Biography

Shrinivas Aiyangar Ramanujan was born on December 22, 1887 in a Brahmin family in Southern India. His father was an accountant for the local traders, and was by no means well off. At the age of five, Ramanujan started attending primary school at Kumbakonam, his father’s place of work. Even during his school days his grasp of mathematical concepts was exceptional. He mystified his teachers and classmates with rapid calculations of long mathematical problems. At home too, his mind appeared to be busy thinking about and mentally playing around with numbers. The society in which he lived was appreciative of learning in general, and of mathematical aptitude in particular.
His school friends recall approaching him for help in Mathematics. This he would readily provide enthusiastically. Though they knew that his grasp of the subject was much more, they could not fathom the depth of his intellect. It was after he entered Town High School at Kumbakonam in 1898 that his genius took wings. In 1900, he began working on summing up of geometric and arithmetic series. Interestingly, in 1902 when he was taught cubic equations he went right ahead and evolved his own method to solve quartics. Going a step further, he tried solving quintics by the same method but failed to do so.[br /]
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The year 1902 marked a turning point in Ramanujan’s life. From the local library he got hold of a copy of a book on pure mathematics by G S Carr entitled Synopsis of Elementary Results in Pure Mathematics. The book was a collection of around 6,000 theorems and formulae with short proofs. Written in a concise manner, by a tutor, the book served to unfold uncharted fields for Ramanujan’s intellectual quests. Carr’s book was fairly outdated being published in 1856. Carr himself was never renowned as a great mathematician. But his book definitely was a scholarly and lively written text by one who obviously enjoyed mathematics. It not only provided the required thrust to Ramanujan’s genius but the influence of the book was to be felt in his works even after he had received much wider exposure to theories concurrent with the times then.[br /]
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In 1904, when he was just 16, Ramanujan began investigating the series of S (1/n) and calculated Euler’s Constant to 15 decimal places. His study of Bernoulli numbers also commenced at this stage. In recognition of his excellent school performance, Ramanujan was offered a scholarship at Government College, Kumbakonam. His preoccupation with mathematics led him to neglect other

subjects, and unfortunately, the college failed to renew his scholarship the following year. This was a setback that he took to heart and without informing his parents, went to Vishakhapatnam about 650 kms. from Madras. He continued his research work and focused on relations between integrals and series.[br /]
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During the years in college, the professors of mathematics particularly Ramanujachari and Mudaliar quickly realized the worth of their precocious student. Often when a complex problem was explained to the class, Ramanujan would stand up and offer another solution which was easy and involved fewer steps.[br /]
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Wishing to enter the University of Madras, Ramanujan got admission to Pachaiyappa’s College for his First Arts Exam. After barely three months of enrolment, he was struck by the first of his major illnesses. Ramanujan had to leave the course but managed to appear for the exam. He failed in all the subjects except mathematics. Given the rigidity of the formal education system, Ramanujan was deprived of a formal university education. The crucial phase of his life when guidance, information and education might have given boost to his brilliance, was spent in self-study. Whether formal education would have shackled his innovative and intuitive thinking, is a moot point for intellectual consideration.[br /]
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Ramanujan continued his independent study, which included research on continued fractions and divergent series. In 1908, he took seriously ill which plagued him for sometime. He had to undergo a major surgery in 1909. On July 14, 1909, on his mother’s insistence he was married to nine-year-old S Janaki Ammal. They however stayed separately in observance of the traditional belief, till Janaki was 12.[br /]
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Ramanujan tryst with mathematics and solution to problems featured in the Journal of Indian Mathematical Society (IMS). He even submitted problems of his own to the Journal. In 1910, he succeeded in developing the relations between elliptic modular equations.[br /]
