This year’s Abel Prize was awarded to Srinivasa Varadhan, currently Professor of Mathematics and Frank J. Gould Professor of Sciences at the Courant Institute of Mathematical Sciences at the New York University, “For his fundamental contributions to the probability theory and in particular for creating a unified theory of large deviations”.

Prof. Kristian Seip, head of the Abel Committee said, “Varadhan’s work has great conceptual strength and ageless beauty. His ideas have been largely influential and will continue to further research for a long time”.
The law of large numbers in the theory of probability states that if we repeat an experiment a large number of times, the number of times a given outcome appears will reflect the true underlying probability of its occurrence. In the simple case of tossing a coin a sufficiently large number of times, the proportion of times either ‘head’ or ‘tail’ appears would approach half.

Today, probability theory has become a mature part of mathematics and is used as a powerful tool in Natural as well as Social Sciences - like describing the behavior of fundamental particles in quantum mechanics, to radioactive decay, to mutations in DNA - the hereditary material, to mundane activities such as installing a telephone network, to fixing the premium for car insurance, and so on.

Large deviations
But there are situations which the classical theory of probability is not equipped to solve.

Let us go back to the simple coin tossing experiment. Even if we flip the coin a thousand times or more there is a finite, but extremely small probability that the coin will show ‘head’ every time it is tossed. There is a slightly larger but still very small probability that the proportion of ‘head’ will be, say, 3/4 instead of the expected half, and so on. These are known as “large deviations”. This is where Prof. Varadhan’s work assumes importance.
Large deviations, though extremely small in probability, may have very high consequences. Hence, such events, though freak, are too severe to be taken lightly.

Take the case of car insurance. There may be a very bad year in which a much larger number of cars are involved in crashes than suggested by the average of the previous years, resulting in huge payoffs. The question then is how large a capital reserve an insurance company should have in order to keep the probability of default at an acceptable level?

Similarly, an unlikely situation in which all customers in a telephone network may pick up the phone at the same, leading to the system-failure due to overload; or an extremely large number of trucks may ply over a bridge one day leading to its collapse.

While in classical theory of probability one is interested only in the number of events, in these cases what is important is not the number of times that large deviations occur but their nature and impact. Roughly speaking, Theory of Large Deviations helps us to accurately calculate the probabilities of unlikely events occurring. 

It was in 1937 that a Swedish mathematician Herald Cramer analysed the problem of large
deviations in car insurance to determine their precise estimates. In the ensuing 30 years Prof. Varadhan discovered the underlying principles of large deviations and developed in collaboration with Prof. Monroe Donsker, a unified theory applicable to various systems governed by chance.

The trail from Chennai
Abel Prize, in memory of the 19th century Norwegian mathematician Niels Henrik Abel, has been regarded as equivalent of the Nobel Prize for mathematics. Instituted only in 2002, it is managed by the Norwegian Academy of Science and Letters on lines similar to Nobel Prize. 

Srinivasa S.R.Varadhan, fondly known to his colleagues and students as ‘Raghu’ was born in Chennai in 1940. His father was a school teacher and there was always a great emphasis on education in the family.  Varadhan obtained B.Sc honors in 1959 and M.A. the following year from the Presidency College in Chennai, and Ph.D from the Indian Statistical Institute, Kolkata in 1963. The distinguished statistician Prof. C.R. Rao was his thesis advisor. The same year he went as a post-doc to the Courant Institute of Mathematical Sciences at the New York University and stayed on there. Currently he is the Professor of Mathematics and Frank J. Gould Professor of Sciences at the Institute.

He has also been elected member of many academic societies including the Third World Academy of Science and The Royal Society. Varadhan is married to Vasundra. They have a son. A tragedy struck the Varadhan family in 2001. His elder son Gopal was one of the victims of 9/11 terrorist attack on the World Trade Center Twin Towers in New York.

Prof. Varadhan plans to use part of the prize money for educational purposes in Chennai.