School of Natural Sciences, discusses the direction of fundamental physics in coming years and decades, including efforts to replace the concept of spacetime and understand how the macroscopic world...