How does it feel to have won the Fields Medal? You are the first person of Indian origin to be getting it...
It is of course a great honour; beyond that, it is a great source of inspiration and encouragement - not just for me, but for my students, collaborators, and colleagues who work with me. Hopefully, it is also be a source of inspiration for young people in India to take up research in the sciences!
You have grown up in Canada... did you have any cultural identity questions? Do you think of yourself as a Canadian, American, Indian or none of these or all of these?
I was born in Canada, but grew up mostly in the U.S. in a very Indian home. I learned Hindi and Sanskrit, read Indian literature, and learned classical Indian music. I ate mostly Indian food! On the other hand, I grew up playing with American kids and went to school mostly in the U.S. I liked growing up in two cultures like that because it allowed me to pick and choose the best of both worlds. My Indian upbringing was very important to me.
I also spent a lot of time in India growing up. Every three or four years, I would take off six months of school to spend it in India -- mostly in our hometown Jaipur -- with my grandparents. There I had the opportunity to truly live in India for extended periods of time, go to school there, brush up on my Hindi and Sanskrit, and learn tabla (as well as some sitar and vocal music). I particularly enjoyed celebrating all the Indian holidays as a child, and flying kites on Makar Sankranti.
I feel very much at home in all three countries. So I definitely think of myself as all three – Canadian, American, and of course Indian.
How did you get interested in Tabla playing? You have learnt the Tabla from Ustad Zakir Husain... Can you tell us how this came about and what it means to you?
I first started learning from my mother, who also plays the tabla. When I was maybe 3 years old, I used to hear my mother playing often, and I asked her to teach me to play a little bit. She tried to teach me the basic sound "na." She demonstrated the sound to me, and I tried to mimic her to reproduce the sound, but nothing came out. I was hooked! I always loved the beauty and the intricacy of the tabla sound and repertoire, and how it also perfectly complemented sounds on the sitar, or vocal, etc. I learned with my mom first, and then with Pandit Prem Prakash Sharma in Jaipur whenever I visited there.
I met Zakir ji when I was an undergraduate at Harvard. He came to perform there when I was a third year student. I had the exciting opportunity to meet him afterwards at a reception, and he invited me to visit him in California (where he lives). I have had the great pleasure and privilege of learning from him a bit off and on since then. More than that, he has been a wonderful and inspirational friend, and he and his whole family -- in both California and Bombay -- have been such a huge source of love, encouragement, and support to me for so long, and I am very grateful to them for that.
Do you collaborate with mathematicians in India? Do you have contacts with the institutes in India?
For many years now, I have been an adjunct professor at TIFR-Mumbai (Tata Institute for Fundamental Research), IIT-Bombay, and the University of Hyderabad. I've spent a lot of time at these three institutes, especially at TIFR and IIT-B, over many years. I've lectured extensively to students at these institutes, as well as collaborated a lot with mathematicians there, such as with Eknath Ghate at TIFR (who recently won the Shanti Swarup Bhatnagar Prize for mathematical sciences).
I've also been involved in starting a new institute in Bangalore called "ICTS" (International Center for Theoretical Sciences). It will be inaugurated next year, and we hope it will be a great success. The director is Professor Spenta Wadia of TIFR, and the head of the International Advisory Board is Nobel Prize Winner Professor David Gross. So hopefully I will spend even more time in India after the inauguration next year!
Recently you have won prizes for your work on the Birch and Swinnerton-Dyer conjecture which was listed as one of the seven millennium prize problems. Can you explain the significance of this work?
In joint work with Christopher Skinner and Wei Zhang, we have shown that the Birch and Swinnerton-Dyer Conjecture is true “most” of the time (more precisely, for more than 66.48 per cent of elliptic curves!). Previously, it was not known that it was true for more than 0 per cent. So that is significant progress, but it is still “not” a complete solution!
Finishing a proof of the Birch and Swinnerton-Dyer Conjecture would be a momentous achievement, and it is one of my favorite problems!, but it is not solved yet.
Do you believe that this is the best time to study math - for instance, number theory is now being applied in cryptography and so on? What does it take to do great mathematics?
It is interesting that pure mathematicians, like myself, rarely think directly about applications. We are instead guided primarily by what directions we find most beautiful, elegant, or most promising. We tend to treat our discipline more as an art than as a science! And indeed, this is the attitude that allows us to be the most creative and productive.
On the other hand, it is also true, historically, that the mathematics that has been the most applicable and important to society over the years has been the mathematics that scientists found while searching for beauty; and eventually all beautiful and elegant mathematics tends to find applications.
That is why it is very important to fund basic science research. When science funding is only application-driven, it does not allow full freedom and creativity. Funding basic science allows a large interconnected database of scientific techniques and knowledge to accumulate, so that when a societal need arises, the science is ready to be applied and adapted to the purpose.
Elliptic curves (and the related Birch and Swinnerton-Dyer Conjecture) are indeed a good example! They were first studied by pure mathematicians, but are now one of the most important mathematical objects in cryptography. So that is indeed exciting, but I just want to emphasize that they were exciting and central to number theory well before these applications were found; but it was inevitable that they would be found, given their fundamental nature.
That is why elliptic curves have fascinated me! They are so fundamental in both pure and applied mathematics. Beyond advancing the subject of number theory in general, a heightened understanding of elliptic curves also has important implications in coding theory and cryptography. Encryption schemes, such as those used to protect our privacy when transmitting information online, often centrally involve the use of elliptic curves.
Math is generally considered a difficult subject but you have been enjoying math since your childhood. What aspect of your education could have contributed to this enjoyment?
I've always enjoyed mathematics as far back as I can remember, since I was two or three years old. Since my mother was a mathematician, I always had her as a resource - I would always go and ask her questions and so I learned a lot from her. She was also a great source of encouragement - she always answered my questions enthusiastically, and always encouraged me to pursue whatever I was interested in - and that probably single-handedly contributed the most to my enjoyment of mathematics (and of all my interests)!
