Mathematician S. R. Srinivasa Varadhan, who was not too long ago named for the Padma Vibhushan, India’s second-highest civilian honour, isn’t any stranger to awards. Prof. Varadhan, who’s at the moment the Frank J. Gould professor of science and a professor of arithmetic at New York University’s Courant Institute of Mathematical Sciences, was awarded the Abel Prize given to excellent worldwide mathematicians in 2007; the Padma Bhushan in 2008 and the National Medal of Science, United States, in 2010, amongst others.
Born in Chennai in 1940, Prof. Srinivasa Varadhan graduated with an Honours diploma in statistics from Presidency College, Chennai in 1959, after he which he joined the Indian Statistical Institute, Kolkata, the place he accomplished his Ph.D in 1963.
In an electronic mail interview with The Hindu, he describes his journey from Chennai to the United States, his specialisation in probability concept, maths for college students, and extra.
Can you inform us a little about your journey as a mathematician and a scientist from Chennai to New York?
I used to be good in math way back to I can keep in mind. [I]was above my class stage, and was quick tracked. During grades 6-11, my father was the headmaster of the college I attended, a authorities college in a small city twenty miles north of Chennai. [I]did nicely, particularly in math and science. I had an uncle in Tambaram, and we tried, and succeeded, in getting a seat in “intermediate” a two-year programme earlier than branching off into medical, engineering, science or humanities [courses].
I stayed with my uncle, together with two of my cousins, and had to resolve after two years what to pursue. I used to be not concerned about engineering. Majoring in arithmetic was not interesting, due to [a] lack of job alternatives. I wanted to get into an “Honours” programme within the primary sciences that led to a Master’s diploma in three years slightly than the 4 years in a common programme. I used to be eligible to apply for established programmes in arithmetic, physics, chemistry and an rising new programme in statistics. It was arduous to get in. The variety of seats had been beneath 20 in the entire State in all faculties mixed, for physics, chemistry or statistics and barely extra in arithmetic.
I used to be informed statistics had good job prospects, and so I attempted, and was fortunate to be admitted as one in every of 13 college students. We had been a close-knit group and stayed collectively for 3 years. After 60-plus years we’re nonetheless in contact and get collectively on Zoom each two weeks. The school that we attended was Presidency College going through the Bay of Bengal and we might watch the ocean from our classroom. It was a lengthy commute for me. My father had retired, and took up a place as headmaster in a personal college in Tambaram and after one 12 months, I persuaded my mother and father to let me keep within the hostel. Those two years had been idyllic. I might spend early evenings on the seashore gossiping with my mates. I didn’t discover schoolwork demanding and will take all of the exams with none preparation. I graduated after three years within the Honours programme having scored the very best marks and was awarded a prize as the very best scholar to graduate that 12 months.
The query now was, what subsequent? The large attraction for a lot of of my classmates was high-level administrative positions in the federal government, banking, insurance coverage and many others. If you probably did nicely in a aggressive examination you had been chosen for a high-level place and as well as to a nice profession, you additionally had the satisfaction of serving the nation. The different possibility was to be skilled as a skilled statistician and work within the business. One ultimate possibility was analysis. I assumed I might strive it. [I] had no concept what it might contain. The concept was, if I didn’t prefer it, I used to be younger sufficient to take the aggressive examination! I used to be chosen to do analysis on the Indian Statistical Institute [Kolkata], the place I confirmed up in August, 1959. I used to be given a desk and there have been a couple of programs that we might attend that lasted three months. I considered doing analysis in utilized statistics and was rapidly disillusioned.
Two senior analysis students, [K. R.] Parthasarathy and [R.] Ranga Rao, persuaded me to work with them in probability concept. They had labored earlier with [Veeravalli S.] Varadarajan, who had left quickly after I arrived in Kolkata, to go to the United States. It was nice for me. Probability was, for me, the correct combination of mathematical rigour and statistical instinct. The three of us labored collectively for over two years. [Then] they each left, one to go to the United States and the opposite to Russia. Varadarajan returned and we labored collectively for a 12 months, earlier than I left for the United States.
Meanwhile, I had completed my thesis and Andrey Kolmogorov, a nice Russian mathematician [who contributed significantly to probability theory] and father of the fashionable concept of probability, was visiting ISI [in 1962]. My advisor, [renowned statistician] Dr. [C.R.] Rao needed him to be one of many readers of my thesis. I used to be to give a one-hour presentation of my work, which I did, besides [that] it went on for almost two hours. I acquired carried away in my presentation. When the discuss ended, the viewers who had been on the finish of their persistence, acquired up and began to go away. Kolmogorov, who had stood up with a piece of chalk to say one thing, threw the chalk down and walked out in anger. My rapid response was: There goes my PhD. Along with fellow college students, I rushed behind Kolmogorov, apologizing profusely for speaking too lengthy. He was calm and mentioned he didn’t thoughts the lengthy lecture however was irritated as a result of, as he put it, “When Kolmogorov speaks, people should listen.” He supplied a very good report on my thesis.
In the spring of 1963, I needed to go to the United States for postdoctoral work, and Varadarajan wrote to Peter D. Lax at the Courant Institute [of Mathematical Sciences – New York University] suggesting my identify for a “visiting member” as they had been then referred to as on the Institute. After a while, a suggestion got here and I ended up as a customer at the Courant Institute. I by no means left!
Your work on giant deviations is taken into account to be one of many cornerstones of contemporary probability concept and it has functions in fields as numerous as insurance coverage threat modelling to predicting outlier climate occasions. Can you clarify what the ‘art of predicting rare events’ is?
You begin with a mannequin of randomness that determines the possibilities of assorted occasions. But it’s arduous to estimate the possibilities when they’re very small. How to measure how small is small? We might have an occasion with small probability beneath our mannequin. We can change the mannequin and make this occasion, one with important probability. By how a lot have we modified the mannequin? That could be measured. There could also be some ways to change the mannequin and we will optimise. That offers a extra precise measure of how small the probability is. To give a easy instance, in the event you toss a honest coin 1,000 occasions, how small is the probability that you simply get 800 heads? If the probability of getting a head had been 0.8 as a substitute of 0.5, 800 heads could be regular. How far is 0.8 from 0.5 for this drawback? There is a measure referred to as relative entropy that serves the aim.
Yours is a storied profession, adorned with accomplishments and honour. In that context what does the conferring of Padma Vibhushan, India’s second-highest civilian honour, imply to you?
I take into account myself fortunate. The world is filled with folks with extraordinary expertise. But solely a few are recognised with excessive awards. Part of it’s being on the proper place on the proper time and selecting the best drawback to work on. I had a very encouraging atmosphere with nice colleagues to work with. We had a fixed stream of holiday makers to our Institute who supplied new views.
Math, for a lot of, is an summary, intimidating topic they examine in faculties. How do you suppose we will make the instructing of arithmetic extra engrossing for school-going youngsters?
Students must be inspired to resolve puzzles. They want to consider problem-solving as a sport, slightly than as a job. Each scholar can discover their very own stage.
At a private stage, what about arithmetic means essentially the most to you? Is it the method of fixing a drawback, or the invention of the inherent magnificence and class of the answer?
First, it’s the problem of making an attempt to show one thing. Once you succeed, you’re happy for a couple of days, after which on to the subsequent drawback. Eventually you see a sample rising and all of the odd items that had been down under seem a part of [a] grand construction when appeared [at] from above. Very satisfying!
