Ideas

Explore firsthand accounts of research and questions posed by IAS scientists and scholars. From art history to string theory, from moral anthropology to the long-term fate of the universe, contributions span the last decade to the research of today.

In colloquial speech the word “duality” connotes two contrasting facets of a single entity, often at odds with one another. The concept is anthropomorphized in mythology by deities or monsters with multiple faces, like the two-faced Janus, Roman god of doorways. It is also enshrined in pop culture in the double visages of Jekyll and Hyde, and in the Batman villain Harvey Dent (alias Two-Face). In physics and mathematics, the concept of “duality” takes on a more positive connotation because of its ubiquity, utility, and power. 

Adventures of a Mathematician

The Institute for Advanced Study distributed $21,742.50 in stipends for mathematics and $10,000 for theoretical physics during the academic year 1935–36. Three hundred dollars, sufficient to secure entry to the United States, was awarded to the Polish mathematician Stanislaw Ulam (1909–84), who had written to John von Neumann about a problem in measure theory in 1934.

Karen Uhlenbeck’s Pioneering Path in Mathematics

[In high school] I remember the book by George Gamow, One, Two, Three, Infinity. I think that was my first mathematical achievement, to understand the differences in the kinds of infinities there are. I really liked that satisfaction of understanding why there was more than one kind of infinity. — Distinguished Visiting Professor Karen Uhlenbeck, the first woman to win the prestigious Abel prize

Knots and Quantum Theory

Much of the theory of knots is best understood in the framework of 20th- and 21st-century developments in quantum physics. In other words, what really fascinates me are not the knots per se but the connections between the knots and quantum physics.

Race After Technology

Like everyone who lives in a heavily policed neighborhood, I grew up with a keen sense of being watched. Family, friends, and neighbors—all of us caught up in a carceral web, in which other people’s safety and freedom are predicated on our containment.

Q&A with John Urschel

John Urschel, Member in the School of Mathematics, is an applied mathematician/theoretical computer scientist as well as a former professional football player, who spent three seasons with the Baltimore Ravens. Urschel retired from the NFL in 2017...

Solving the Mysteries of Deep Learning

Sanjeev Arora, Distinguished Visiting Professor in the School of Mathematics, specializes in the theory of deep learning, with an interest in natural language processing and privacy. He speaks with IAS's Joanne Lipman about why deep learning is a “black box,” and navigating ethical issues of bias and privacy.

Antiquities in the Dining Hall

Hanging on the walls of Simons Hall are four late antique mosaics. Their migration from the floors of private houses in a Near Eastern city under Roman rule to a research institute in North America is a story of affluence, oblivion, and rediscovery.