Manjul Bhargava

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Manjul Bhargava
Manjul Bhargava.jpg
Born (1974-08-08) August 8, 1974 (age 39)
Hamilton, Ontario
Nationality Canadian, America
Fields Mathematics
Institutions Princeton University
Alma mater Harvard University
Princeton University
Doctoral advisor Andrew Wiles
Doctoral students Michael Volpato
Melanie Wood
Wei Ho
Arul Shankar
Known for Gauss composition laws
15 and 290 theorems
factorial function
ranks of elliptic curves
Notable awards Infosys Prize (2012)
Fermat Prize (2011)
Cole Prize (2008)
Clay Research Award (2005)
SASTRA Ramanujan Prize (2005)
Hasse Prize (2003)
Morgan Prize (1996)
Hoopes Prize (1996)

Manjul Bhargava (मञ्जुल भार्गव) (born August 8, 1974[1]) is an Canadian-American mathematician. He is the R. Brandon Fradd Professor of Mathematics at Princeton University. He is known primarily for his contributions to number theory.


Bhargava's mother, Mira Bhargava, is a mathematician at Hofstra University and his father a chemist.[2] Bhargava grew up in Long Island, New York.[3] Manjul Bhargava completed all of his high school math and computer courses by age 14.[4] He attended Plainedge High School, graduating 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 receive his doctorate from Princeton in 2001, supervised by Andrew Wiles. He was a visiting scholar at the Institute for Advanced Study in 2001-02.[5] Princeton hired him at the rank of tenured full professor within only two years of finishing graduate school, which is considered a record in the Ivy League.[6]

Bhargava is also an accomplished tabla player, having studied under gurus such as Zakir Hussain.[7] He has also studied Sanskrit. His grandfather Purushottam Lal Bhargava is a well-known scholar of Sanskrit and ancient Indian history.


His Ph.D. thesis generalized the classical Gauss composition law for quadratic forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study of asymptotic behavior of arithmetic properties of these orders and fields.

His research also includes fundamental contributions to the representation theory of quadratic forms, to interpolation problems and p-adic analysis, to the study of ideal class groups of algebraic number fields, and to the arithmetic theory of elliptic curves.[8] A short list of his specific mathematical contributions are:

  • 14 new Gauss-style composition laws.
  • Determination of the asymptotic density of discriminants of quartic and quintic number fields.
  • Proofs of the first known cases of the Cohen-Lenstra-Martinet heuristics for class groups.
  • Proof of the 15 theorem, including an extension of the theorem to other number sets such as the odd numbers and the prime numbers.
  • Proof (with Jonathan Hanke) of the 290 theorem.
  • A novel generalization of the factorial function, resolving a decades-old conjecture by George Pólya.
  • Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded.

In July 2010 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.[9]

Awards and Honors[edit]

Bhargava is the second youngest full professor in Princeton University's history, after Charles Fefferman (professor at Princeton at age 24).

Bhargava has won several awards for his research, including the Morgan Prize[10] in 1996, a Clay 5-year Research Fellowship, the Merten M. Hasse Prize from the MAA in 2003,[11] 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.

Peter Sarnak of Princeton University has said of Bhargava:[12]

At mathematics he's at the very top end. For a guy so young I can't remember anybody so decorated at his age. He certainly started out with a bang and has not let it get to his head, which is unusual. Of course he couldn't do what he does if he wasn't brilliant. It's his exceptional talent that's so striking

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 Tanjavur, India, for his outstanding contributions to number theory.

In 2008, Bhargava was awarded the American Mathematical Society's Cole Prize.[13] The citation reads:

Bhargava’s original and surprising contribution is the discovery of laws of composition on forms of higher degree. His techniques and insights into this question are dazzling; even in the case considered by Gauss, they lead to a new and clearer presentation of that theory

In 2011, Bhargava 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".[14]

Bhargava is also a sought-after speaker, having given numerous public lectures around the world. In 2011, he delivered the prestigious Hedrick lectures of the MAA in Lexington, Kentucky.[15] He was also the 2011 Simons Lecturer at MIT.[16]

In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,[17] and became a fellow of the American Mathematical Society in its inaugural class of fellows.[18]

Bhargava was also awarded the 2012 Infosys Prize in mathematics for his “extraordinarily original work in algebraic number theory, which has revolutionized the way in which number fields and elliptic curves are counted".[19]

In 2013, Bhargava was elected to the National Academy of Sciences.[20]

Selected Publications[edit]


External links[edit]