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SRINIVASA RAMANUJAN.

INTRODUCTION Srinivasa Ramanujan Aiyangar (22 December 1887 – 26 April 1920)was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: according to Hans Eysenck: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered".[4] Seeking mathematicians who could better understand his work, in 1913 he began a postal correspondence with the English mathematician G. H. Hardy at the University of Cambridge, England..

HIS WORKS. Recognising Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that "defeated me completely; I had never seen anything in the least like them before", and some recently proven but highly advanced results. During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Of his thousands of results, all but a dozen or two have now been proven correct..

Pursuit of career in mathematics. In 1910, Ramanujan met deputy collector V. Ramaswamy Aiyer , who founded the Indian Mathematical Society.Wishing for a job at the revenue department where Aiyer worked, Ramanujan showed him his mathematics notebooks. As Aiyer later recalled.I was struck by the extraordinary mathematical results contained in [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department.Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends in Madras.Some of them looked at his work and gave him letters of introduction to R. Ramachandra Rao, the district collector for Nellore and the secretary of the Indian Mathematical Society. Rao was impressed by Ramanujan's research but doubted that it was his own work. Ramanujan mentioned a correspondence he had with Professor Saldhana , a notable Bombay mathematician, in which Saldhana expressed a lack of understanding of his work but concluded that he was not a fraud. Ramanujan's friend C. V. Rajagopalachari tried to quell Rao's doubts about Ramanujan's academic integrity. Rao agreed to give him another chance, and listened as Ramanujan discussed elliptic integrals, hypergeometric series, and his theory of divergent series, which Rao said ultimately convinced him of Ramanujan's brilliance. When Rao asked him what he wanted, Ramanujan replied that he needed work and financial support. Rao consented and sent him to Madras. He continued his research ..

HIS EARLY LIFE. Ramanujan , "younger brother of Rama", a Hindu deity was born on 22 December 1887 into a Tamil Brahmin Iyengar family in Erode, Mysore Kingdom (now Tamil Nadu, India), at the residence of his maternal grandparents. His father, Kuppuswamy Srinivasa Iyengar, originally from Thanjavur district, worked as a clerk in a sari shop. His mother, Komalatammal , was a housewife and sang at a local temple. They lived in a small traditional home on Sarangapani Sannidhi Street in the town of Kumbakonam.The family home is now a museum. When Ramanujan was a year and a half old, his mother gave birth to a son, Sadagopan , who died less than three months later. In December 1889, Ramanujan contracted smallpox, but recovered, unlike the 4,000 others who died in a bad year in the Thanjavur district around this time. He moved with his mother to her parents' house in Kanchipuram, near Madras (now Chennai). His mother gave birth to two more children, in 1891 and 1894, both of whom died before their first birthdays..

Ramanujan departed from Madras aboard the S.S. Nevasa on 17 March 1914.When he disembarked in London on 14 April, Neville was waiting for him with a car. Four days later, Neville took him to his house on Chesterton Road in Cambridge. Ramanujan immediately began his work with Littlewood and Hardy. After six weeks, Ramanujan moved out of Neville's house and took up residence on Whewell's Court, a five-minute walk from Hardy's room.Hardy and Littlewood began to look at Ramanujan's notebooks. Hardy had already received 120 theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks. Hardy saw that some were wrong, others had already been discovered, and the rest were new breakthroughs. Ramanujan left a deep impression on Hardy and Littlewood. Littlewood commented, "I can believe that he's at least a Jacobi",while Hardy said he "can compare him only with Euler or Jacobi."Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. Hardy and Ramanujan had highly contrasting personalities. Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades, the foundations of mathematics had come into question and the need for mathematically rigorous proofs recognised . Hardy was an atheist and an apostle of proof and mathematical rigour , whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights. Hardy tried his best to fill the gaps in Ramanujan's education and to mentor him in the need for formal proofs to support his results, without hindering his inspiration—a conflict that neither found easy..

