This collection of thousands of theoremsmany presented with only the briefest of proofs and with no material newer thanaroused his genius. In he secured a scholarship to the University of Madras but lost it the following year because he neglected all other studies in pursuit of mathematics. Ramanujan continued his work, without employment and living in the poorest circumstances.
The second was new to Hardy, and was derived from a class of functions called hypergeometric serieswhich had first been researched by Leonhard Euler and Carl Friedrich Gauss. Hardy found these results "much more intriguing" than Gauss's work on integrals. Littlewoodto take a look at the papers.
Littlewood was amazed by Ramanujan's genius. After discussing the papers with Littlewood, Hardy concluded that the letters were "certainly the most remarkable I have received" and said that Ramanujan was "a mathematician of the highest quality, a man of altogether exceptional originality and School essay on srinivasa ramanujan.
Nevillelater remarked that "not one [theorem] could have been set in the most advanced mathematical examination in the world". Hanumantha Rao, a mathematics professor at an engineering college, invited Ramanujan's colleague Narayana Iyer to a meeting of the Board of Studies in Mathematics to discuss "what we can do for S.
In one instance, Narayana Iyer submitted some of Ramanujan's theorems on summation of series to the journal, adding, "The following theorem is due to S.
Ramanujan, the mathematics student of Madras University.
Ross of Madras Christian Collegewhom Ramanujan had met a few years before, stormed into his class one day with his eyes glowing, asking his students, "Does Ramanujan know Polish?
Working off Giuliano Frullani's integral theorem, Ramanujan formulated generalisations that could be made to evaluate formerly unyielding integrals. Hardy enlisted a colleague lecturing in Madras, E. Neville, to mentor and bring Ramanujan to England. Ramanujan apparently had now accepted the proposal; as Neville put it, "Ramanujan needed no converting and that his parents' opposition had been withdrawn".
Life in England[ edit ] Ramanujan centre and his colleague G. Hardy extreme rightwith other scientists, outside the Senate House, Cambridgec. Nevasa on 17 March 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 had already received 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. Littlewood commented, "I can believe that he's at least a Jacobi ",  while Hardy said he "can compare him only with Euler or Jacobi. 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 recognized.
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. While in England, 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.
Ramanujan was awarded a Bachelor of Science degree by research this degree was later renamed PhD in March for his work on highly composite numbersthe first part of which was published as a paper in the Proceedings of the London Mathematical Society.
The paper was more than 50 pages and proved various properties of such numbers. Hardy remarked that it was one of the most unusual papers seen in mathematical research at that time and that Ramanujan showed extraordinary ingenuity in handling it.
At age 31 Ramanujan was one of the youngest Fellows in the history of the Royal Society. He was elected "for his investigation in Elliptic functions and the Theory of Numbers.
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 in England and wartime rationing during — He was diagnosed with tuberculosis and a severe vitamin deficiency at the time, and was confined to a sanatorium.
In he returned to KumbakonamMadras Presidencyand soon thereafter, indied at the age of After his death, his brother Tirunarayanan chronicled Ramanujan's remaining handwritten notes consisting of formulae on singular moduli, hypergeometric series and continued fractions and compiled them.
Janaki Ammal, moved to Bombay ; in she returned to Madras and settled in Triplicanewhere she supported herself on a pension from Madras University and income from tailoring. Inshe 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 was also granted pensions from, among others, the Indian National Science Academy and the state governments of Tamil NaduAndhra Pradesh and West Bengal.
She continued to cherish Ramanujan's memory, and was active in efforts towards increasing his public recognition; prominent mathematicians, including George Andrews, Bruce C.
She died at her Triplicane residence in Young  concluded that his medical symptoms —including his past relapses, fevers, and hepatic conditions—were much closer to those resulting from hepatic amoebiasisan illness then widespread in Madras, rather than tuberculosis.
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Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series. Ramanujan was born in his grandmother's house in Erode on December 22, When Ramanujan was.
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