Number Theory

When Ellen Eischen, von Neumann Fellow (2024–25) in the School of Mathematics, followed a stray thread of “lost math” into the Institute’s Shelby White and Leon Levy Archives Center, she uncovered the story of Hel Braun—and a mid-century perspective that still has consequences for research today. Eischen's investigations show what mathematics can forfeit when it treats its truths as untouched by the human, institutional, and political realities that shape them.

Peter Sarnak, Professor Emeritus in the School of Mathematics, has emerged as a pivotal "connector" between the fields of pure math and computer science. His legacy reveals how seemingly esoteric mathematical investigations can yield unexpected and transformative insights.

Meet Ellen Eischen, von Neumann Fellow in the School of Mathematics, who works in the field of number theory, exploring the nature of whole numbers. In this Q&A, she shares her journey through math, from the secret math journal she kept in high school, to a Women in Numbers program that facilitated her research, to joining the Institute for the 2024–25 academic year.

The official award video produced by the International Mathematical Union and the Simons Foundation honors 2018 Fields Medalist Akshay Venkatesh, Professor in the Institute's School of Mathematics.

"A lot of the time when you do math, you're stuck,"...

Thanks to the rabbit I pulled out of my hat on my returning from the museum the other evening, I’ve been able to get back on track. But today I’m filled with a strange mixture of optimism and dread. . . . the complexity of the mathematical landscape that’s now opened up makes my head spin if I think about it for more than a few moments.

A year ago in April, the editors of the Annals of Mathematics, a journal published by the Institute and Princeton University, received an email with a submission by an unknown mathematician. “Bounded Gaps Between Primes” by Yitang Zhang, an adjunct...

From the data, you have this remnant of a real object that you want to resurrect. Before you can start to do that, the first thing you need to know is, is it really coming from such and such an object? Are there some good tests or signatures for that?

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, articulated...

During the first term of 2007–08, School of Mathematics Professor Jean Bourgain and Member Van Vu of Rutgers, The State University of New Jersey, ran a program on arithmetic combinatorics. The Members in residence for the program ranged from Endre...