# A professor who sees common thread in Sanskrit, music and mathematics

**Bibhu Ranjan Mishra |**Bangalore

**August 14, 2014**

Manjul Bhargava

**Manjul Bhargava wins Fields Medal, considered Nobel Prize for maths**

Do Indian classical music and Sanskrit have a direct correlation with mathematics? In case you are confused, ask Manjul Bhargava. The mathematics professor at Princeton University who just turned 40 took inspiration from both music and Sanskrit to pursue mathematics, his pet subject - and how. On Wednesday, he won Fields Medal, often described as the 'Nobel Prize of Mathematics', and was chosen one of the four best mathematicians globally. He is the first Indian-origin person to win this medal.

"As a child, I enjoyed studying Sanskrit, Sanskrit poetry and Indian classical music. I saw maths in all these things; that further inspired me to pursue mathematics. When I went to college, I took Sanskrit, a lot of music, computer science and physics, and also mathematics. To me, mathematics was the common thread in all these subjects," he says.

A graduate in mathematics from Harvard University and a PhD from Princeton University in 2001, Bhargava is also a recipient of the Infosys Prize for Mathematical Sciences, which he received in 2012.

"Today is an incredible day of celebration for all of us Indians… This (Fields Medal) in some sense is harder to win than the Nobel, since it is awarded once every four years and the winner has to be younger than 40 years old. This is an extraordinary and rare achievement," says N R Narayana Murthy, co-founder & chairman of Infosys, the country's second-largest IT services firm.

In a world where students are losing interest in research in pure basic sciences, Bhargava is an exception. As a child, mathematics always fascinated him. "One of my early childhood memory was stacking oranges in the form of a pyramid. My work primarily revolves around understanding whole numbers like prime and square," he says.

After finishing his PhD, Bhargava joined Princeton University as a professor in 2003. His primary research interests lie in the number theory, representation theory, and algebraic geometry. Since then, he has earned several awards and citations for his contribution to many critical areas of mathematical research and algorithm, including Derek Bok Awards for Excellence in Teaching, Hoopes Prize for Excellence in Scholarly Work and Research from Harvard University and AMS-MAA-SIAM Morgan Prize for Outstanding Undergraduate Research in Mathematics.

The Fields Medal this year was conferred on him 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.

Named after Canadian mathematician John Charles Fields and instituted by International Mathematical Union, Fields medal is awarded once every four years to exceptional talents under the age of 40. Though the award carries cash prize of around 15,000 Canadian dollars, it is considered the highest honour in the field of mathematical research.

He was born in Canada and brought up in the US but Bhargava, with roots in Jaipur, has a strong connection with India. "We speak Hindi at home and celebrate all Indian festivals. I am pretty much an Indian at heart."

Besides mathematics, which is his first love, he is also an accomplished tabla player; he learnt that art with Pandit Prem Prakash Sharma and Ustad Zakir Hussain.

"I first met him when he won the Infosys Science prize three years ago. If you meet or talk to Manjul, you will find he is very passionate about India and has his interests close to his heart. He is as unassuming and friendly as he is brilliant," Murthy adds.

Bhargava feels very sad about the state of scientific research in India. Despite having very good mathematical talent, many are getting attracted to engineering and medicines for "easy money", he says, adding this is a mistake that might prove costly, not only to the individual but to the country.

"Science is also a very collaborative discipline... So, doing scientific research is like a big venture that gives you an amazing feeling… it is a lot of fun and it is very important for the world," Bhargava says.

"As a child, I enjoyed studying Sanskrit, Sanskrit poetry and Indian classical music. I saw maths in all these things; that further inspired me to pursue mathematics. When I went to college, I took Sanskrit, a lot of music, computer science and physics, and also mathematics. To me, mathematics was the common thread in all these subjects," he says.

A graduate in mathematics from Harvard University and a PhD from Princeton University in 2001, Bhargava is also a recipient of the Infosys Prize for Mathematical Sciences, which he received in 2012.

"Today is an incredible day of celebration for all of us Indians… This (Fields Medal) in some sense is harder to win than the Nobel, since it is awarded once every four years and the winner has to be younger than 40 years old. This is an extraordinary and rare achievement," says N R Narayana Murthy, co-founder & chairman of Infosys, the country's second-largest IT services firm.

In a world where students are losing interest in research in pure basic sciences, Bhargava is an exception. As a child, mathematics always fascinated him. "One of my early childhood memory was stacking oranges in the form of a pyramid. My work primarily revolves around understanding whole numbers like prime and square," he says.

After finishing his PhD, Bhargava joined Princeton University as a professor in 2003. His primary research interests lie in the number theory, representation theory, and algebraic geometry. Since then, he has earned several awards and citations for his contribution to many critical areas of mathematical research and algorithm, including Derek Bok Awards for Excellence in Teaching, Hoopes Prize for Excellence in Scholarly Work and Research from Harvard University and AMS-MAA-SIAM Morgan Prize for Outstanding Undergraduate Research in Mathematics.

The Fields Medal this year was conferred on him 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.

