He attended MIT as an undergraduate, despite obtaining the first rank in the entrance examination for the Indian Institute of Technology (out of a few hundred thousand applicants). He received S.B. degrees in EECS, mathematics and physics from MIT in 2002. A two-time Putnam Fellow, Kumar received the Jon A. Bucsela Prize for the strongest undergraduate in mathematics at MIT. He also received the Harvard Putnam and GSAS fellowships for graduate school at Harvard, where he completed a Ph.D. mathematics in 2006 under the supervision of Noam Elkies and Barry Mazur. Kumar then took a postdoctoral research appointment at Microsoft, 2006-07, before joining the MIT mathematics faculty as assistant professor in 2007. He was promoted to associate professor in 2012. Professor Kumar works in the field of arithmetic algebraic geometry, lattices and sphere packings, and combinatorics and discrete geometry.