P. C. Mahalanobis: the physicist who taught India to count itself

A physics student who found a journal

Mahalanobis was born in Calcutta on 29 June 1893. He went to the Brahmo Boys' School, which his grandfather had founded, and then studied physics at Presidency College, completing a BSc with honours in 1912.

In 1913 he joined Cambridge University. The science magazine Bhāvanā records that he took both parts of the Tripos examinations in 1914 and 1915, struggled in the mathematics part, and came first in the physics part. While at Cambridge he became friendly with Srinivasa Ramanujan.

The turning point was small. After his exams he spent time in the library, and his tutor, W. H. Macaulay, showed him bound volumes of Biometrika, a statistics journal edited by Karl Pearson. Mahalanobis bought a complete set, read them on the ship home and kept working through the exercises on his own in Calcutta.

“What at first most strongly attracted my admiration was that the Professor's work was not imitative”

— Ronald Fisher, on Mahalanobis, via vvmwb.org

From a borrowed room to an institute

He meant to visit India briefly in 1915, but the First World War kept him there. Presidency College offered him a temporary teaching post in physics, and he stayed. He became a full professor in 1922 and taught at the college until 1948.

He began applying statistics to whatever problems he met: examination results, weather and the human body. In 1922 he published a study of anthropometric measurements of Anglo-Indians in Calcutta. From this work came the D-squared statistic, now called the Mahalanobis distance, a way of measuring how far apart two groups are while taking into account how their characteristics are related. It is still used in classification, data science and anomaly detection.

When engineers proposed raising embankments after a severe flood in Orissa in 1926, he studied about sixty years of river data and argued that the riverbed had not risen as they believed. Questions like these kept arriving, and colleagues gathered around his statistical laboratory in the physics department. On 17 December 1931 that group became the Indian Statistical Institute, registered as a society in 1932. In 1933 he started Sankhyā, the Indian Journal of Statistics, and edited it for the rest of his life.

Sample surveys and national planning

His best-known practical work was the large-scale sample survey. The Indian Statistical Institute explains that he showed reliable data could be gathered without a complete census. He used carefully chosen samples to estimate crop yields, sending field workers to cut crops in small circles, and extended the method to consumer spending, public opinion and plant disease. After the Bengal famine of 1943 he led a sample survey of its after-effects.

Within the Institute he set up the National Sample Survey, which collected socio-economic and demographic data across the country through continuing surveys. It became so important that the government took it over.

After independence he played a central role in economic planning. According to the Institute, he was a key architect of the Second Five-Year Plan, which emphasised industrialisation and heavy industry and rested on statistical analysis. He was elected a Fellow of the Royal Society and received the Padma Vibhushan. He remained director of the Institute until he died on 28 June 1972, a day before his seventy-ninth birthday.

The skills and habits that made the difference

The first was self-study. Nobody taught him statistics; he worked through Biometrika on his own, alongside a full teaching job in physics.

The second was always starting from a real problem. The Mahalanobis distance came out of measurements of people, and his survey methods came out of the need to know crop yields. University of Minnesota statisticians note that his work could always be linked to some field of application.

The third was building institutions. He did not stop at papers; he created an institute, a journal and a national survey so that others could keep doing the work.