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. Awards and honours 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. Bhargava was conferred a Fellowship at the Royal Society in 2019. Bhargava is the third-youngest full professor in Princeton University's history, after Charles Fefferman and John Pardon. 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. Peter Sarnak of Princeton University has said of Bhargava: 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