Manjul Bhargava

Princeton University

Manjul Bhargava is a Canadian-American number theorist and the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, awarded the Fields Medal in 2014. As a graduate student he stunned the mathematical world by discovering thirteen new composition laws generalizing Carl Friedrich Gauss's two-hundred-year-old law of composition for binary quadratic forms, reframing classical questions through the lens of higher composition laws and the geometry of numbers. His subsequent work on arithmetic statistics, much of it joint with collaborators including Arul Shankar, produced breakthrough results on the average size of class groups, the distribution of discriminants of number fields, and bounds on the average rank of elliptic curves, including proofs that a positive proportion of elliptic curves satisfy the Birch and Swinnerton-Dyer conjecture. He also developed novel methods for counting number fields of small degree. Beyond his Princeton chair, Bhargava holds the Stieltjes Professorship at Leiden University and adjunct positions at the Tata Institute of Fundamental Research, IIT Bombay, and the University of Hyderabad, and is a Fellow of the Royal Society. A celebrated expositor and accomplished tabla player, he draws connections between mathematics, Sanskrit poetry, and music. His foundational results in number theory underpin modern arithmetic geometry and remain reference material for research programs across pure mathematics.