Ideas

Hong Wang, Member (2019–21) in the School of Mathematics, and Joshua Zahl of the University of British Columbia have announced a solution of the three-dimensional Kakeya conjecture. Their groundbreaking work builds on that of other IAS scholars, including Jean Bourgain, Professor (1994–2018), and Terence Tao, Member (2005, 2023), in the School.

Motivated by the growing interest in using artificial intelligence for teaching purposes, IAS scholars from the Schools of Mathematics and Natural Sciences have conducted an innovative study to assess the correctness and helpfulness of large language models in STEM education. Their research yielded surprising results, including highlighting the importance of training models on conversations rather than textbooks.

In a groundbreaking study, Pravesh Kothari, Visiting Professor (2024) in the School of Mathematics, and Peter Manohar, Member (2024–26) in the School, have transformed theoretical computer scientists’ knowledge of locally correctable codes (LCCs), showing that such codes must grow exponentially as the amount of original data increases.

Learn how Peter Sarnak, Professor Emeritus in the School of Mathematics, emerged as a pivotal "connector," bridging pure mathematics and computer science through his work on Ramanujan graphs, and revealing how seemingly esoteric mathematical investigations can yield unexpected and transformative insights.

From unraveling the mysteries of high-dimensional expanders to exploring the intricate nuances of topology, three new appointments to the Institute's School of Mathematics promise to push the boundaries of fundamental knowledge and inspire groundbreaking discoveries in theoretical computer science, dynamical systems, and geometric analysis.

Suparna Mahableshwarkar, Academic Assistant in the School of Mathematics, describes the wide variety of lectures and events that she has been able to attend while working at the Institute for Advanced Study, ranging from a math magic show to a night of stargazing.

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.

Pravesh Kothari, Visiting Professor in the School of Mathematics (2024), describes his experiences of interacting with “celebrities” from the worlds of pure mathematics and computer science at the Institute for Advanced Study, and how these two fields strongly interconnect at IAS.

The “Paths to Math” series comes to a close with this special edition video, featuring one of our most beloved veteran mathematicians: Distinguished Visiting Professor Karen Uhlenbeck. Watch to see Karen describe the introduction to calculus course that awakened her love for math and her spirited female colleagues in Chicago, who helped to dispel any lingering doubts about being a woman mathematician.

"Imagine that you are blowing a soap bubble using a simple wand. Why does the bubble that you create take the form of a sphere? Why not an ovoid? Or a cylindrical shape? Or something totally random?" Explore the minimization principles that govern such systems with geometric measure theorist Paul Minter, who serves as a Veblen Fellow in the School of Mathematics.