Home / News / World /  Indian-origin mathematician Manjul Bhargava wins Fields Medal

New Delhi: Manjul Bhargava, a Canadian mathematician of Indian origin, has been awarded the prestigious 2014 Fields Medal at the International Mathematical Union’s (IMU) International Congress of Mathematicians held in Seoul.

Bhargava, 40, is the first person of Indian origin to receive the prestigious medal, which has been awarded since 1936 and recognizes outstanding mathematical achievement for existing work and the “promise of future achievement".

Known to colleagues as a gifted mathematician who would devise new and simple methods to prove centuries-old theorems in number theory, Bhargava’s work has been described by IMU as based both on a deep understanding of the representations of arithmetic groups and a unique blend of algebraic and analytic expertise.

Bhargava was awarded the medal “for developing powerful new methods in geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves", IMU said. One of Bhargava’s most prominent discoveries was a thesis that threw a new light on Gauss’s Law for the composition of two binary quadratic forms.

When Bhargava was a graduate student, he read Disquisitiones Arithmeticae, where Gauss developed his composition law which gives a method for composing two binary quadratic forms to obtain a third one. According to IMU’s description of his work, Bhargava one day came up with the idea that if he cut off the Rubik’s mini-cube into half and labelled each corner of the cube with two sets of numbers, that would lead to a cubic analogue of the Gauss Composition. After being cut, a Rubic’s mini-cube could generate three quadratic forms. From the three ways of slicing the cube, three binary forms emerged, and so Bhargava had discovered a simple way to prove the law.

“It’s all about contributing to the understanding of ourselves and the world around us. One of the keys to understanding mathematical problems that people have been thinking about for years is to think about them in a totally different way," said Bhargava in an interview with Simons Foundation and IMU.

He went on to discover 12 other analogues of Gauss compositions over the years. He received his Ph.D in 2001 from Princeton University for a thesis that has been described as “stunning" and a “breakthrough". It generalized the classical Gauss composition law for quadratic forms to many other situations, according to the Tata Institute of Fundamental Research. By 2003, Bhargava had become a professor at Princeton .

Born in 1974 in Canada, Manjul Bhargava grew up in the US and often visited Jaipur to stay with his grandparents. His grandfather was a professor in Sanskrit from whom Bhargava learnt Sanskrit poetry, while his mother was a mathematics professor who allowed Bhargava to attend her college-level classes as a child, according to interviews.

“He is an extremely original mathematician, who has developed a style which is distinctly his own," said Benedict Gross, professor of mathematics at Harvard University, who has known Bhargava since his days as a Harvard undergraduate. “His method—combining the arithmetic interpretation of integral orbits with their enumeration, using the geometry of numbers—has led to the solution of a large number of problems in number theory. I think his mathematical work is tremendously important, and has changed the face of the subject," added Gross, who himself is a renowned mathematician for his work on the Gross-Zagier Theorem that won him the Cole Prize along with his collaborators.

Bhargava has also collaborated with mathematicians to increase the understanding of elliptic curves, which are one of the fundamental objects in number theory with applications in the fields of cryptography and data security.

Describing the uniqueness of his work, Gross said, “He obtains results ‘on average’ that we can’t obtain in individual cases. For example, for a cubic equation (an elliptic curve), it is quite difficult to determine the size of the group of rational solutions. Bhargava determines an upper bound on the average size, over all cubic equations with rational coefficients."

Bhargava is an accomplished tabla player, having trained under Ustad Zakir Hussain, one of the greatest exponents of the percussion instrument. He is also an impressive and lucid orator. “He is a very kind person, who shares his ideas freely with others. He is also a talented tabla player, who loves music and other arts," said Gross.

Peter Sarnak, professor in the department of mathematics at Princeton University, said, “Bhargava has developed fundamental new tools geometric and diophantine, to count objects in algebraic number theory, that before his work seemed hopeless. His work reminds me of the great German mathematician Hermann Minkowski’s work in number theory: it is brilliant, clear and beautiful and has reshaped the landscape."

Three others received the Fields medal—Maryam Mirzakhani, the first Iranian and the first woman to be awarded the medal; Artur Avila, the first Brazilian to be awarded, and Martin Hairer, the first Austrian to win the medal.

Subhash Khot, an Indian-origin scientist from New York University, was awarded the Nevanlinna Prize in Seoul for his prescient definition of the “Unique Games" problem, and his efforts to understand its role in the study of efficient approximation of optimization problems, which have produced breakthroughs in algorithmic design and approximation hardness, according to ICM.

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