Bhargava was born in an Indian family in Hamilton, Ontario, Canada, but grew up and attended school primarily in Long Island, New York. His mother Mira Bhargava, a mathematician at Hofstra University, was his first mathematics teacher. He completed all of his high school math and computer science courses by age 14. He attended Plainedge High School in North Massapequa, and graduated in 1992 as the class valedictorian. He obtained his B.A. from Harvard University in 1996. For his research as an undergraduate, he was awarded the 1996 Morgan Prize. Bhargava went on to pursue graduate studies at Princeton University, where he completed a doctoral dissertation titled “Higher composition laws” under the supervision of Andrew Wiles and received his Ph.D. in 2001, with the support of a Hertz Fellowship. He was a visiting scholar at the Institute for Advanced Study in 2001–02, and at Harvard University in 2002–03. Princeton appointed him as a tenured Full Professor in 2003. He was appointed to the Stieltjes Chair in Leiden University in 2010.

In addition, he won the Morgan Prize and Hertz Fellowship in 1996, a Clay 5-year Research Fellowship, the Merten M. Hasse Prize from the MAA in 2003, the Clay Research Award in 2005, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005.

He was named one of Popular Science magazine’s “Brilliant 10” in November 2002. He won the $10,000 SASTRA Ramanujan Prize, shared with Kannan Soundararajan, awarded by SASTRA in 2005 at Thanjavur, India, for his outstanding contributions to number theory.

In 2008, Bhargava was awarded the American Mathematical Society’s Cole Prize. The citation reads:

In 2009, he was awarded the Face of the Future award at the India Abroad Person of the Year ceremony in New York City. In 2014, the same publication, the most prestigious and most widely read of the diaspora publications, gave him a second prize, India Abroad Publisher’s Prize for Special Excellence.

In 2011, he was awarded the Fermat Prize for “various generalizations of the Davenport-Heilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves”.

In 2011, he delivered the Hedrick lectures of the MAA in Lexington, Kentucky. He was also the 2011 Simons Lecturer at MIT.

In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award, and became a fellow of the American Mathematical Society in its inaugural class of fellows.

In 2013, he was elected to the National Academy of Sciences.

Bhargava has won several awards for his research, the most prestigious being the Fields Medal, the highest award in the field of mathematics, which he won in 2014.

In 2014, Bhargava was awarded the Fields Medal at the International Congress of Mathematicians in Seoul for “developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves”.

In 2015 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.

In 2015, he was awarded the Padma Bhushan, the third-highest civilian award of India.

In 2017, Bhargava was elected as a member of the American Academy of Arts and Sciences.

In 2018 Bhargava was named as the inaugural occupant of The Distinguished Chair for the Public Dissemination of Mathematics at The National Museum of Mathematics (MoMath). This is the first visiting professorship in the United States dedicated exclusively to raising public awareness of mathematics.

Bhargava was conferred a Fellowship at the Royal Society in 2019.