born 22 December in Erode (Madras Presidency = Tamil Nadu) named Srinivasa Ramanujan Iyengar. Christian Krattenthaler. Srinivasa Ramanujan. Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in Media links; Biographical links; Other links and His Heritage: Years of Civilization and Science in Europe (PDF). Turnhout. An introduction to RAMANUJAN's mathematics. Michel Waldschmidt http://www. terney.info miw/. 1. Biography of. Srinivasa Ramanujan.

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When he was 15 years old, he obtained a copy of George Shoobridge Carr's Synopsis of Elementary Results in Pure and Applied Mathematics. tribute commemorates Ramanujan the Mathematician and. Ramanujan contributions is given to describe the gifted talent of Srinivasa RamanuJan. As an The biographical sketch of Srinivasa RamanuJan described in this article is based. Letter to Hardy. • Dear Sir: I beg to introduce myself as an accounts clerk in the Port Trust.. • I remain, Dear Sir, Yours truly,. • S. Ramanujan.

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 considered to be unsolvable. Ramanujan initially developed his own mathematical research in isolation: What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Hardy at the University of Cambridge , England. Recognizing the extraordinary work sent to him as samples, Hardy arranged travel for Ramanujan to Cambridge.

His family enlisted a local constable to make sure the boy attended school. He had a close relationship with her. From her, he learned about tradition and puranas. He learned to sing religious songs, to attend pujas at the temple, and to maintain particular eating habits — all of which are part of Brahmin culture.

Just before turning 10, in November , he passed his primary examinations in English, Tamil, geography and arithmetic with the best scores in the district. That year, Ramanujan entered Town Higher Secondary School, where he encountered formal mathematics for the first time.

He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series. Ramanujan reportedly studied the contents of the book in detail.

The book is generally acknowledged as a key element in awakening his genius. Ranganatha Rao prize for mathematics.

On 14 July , Ramanujan married Janaki a girl whom his mother had selected for him a year earlier. It was not unusual for marriages to be arranged with girls. After his successful surgery, Ramanujan searched for a job. To make money, he tutored students at Presidency College.

Ramaswamy Aiyer, who had founded the Indian Mathematical Society. Wishing for a job at the revenue department where Aiyer worked. He lasted only a few weeks.

Toward the end of that assignment, he applied for a position under the Chief Accountant of the Madras Port Trust. Out of these, G. Hardy asked a colleague, J. Littlewood, to take a look at the papers. On 8 February , Hardy wrote Ramanujan a letter expressing his interest in his work. Hardy enlisted a colleague lecturing in Madras, E. Neville, to mentor and bring Ramanujan to England.

Ramanujan traveled to England by ship, leaving his wife to stay with his parents in India. Nevasa on 17 March 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. Hardy had already received theorems from Ramanujan in the first two letters, but there were many more results and theorems in the notebooks.

On 8 February , Hardy wrote Ramanujan a letter expressing his interest in his work, adding that it was "essential that I should see proofs of some of your assertions". To supplement Hardy's endorsement, Gilbert Walker , a former mathematical lecturer at Trinity College, Cambridge , looked at Ramanujan's work and expressed amazement, urging the young man to spend time at Cambridge. 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 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's correspondence with Ramanujan soured after Ramanujan refused to come to England. 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".

Ramanujan departed from Madras aboard the S. 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 ", [52] 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 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 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 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. Throughout his life, Ramanujan was plagued by health problems. 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 Kumbakonam , Madras Presidency , and soon thereafter, in , died 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.

Ramanujan's widow, Smt. 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 , 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 was also granted 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 towards increasing his public recognition; prominent mathematicians, including George Andrews, Bruce C. She died at her Triplicane residence in A analysis of Ramanujan's medical records and symptoms by Dr. Young [54] 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, rather than tuberculosis.

He had two episodes of dysentery before he left India. When not properly treated, dysentery can lie dormant for years and lead to hepatic amoebiasis, whose diagnosis was not then well established.

Ramanujan has been described as a person of a somewhat shy and quiet disposition, a dignified man with pleasant manners. He looked to her for inspiration in his work [12]: Afterward he would receive visions of scrolls of complex mathematical content unfolding before his eyes.