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Poverty continued to dog Ramanujan’s life but fire of his genius continued to glow unabated. In his days of penury, Ramanujan would scribble his workings on a slate and rub it off to continue with his work. When he was asked why he did not use paper, he said that he would require four reams of paper every month and if he spent the little that he was getting on buying paper, he would have nothing to eat. Working on the slate however, became a habit, which stayed with him till the end. Ramanujan wore a buttoned up coat, which covered the fact that he had no shirt underneath. Once, he entered college without the required cap on his head. When reprimanded, he stated that his old cap had blown off in a gust of wind and had no money to buy a new one, though it cost less than a rupee.[br /]
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Though poor, Ramanujan was a man of self-respect. He hated to seek any help and was not happy to use the stipend that Rao had given him in recognition of his work. He augmented his income by giving tutions in mathematics and showed great concern for his student’s performance.Gopalachary, a contemporary of Ramanujan recalls Ramanujan’s compassion

towards fellow human beings. His old drillmaster at school went mad after having a vision of Lilliputian like beings surrounding him. This drove him insane and by the time he recovered he had lost his job. Ramanujan used to beg food from other houses and give it to his old teacher. Ramanujan also believed that the teacher was an ‘evolved soul’ who had a vision of things not seen by mortal eyes.[br /]
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In his later life when failing health prevented him from putting in as much work as he would have liked to, the thought of not ‘earning his pay’ weighed very heavily on his mind. In 1918, at the peak of his career, Ramanujan was granted £250 per year by both Trinity College Cambridge and Madras University. The total sum of £500 was much beyond what Ramanujan perceived as necessary. He promptly wrote to the Registrar of the University of Madras, that he wished to provide books and fees for needy students out of the remaining balance, after the payment of his expenses and a sum of £50 p. a. payment to his parents.[br /]
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In 1911, he submitted a brilliant research paper on Bernoulli numbers to the Journal of the IMS. The publication of this gained him recognition as a talented mathematician. Marriage had made the earning for a living, an imperative for Ramanujan. He sought help from the founder of the IMS. In 1911, he got his first job, a temporary one, in the Accountant General’s office in Madras. Somebody suggested he meet Dewan Bahadur Ramchandra Rao, who was collector at Nellore and a keen mathematician and founder member of the IMS. Ramachandra Rao recollected his first meeting with Ramanujan in these words :[br /]
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"A short figure…. with one conspicuous feature – shining eyes…walked in with a frayed notebook under his arm. He was miserably poor…. He opened his book and began to explain some of his discoveries, I saw quite at once that there was something out of the way, but my knowledge did not permit me to judge whether he talked sense or nonsense. I asked him to come over again. He did. Then he had gauged my ignorance and showed me some of his simpler results… at last his theory of divergent series not yet announced to the world converted me." Ramachandra Rao provided him with a modest subsidy and tried to get him a scholarship at Madras but was unsuccessful. Ramanujan was unwilling to live on charity and applied for a clerical job in the accounts section of the Madras Port Trust. His references included one from E W Middlemast, a professor of Mathematics at the Presidency College in Madras. It read "I can strongly recommend the applicant. He is a young man of quite exceptional capacity in mathematics and especially in work relating to numbers. He has a natural aptitude for computation and is very quick at figure work."[br /]
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Ramanujan was appointed to the job and took up his duties from March 1, 1912. Ramanujan was lucky that his brilliance was recognized by many who came in his touch. The Chief Accountant at Madras Port Trust, S N Aiyar wrote a paper based on Ramanujan’s work. L L T Griffith was a professor at Madras Engineering College. He knew the professor of mathematics at University College, London, M J M Hill. Griffith sent him some of Ramanjan’s work including his paper on Bernoulli numbers. Hill was very encouraging but not quite convinced. He recommended some books for further reading. Ramanujan approached a few others in London but failed to get any reply. Ramanujan had then read a book ‘Order of Infinity’ by G H Hardy and in January 1913, he wrote to Hardy, a long list of theorems professed by him.[br /]
