Version for printing Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functionscontinued fractionsand infinite series.

Ramanujan was born in his grandmother's house in Erode, a small village about km southwest of Madras. When Ramanujan was a year old his mother took him to the town of Kumbakonam, about km nearer Madras.

His father worked in Kumbakonam as a clerk in a cloth merchant's shop. In December he contracted smallpox. When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several *brief biography of srinivasa ramanujan* primary schools before entering the Town High School in Kumbakonam in January At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar.

In he began to work on his own on mathematics summing geometric and arithmetic series. Ramanujan was shown how to solve cubic equations in and he went on to find his own method to solve the quartic.

The following year, not knowing that the quintic could not be solved by radicalshe brief biography of srinivasa ramanujan and of course brief biography of srinivasa ramanujan to solve the quintic. It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics, but the style of the book was to have a rather unfortunate effect on the way Ramanujan was later to write down mathematics since it provided the only model that he had of written mathematical arguments.

The book contained theorems, formulae and short proofs. It also contained an index to papers on pure mathematics which had been published in the European Journals of Learned Societies during the first half of the 19th century. The book, published inwas of course well out of date by the time Ramanujan used it.

By Ramanujan had begun to undertake deep research. He began to study the Bernoulli numbersalthough this was entirely his own independent biography of addisu legesse. Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in Kumbakonam which he entered in However the following year his scholarship was not renewed because Ramanujan devoted more and more of his time to mathematics and brief biography of srinivasa ramanujan his other subjects.

Without money he was soon in difficulties and, without telling his parents, he ran away to the town of Vizagapatnam about km north of Madras.

He continued his mathematical work, however, and at this time he worked on hypergeometric series and investigated relations between integrals and series. He was to discover later that he had been studying elliptic functions. In Ramanujan went to Madras where he entered Pachaiyappa's College. His aim was to pass the First Arts examination which would allow him to be admitted to the University of Madras. He attended lectures at Pachaiyappa's College but became ill after three months study.

He took the First Arts examination after having left the course. He passed in mathematics but failed all his other subjects and therefore failed the examination. This meant that he could not enter the University of Madras. In the following years he worked on mathematics developing his own ideas without any help and without any real idea of the then current research topics other than that provided by Carr's book. Continuing his *brief biography of srinivasa ramanujan* work Ramanujan studied continued fractions and divergent series in At this stage he became seriously ill *brief biography of srinivasa ramanujan* and underwent an operation in April after which he took him some considerable time to recover.

He married on 14 July when his mother arranged for him to marry a ten year old girl S Janaki Ammal. Ramanujan did not live with his wife, however, until she was twelve years old. Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society.

He devoloped relations between elliptic modular equations in After publication of a brilliant research paper on Bernoulli numbers in in the Journal of the Indian Mathematical Society he gained recognition for his work. Despite his lack of a university education, he was becoming well known in the Madras area as a mathematical genius.

In Ramanujan approached the founder of the Indian Mathematical Society for advice on a job. After this he was appointed to his first job, a temporary post in the Accountant General's Office in Madras.

It was then suggested that he approach Ramachandra Rao who was a Collector at Nellore. Ramachandra Rao was a founder member of the Indian Mathematical Society who had helped start the mathematics library. He writes in [ 30 ]: He was **brief biography of srinivasa ramanujan** poor. He opened his book and began to explain brief biography of srinivasa ramanujan of his discoveries. I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense.

I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches.

Ramachandra Rao told him to return to Madras and he tried, unsuccessfully, to arrange a scholarship for Ramanujan. In Ramanujan applied for the post of clerk in the accounts section of the Madras Port Trust. In his letter of application he wrote [ 3 ]: I have, however, been devoting all my time to Mathematics and developing the subject. Despite the fact that he had no university education, Ramanujan was clearly well known to the university mathematicians in Madras for, with his letter of application, Ramanujan included a reference from E W Middlemast who was the Professor of Mathematics at The Presidency College in Madras.

Middlemast, a graduate of St John's College, Cambridge, wrote [ 3 ]: He is a young man of quite exceptional capacity in mathematics and especially in work relating to numbers.

He has a natural aptitude for computation and is very quick at figure work.

On the strength of the recommendation Ramanujan was appointed to the post of clerk and began his duties on 1 March Ramanujan was quite lucky to have a number of people working round him with a training in mathematics. In fact the Chief Accountant for the Madras Port Trust, S N Aiyar, was trained as a mathematician and published a paper On the distribution of primes in on Ramanujan's work.

The professor of civil engineering at the Madras Engineering College C L T Griffith was also interested in Ramanujan's abilities and, having been educated at University College London, knew the professor of mathematics there, namely M J M Hill.

He wrote to Hill on 12 November sending some of Ramanujan's work and a copy of his paper on Bernoulli numbers. Hill replied in a fairly encouraging way but showed that he had *brief biography of srinivasa ramanujan* to understand Ramanujan's results on divergent series. The recommendation to Ramanujan that he read Bromwich 's Theory of infinite series did not please Ramanujan much.

Ramanujan wrote to E W Hobson and H F Baker trying to interest them in his results but neither replied. In January Ramanujan wrote to G H Hardy having seen a copy of his book Orders of infinity. In Ramanujan's letter to Hardy he introduced himself and his work [ 10 ]: After leaving school I have been employing the spare time at my disposal to work at mathematics.

I have not trodden through the conventional regular course which is followed in a university course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as 'startling'.

Hardytogether with Littlewoodstudied the long list of unproved theorems which Ramanujan enclosed with his letter. On 8 February he replied to Ramanujan [ 3 ], the letter beginning: You will however understand that, before I can judge properly of the value of what you have done, it is essential that I should see proofs of some of your assertions.