Hardy cites Ramanujan as remarking that all religions seemed equally true to him. At the same time, he remarked on Ramanujan's strict vegetarianism. In mathematics, there is a distinction between insight and formulating or working through a proof. Ramanujan proposed an abundance of formulae that could be investigated later in depth. Hardy said that Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye.

As a byproduct of his work, new directions of research were opened up. This might be compared to Heegner numbers , which have class number 1 and yield similar formulae.

See also the more general Ramanujan—Sato series. One of Ramanujan's remarkable capabilities was the rapid solution of problems, illustrated by the following anecdote about an incident in which P.

Mahalanobis posed a problem:. Imagine that you are on a street with houses marked 1 through n. There is a house in between x such that the sum of the house numbers to the left of it equals the sum of the house numbers to its right. If n is between 50 and , what are n and x? Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction. The unusual part was that it was the solution to the whole class of problems.

Mahalanobis was astounded and asked how he did it. The minute I heard the problem, I knew that the answer was a continued fraction. Which continued fraction, I asked myself. Then the answer came to my mind', Ramanujan replied. His intuition also led him to derive some previously unknown identities , such as. In Hardy and Ramanujan studied the partition function P n extensively. They gave a non-convergent asymptotic series that permits exact computation of the number of partitions of an integer.

Hans Rademacher , in , was able to refine their formula to find an exact convergent series solution to this problem. Ramanujan and Hardy's work in this area gave rise to a powerful new method for finding asymptotic formulae called the circle method.

In the last year of his life, Ramanujan discovered mock theta functions. Although there are numerous statements that could have borne the name Ramanujan conjecture, there is one that was highly influential on later work. It was finally proven in , as a consequence of Pierre Deligne 's proof of the Weil conjectures. The reduction step involved is complicated.

Deligne won a Fields Medal in for that work. This congruence and others like it that Ramanujan proved inspired Jean-Pierre Serre Fields Medalist to conjecture that there is a theory of Galois representations which "explains" these congruences and more generally all modular forms.

Pierre Deligne in his Fields Medal-winning work proved Serre's conjecture. The proof of Fermat's Last Theorem proceeds by first reinterpreting elliptic curves and modular forms in terms of these Galois representations. Without this theory there would be no proof of Fermat's Last Theorem. While still in Madras, Ramanujan recorded the bulk of his results in four notebooks of loose-leaf paper. They were mostly written up without any derivations.

This is probably the origin of the misapprehension that Ramanujan was unable to prove his results and simply thought up the final result directly. Mathematician Bruce C. Berndt , in his review of these notebooks and Ramanujan's work, says that Ramanujan most certainly was able to prove most of his results, but chose not to.

This may have been for any number of reasons. Since paper was very expensive, Ramanujan would do most of his work and perhaps his proofs on slate , and then transfer just the results to paper.

Using a slate was common for mathematics students in the Madras Presidency at the time.

He was also quite likely to have been influenced by the style of G. Carr 's book, which stated results without proofs. Finally, it is possible that Ramanujan considered his workings to be for his personal interest alone and therefore recorded only the results.

The first notebook has pages with 16 somewhat organised chapters and some unorganised material. The second notebook has pages in 21 chapters and unorganised pages, with the third notebook containing 33 unorganised pages. The results in his notebooks inspired numerous papers by later mathematicians trying to prove what he had found. Hardy himself created papers exploring material from Ramanujan's work, as did G.

Watson , B. Wilson , and Bruce Berndt. The number is known as the Hardy—Ramanujan number after a famous visit by Hardy to see Ramanujan at a hospital.

In Hardy's words: I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number and remarked that the number seemed to me rather a dull one , and that I hoped it was not an unfavorable omen. Immediately before this anecdote, Hardy quoted Littlewood as saying, "Every positive integer was one of [Ramanujan's] personal friends.

Generalizations of this idea have created the notion of " taxicab numbers ". In his obituary of Ramanujan, which he wrote for Nature in , Hardy observed Ramanujan's work primarily involved fields less known even amongst other pure mathematicians, concluding:.

