Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society. Ramanujan did not live with his wife, however, until she was twelve years old. He married on 14 July 1909 when his mother arranged for him to marry a ten year old girl S Janaki Ammal. At this stage he became seriously ill again and underwent an operation in April 1909 after which he took him some considerable time to recover. 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.Ĭontinuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908. This meant that he could not enter the University of Madras. He passed in mathematics but failed all his other subjects and therefore failed the examination. He took the First Arts examination after having left the course. He attended lectures at Pachaiyappa's College but became ill after three months study. His aim was to pass the First Arts examination which would allow him to be admitted to the University of Madras. In 1906 Ramanujan went to Madras where he entered Pachaiyappa's College. He was to discover later that he had been studying elliptic functions. He continued his mathematical work, however, and at this time he worked on hypergeometric series and investigated relations between integrals and series. Without money he was soon in difficulties and, without telling his parents, he ran away to the town of Vizagapatnam about 650 km north of Madras. 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. Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in Kumbakonam which he entered in 1904. He began to study the Bernoulli numbers, although this was entirely his own independent discovery. He investigated the series ∑ ( 1 n ) \sum (\large\frac\normalsize ) ∑ ( n 1 ) and calculated Euler's constant to 15 decimal places. The book, published in 1886, was of course well out of date by the time Ramanujan used it.īy 1904 Ramanujan had begun to undertake deep research. 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 19 th century. The book contained theorems, formulae and short proofs. 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. 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. The following year, not knowing that the quintic could not be solved by radicals, he tried (and of course failed ) to solve the quintic. Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the quartic. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series. At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar. 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. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras (now Chennai ). He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series. Biography Srinivasa Ramanujan was one of India's greatest mathematical geniuses.
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