Ramanujan continued his work, without employment and living in the poorest circumstances. After marrying in he began a search for permanent employment that culminated in an interview with a government official, Ramachandra Rao. In Ramanujan published the first of his papers in the Journal of the Indian Mathematical Society.
His genius slowly gained recognition, and in he began a correspondence with the British mathematician Godfrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge. Overcoming his religious objections, Ramanujan traveled to England in , where Hardy tutored him and collaborated with him in some research. Facts Matter. Although he was almost completely unaware of modern developments in mathematics, his mastery of continued fractions was unequaled by any living mathematician.
He worked out the Riemann series, the elliptic integrals , hypergeometric series, the functional equations of the zeta function , and his own theory of divergent series. Though brilliant, many of his theorems on the theory of prime numbers were wrong. In England Ramanujan made further advances, especially in the partition of numbers the number of ways that a positive integer can be expressed as the sum of positive integers; e. Ross of Madras Christian College , whom 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had now accepted the proposal; Neville said, "Ramanujan needed no converting" and "his parents' opposition had been withdrawn".
Life in England[ edit ] Ramanujan centre and his colleague G. Hardy extreme right , with other scientists, outside the Senate House, Cambridge , c. 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. 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 numbers , the first part of which was published as a paper in the Proceedings of the London Mathematical Society. The paper was more than 50 pages long and proved various properties of such numbers. Hardy remarked that it was one of the most unusual papers 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 there and because of wartime rationing in — He was diagnosed with tuberculosis and a severe vitamin deficiency, and confined to a sanatorium.Janaki Ammal, moved to Bombay ; in she returned to Madras and settled in Triplicane , where she supported herself on a pension from Madras University and income from tailoring. In one instance Iyer submitted some of Ramanujan's theorems on summation of series to the journal, adding, "The following theorem is due to S. ET today read comments Most Viewed B? And it was decided to send him back to India for some time. Facts Matter. These qualities he had inherited from his mother.
His mastery of certain areas of mathematics was really fantastic and unbelievable.
Littlewood was amazed by Ramanujan's genius. If you see something that doesn't look right, contact us! Hardy enlisted a colleague lecturing in Madras, E.
Visit Website When at age 15 he obtained an out-of-date book called A Synopsis of Elementary Results in Pure and Applied Mathematics, Ramanujan set about feverishly and obsessively studying its thousands of theorems before moving on to formulate many of his own. I just prefer to take the time to socialize and end up paying for it at a later time, maintain.
He left behind him about formulae and theorems. At the same time, he remarked on Ramanujan's strict vegetarianism.
Not much is known about his early life and schooling except that he was a solitary child by nature. In she adopted a son, W. Their lands included most of the present state of Delaware, youre only going to get the best essay mark twain essay titles service from us, this scholarships for high school seniors in texas prove anything, maybe easier than that , there are professional custom writing companies such as MyHomeworkDone.