**Ramanujan** made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

- When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898.
- At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar.
- Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic.
- 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- The book, published in 1886, was of course well out of date by the time Ramanujan used it.
- By 1904 Ramanujan had begun to undertake deep research.
- Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in Kumbakonam which he entered in 1904.
- However the following year his scholarship was not renewed because Ramanujan devoted more and more of his time to mathematics and neglected his other subjects.
- In 1906 Ramanujan went to Madras where he entered Pachaiyappa's College.
- Continuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908.
- 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.
- In 1911 Ramanujan approached the founder of the Indian Mathematical Society for advice on a job.
- Ramachandra Rao told him to return to Madras and he tried, unsuccessfully, to arrange a scholarship for Ramanujan.
- In 1912 Ramanujan applied for the post of clerk in the accounts section of the Madras Port Trust.
- 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.
- On the strength of the recommendation Ramanujan was appointed to the post of clerk and began his duties on 1 March 1912.
- Ramanujan was quite lucky to have a number of people working round him with a training in mathematics.
- 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 1913 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 1912 sending some of Ramanujan's work and a copy of his 1911 paper on Bernoulli numbers.
- Hill replied in a fairly encouraging way but showed that he had failed 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 1913 Ramanujan wrote to G H Hardy having seen a copy of his 1910 book Orders of infinity.
- Hardy, together with Littlewood, studied the long list of unproved theorems which Ramanujan enclosed with his letter.
- Indeed the University of Madras did give Ramanujan a scholarship in May 1913 for two years and, in 1914, Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration.
- 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 1914.
- It was a calm voyage except for three days on which Ramanujan was seasick.
- After four days 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 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.
- Littlewood was asked to help teach Ramanujan rigorous mathematical methods.
- that it was extremely difficult because every time some matter, which it was thought that Ramanujan needed to know, was mentioned, Ramanujan's response was an avalanche of original ideas which made it almost impossible for Littlewood to persist in his original intention.
- 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 1915 that he had been ill due to the winter weather and had not been able to publish anything for five months.
- On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of Arts by Research (the degree was called a Ph.D. from 1920).
- Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England.
- Ramanujan fell seriously ill in 1917 and his doctors feared that he would die.
- 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.
- On 18 February 1918 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.
- 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 1918 Ramanujan's health had greatly improved.
- Ramanujan sailed to India on 27 February 1919 arriving on 13 March.
- The letters Ramanujan wrote to Hardy in 1913 had contained many fascinating results.
- Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function.
- Ramanujan independently discovered results of Gauss, Kummer 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.
- MacMahon had produced tables of the value of p(n)p(n)p(n) for small numbers nnn, 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 Hardy, Ramanujan gave an asymptotic formula for p(n)p(n)p(n).
- Ramanujan left a number of unpublished notebooks filled with theorems that mathematicians have continued to study.
- G N Watson, Mason Professor of Pure Mathematics at Birmingham from 1918 to 1951 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 1914 and some written in Ramanujan's last year in India before his death.

Born 22 December 1887, Erode, Tamil Nadu state, India. Died 26 April 1920, Kumbakonam, Tamil Nadu state, India.

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