Tag Archives: Nobel prize in Maths

Major Mathematics awards to two Indian origin scientists


The Hindu Aug 14 2014

Manjul Bhargava and Subhash Khot, are among the eight winners of the prestigious International Mathematical Union awards

Two mathematicians of Indian origin, Manjul Bhargava and Subhash Khot, are among the eight winners of the prestigious awards of the International Mathematical Union (IMU) that were announced at the inaugural of the 9-day International Congress of Mathematicians (ICM) which began today at Seoul, Republic of Korea. The President of Korea, Park Geun-hye, gave away the awards.

The ICM is held every four years and, traditionally, the IMU awards are presented at this quadrennial event. The awards include the Fields Medal, the highest award in mathematics, the Rolf Nevanlinna Prize and the Carl Friedrich Gauss Prize. At the last ICM held at Hyderabad, India, two new awards, the Chern Medal and the Leelavati Prize, were added to the existing three awards.

The 40 year-old Canadian-American Manjul Bhargava, a number theorist from Princeton University, is one of the four Fields Medalists chosen for the ICM2014 awards. The Fields Medal is awarded “to recognize outstanding mathematical achievement for existing work and for the promise of future achievement”. A minimum of two and a maximum of four Fields Medals are given to mathematicians under the age of 40 on January 1 of the year of the Congress.

“Manjul Bhargava has developed powerful new methods in the geometry of numbers and applied them to count rings of small rank and to bound the average rank of elliptic curves,” said the IMU citation for the award.

The other three Fields Medalists are:

The Brazilian mathematician Arthur Avila (35) of the Paris Diderot University-Paris 7 and Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, who has been awarded “for his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalizations as a unifying principle”; the British mathematician Martin Hairer (39) of the University of Warwick “for his outstanding contributions to stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations”; and, the Iranian mathematician Maryam Mirzakhani (37) of Stanford University “for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their modulii spaces”.

The 36 year-old IIT Bombay alumnus Subhash Khot, an Indian-American theoretical computer scientist at the Courant Institute of Mathematical Sciences of New York University has been chosen for the ICM2014 Rolf Nevanlinna Prize. The Nevanlinna Prize is awarded “for outstanding contributions in mathematical aspects of information sciences”.

“Subhash Khot’s prescient definition of the “Unique Games” problem, and his leadership in the effort to understand its complexity and its pivotal role in the study of efficient approximation of optimization problems, have produced breakthroughs in algorithmic design and approximation hardness, and new exciting interactions between computational complexity, analysis and geometry,” the award citation said.

The Gauss Prize in Applied Mathematics is awarded “to honor scientists whose mathematical research has had an impact outside mathematics – either in technology, in business, or simply in people’s everyday lives”.

The winner of the ICM2014 Gauss Prize is Stanley Osher (72) of University of California, Los Angeles, who has been awarded the Prize “for his influential contributions to several fields in applied mathematics, and for far reaching inventions that have changed our conception of physical, perceptual and mathematical concepts, giving us new tools to apprehend the world.”

The Chern Medal is given “to an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics”.

The Chern Medal this time goes to the American algebraic geometer Phillip Griffiths (76) “for his groundbreaking and transformative development of transcendental methods in complex geometry, particularly his seminal work in Hodge theory and periods of algebraic varieties”.

Unlike the other awards, the Leelavati Prize is not given for achievements in mathematics research but for outstanding public outreach work in mathematics. Proposed by India, it was originally intended as a one-time award using the grant from the Norwegian Abel Foundation. Thanks to the efforts by Indian mathematicians in finding a sponsor to make it a regular affair, it has now been instituted as a recurring four-yearly award under the IMU charter to be given away at the closing ceremony of the ICM. The award is now being sponsored by Infosys, the Indian IT major.

The ICM2014 Leelavati Prize has been given to the Argentine Adrián Paenza (65) “for his decisive contributions to changing the mind of a whole country about the way it perceives mathematics in daily life, and in particular for his books, his TV programmes, and his unique gift of enthusiasm and passion in communicating the beauty and joy of mathematics”.

Hope Indian youth take up research in sciences: Fields Medal winner


The Hindu Aug 14 2014.

Manjul Bhargava, one of the recipients of the Fields Medal, speaks about mathematics, music and more.

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)!