Manjul Bhargava
Canadian-American mathematician (born 1974)
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Through India and Computer science
Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation, he was awarded the prize "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". He was also a member of the Padma Award committee in 2023.
In February 2026, he became the first president of the National Museum of Mathematics (MoMath) in New York city.
Education and career
Bhargava was born to an Indian family in Hamilton, Ontario, Canada, but grew up and attended school primarily on 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 AB from Harvard University in 1996, where he was elected to Phi Beta Kappa. For his research as an undergraduate, he was awarded the 1996 Morgan Prize. The research was eventually published in The American Mathematical Monthly in 2000, and established the Bhargava factorial. 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 PhD 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.
Bhargava has also studied the tabla under gurus such as Zakir Hussain. He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a scholar of Sanskrit and ancient Indian history. He is an admirer of Sanskrit poetry.
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Career and research
Bhargava’s PhD thesis generalized Gauss's classical law for composition of binary 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 the asymptotic behavior of the 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. A short list of his specific mathematical contributions are:
- Fourteen 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, Bhargava factorial, providing an answer to a decades-old question of George Pólya.
- Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded.
- Proof that most hyperelliptic curves over Q have no rational points.
In 2015, Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.