His insight into formulae was quite amazing, and altogether beyond anything I have met with in any European mathematician. It is perhaps useless to speculate as to his history had he been introduced to modern ideas and methods at sixteen instead of at twenty-six. It is not extravagant to suppose that he might have become the greatest mathematician of his time.

What he actually did is wonderful enough He combined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling, and made him, in his own peculiar field, without a rival in his day. The limitations of his knowledge were as startling as its profundity.

Here was a man who could work out modular equations and theorems When asked about the methods Ramanujan employed to arrive at his solutions, Hardy said that they were "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to , Hardy gave himself a score of 25, J.

Littlewood 30, David Hilbert 80 and Ramanujan In his book Scientific Edge , the physicist Jayant Narlikar spoke of "Srinivasa Ramanujan, discovered by the Cambridge mathematician Hardy, whose great mathematical findings were beginning to be appreciated from to His achievements were to be fully understood much later, well after his untimely death in For example, his work on the highly composite numbers numbers with a large number of factors started a whole new line of investigations in the theory of such numbers.

The year after his death, Nature listed Ramanujan among other distinguished scientists and mathematicians on a "Calendar of Scientific Pioneers," who had achieved eminence. Stamp picturing Ramanujan were issued by the Government of India in , , and A prize for young mathematicians from developing countries has been created in Ramanujan's name by the International Centre for Theoretical Physics ICTP in cooperation with the International Mathematical Union , which nominate members of the prize committee.

House of Ramanujan Mathematics, a museum on life and works of the Mathematical prodigy, Srinivasa Ramanujan, also exists on this campus. In , on the th anniversary of his birth, the Indian Government declared that 22 December will be celebrated every year as National Mathematics Day. From Wikipedia, the free encyclopedia. This is the latest accepted revision , reviewed on 14 April Indian mathematician.

For other uses, see Ramanujan disambiguation. In this Indian name , the name Srinivasa is a patronymic , not a family name , and the person should be referred to by the given name , Ramanujan.

Hardy J. Main article: Ramanujan—Petersson conjecture. Further information: Ramanujan's lost notebook. List of things named after Srinivasa Ramanujan. Berndt, Bruce C. Butzer, P. Charlemagne and His Heritage: Turnhout, Belgium: Brepols Verlag. Ramanujan's Lost Notebook. Part I. New York: Part II. Part III. Part IV. Letters and Commentary. Providence, Rhode Island: American Mathematical Society.

Essays and Surveys. Number Theory in the Spirit of Ramanujan. Ramanujan's Notebooks. Part V. Hardy, G. March The American Mathematical Monthly.

Chelsea Pub. Henderson, Harry Modern Mathematicians. Facts on File Inc. Kanigel, Robert The Man Who Knew Infinity: Charles Scribner's Sons. Leavitt, David The Indian Clerk paperback ed. Narlikar, Jayant V. Scientific Edge: New Delhi, India: Penguin Books. Ono, Ken ; Aczel, Amir D. My Search for Ramanujan: How I Learned to Count. Sankaran, T. Kochi, India: Kerala Sastra Sahithya Parishath. Ramanujan, Srinivasa; Hardy, G. Collected Papers of Srinivasa Ramanujan.

This book was originally published in [] after Ramanujan's death. It contains the 37 papers published in professional journals by Ramanujan during his lifetime. The third reprint contains additional commentary by Bruce C. Ramanujan Notebooks 2 Volumes. Tata Institute of Fundamental Research. These books contain photocopies of the original notebooks as written by Ramanujan.

New Delhi: This book contains photo copies of the pages of the "Lost Notebook". This was produced from scanned and microfilmed images of the original manuscripts by expert archivists of Roja Muthiah Research Library, Chennai. Mathematics portal Biography portal India portal. Oxford Dictionaries. Archived from the original on 30 July Retrieved 30 July Oxford Dictionary of National Biography online ed.

Oxford University Press. Subscription or UK public library membership required. Genius, p. Ramanujan's Notebooks, Part 5. Notices of the American Mathematical Society. Archived PDF from the original on 21 June Retrieved 23 June August Archived from the original on 25 September Retrieved 20 December Analytic and Elementary Number Theory: New Scientist.

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Science, New Series. Janakiammal Janaki " PDF.