Your results seem to me to fall into brief biography of srinivasa ramanujan three classes: Ramanujan was delighted with Hardy 's reply and when he wrote again he said [ 8 ]: I am already a half starving man. To preserve my brains I want food and this is my first consideration.

Any sympathetic letter from you will be helpful to me here to get a scholarship brief biography of srinivasa ramanujan from the university of from the government. Indeed the University of Madras did give Ramanujan a scholarship in May for two years and, inHardy brought Ramanujan to Trinity College, Cambridge, to begin an brief biography of srinivasa ramanujan collaboration.

Setting this up was not an easy matter. Ramanujan was an orthodox Brahmin and so was a strict vegetarian. His religion should have prevented him from travelling but this difficulty was overcome, partly by the work of E H Neville who was a colleague of Hardy 's at Trinity College and who met with Ramanujan while lecturing in India. Ramanujan sailed from India on 17 March It was a brief biography of srinivasa ramanujan voyage except for three days on which Ramanujan was seasick.

He arrived in London on 14 April and was met by Neville. After four brief biography of srinivasa ramanujan in London they went to Cambridge and Ramanujan spent a couple of weeks in Neville's home before moving into rooms in Trinity College on 30th April. Right from the beginning, however, he had problems with his diet.

The outbreak of World War I made obtaining special items of food harder and it was not long before Ramanujan had health problems. Right from the start Ramanujan's collaboration with Hardy led to important results. Hardy was, however, unsure how to approach the problem of Ramanujan's lack of formal education. He wrote [ 1 ]: The limitations of his knowledge were as startling as its profundity.

Littlewood was asked to help teach Ramanujan rigorous mathematical methods. However he said [ 31 ]: The war soon took Littlewood away on war duty but Hardy remained in Cambridge to work with Ramanujan. Even in his first winter in England, Ramanujan was ill and he wrote in March that he had been ill due to the winter weather and had not been able to publish anything for five months. What he did publish was the work he did in England, the decision having been made that the results he had obtained while in India, many of which he had communicated to Hardy in his letters, would not be published until the war had ended.

On 16 March Ramanujan graduated from Cambridge with a Bachelor of Science by Research the degree was called a Ph. He had been allowed to enrol in June despite not having the proper qualifications. Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England. Ramanujan brief biography of srinivasa ramanujan seriously ill in and his doctors feared that he would die. He did improve a little by September but spent most of his time in various nursing homes.

In February Hardy wrote see [ 3 ]: His worst theory was that this had really been for the removal of a malignant growth, wrongly diagnosed. In view of the fact that Ramanujan is no worse than six months ago, he has now abandoned this theory - the other doctors never gave it any support.

Tubercle has been the provisionally accepted theory, apart from this, since the original idea of gastric ulcer was given up. Like all Indians he is fatalistic, and it is terribly hard to get him to take care of himself. On 18 February Ramanujan was elected a fellow of the Cambridge Philosophical Society and then three days later, the greatest honour that he would receive, his name appeared on the list for election as a fellow of the Royal Society of London.

He had been proposed by an impressive list of mathematicians, namely HardyMacMahonGrace, LarmorBromwichHobsonBakerLittlewoodNicholson, YoungWhittakerForsyth and Whitehead. His election as a fellow of the Royal Society was confirmed on 2 Maythen on 10 October he was elected a Fellow of Trinity College Cambridge, the fellowship to run for six years. The honours which were bestowed on Ramanujan seemed to help his health improve a little and he renewed his effors at producing mathematics.

By the end of November Ramanujan's health had greatly improved. Hardy wrote in a letter [ 3 ]: His temperature has ceased to be irregular, and he has gained nearly a stone in weight. There has never been any sign of any diminuation in his extraordinary mathematical talents. He has produced less, naturally, during his illness but the quality has been the same.

He will return to India with a scientific standing and reputation such as no Indian has enjoyed before, and I am confident that India will regard him as the treasure he is. His natural simplicity and modesty has never been affected in the least by success - indeed all that is wanted is to get him to realise that he really is a success.

Ramanujan sailed to India on 27 February arriving on 13 March. However his health was very poor and, despite medical treatment, he died there the following year.

The letters Ramanujan wrote to Hardy in had contained many fascinating results. Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function. On the other hand he had only a vague idea of what constitutes a mathematical proof. Despite many brilliant results, some of his theorems on brief biography of srinivasa ramanujan numbers were completely wrong.

Ramanujan independently discovered results of GaussKummer and others on hypergeometric series. Ramanujan's own work on partial sums and products of hypergeometric series have led to major development in the topic.

Perhaps his most famous work was on the number p n of partitions of an integer n into summands. MacMahon had produced tables of the value of p n for small numbers n, and Ramanujan used this numerical data to conjecture some remarkable properties some of which he proved using elliptic functions. Other were only proved after Ramanujan's death. In a joint paper with HardyRamanujan gave an asymptotic formula for p n. It had the remarkable property that it appeared to give the correct value of p nand this was later proved by Rademacher.

Ramanujan left a number of unpublished notebooks filled with theorems that mathematicians have continued to study. G N WatsonMason Professor of Pure Mathematics at Birmingham from to published 14 papers under the general title Theorems stated by Ramanujan and in all he published nearly 30 papers which were inspired by Ramanujan's work.

Hardy passed on to Watson the large number of manuscripts of Ramanujan that he had, both written before and some written in Ramanujan's last year in India before his death.

The picture above is taken from a stamp issued by the Indian Post Office to celebrate the 75th anniversary of his birth.

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