Interview with Dr. Ramdorai Sujatha

Dr. Ramdorai Sujatha of the Tata Institute of Fundamental Research (TIFR) received all her education in India and has been with TIFR since 1985, where she is now Associate Professor in the School of Mathematics. The international selection committee consisted of Professors Bernt Øksendal (Oslo), Jacob Palis (IMPA), Peter Sarnak (Princeton), Le Dung Trang (ICTP) and Srinivasa Varadhan (Courant). The Prize is awarded to Dr. Sujatha in recognition of her work on the arithmetic of algebraic varieties and her substantial contributions to non-commutative Iwasawa theory. In particular, together with Coates, Fukaya, Kato, and Venjakob, she formulated a non-commutative version of the main conjecture of Iwasawa theory, which now drives much of the work in this important subject.

What is your field of study in mathematics? Please explain in simple words for the general public.

My thesis subject was the algebraic theory of quadratic forms over fields; which basically means studying the solutions of degree 2 equations of the form x_1^2 + x_2^2 +....+ x_n^2 (here ^ denotes superscript and _ denotes subscript) over fields. This has a very rich algebraic theory with connections to various other fields in pure mathematics. But in the last decade I have been working in the theory of elliptic curves. This is at the interface of algebra and number theory. Elliptic curves are very special curves with an enormously rich structure, multi-layered, with connections to complex geometry, topology, number theory, some areas of theoretical physics, etc. But for number theorists they are deeply fascinating as there are a lot of problems that can be explained rather simply but have remained open for decades. Elliptic curves have become fashionable now with their applications to cryptology, but I do not work in these aspects.

What are the most difficult obstacles you have encountered in your research, as a women scientist working in a developing country? How many female mathematicians are there in India?

I always like to tell people that there is more to anything than meets the eye in India! People have the image of the status of women being low in India. This is no doubt true, but on the other hand, given any field, one is surprised that there are women at the top echelons, albeit few but sometimes more than in developed countries! This applies for science and technology as well, In my department, roughly about a tenth of the Faculty consists of women. I have never encountered any obstacles in my work place on account of my gender. It is true that the scientific policies could be shaped towards making them sensitive to the problems of women and this is happening to a certain extent.

What do you think is the role of mathematics in our everyday life? Please give examples.

Mathematics underpins many of the research in the Sciences and also much of the technology. Some simple examples of ideas from pure mathematics being used in different forms: Signalling and telecommunications research, Internet security and cryptography, Search engines, Data compression, Efficient packing solutions, etc

When did you first realize that you had a special talent for mathematics?

Well, I do not know if I realised I had a special talent; in those days people did not watch out for such pointers! I think my answer would be to the question `When did I realize that I liked mathematics'.... Initially, I thought I liked it because that was the one subject where one could score full marks, but then in high school it went deeper. I eagerly used to wait for the text books of the next year during my school holidays before the school reopened, in order to read and try and solve the math problems. English was the other such subject. My brother and I would usually finish reading the English text books before the school reopened! I had no idea that there was a career in mathematical research that was possible, and when a senior in my pre-University years told me that if I liked abstract thinking, I should go for higher studies in pure science (rather than engineering), and I followed his advice.

Could you say in few words why young people in Italy ought to study mathematics? What is the message you would send to young (women) high-school / university students that dream of a scientific career?

I think we scientists do a bad job of promoting ourselves or in conveying the excitement of research! I know of many young students in India who get sucked in to the Information Technology madness and then complain that they feel frustrated after a few years of work as they do not find anything challenging enough, in spite of the money and other tangible perks. I think the freedom that we scientists have in our work is something valuable; of course with it comes the responsibility, frustrations etc but the challenge, should we seek it, is there all through the life. And learning is a process that never ends. Now why should young people in Italy (or anywhere else) study mathematics? My first reaction would be to say because it is so beautiful! The purity and structure in the subject never fails to inspire awe and respect in me. For the younger women students who dream of a scientific career, I want to tell them it is rewarding, possibly much more than other careers, and often offers the flexibility of combining a career with a personal life.

What are the skills and requirements needed to become a good mathematician? Please describe a typical day of work.

Patience, discipline, and rigour are the requirements....skill is more difficult--I guess the simplest answer would be the capacity to think abstractly and to like doing it. A typical day of work is one where I sit on my desk if I am working on a problem, with paper and pencil and try to think about how to attack it. Of course the problem is usually part of a bigger thing that one is trying to prove, and often, in rigorously writing out things, there are so many creases that need to be smoothened. This thinking is interspersed with lectures and discussions. Often, one can spend frustrating days not seeing the light and then one sees it in a flash at some point; that joy and the eventual beauty of everything fitting together so intrinsically is worth all the previous days or weeks of frustration! I collaborate a lot with other mathematicians, which sometimes lightens this process of chipping away by oneself on a difficult problem.

Mathematics is a very old, theoretical and traditional science, to what degree does mathematicians of today use computers in their research?

Computers have been of enormous use in guiding pure research, especially in number theory, and also in computational aspects of other areas of pure mathematics. To give an example, a pure mathematician, by pure thought, might feel intuitively that a certain statement has to be correct. In many areas of number theory, such an intuition can then be put to test by using computers which can probably check the statement for a small range....There is one famous story of a computer chip (Intel, I think) which was used in one such situation and the results did not fit with the mathematician's intuition. He went back and checked his arguments and found no flaw in them. Eventually, it turned out that there was a bug in the chip design! This is of course an example in the opposite spirit, to what I was saying, but I want to underline that computations with computers are helpful in guiding mathematicians towards very abstract general results. But the percentage of pure mathematicians who use computers for their research on an everyday basis is still small.

How familiar are you with ICTP? What is the role the centre - Trieste (could) play(s) in the international scientific community?

Well, familiarity in the sense of having been there? I have been there just once for a long workshop and conference around 10 years ago which was immensely useful for me. I am of course aware of the role it is supposed to play and think it is unique in its mission to nurture and encourage scientific activities and interactions between developing nations and the others. Centres like the ICTP, the Max Planck Institute in Bonn, etc has played an important role in exposing young mathematicians and other scientists to frontline research.

What does it mean to a scientist to receive a prize like the Ramanujan prize?

As I learnt, the Ramanujan prize was started just two years ago. I am aware that in the last few years there has been a flurry of various prizes instituted for mathematical research, but none that was addressed to support mathematics in developing nations. I think it was very enlightened of the IMU, ICTP and the Abel foundation to have instituted such a prize. It is an important recognition and serves well to integrate mathematics globally. It will certainly inspire working mathematicians in the developing nations.

How do you see the future of the Ramanujan prize?

I feel it can only grow in stature over the years! Mathematical research is possibly a fledgling area of research in many Asian and African countries but if it spreads and gathers strength, the number of contenders will of course increase. I already see it happening in China and Vietnam, to a certain extent.