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This one act was going to be the catalyst for Ramanujan’s trailblazing achievements and recognition in the international arena. G H Hardy was of a true scholastic spirit. He studied the theorems sent by an unknown Indian clerk, discussed them with colleagues particularly Littlewood and concluded, "Only a mathematician of a highest class could have written them. They had to be true, for if they were not, no one would have the imagination to invent them."[br /]
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Hardy’s prompt response sent Ramanujan’s spirits soaring. He sought Hardy’s help in the following words : "I have found a friend in you who views my labors sympathetically… I am already a half-starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university or from the government." One gets the picture of a self-respecting genius, desperate to get on with the passion of his life but, held back by the necessities of providing for himself and his family.[br /]
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During this period, T C Walker, Director General of Observatories, Shimla also happened to visit Madras. The Chairman of Madras Port Authority took the opportunity to bring Ramanujan’s talent to his notice. Walker was impressed and urged the Madras University to provide him a stipend which would allow Ramanujan to concentrate on research without financial worries.The University of Madras, at this point, bent its rules to grant a scholarship to Ramanujan who was then able to leave his job and devote his time to research.[br /]
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Meanwhile, Hardy was keen on bringing Ramanujan over to Cambridge. He felt that when exposed to newer ideas and thinking of many more shrewd mathematical minds, Ramanujan’s creative abilities will flourish. Lack of funds coupled with religious taboos regarding crossing the seas held Ramanujan back. He also knew that life in England was not likely to be easy for a strict vegetarian like him. In the beginning of 1914, the University of Madras invited E H Neville, a fellow of Trinity to conduct some classes. Hardy lost no time in requesting Neville to try and persuade Ramanujan to go to Cambridge. Neville tried and succeeded not only in persuading Ramanujan but also the University of Madras to award him a scholarship for his study at Cambridge.[br /]
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Ramanujan’s mother finally agreed to her son’s crossing the seas, after she received a sign from the Goddess of Nammakkal, in her dreams. Ramanujan had now to be outfitted for England. His traditional tuft of hair was shaved off and the turban replaced by a hat. His Indian clothes were exchanged for European outfits. He is believed to have been very uncomfortable with these changes but succumbed to them for the benefit of his beloved mathematics. He, however refused to give up vegetarianism. Mrs Neville later recalled with sympathy, the discomfort that Ramanujan had to conform to the British way of life and wondered if it could have been avoided.[br /]
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On March 17, 1914, Ramanujan left India. As a voyage it was uneventful except for a bout of seasickness but it was indeed a remarkable journey, for the child of an nondescript Indian family of limited means, to have set sail towards greater achievements and fame. Ramanujan stayed for a few weeks with Neville and then moved to his room in Trinity College. Though lacking the proper qualifications, Ramanujan was allowed to enroll for his Bachelor of Science by Research Degree Course at Cambridge.[br /]
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Ramanujan’s collaboration with his mentor Hardy started yielding impressive results. Hardy was puzzled on how to teach the foundation of modern Mathematics to Ramanujan. He sought the help of Littlewood who found it a daunting task. Often when some matter was introduced to Ramanujan, he would come up with "an avalanche of original ideas which made it almost impossible for Littlewood to persist in his original intention."[br /]
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1914 – the year Ramanujan reached England also saw the beginning of World War I. Littlewood was enlisted in war duty but Hardy and Ramanujan continued their work. The war meant a scarcity of food items amongst other things and Ramanujan found it more difficult to obtain the requirements for his vegetarian diet. This along with the British winter affected his already frail health. He could not do much serious work during the cold months. This fact also seemed to bear heavily on him. However, he published the work that he had done in England till then. Ramanujan completed his dissertation on Highly Composite Numbers and on March 16, 1916 was awarded a Ph D (then called Bachelor of Science by Research) from Cambridge University.[br /]
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Many Indians recall their meeting with Ramanujan in London. He would often invite them over for a meal which he cooked himself. Mr Ayyangar (Editor of The Hindu), Dr C D Deshmukh, Dr P C Mahalanobis, Mr K Ananda Rao were amongst the few, who fondly recalled having partaken of his hospitality.[br /]
