#### by Linda Kirby

Srinivasa Varadhan had planned to go into industry after graduation and assumed that the field of statistics would be a better preparation. However, after meeting several mathematical probabilists, he realized that mathematics was far more interesting and productive, and switched his subject areas, eventually winning the Abel Prize in Mathematics in 2007.

Srinivasa Varadhan — or Raghu to his friends — was born on 2 January 1940, in Chennai (formerly called Madras), India. His father, Ranga Iyengar, was a science teacher who became the Principal of the Board High School in Ponneri, a small town about 30 km from Chennai.

After his graduation from high school in 1955, Varadhan was accepted at Presidency College at the University of Madras and received both his Bachelor’s (1959) and Master’s (1960) degrees in statistics. He continued his studies at The Indian Institute in Kolkata studying statistical control, which left him “totally unsatisfied”. The mathematicians Varadarajan, Parthasarathy and Ranga Rao convinced him that mathematics would be more productive, and they began to work on a problem concerning probability distributions on groups. In 1963, Varadhan got his Ph.D. in mathematics from the Indian Institute, with a thesis on “Convolution Properties on Distribution of Topological Groups” [e1]. Perhaps pre-planned, the well-known Russian mathematician Kolmogorov was one of the examiners of Varadhan’s thesis. Kolmogorov was so impressed with Varadhan that he wrote, “This is not the work of a student, but of a mature master”.

In 1963, Varadhan came from India as a postdoctoral fellow to the Courant Institute in New York and never left, spending his entire professional life there, including serving two terms as its director (1980–1984; 1992–1994). He is currently its Frank J.Gould Professor of Science. It is at Courant that he met Daniel Stroock, his future collaborator.

In 1964, he married Vasundra, who was born in 1947 in Chennai but had spent most of the first twelve years of her life in New York. Vasu is a professor in media studies at Gallatin School of Individualized Study at New York University. They had two children, Gopal (born in 1969) and his younger brother Ashok. In August 2001, Gopal joined Cantor Fitzgerald as the Managing Director of its interest-rate derivatives business, and died in the north tower of the World Trade Center on September 11, 2001.

Varadhan enjoys traveling and the arts — movies and both classical Indian and western music. He particularly likes reading Tamil literature. “Not many people in the world are familiar with Tamil as a language. It is a language which is 2,000-years old, almost as old as Sanskrit. It is perhaps the only language which today is not very different from the way it was 2,000 years ago. So, I can take a book of poetry written 2,000 years ago, and I will still be able to read it.” [source]

In 2010, Varadhan received the Abel Prize in Mathematics by the Norwegian Academy of Science and Letters “for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations.”

Probability theory is the mathematical tool for analyzing situations governed by chance. The law of large numbers, discovered by Jacob Bernoulli in the eighteenth century, shows that the average outcome of a long sequence of coin tosses is usually close to the expected value. Yet the unexpected happens, and the question is, how? The theory of large deviations studies the occurrence of rare events. This subject has concrete applications to fields as diverse as physics, biology, economics, statistics, computer science, and engineering.

The law of large numbers states that the probability of a deviation beyond a given level goes to zero. However, for practical applications, it is crucial to know how fast it vanishes. For example, what capital reserves are needed to keep the probability of default of an insurance company below acceptable levels? In analyzing such actuarial “ruin problems,” Harald Cramér discovered in 1937 that standard approximations based on the Central Limit Theorem (as visualized by the bell curve) are actually misleading. He then found the first precise estimates of large deviations for a sequence of independent random variables. It took 30 years before Varadhan discovered the underlying general principles and began to demonstrate their tremendous scope, far beyond the classical setting of independent trials. [Abel Prize website]

Upon Varadhan’s receipt of the Abel prize, the President of New York University, John Sexton, said:

We are so happy and proud of Raghu. Not only is he an outstanding scholar, he is also a kind and wonderful colleague, a devoted teacher, and an exemplary “University citizen,” serving with dedication and professionalism as director of the Courant Institute and on such bodies as the University Senate. This distinction is a well-deserved honour for a faculty member whose modesty and discretion are almost as great as his scholarly contributions. In the time that Raghu has been at NYU, our University has changed a great deal, but it is the persistent presence of scholars such as he that has enabled us to build NYU into what it is today and to continue to attract top scholars and researchers to our midst.

In 1996, Varadhan and Daniel Stroock received the American Mathematical Society’s Leroy Steele Prize for fundamental contributions to research. Their citation [e6] reads,

To Daniel Stroock and Srinivasa Varadhan for their four papers “Diffusion Processes with continuous coefficients, I and II” (1969) [e3], [e2], “On the support of diffusion processes with applications to the strong maximum principle” (1970) [e4], “Multidimensional diffusion processes” (1979) [e5], in which they introduced the new concept of a martingale solution to a stochastic differential equation, enabling them to prove existence, uniqueness, and other important properties of solutions to equations which could not be treated before by purely analytic methods; their formulation has been widely used to prove convergence of various processes to diffusions.

In addition, Varadhan is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the Royal Society of London, and the Third World Academy of Sciences.

He also has honorary degrees from Université Pierre et Marie Curie in Paris (2003) and from the Indian Statistical Institute in Kolkata, India (2004).

In addition, Varadhan received the following prizes: The Birkhoff Prize in 1994 from the American Mathematical Society; The Margaret and Herman Sokol Award of New York University’s Faculty of Arts and Science in 1995; an Alfred P. Sloan fellowship, and a Guggenheim Fellowship. He is a fellow of the Institute of Mathematical Statistics of the Indian Academy of Sciences.

In 2008, the government of India awarded him the Padma Bhushan, one of the country’s highest civilian honors.

Daniel Stroock describes [e7] his co-author and collaborator as follows:

I am not going to claim that Varadhan does not enjoy his success; he does. Nor am I about to say that he is some sort of saint; we could never have become friends if he were. Nonetheless, what distinguishes Varadhan from nearly all the other gifted people whom I have met is the remarkable command he exercises over his own gift. In particular, he has learned how to prevent his unusual intellectual powers from poisoning his relations with lesser intellects. For example, Varadhan can tolerate being wrong, at least occasionally. In addition, he is not one of the many mathematical princes who espouse the notion that all their obligations to humanity can be met through their contributions to mathematical research.