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*Srinivasa Ramanujan*

*Srinivasa Ramanujan*

**(1887-1920)**

## biography

**Srinivasa Ramanujan was one of the greatest mathematicians India has produced. He was born at Erode in Tamil Nadu on 22 December 1887. His father was a petty clerk in a cloth Shop at Kumbakonam.**

**The family was not well-to-do. Ramanujan went to school at the age of five. Two years later (1894) he joined the Town High School at Kumbakonam, where he got a free studentship. He passed the matriculation examination in 1904 and won the Subrahmanyam Scholarship by topping in mathematics, which enabled him to join Government College at Kumbakonam.**

**He had such a fascination for mathematics that he devoted all his time to the subject, neglecting others, including the English language. The result was that he failed twice in his first year arts examination and had to leave college. That was the end of his formal education.**

**But from his early childhood it was evident that he was a mathematical prodigy, and Nature had gifted him an uncanny memory which he put entirely at the service of numbers. As a result “he remembered the idiosyncrasies of every one of the first ten thousand integers”. His talent for mathematics was sharpened while still in school. He borrowed from the school library G.S. Carr’s the**

*Synopsis**of**Elementary**Results**in**Pure**and**Applied**Mathematics*. For a boy of fifteen, the title of the book can be frightening, but Ramanujan was delighted as if he had got a fascinating mystery story to read. He devoured the book and found delight in verifying some of the formulae given in it and began to make new theorems and formulae. It triggered the mathematical genius in him. Mathematical ideas came rushing to his mind with great speed. He started doing problems on loose sheets of paper. By the time he left for England, he had filled three big sized notebooks, which later were known as Ramanujan’s*Frayed**Notebooks*. Even today scientists at the Bhabha Atomic Research Centre and Tata Institute of Fundamental Research are trying to decipher his*Notebooks*and his other works to prove or disprove the results given in them, and to find out if any of them could help them in their atomic energy research.**But this mathematical genius did not have adequate qualifications for a job. He would visit offices, showing his**

*Frayed**Notebooks*, trying to convince the officials that he knew mathematics and could do a clerical job. But people could not understand what was scribbled in the*Notebooks*until he met Francis Spring, director of the Madras Port Trust, who was impressed by his*Notebooks*. Spring offered Ramanujan a clerical job on a monthly salary of rupees twenty-five. Ramanujan desperately needed a job because his parents had got him married in 1909, at the age of twenty-two, to an eight-year-old girl Janaki.**Ramanujan had continued his mathematical work after leaving college. His earliest contribution to the**

*journal**of**Indian**Mathematical**Society*was in the form of questions, which appeared in 1911. The same year was published his article ‘*Some**Properties**of**Bernoulli’s**Numbers’*. But because of his scanty knowledge of the English language he could not express himself properly. At that time, Ramanujan was working on theorems of prime numbers. In Cambridge University, Professor G.H. Hardy, in his tract on ‘*Orders**of**Infinity’,*had posed some problems which were yet to be solved. Ramanujan had found the solution to those problems. These were communicated to Professor Hardy. This started a very fruitful friendship which resulted in Ramanujan going to England and Working in collaboration with Professor Hardy.**While Working in the Port Trust, Ramanujan was introduced to Dr. G.T. Walker, director of Meteorology, Government of India, who at once recognized the quality of Ramanujan’s work and succeeded in arranging a monthly scholarship of rupees seventy-five for Ramanujan from the University of Madras in May, 1913. All that time Professor Hardy was trying to get him a research scholarship at Trinity College, Cambridge, which he succeeds soon after. It was conveyed to Ramanujan and he left for England in April 1914. The scholarship was worth 250 Euro. In addition, he was also awarded an exhibition (scholarship) amounting to fifty pounds. As a scholar, Ramanujan had no assigned duties at Cambridge and was free to work as he pleased. He devoted himself wholeheartedly to his research work and in collaboration with Professor Hardy put his genius to work in number theory. Ramanujan played with numbers as a child plays with toys. In Ramanujan, Hardy found an unsystematic mathematician. The several discrepancies in his research could be due to his lack of formal education. His inadequate knowledge of English did not help matters either. But Hardy and their other collaborator, J.E. Littlewood, took care of his deficiencies. His achievements at Cambridge include the Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan identities in partition of integers, a long list of the highest composite numbers, besides work on the number theory and the algebra of inequalities. In algebra, his work on continued fractions is considered to be equal in importance to that of the great Swiss mathematician Leonard Euler (1707-83) and the German mathematician Karl Jacobi (1804-51).**

**Ramanujan was elected Fellow of the Royal Society on 18 February 1918 and in October the same year became the first Indian to be elected Fellow of Trinity College.**

**His stay in England was cut short due to his ill-health. The extreme cold of Cambridge for a south Indian used to tropical climate was not easy to bear. His orthodoxy with regard to diet further contributed to the deterioration of his health. He had developed tuberculosis which was incurable at that time. He was removed to a nursing home at Cambridge. As his condition did not improve, he was kept at different sanatoria at Wales, at Matlock and London. When in autumn 1918 he showed signs of improvement, he resumed his research work and discovered some of his most beautiful theorems. Fearing that he may again become bedridden, the university authorities sent him back to India. On his return to India, he resumed his research work but his health went on deteriorating and on 26 April 1920 he breathed his last in Madras.**

**Ramanujan was a pure mathematician of the highest order, whose prime interest was the theory of numbers. As a pure mathematician, he wanted to keep his work away from any kind of technological application. “But what, one may enquire is the use of all this ado about splitting numbers in various ways? If Ramanujan had to answer the question, he likes his mentor and discoverer, G.H. Hardy, would have been the First to agree that such work was completely useless. I have no doubt that he would have wholeheartedly endorsed the famous toast which Hardy is said to have proposed at Cambridge some years after Ramanujan’s death ‘To pure mathematics_ and May it remain useless for ever.**

**However, to the chagrin of Ramanujan and Hardy, even pure mathematics may not remain ‘useless’ for all times to come. It is gradually being made use of in technology. Ramanujan’s mock-theta functions, modular equations, identities, theories of continued fractions and elliptic functions or some other of his numerous creations are being extensively studied with a view to ascertaining the possibility of understanding and regulating atomic furnaces. Some other uses may be invented in course of time. For posterity, Hardy and others have edited Ramanujan’s works in a volume which came out in 1927. Like the unknown inventor of' zero centuries ago, Ramanujan has put India on the map of the world of mathematics. No greater tribute could be paid to Ramanujan than what his mentor Hardy said: “I still say to myself when I am depressed and find forced to listen to pompous and tiresome people: Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms”.**

**Jawaharlal Nehru Writes in his book**

*Discovery**of**lndia*: “Mathematics in India inevitably makes one think of one extraordinary figure in recent times. This was Srinivasa Ramanujan”. And all that he achieved was in a short span of thirty-three year.
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