Posthumous Recognition. The year after his death, Nature listed Ramanujan among other distinguished scientists and mathematicians on a "Calendar of Scientific Pioneers" who had achieved eminence.Ramanujan's home state of Tamil Nadu celebrates 22 December (Ramanujan's birthday) as 'State IT Day'. Stamps picturing Ramanujan were issued by the government of India in 1962, 2011, 2012 and 2016.Since Ramanujan's centennial year, his birthday, 22 December, has been annually celebrated as Ramanujan Day by the Government Arts College, Kumbakonam , where he studied, and at the IIT Madras in Chennai. The International Centre for Theoretical Physics (ICTP) has created a prize in Ramanujan's name for young mathematicians from developing countries in cooperation with the International Mathematical Union, which nominates members of the prize committee. SASTRA University, a private university based in Tamil Nadu, has instituted the SASTRA Ramanujan Prize of US$10,000 to be given annually to a mathematician not exceeding age 32 for outstanding contributions in an area of mathematics influenced by Ramanujan.[85]Based on the recommendations of a committee appointed by the University Grants Commission (UGC), Government of India, the Srinivasa Ramanujan Centre, established by SASTRA, has been declared an off-campus centre under the ambit of SASTRA University. House of Ramanujan Mathematics, a museum of Ramanujan's life and work, is also on this campus. SASTRA purchased and renovated the house where Ramanujan lived at Kumabakonam.In 2011, on the 125th anniversary of his birth, the Indian government declared that 22 December will be celebrated every year as National Mathematics Day.Then Indian Prime Minister Manmohan Singh also declared that 2012 would be celebrated as National Mathematics Year..

Ramanujan has been described as a person of a somewhat shy and quiet disposition, a dignified man with pleasant manners.He lived a simple life at Cambridge. Ramanujan's first Indian biographers describe him as a rigorously orthodox Hindu. He credited his acumen to his family goddess, Namagiri Thayar (Goddess Mahalakshmi) of Namakkal . He looked to her for inspiration in his work and said he dreamed of blood drops that symbolised her consort, Narasimha. Later he had visions of scrolls of complex mathematical content unfolding before his eyes. He often said, "An equation for me has no meaning unless it expresses a thought of God." Hardy cites Ramanujan as remarking that all religions seemed equally true to him. Hardy further argued that Ramanujan's religious belief had been romanticised by Westerners and overstated—in reference to his belief, not practice—by Indian biographers. At the same time, he remarked on Ramanujan's strict vegetarianism. Similarly, in an interview with Frontline, Berndt said, "Many people falsely promulgate mystical powers to Ramanujan's mathematical thinking. It is not true. He has meticulously recorded every result in his three notebooks," further speculating that Ramanujan worked out intermediate results on slate that he could not afford the paper to record more permanently ..

ILLNESS AND DEATH. Ramanujan was plagued by health problems throughout his life. His health worsened in England; possibly he was also less resilient due to the difficulty of keeping to the strict dietary requirements of his religion there and because of wartime rationing in 1914–18. He was diagnosed with tuberculosis and a severe vitamin deficiency, and confined to a sanatorium. In 1919, he returned to Kumbakonam , Madras Presidency, and in 1920 he died at the age of 32. After his death, his brother Tirunarayanan compiled Ramanujan's remaining handwritten notes, consisting of formulae on singular moduli, hypergeometric series and continued fractions.Ramanujan's widow, Smt. Janaki Ammal, moved to Bombay. In 1931, she returned to Madras and settled in Triplicane , where she supported herself on a pension from Madras University and income from tailoring. In 1950, she adopted a son, W. Narayanan, who eventually became an officer of the State Bank of India and raised a family. In her later years, she was granted a lifetime pension from Ramanujan's former employer, the Madras Port Trust, and pensions from, among others, the Indian National Science Academy and the state governments of Tamil Nadu, Andhra Pradesh and West Bengal. She continued to cherish Ramanujan's memory, and was active in efforts to increase his public recognition; prominent mathematicians, including George Andrews, Bruce C. Berndt and Béla Bollobás made it a point to visit her while in India. She died at her Triplicane residence in 1994.1994 analysis of Ramanujan's medical records and symptoms by Dr. D. A. B. Young concluded that his medical symptoms—including his past relapses, fevers, and hepatic conditions—were much closer to those resulting from hepatic amoebiasis, an illness then widespread in Madras, than tuberculosis. He had two episodes of dysentery before he left India. When not properly treated, amoebic dysentery can lie dormant for years and lead to hepatic amoebiasis, whose diagnosis was not then well established . At the time, if properly diagnosed, amoebiasis was a treatable and often curable disease,British soldiers who contracted it during the First World War were being successfully cured of amoebiasis around the time Ramanujan left England..