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.
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 Carr’s book was fairly outdated being published in 1856.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.
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.
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.
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.
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.
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.
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.
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.
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.
(1887 - 1920)
Galileo Died At The Hands Of Inquisition And I Will Die Of Poverty
Shrinivas Ramanujan in his short life-span, proved to be a mathematical genius comparable to the likes of Karl Jacobi and Leonhaed Euler. Despite lack of formal higher education and battling against heavy odds like poverty and ill health, his mathematical genius flowed unhindered. His contribution in the fields of elliptic functions, infinite series and the analytical theory of numbers is immeasurable. Even after his death at the young age of 32, his notes continued to be a subject of research and a source of further mathematical theorems, formulae and solutions.
Born in India, which was then under British rule, he received encouragement and recognition not only from discerning Indians but also from his contemporary British mathematicians. Against the dictum of his religion, he traveled overseas to Britain where he collaborated with Prof. Hardy at the Trinity College. Between 1914-1918, which coincided with World War I, Ramanujan stayed and worked at the Trinity College. Though his health was deteriorating, his mental faculties and mathematical genius flourished. It took an impressive list of eminent mathematicians to propose his name for election as a Fellow at The Royal Society of London. This unique honor was conferred on him on May 2, 1918. Read on to have an insight into the life and mind of one of the most prolific and yet elusive Indian personality who left behind a mathematical legacy, for others to reveal.
December 22, 1887
Born in Erode, Tamilnadu, India.
1898
Entered Town High School in Kumbakonam.
1900
Commenced work on summing geometric and arithmetic series.
1902
Was taught how to solve quartics but evolved his own method.
1902 (approx)
Perused G S Carr’s Synopsis of Elementary Results in Pure Mathematics. This book proved to be a major influence on Ramanujan.
1904
Investigated series S (1/n) and calculated Euler’s constant to 15 decimal places. Began study of Bernoulli numbers. Obtained scholarship and entered the Government College in Kumbakonam.
1905
Scholarship not renewed due to lack of application to other subjects.
1906
Gained admission to Pachayappa’s College in Madras. Began study of elliptic functions.
Took ill after three months in college. Took his exams after having left the course where he failed in all subjects except Mathematics.
1908
Study of continued fractions and divergent series. His health seriously deteriorated.
July 14, 1909
Was married to S Janaki Ammal.
1910
Came into contact with Diwan Bahadur Ramchandra Rao, Collector of Nellore, who recognized his genius and financially supported him for some time.
1911
Developed relations between elliptic modular equations. First paper published in Journal of Indian Mathematical Society on Bernoulli numbers.
1912
Took up a job as a clerk in the accounts section of the Madras Port Trust to maintain himself and his family.
1913
Began correspondence with British mathematician Godfrey H Hardy.
May 1913
University of Madras grants him a scholarship.
March 17, 1914
Ramanujan leaves India for Trinity College, Cambridge, England, on Hardy’s invitation.
March 16, 1916
Graduated from Cambridge with a Bachelor of Science for Research (later called the Ph D). His thesis was on Highly Composite Numbers.
1917
Fell seriously ill with tuberculosis.
February 18, 1918
Elected Fellow of the Cambridge Philosophical Society.
May 2, 1918
Elected Fellow of the Royal Society of London.
October 10, 1918
Elected Fellow of Trinity College, Cambridge, for six years.
February 27, 1919
Failing health forced him to sail back to India.
April 26, 1920
Died in Madras.
Not Available
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• At the age of 24, published his first paper on Bernoulli numbers in the Journal of Indian Mathematics.
• 1918
Elected Fellow of the Royal Society of London.
Elected Fellow of Trinity College, Cambridge.
Elected Fellow of the Cambridge Philosophical Society.
