The Most Touching Story In Mathematics

The most touching story in Mathematics ``And if you divide any number by itself, you get 1.'' The teacher in a small high school in southern India turned round to see a tiny hand trying to reach the ceiling. Oh by the gods, him again! That Aiyangar boy with his horribly difficult and quite irrelevant questions. Like last week, when he wanted to know how long it would take for a steam train to reach Alpha Centauri. As if he would be able to afford the fare if he knew. Well, he couldn't let him exercise his hands too much. ``Yes Ramanujan?'' The small boy with shining eyes stood up. He spoke slowly, with the calm confidence of one who did not need to be told he was the best in the class. ``Is zero divided by zero also equal to one?'' Unfortunately for all those other teachers who've been asked this question at least twenty times in their lives, the response to the question is unknown. But the life of the boy, Srinivasa Ramanujan Aiyangar, certainly isn't. The eldest son of a poor Brahmin clerk was born on December 22, 1887 in Erode in present day Tamil Nadu. An intelligent mind had seen him get through high school on scholarships, and stories abound of his youthful brilliance. For instance, when he was the fourth form, he was helping his undergraduate neighbour with difficult mathematics problems. A year later he independently obtained formulae of the form eiA=cos A + i sin A, which the great Euler had introduced to the world less than a century before. When he was sixteen and in the sixth form, he came across ``A synopsis of elementary results in pure and applied mathematics" by George Carr. This book, an elucidation of 6000 theorems, served to introduce Ramanujan to the real world of mathematics, but in a highly personal style that relegated the proofs, if any, to mere footnotes. Ramanujan went through the entire book methodically and excitedly, proving its theorems by himself, often as he got up in the morning. He claimed that the goddess of Namakkal inspired him with formulae in dreams. (Any ideas on how to verify this claim should be sent to Psychoanalysts International.) In December 1903, he won a scholarship to the Government College in the nearby town of Kumbakonam. But now he was really addicted to mathematics and could not kick the habit, even in classes for other subjects. Many were the English or Physiology lectures spent proving some erudite theorem or simply having fun with numbers. After all, this was the guy who would later be described as having each of the positive integers as one of his personal friends. The result? He went into a frantic moment of final-two-weeks study and passed all his exams, which he managed to do year after year? No, he failed all his nonmathematical exams. His scholarship was not renewed, and he had to leave university. Further attempts to complete his degree failed. He continued with mathematics, working on his slate (he could not afford much paper) and in his head to obtain results which he then committed to a notebook. His needs were simple and he did not feel he

lacked much. But he looked miserably poor, and his appearance was not a biased representation of the truth. At 22, he married and wanted to settle down. He approached Ramaswami Aiyar, the founder of the Indian Mathematical Society, to see if he could help him find a clerical job in his municipal office. Aiyar looked at some of Ramanujan's results and was shocked that such a talent should be wasted in a tedious office job. Contacts were made with his fellow-academics Seshu Aiyar and Ramachandra Rao (who would later become Ramanujan's biographers) and they tried hard to find him a job in academia. But the inelastic institutions of the day did not think much of employing a first year drop-out. Not even the fact that he had already published some research papers made a difference. Oh, what a change there might have been if they had only seen enough light to provide him with a roof and food! The world would have seen much more of this original mind. Eventually, they contacted Mr Griffith of the Madras Engineering College, and he contacted Sir Francis Spring, the Chairman of the Madras Port Trust, who promptly offered Ramanujan a light clerical job there. Never the sort who enjoyed living on friends' charity, Ramanujan accepted. It gave him enough time to continue his research, and plenty of scrap papers to take home and work on! The fact that Narayana Aiyar, the head of the Port Trust, was a keen mathematician, certainly helped. But all this encouragement from friends did not provide him with the things a mathematician most needs --- good teachers, an active research environment and access to the latest works. He was approaching 25, which meant his nascent years had been basically wasted. God knows what might have happened had history been less cruel. This was the real tragedy of Ramanujan. At least his friends knew this. They encouraged him to write to a leading pure mathematician of the day, Godfrey Hardy of Cambridge. So in January 1913 Professor Hardy received a letter with a Madras postmark from an unknown clerk with over a hundred theorems. Hardy looked at the letter. At least it was not one of those bombastic pieces from some smart alec who thought he was the next Newton. He looked at the papers. Not bad. He put them down and looked at the papers --- this time the ones with the latest cricket scores. Then he went to his lectures. But the theorems! Some were unusual and played havoc with his intellect as he played his regular tennis game that afternoon. What if... could it be... had the unimaginable happened? Was this guy more than a crank? He talked to his friend John Littlewood about it that night at supper. Sure, John would have a look at the papers with him. So the theorems were finally seen by people who could judge their worth. Most were rediscoveries, but what rediscoveries! Those who had beaten this clerk were the very best. And some of his results were so incredible! They had never seen the like! He had hardly any proofs, but they had to be correct, for the simple reason that no one could have had the imagination to invent them. A few were definitely wrong, but that only added weight to their increasingly shocked feeling that this stuff was totally genuine. This was no crank, this was a genius of the highest order! And he was still alive, and wanting help. Help? Of course they'd help --- they'd get him to Cambridge regardless of whether it was humanly possible or not.

