Sathamangalam Ranga Iyengar Srinivasa Varadhan Express Illustrations by Sourav Roy
The Sunday Standard

Making sense of the improbable

In an interview with the excellent mathematics magazine Bhavana, Varadhan recalled that a teacher nudged him towards statistics, predicting it would become an important discipline.

Prasanna R S

Markets routinely absorb bad news every day—even missile strikes and sanctions threats—with only mild volatility that headlines tend to magnify. But if investors were to suddenly wake up to the fact that a US–Israel attack on Iran had unleashed the largest energy shock in history, and global stock indices plunged in a way seen only once in decades, that would be a rare event far outside ordinary expectations. So too would one person winning a million-dollar lottery twice—an outcome so improbable that it once prompted accusations of fraud, until it was shown to lie within the realm of probability.

Understanding such extraordinary departures from the ordinary is at the heart of the mathematical theories for which one of the greatest living mathematicians of Indian origin is best known.

This mathematician has been trending online recently. Did he win another award to add to his already extensive collection, which includes an Abel Prize and a Padma Vibhushan? It appears instead that he is going viral thanks to a social media handle that spreads awareness about Indian and Indian-origin scientists, perhaps compiling at least some of its information using LLMs.

If the use of AI helps more people hear about Sathamangalam Ranga Iyengar Srinivasa Varadhan, why not? After all, Raj Reddy—another US-based Indian pioneer, this time in artificial intelligence—recently told this newspaper that his first advice to students would be to ask their parents to get them smartphones and download Google Gemini.

Today, artificial intelligence dominates the imagination, and higher studies in AI (perhaps not the best idea for most people) seem the obvious path for many students—and especially their parents. But when Varadhan was growing up in Madras in the 1950s, the future looked very different. He initially wanted to become a doctor—a choice many parents would still applaud—until he realised he could not stand the sight of cut-up bodies.

In an interview with the excellent mathematics magazine Bhavana, Varadhan recalled that a teacher nudged him towards statistics, predicting it would become an important discipline. After the structured rigour of Presidency College—where his Master’s marks at the University of Madras were the highest in its history—Varadhan entered the Indian Statistical Institute, Kolkata, and initially embraced its freedoms with enthusiasm.

Since applied statistics held little appeal for him, his first year was spent enjoying the city, playing badminton and cards, until a sharp intervention from fellow student and future doyen K R Parthasarathy pushed him toward the self-driven mathematical life that defined ISI.

Within a few years, that disciplined turn had produced a PhD—and with it, a story that has only grown grander in retelling. Even the Abel Prize website presents Varadhan’s thesis defence as a dramatic encounter with an incognito Andrey Kolmogorov, the legendary Russian mathematician, in the examination room.

Varadhan’s own version, as he told Bhavana with amusement, is less theatrical and more charming. Kolmogorov, the father of modern probability theory, agreed during an ISI visit to examine Varadhan’s thesis, took it back to Moscow, and then had to be reminded by Parthasarathy to send in the overdue report.

Varadhan was only about 22 when another decisive chapter in his life began: his marriage to Vasundhara, or Vasu, who was then just 16. Soon after, he left for the United States as a postdoctoral fellow at the Courant Institute of Mathematical Sciences, which would become his enduring academic home.

As Vasu recounts in her memoir On My Own Terms, written after the family’s deepest tragedy—the loss of their son Gopal in the 9/11 attacks—even her husband’s name had to be remade in America. Thanks to US immigration authorities, Srinivasa became his first name, Varadhan his surname.

At Courant, Varadhan built the body of work that made him one of the defining figures of modern probability. His most celebrated achievement was turning the theory of large deviations into a general mathematical framework—one that explains the likelihood of rare but decisive departures from the norm. As Professor Tom Louis Lindstrøm has noted, Varadhan’s Large Deviation Principle transformed a specialised technique into “a very strong and versatile tool with applications in many areas of mathematics and related sciences.” His ideas have become indispensable in fields ranging from statistical physics to finance.

His combination of depth and clarity has inspired admiration from unexpected quarters. Author, statistician, and part-time provocateur Nassim Nicholas Taleb once captured Varadhan’s stature succinctly: “Learning probability from Varadhan,” Taleb wrote in reviewing his book Probability Theory, “is like learning from Aristotle.” Few mathematicians have made the mathematics of uncertainty seem so lucid.

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