School of Mathematics

Catherine Eva Pfaff, Member in the School of Mathematics (2024–25), discusses the ways in which geometric group theorists and theoretical computer scientists at the Institute for Advanced Study approach mathematical constructions and learn from one another’s insights.

Theresa Arzadon-Labajo, Senior System Administrator in the Institute for Advanced Study's School of Mathematics, reflects on fond memories that she has of working alongside Professor Emeritus Pierre Deligne.

Mikaela Iacobelli, von Neumann Fellow in the School of Mathematics (2024–25), describes her work on plasma—often called "the first state of matter"—and her exploration of convex integration, a new field she is investigating at the Institute for Advanced Study.

Jean Gutt, von Neumann Fellow in the Institute for Advanced Study's School of Mathematics (2024–25), recounts how dialogue with a School of Historical Studies colleague over lunch revealed connections between disparate fields.

Bennett Chow, Member in the Institute for Advanced Study's School of Mathematics (2024–25), traces new paths of discovery being undertaken in the field of geometric analysis, influenced in particular by Professor Aaron Naber.

Aaron Naber, Professor in the School of Mathematics, explores singularities that emerge when mathematical solutions break. He also shares his journey to finally solving the energy identity conjecture at the Institute for Advanced Study after years of dedicated work.

Ellen Eischen, von Neumann Fellow in the School of Mathematics (2024–25), shares her journey of discovery through the Institute for Advanced Study's archives, uncovering the story of Hel Braun, Member (1947–48) in the School, a significant yet overlooked pioneer in number theory.

Mark Goresky, Visitor in the School of Mathematics (2024–29), recounts how Institute for Advanced Study scholars have weathered storms to advance their scholarship.

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. 

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.