The story Of Srinivasa Ramanujan

   

The story Of Srinivasa Ramanujan - The Man Who Knew Infinity

                  One morning early in 1913, G. H.  Hardy (Professor Of  Srinivasa Ramanujan) found, among the letters on his breakfast table, a large untidy envelope decorated with Indian stamps. When he opened it, he found sheets of paper by no means clean, on which, in a non - English script, were line after line of symbols. Hardy glanced at them without enthusiasm.

                He felt, more than anything, bored. He glanced at the letter, written in halting English, signed by an unknown Indian, asking him to give an opinion of these mathematical discoveries. The script appeared to consist of theorems, most of them, wild or fantastic looking, one or two already well - known, laid out as though they were original. There were no proofs of any kinds. Hardy was not only bored, but also irritated. It seemed like a curious kind of fraud. He put the manuscript aside and went on with his day’s routine. 

             After lunch he loped off for a game of real tennis in the university court. (If it had been summer, he would have walked down to Fenner’s to watch cricket.) In the late afternoon, he strolled back to his rooms. That particular day, though, while the timetable wasn’t altered, internally things were not going according to plan. At the back of his mind, getting in the way of his complete pleasure in his game, the Indian manuscript nagged away. Wild theorems. Theorems such as he had never seen before, nor imagined. A fraud of genius ? A question was forming itself with epigrammatic clarity : is a fraud of genius more probable than an unknown mathematician of genius ? Clearly the answer was no. Back in his rooms in Trinity, he had another look at the script. He sent word to Littlewood (probably by messenger, certainly not by telephone, for which, like all mechanical contrivances including fountain pens, he had a deep distrust) that they must have a discussion after hall.

            Before midnight they knew, and knew for certain. The writer of these manuscripts was a man of genius. That was as much as they could judge, that night. It was only later that Hardy decided that Srinivasa Ramanujan was, in terms of natural mathematical genius, in the class of Gauss and Euler : but that he could not expect, because of the defects of his education and because he had come on the scene too late in the line of mathematical history, to make contribution on the same scale.

              The following day Hardy went into action. Srinivasa Ramanujan must be brought to England, Hardy decided. Money was not a major problem. Trinity had usually been good at supporting unorthodox talent (the college had been the same for Kapitsa a few years later). Once Hardy was determined, no human agency could have stopped Ramanujan, but they needed certain amount of help from a superhuman one. 

                  Ramanujan turned out to be a poor clerk in Madras (Chennai), living with his wife on twenty pounds a year. He was usually strict about his religious observances, with a mother who was even stricter. It seemed impossible that he could break the ban and cross the water. Fortunately his mother had the highest respect for the goddess of Namakkal. One morning Ramanujan’s mother made a startling announcement. She had a dream the previous night, in which she saw her son seated in a big hall among a group of Europeans and the goddess of Namakkal had commanded her not to stand in the way of her son fulfilling his life’s purpose. This, say Ramanujan’s Indian biographers, was a very agreeable surprise to all concerned.

              In 1914, Ramanujan arrived in England. So far as Hardy could detect (though in this respect I should not trust his insight far) Ramanujan, despite the difficulties of breaking the caste laws, did not believe much in theological doctrine, except for a vague pantheistic benelolence, any more than Hardy did himself. But he did certainly believe in ritual. When Trinity put him up in college within four years he became a fellow. There was no ‘‘Alan St. Aubyn” self - indulgence for him at all. Hardy used to find him ritually changed into his pyjamas, cooking vegetables rather miserably in a frying pan in his own room.

             Their association was strangely touching one. Hardy did not forget that he was in the presence of a genius, but genius that was, even in mathematics, almost untrained. Ramanujan had not been able to enter Madras (Chennai) University because he could not matriculate in English. According to Hardy’s report, he was always amiable and good - natured, but no doubt he sometimes found Hardy’s conversation outside mathematics more than a little baffling. He seems to have listened with a patient smile on his good, friendly, homely face. Even inside mathematics they had to come to terms with the difference in their education. Ramanujan was self - taught : he knew nothing of the modern rigour, in a sense he didn’t know what a proof was. In an uncharacteristically sentimental moment, Hardy once wrote that if he had been better educated, he would have been less ‘Ramanujan’. Coming back to his ironic senses, Hardy later corrected himself and said that the statement was nonsense. If Ramanujan had been better educated, he would have been even more wonderful than he was. In fact, Hardy was obliged to teach him some formal mathematics as though Ramanujan had been a scholarship candidate at Winchester. Hardy said that this was the most singular experience of his life . What did modern mathematics look like to someone who had the deepest insight, but who had literally never heard of most of it ?

               It is good to remember that England gave Ramanujan such honours as were possible. The Royal Society elected him a Fellow at the age of thirty (which, even for a mathematician, is very young). Trinity also elected him a Fellow in the same year. He was the first Indian to be given either of these distinctions. He was amiably grateful. But he soon became ill.

                    Hardy used to visit him, as he lay dying in hospital at Putney. It was on one of those visits that there happened the incident of the taxi - cab number. Hardy had gone out to Putney by taxi as usual, his chosen mehod of conveyance. He went into the room where Ramanujan was lying. Hardy, always clumsy about introducing a conversation, said, probably without a greeting and certainly as his first remark : “The number of my taxi cab was 1729. It seemed to me rather a dull number.” To which Ramanujan replied : “No, Hardy ! 

                 It is a very interesting number : It is the smallest number expressible as the sum of two cubes in two different ways”.

               It was difficult, in war - time, to move Ramanujan to a kinder climate. He died of tuberculosis, back in Madras (Chennai), two years after the war. As Hardy wrote in the Apology, his roll - call of mathematicians : ‘Galois died at twenty - one. Abel at twenty - seven, Ramanujan at thirty - three, Riemann at forty. I do not know an instance of a major mathematical advance initiated by a man past fifty’.