The Hardy Connection: East Meets West

The legendary collaboration between Ramanujan and G.H. Hardy

Trace the remarkable intellectual partnership between Srinivasa Ramanujan and G.H. Hardy, from the nine page letter that arrived in Cambridge in January 1913 through five years of collaboration that reshaped twentieth century number theory.

The Hardy Connection: East Meets West

On the morning of 16 January 1913, a nine page letter written in careful if slightly nonstandard English arrived at Trinity College, Cambridge, addressed to the mathematician Godfrey Harold Hardy. The letter was from a twenty five year old clerk in the Port Trust office in Madras named Srinivasa Ramanujan, who introduced himself as a man with no university education, no formal mathematical training beyond high school, and a modest salary of twenty pounds a year. Attached to the letter were roughly 120 mathematical results, stated as bald assertions without proof, ranging from the elementary to the staggeringly deep. Hardy read the letter over breakfast. He was, at that point, the leading pure mathematician in England and one of the two or three most rigorous analytic number theorists in the world. His first reaction, he later admitted, was that the letter must be a hoax. His second reaction, after an afternoon reviewing the claims with his longtime collaborator John Edensor Littlewood in Trinity's rooms, was that nobody could possibly have made up a letter like this, because nobody with enough mathematical sense to fabricate half of these results would have bothered to fabricate the other half. The letter was real. Its author was real. And in late afternoon of 16 January 1913, the history of twentieth century mathematics quietly pivoted.

A Clerk in Madras Writes to Cambridge

The letter had not been a first attempt. Ramanujan had written to M.J.M. Hill and to H.F. Baker and to E.W. Hobson, three other eminent British mathematicians of the period, and had been ignored or dismissed. He was running out of people to try. The letter to Hardy was both a scientific announcement and a personal plea. Its opening paragraph described the writer's circumstances in plain terms, declared that he had after much work achieved several results unlikely to be known in Europe, and asked, with as much dignity as a twenty five year old with no connections could muster, that the recipient give the attached work a fair reading. The attached results included identities in continued fractions, new asymptotic formulas, definite integrals that even Hardy could not evaluate on sight, and a handful of theorems in the analytic theory of numbers that were, as Hardy later put it in his famous essay on Ramanujan, of a kind one would not even have dared to conjecture unless one already had some sense of their being true.