G. H. Hardy on Srinivasa Ramanujan

“In his insight into algebraical formulae, transformation of infinite series, and so forth, that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler or Jacobi.”

“The formulae... defeated me completely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only have been written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.”

“The formulae (1.10) - (1.13) are on a different level and obviously both difficult and deep... (1.10) - (1.12) defeated me completely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.”

“He could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."”

“The years between 18 and 25 are the critical years in a mathematician's career, and the damage had been done. Ramanujan's genius never had again its chance of full development. ... a mathematician is often comparatively old at 30, and his death may be less of a catastrophe than it seems. Abel died at 26 and, although he would no doubt have added a great deal more to mathematics, he could hardly have become a greater man. The tragedy of Ramanujan was not that he died young, but that, during his five unfortunate years, his genius was misdirected, side-tracked, and to a certain extent distorted.”

“It has not the simplicity and the inevitableness of the very greatest work; it would be greater if it were less strange. One gift it shows... profound and invincible originality. He would probably been a greater mathematician if he could have been caught and tamed a little in his youth; he would have discovered more that was new, and... of greater importance. On the other hand he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain... the last sentence is... ridiculous sentimentalism. There was no gain at all when the College at Kumbakonam rejected the one great man they had ever possessed, and the loss was irreparable...”

“He was sent at seven to the High School at Kumbakonam, and remained there nine years. ...His biographers say ...that soon after he had begun the study of trigonometry, he discovered for himself "Euler's theorems for the sine and cosine (by which I understand the relations between the circular and exponential functions), and was very disappointed when he found later, apparently from the second volume of Loney's Trigonometry that they were known already. Until he was sixteen he had never seen a mathematical book of higher class. Whittaker's Modern Analysis had not yet spread so far, and Bromwich's Infinite Series did not exist. ...[E]ither of these books would have made a tremendous difference ...”

“Ramanujan did not seem to have any definite occupation, except mathematics, until 1912. In 1909 he married, and it became necessary for him to have some regular employment, but he had great difficulty in finding any because of his unfortunate college career. About 1910 he began to find more influential Indian friends, Ramaswami Aiyar and his two biographers, but all their efforts to find a tolerable position for him failed, and in 1912 he became a clerk in the office of the Port Trust of Madras, at a salary of about £30 per year. He was nearly twenty-five. The years between eighteen and twenty-five are the critical years in a mathematician's career, and the damage had been done. Ramanujan's genius never had again its chance of full development.”