He took his BA from Elphinstone College in Bombay in 1912, in economics and political science. The following year Sayajirao Gaekwad III, the ruler of the princely state of Baroda, awarded him a scholarship to study abroad on the condition that he return and serve the state for ten years. In July 1913 he sailed for New York and enrolled at Columbia University.

It is worth pausing on how narrow that door was. The scholarship was a personal decision by one reforming prince, taken for a handful of students, and it carried an obligation rather than a gift. There was no scheme behind it, no quota, no second award, and no second chance if it went badly. The whole of his access to the education that made the rest of his life possible rested on the continuing goodwill of one man, and he knew it.

He read economics, sociology, history, anthropology and philosophy, and took his MA in June 1915 with a thesis on ancient Indian commerce. He worked under Edwin Seligman, the public finance economist, who supervised his doctoral work; and he sat under John Dewey, whose argument that democracy is not a form of government but a way of living alongside other people — a mode of associated living, in Dewey's phrase — stayed with him for the rest of his life. He was still making that argument, in almost those words, in the Constituent Assembly thirty-four years later.

New York did something else that no reading list accounts for. For three years the first thing known about him in a room was not his caste. He said afterwards that his classmates and professors at Columbia were the best friends he had ever had, and the remark is usually quoted as warmth. It is warmth, but it also tells you what the absence of the thing felt like to someone who had never once been without it.

On 9 May 1916, in an anthropology seminar run by Alexander Goldenweiser, he read a paper called Castes in India — Their Mechanism, Genesis and Development. He was twenty-five. It was published in the journal Indian Antiquary in May 1917. The paper does what almost nothing written on caste before it had done: it treats caste as a mechanism with working parts that can be taken apart and named, rather than as an ancient mystery of the East to be described and marvelled at.

The third point is the one that has aged least and is quoted least. He was arguing, in 1916, that the position of women in a caste society is not a separate grievance running alongside caste but the mechanism by which caste reproduces itself. Thirty-five years later that argument is what he resigned from the Cabinet over.

His doctoral thesis was on the evolution of provincial finance in British India — a study of how the imperial government devolved revenue and spending onto the provinces, and what that did to both. Columbia required a doctoral thesis to be published before the degree was conferred, and publication took years, so the doctorate itself was awarded in 1927, eleven years after the work was finished. He left New York in 1916 for London, still under the Baroda obligation, with the clock running.