Princeton University mathematician Manjul Bhargava has been awarded the 2014 Fields Medal, one of the most prestigious awards in mathematics, in recognition of his work in the geometry of numbers. The International Mathematical Union (IMU) presents the medal every four years to researchers under the age of 40 based on the influence of their existing work and on their "promise of future achievement."

The honor, often referred to as the "Nobel Prize of mathematics," has been awarded to four young researchers at the 2014 IMU International Congress of Mathematicians held in Seoul, South Korea. Bhargava is the eighth Fields Medal recipient from Princeton since 1954 and the third consecutive awardee from the University, following recipients in 2006 and 2010.

Born in 1974 in Canada, Manjul Bhargava grew up in the US and also spent much time in India. Manjul Bhargava is the first Indian origin Mathematician to win a Fields Medal. The other three winners this year are Maryam Mirzakhani, Martin Hairer and Artur Avila. Iranian-born mathematician and Stanford University professor Maryam Mirzakhani has become the first woman to win the prize.

The prize committee commended Bhargava, the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton, "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." The IMU further wrote that his "work in number theory has had a profound influence on the field. A mathematician of extraordinary creativity, he has a taste for simple problems of timeless beauty, which he has solved by developing elegant and powerful new methods that offer deep insight…. He surely will bring more delights and surprises to mathematics in the years to come."

Bhargava, who joined the Princeton faculty in 2003 after receiving his Ph.D. in mathematics from the University in 2001, said that the honor extends beyond himself to include those who have worked alongside him during his career. "I am of course very honored to be receiving the Fields Medal," Bhargava said. "Beyond that, it is a great source of encouragement and inspiration, not just for me, but I hope also for my students, collaborators and colleagues who work with me. Needless to say, this is their prize, too!"

Bhargava's mother, Mira Bhargava, is a mathematician at Hofstra University and his father a chemist. Bhargava was born in Hamilton, Ontario, but grew up in Long Island, New York. Manjul Bhargava completed all of his high school math and computer courses by age 14. 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. 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.

Bhargava is also an accomplished tabla player, having studied under gurus such as Zakir Hussain. 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. 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.

Bhargava has received numerous awards for his work, including the 2012 Infosys Prize; the 2011 Fermat Prize presented by the Toulouse Mathematics Institute in France; the 2005 SASTRA Ramanujan Prize from the Shanmugha Arts, Science, Technology and Research Academy in India; the AMS Blumenthal Award for the Advancement of Pure Mathematics in 2005; and the Packard Foundation Fellowship in Science and Engineering in 2004. He was elected to the U.S. National Academy of Sciences in 2013. He also was named one of Popular Science magazine's "Brilliant 10" in 2002.

"Bhargava has developed a unique mathematical style", Benedict Gross, a mathematician at Harvard University who has known Bhargava since the latter’s undergraduate days,

said, “You could look at a paper and say, ‘Manjul’s the only one who could have done that.’ It’s the mark of a really great mathematician that he doesn’t have to sign his work.”

Courtesy: Wikipedia and Princeton University official website.

## Sameen Ahmed Khan

16 September

Heartiest Congratulations!

With warm regards + best wishes

Sameen Ahmed KHAN

Engineering Department

Salalah College of Technology,

Salalah, Sultanate of OMAN. http://SameenAhmedKhan.webs.com/