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In 1917, his health further deteriorated and the doctors made a prognosis of tuberculosis. Ramanujan was seriously ill and spent most of his time in hospitals and nursing homes. He must have found it hard to take care of himself in a foreign country, far away from home. Due care by his hosts and partial recovery coupled with his never-say-die spirit saw him weather such times. [br /]
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His tenacity was to be soon rewarded and on February 18, 1918, Ramanujan had the distinction of being elected as a Fellow of the Cambridge Philosophical Society and shortly thereafter, a list of distinguished mathematicians including Hardy, Littlewood, MacMohan, Grace, Young, Whittaker and Whitehead, proposed Ramanujan’s name for election as a Fellow of The Royal Society of London. This honor was duly conferred on him on May 2, 1918 making him the first Indian to be honored. On October 10, 1918, he was elected Fellow of Trinity College Cambridge for a period of six years. The year 1918 thus proved to be a year of recognition of Ramanujan’s outstanding talents and achievements. His health too showed a slight improvement for a brief while. On February 27, 1919, Ramanujan sailed back for India. His health had started failing again. Despite medical treatment, Ramanujan passed away in Madras on April 26, 1920, at the age of young of 32.[br /]
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As a man Ramanujan was by nature shy and contemplative; but none has accused him of arrogance which he could have justly felt. His contemporaries have always described him as modest and unassuming. He is believed to be pale and anemic though a little plump. His eyes were an arresting feature in his face and they bespoke of his intellect. His wit and humor stayed with him till his end. During his last days the government shifted him to a place called Chetpet in Madras hoping to seek some change in his health. Ramanujan remarked to his wife, "They have brought me to this place where everything will be ‘chat’ – ‘pat’." He meant that his death would be ‘chat-pat’ – meaning ‘very soon’ in Tamil.[br /]
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Ramanujan had a great interest in Indian Philosophy and Religion. He would become quite animated and warm while discussing those subjects. Ramanujan would say that God could be symbolically represented as the product of ‘zero’ and ‘infinity’ – being attributeless as also the abode of all attributes. Ramanujan had psychic experiences but was not overwhelmed by them. His work revealed that intuition played a role in his intellectual pursuit of Mathematics.[br /]
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His mother’s influence on his life appears to have been great. He hardly spent any time with his wife except in the last year of his life when he returned from England, a dying man. His wife looked after him well and is believed to have been keen to go to London to tend him during his period of ill health. Ramanujan’s mother objected to this and records suggest that on consulting an astrologer, she was advised to keep the two separated for the sake of his good health. She did not succeed in this effort as after his return from England Ramanujan insisted on having Janaki with him. On his return from England many observed that Ramanujan was a changed man. His ill health may have much to do with this. Whilst in England, he could intellectually and socially stand up amongst his foreign contemporaries. He has never been portrayed as an object of curiosity or ridicule although he insisted on continuing with many of his Indian customs. His innate goodness, unmistakable intellect and an inborn humility and compassion may have had much to do with this.[br /]
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Ramanujan’s life was a blaze of talent. He is reported to have woken up from sleep and started jotting down new formulae and theorems in his notebook at a feverish pace. Much of his earlier studies appear to be inspired and intuitive. He often attributed his mathematical deductions to inspiration from the goddess of Nammakkal. Along with a remarkable talent, Ramanujan was fortunate enough to find friends at each stage who would encourage him and further his interests. Neither petty jealousies nor racial prejudices appear to have obstructed his path. His genius seems to have caught the respect, and imagination of all that was purely scholastic in different people. His completed and unfinished works have served as beacons for many mathematicians who came after him. His ‘Lost Note Book’ which was later discovered has been the subject of much further study and research. Indeed, he has left behind a legacy, which would be the matter of pride of any scholar as well as for his country.[br /]
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