Soon Ramanujan was contacted by the Cambridge mathematicians and invited to come there on a full scholarship. No longer would he have any financial woes, and he could play with mathematics to his heart's (and head's) content. By now, Ramanujan was already a professional mathematician, having received a special scholarship (from which he promptly sent a sizable fraction to his parents) from the University of Madras, thanks to the recommendation of another Cambridge Fellow, Dr G. T. Walker. He refused Hardy's invitation, for it was unclean for a Brahmin to leave Indian shores. ``What!'' his friends exclaimed, ``This is what you have been waiting for! You have come so far, you cannot turn this down! Do you think the gods would really mind that their son show himself to the world?'' Hardy too, was very persistent, and Ramanujan agreed to go. But would his mother agree? Not by any means. Then one morning she announced that the family goddess Namagiri had ordered her to let him go, having shown her son in a large hall with a bunch of Europeans. Thus India's greatest mathematician sailed for the heathen shores of England on 17 March 1914. He arrived and got down to work at once. While his mind had been hardened by time, he could still learn new things, and learn them well. It was impossible to teach him systematically, but he gradually absorbed new points of view (like why proofs were important!). The line between what he learnt from books and learnt for himself was always very hazy. In his favourite topics, like infinite series and continued fractions, he had no equal. But in other topics, like elliptic functions, a subject that relied so much on proof, a subject where intuition had a bad habit of coming unstuck, he produced much that was false. But this should merely add to our respect for one who did not fear to let his mind run free and unblinkered. Always faithful in observing his Brahmin heritage, Ramanujan cooked his own food (vegetarian of course), dressed comfortably in his dhoti (the traditional clothing worn by many Indian men at home). Whether he was actually religious has been argued. He once surprised Hardy by saying that all religions seemed to him to be more or less equally true. It was an open secret that he had a high regard for Namagiri, and accepted all the tenets of Hinduism, such as nirvana and kharma. He was a regular attender at popular lectures on the ancient Hindu legends, often entering into discussions with the experts giving the talks. Like Hardy, he was a fervent pacifist. He was not very interested in literature, though he certainly knew enough to tell good stuff from bad. And he had a passion for the oddities of this world, with more than a few books written by cranks such as circle-squarers! In short, he was a man in whom society could take pleasure, with whom one could sip tea and discuss philosophy, politics or mathematics. To quote Hardy, "...He was a normal human being who happened to be a great mathematician.'' Then, in May 1917, Ramanujan was taken ill with what was probably an incurable disease. He entered a nursing home, where he remained for well over a year. In early 1918, he became the first Indian Fellow of the Royal Society, and this stirred him to more excellent research\ldots from bed. Early the next year he returned to India, a physically (but not mentally) emaciated shadow of his former self. But his health only declined (the fact that he didn't like taking his medicine didn't help) and he died on 26

April 1920. His last paper was done on his death-bed a few days before he left his widow Janakiammal (but no children) behind. She died on April 13, 1994.