CR Rao: A statistician who forced students to reason for themselves 

Calyampudi Radhakrishna Rao, the centenarian who was awarded the prestigious International Prize in Statistics on Monday, is known as a teacher who forced his students to think for themselves, before introducing them to a new concept, says R Thyagarajan, the founder and patriarch of Shriram group, who was Rao’s student. 

Thyagarajan remembers his first class with Rao, at the Indian Statistical Institute, Kolkata. Prof Rao, then just 37, was already a Fellow of the Royal Society, UK, a body of eminent scientists, engineers and technologists from the UK and the Commonwealth. So, he was already a celebrity. 

Rao, recalls Thyagarajan, asked each of the 23 students in class to walk to the blackboard and write down the names of their family members. He then asked the students for the male-female ratio in the names.  

Many said 50:50 while some, with the country’s gender ratio in mind, said 52:48. But when they actually counted, it was found to be 72 per cent males and 28 per cent females. 

What could explain this male skew, Rao asked the flummoxed students. “We were intrigued,” Thyagarajan remembers. A brainstorming session ensued and, in the end, Rao explained that the reason could be that families that had all-female children were poorly represented in the class. Second, families that had just one boy were disinclined to send him to far-off Kolkata. At the end of this session, he introduced a theory that explained such skewness. 

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Typically, mathematics or statistics teachers would teach a theorem and then ask students questions, but Rao invariably did it the opposite way, says Thyagarajan. 

Rao (not to be confused with CNR Rao, the Bharat Ratna-awarded Indian chemist) was not a ‘mathematician who happened to take an interest in statistics’, but a pure-blood statistician who applied mathematics to further the discipline, says Thyagarajan. The 2001 Padma Vibhushan awardee has been immortalised by at least two of his contributions that bear his name — the Cramer-Rao inequality and the Rao-Blackwell theorem — that are familiar to every graduate student of statistics. In pure statistical thinking — as opposed to looking at statistics as an adjunct of mathematics — Rao was perhaps influenced by his guru Ronald Fisher, the British polymath who is regarded as the father of statistics. 

Thyagarajan further recalls Rao as a pleasant and caring person, though not one to back-slap or crack jokes. He recalls an instance where a person named Sethuraman, who had a brilliant academic record, got admission to ISI but was forced to give it upand take up a job due to his family’s straitened circumstances. Rao telegrammed Sethuraman to tell him that ISI would offer him the position of a research scholar to help tide over the financial situation. That meant a pay of ₹250, twice as much as what the job would pay or the stipend that students got. Still, Sethuraman’s father remained unconvinced as he feared that research scholars could lose their position if they did not discover something new. Rao telegrammed Sethuraman again and got both father and son to travel to Kolkata and assured them that there was no danger of losing the position. Sethuraman went on to become a brilliant statistician and settled abroad. 

SR Srinivasa Varadhan, the Indian-American mathematician who received the Padma Vibhushan award in January this year, was also a student of Rao. Thyagarajan remembers how Rao introduced Varadhan to Andrey Kolmogorov, a visiting renowned statistician of the Soviet era, and requested the Russian to mentor Varadhan. Varadhan went on to become the only Indian to win the Abel Prize, which is the Nobel for mathematics, also given by Norway. 

At 102, Rao has a lot to look back on and smile. 

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