Named after Canadian mathematician John Charles Fields and instituted by International Mathematical Union, Fields medal is awarded once every four years to exceptional talents under the age of 40. Though the award carries cash prize of around 15,000 Canadian dollars, it is considered the highest honour in the field of mathematical research.

He was born in Canada and brought up in the US but Bhargava, with roots in Jaipur, has a strong connection with India. "We speak Hindi at home and celebrate all Indian festivals. I am pretty much an Indian at heart."

Besides mathematics, which is his first love, he is also an accomplished tabla player; he learnt that art with Pandit Prem Prakash Sharma and Ustad Zakir Hussain.

"I first met him when he won the Infosys Science prize three years ago. If you meet or talk to Manjul, you will find he is very passionate about India and has his interests close to his heart. He is as unassuming and friendly as he is brilliant," Murthy adds.

Bhargava feels very sad about the state of scientific research in India. Despite having very good mathematical talent, many are getting attracted to engineering and medicines for "easy money", he says, adding this is a mistake that might prove costly, not only to the individual but to the country.

"Science is also a very collaborative discipline... So, doing scientific research is like a big venture that gives you an amazing feeling… it is a lot of fun and it is very important for the world," Bhargava says.

#
Indian math: from Bhaskara to Bhargava The story of Indian mathematics is like a non-linear equation http://www.livemint.com/Opinion/RhfpRwTSarIkqxUAmjZdPJ/Indian-math-from-Bhaskara-to-Bhargava.html

Aug. 13, 2014

## Indian math: from Bhaskara to Bhargava

The story of Indian mathematics is like a non-linear equation

Illustration: Jayachandran/Mint

A Princeton University mathematician of Indian origin has won the Fields Medal this year. He is among four winners, including Maryam Mirzakhani, a mathematician from Iran who is currently at Stanford University, and the first woman to win the prestigious medal.

Manjul Bhargava is a specialist in number theory who has proved a number of important results among them a special case of the Birch and Swinnerton-Dyer conjecture, one of the seven Millennium Prize Problems that have, historically, remained unproven. The Fields Medal is only one more milestone in this young mathematician’s journey that has involved proving many creative theorems and problems.

Mathematics, of all the arenas of human endeavour, is removed from nationalistic feeling. But the award of the prize to a person of Indian origin is an apposite occasion to ask another question: whatever happened to India’s indigenous tradition of mathematics? Incidentally, 2014 also marks the 1,000th birth anniversary of the medieval Indian mathematician Bhaskaracharya, who penned a treatise called the

*Lilavati*. While Bhargava may be of Indian origin, the tradition to which he belongs is of Western origin, dating back to at least Pierre de Fermat (1607-1665).
There is no doubt about an Indian mathematical school that began with Aryabhatta in late fifth century AD. But at the same time, there can be no denying—except for modern day mythologists who believe that Indian mathematicians knew it all—India’s mathematical tradition was arrested before it could develop. The tradition had potential for sure. For example, Bhaskaracharya studied, among other things, Pell’s Equation—a polynomial equation of the type x2-ny2=1—but then matters stopped there. Between Bhaskaracharya and some medieval writers of mathematical commentaries, India’s mathematical history is obscure until 20th century when Srinivasa Ramanujan carried out respectable mathematical work. (Incidentally, one of the theorems that Bhargava proved—the 15 Theorem of John Conway and WA Schneeberger—involves quadratic forms, a subject that Ramanujan studied).

So, whatever happened to Indian mathematics? There are many ways to look at the story. One is to ask an Indian version of the “Needham Question”: If India indeed was ahead in scientific discoveries at one point in its history, how did the West march ahead not only in economic growth and prosperity but also in the creation of mathematical knowledge? Unlike Europe, where even during the Dark Ages, universities never ceased to exist, India never knew an organized system of producing and disseminating knowledge during this period. While, at the end of its feudal age, Europe took off—intellectually and economically, India experienced a reverse journey into servitude as Britain colonized her.

But here is where the story takes a twist: It was the British who opened the first universities in India in the 19th century as part of a modernizing colonialism and did not “kill” an indigenous tradition which, in any case, had wilted away a long time ago. The story of India’s mathematical poverty, to use a mathematical analogy, is not a linear equation; it is more like a non-linear differential equation.

While India’s lost mathematical tradition is worthy of historical exploration, there is no cause for mourning. In recent years and decades, Indians and people of Indian origin have made creative contributions to mathematics. Recognition of such efforts, while important, is only second to the mission of proving beautiful theorems and interesting discoveries. A young crop of mathematicians trained within the country is now among the best in the world.

A concluding word about the Fields Medal. While it occupies a special place in the scholarly awards, is not the final word in the recognition of mathematical genius and creativity. Consider number theory itself where a number of outstanding mathematicians did not win the prize. Chief among them Andrew Wiles, who proved Fermat’s Last Theorem and Goro Shimura and Yutaka Taniyama, the two mathematicians who made an important cross connecting discovery that made Wiles’ proof possible.

*What halted the march of mathematics in India? Tell us at views@livemint.com*

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