Manjul Bhargava

The 2005 Clay Research Award was made to Manjul Bhargava for his discovery of new composition laws for quadratic forms and for his work on the average size of ideal class groups.

The field of composition laws had lain dormant for 200 years since the pioneering work of C.F Gauss. The laws discovered by Bhargava were a complete surprise, and led him to another major breakthrough, namely, counting the number of quartic and quintic number fields with given discriminant. The ideal class group is an object of fundamental importance in number theory. Nonetheless, despite some conjectures of Cohen and Lenstra about this problem, there was not a single proven case before Bhargava’s work. Bhargava solved the problem for the 2-part of the class groups of cubic fields, in which case, curiously, the numerical evidence had led people to doubt the Cohen-Lenstra heuristics.