In 1915, against the backdrop of World War I, an Indian student at Cambridge found that his ship from England to India had been delayed. PC Mahalanobis spent some of his waiting time in the library of King’s College, where a tutor brought some statistics books to his notice, quite by chance. He would go on become the founder of the Indian Statistical Institute and a giant of the discipline. A quarter of a century later, in 1940, when World War II was raging, the spectacular journey of another statistical doyen began – as a last resort.

Nineteen-year-old Calyampudi Radhakrishna Rao or CR Rao had stood first-class first in mathematics from Andhra University. However, due to administrative formalities, his application for a research scholarship was turned down. He then applied for a mathematician’s job at an army survey unit and went to Calcutta for an interview, but he was deemed too young for the job. As luck would have it, during his stay at a South Indian hotel in Calcutta, he met a man named Subramanian, who was employed in Bombay, but had been sent to Calcutta to be trained at the Indian Statistical Institute.

CR Rao applied for a one-year training programme in statistics at the Institute, hoping that this additional qualification would help him getting a job. He received a prompt positive reply from Mahalanobis.

That was certainly a defining moment in the history of statistical science. It marked the beginning of Rao’s four-decade-long stay at the Indian Statistical Institute. When Calcutta University launched its master’s degree programme in statistics in 1941, Rao enrolled there. In 1943, he stood first-class first.

‘A new mantra’

As he turned 100 on September 10, Rao is a living legend. Today, many of his works are included in standard textbooks. The National Award in Statistics in India is called the Prof CR Rao Award. The CR Rao Advanced Institute of Mathematics, Statistics and Computer Science is located within the University of Hyderabad Campus. The road outside the university has been named Prof CR Rao Road.
An article in Forbes in 1969 refers to orthogoal arrays, a contribution of Rao as early in 1949, as “a new mantra” in a variety of industrial establishments. A Times of India article in 1988 listed Rao as one of the top 10 scientists of India considering all disciplines. In 2002, he was awarded with the National Medal of Science, the highest scientific award in the US, by US President George W Bush.

The supportive environment of his early years helped Rao’s research career to flourish. Two of his early papers, published in 1945 and 1947, were reproduced in a book titled Breakthroughs in Statistics, 1890-1990 edited by S Kotz and NL Johnson. According to Australian statistician Terry Speed, “The 1940s were ungrudgingly CR Rao’s. His 1945 paper, which contains the Cramér-Rao Inequality, Rao-Blackwell Theorem, and the beginning of differential geometry of parameter space will guarantee that, even had he done nothing else – but there was much else.”

While Rao was teaching the lower bound of the asymptotic variance, one student asked him, “Why don’t you prove it for finite samples?” Rao went back home and devised his famous inequality in one night of 1944.

Rao’s PhD started with a letter from JC Trever of Cambridge University, who in 1946 requested help from the Indian Statistical Institute to analyse measurements of human skeletons obtained from Jebel Moya in Sudan. Rao was among the two people deputed by Mahalanobis for the job. Rao worked at the Cambridge University Museum of Archaeology and Anthropology from 1946 to 1948, and simultaneously did his PhD.

In 1948, he received the degree at King’s College of Cambridge University under the supervision of Ronald Fisher, widely regarded as the father of modern statistics.

A high place in the world

Mahalanobis was possibly keen to retain Rao at the Indian Statistical Institute. In 1948, Mahalanobis made him a professor at Institute at the age of only 28. Rao stood firm with Mahalanobis when others left and, in effect, helped in building the Institute. After Mahalanobis’ died in 1972, Rao took over as the secretary of the Institute.

Rao developed various statistics courses that were later converted into Bachelor’s and Master’s degrees at the Institute. He also initiated the PhD programme at the Institute. SRS Varadhan, who would go on to win the prestigious Abel prize awarded by the King of Norway to outstanding mathematicians, was among Rao’s PhD students.

In a 1963 speech at the Indian Statistical Institute, Fisher said: “For its educational programmes, the institute needs leaders of mathematical thought like Professor Rao, who can uphold and maintain the high place in the world opinion that Indians have already won.”

Though Rao moved to the US after he retired from the Indian Statistical Institute, his work demonstrates the immense potential in Indian academia. With his mathematical ingenuity, Rao was among the people who brought statistical theory to maturity. As Stanford statistician Bradley Efron noted, “The first half of the 20th century was the golden age of statistical theory, during which our field grew from ad hoc origins similar to the current state of computer science to a firmly grounded mathematical science.”

This is how the legendary statistician envisages the discipline: “All knowledge is, in the final analysis, history. All sciences are, in the abstract, mathematics and all methods of acquiring knowledge are essentially statistics.”

Atanu Biswas, a professor of statistics at the Indian Statistical Institute, Kolkata, was the recipient of the Prof CR Rao Award for 2008-’09.