SRINIVASA RAMANUJAN
Born: Dec.22, 1887 ,Erode
Died:Apil26,1920,Kumbakonam, Tamil Nadu
Srinivasa Ramanujan, one of India's greatest mathematical geniuses, was born in his grandmother's housi n Erode, a small village about 400 km southwest of Madras on 22nd Dec,1887.His father K.Srinivasa Lyengar, worked as a clerk in a sari shop and hailed from the ditrict of Thanjavur.His mother, Komalatammal, was a housewife and also sang at a local temple. After one year he was brought to his father's town Kumbakonam. He passed his primary eaxamination in 1897 scoring first in the district and then he joined the Towm High School. In1904 he entered Kumbakonam's Govt.College F.A. student. He was awarded a scholarship. However after school, Ramanujan total concentration was focused on mathematics. The result was that his formal education did not continue for long, He first failed in Kumbakonam's Govt. College. He tried once again in Madras from Pachaiyappa's college but he failed again it was at this time that he came across the book ‘Synopsis of Elementary Results im Pure Mathematics’by GS. Carr.This book had a profound effect on Ramanujan.That's why he failed because he obsessed with mathematics, spending almost all of his time and energy on mathematics and ignoring other subiects,
Srinivasa Ramanujan, the wonderftul young Indian mathematician of the 20Century asked his teacher in primary school, "Is zero divided by Zero also unity?", When his teacher tried to generalize that any number divided by itself was untiy.As a student of class Ⅲ of a primary school he successfully worked out the properties of Arithmetical, Geometrical and Harmonic progression and upto class IV he almost solve all the problems of Lony's Trignometry meant for degree classes. He was So bright that he was declared 'Child Mathematician'at the age of 12 by his teachers. He used to entertain his friends with theorems and formulae with the recitation of Complete list of Sanskrit roots and with repeating the value of π and square root of two to any number of decimal places. Ramanujan, on the strength of his good School work,was given a scholarship in 1904 but was not renewed because he devoted more and more of his time to mathematics and neglected his other subjects.
Continuing his mathematical work Ramanujan studied continued fractions and divergent series in 1908.He became seriously ill and underwent an operation in April 1909 after which it took him some considerable time to recover. He married on 14th July 1909 when his mother arranged for him to marry a ten year old girl Janaki. Ramanujan did not live with his wife, however, until,she was twelve years old.
In the course of his search for work, he was got introduced to a true lover of mathematics, Diwan Bahadur R. Ramachandra Rao. For some months he was suported by Sri Rama Chandra Rao. Then he acepted his appointment as a clerk in the offce of Madras Port Trust. While working as a clerk he never slackened his interest in mathematics. He made his one of the works puoblished in the Journal of Indian Mathematical Society in 1911 at the age of 23. He wrote a long article onproperties of Bernoull's numbers. Meanwhile he began correspondence with professor G.H. Hardy, a leading mathematician of his time.To his first letter heatached 120 theorems of his own creation. Hardy made efforts to bring Ramanujan to Cambridge and helped him to learn modern mathematics In 1916he got honorary BA.degree of the University of Cambridge.
In the spring of 1917, Ramanujan first appeared to be unwell. He went to Nursing home at Cambridge in the early summer and was never out of bed for any length of time again. For a brief period he resumed some active work, stimulated perhaps by his election to the Royal Society and Trinity fellowship. In 1918, hebecame the first Indian to be elected a fellow of the Royal society. He continued to suffer from poor health and returned to India in 1919.On April26,1920 he died due toTuberculosis in the town of Kumbakonam in Tramil Nadu. He wasonly thirty-two years old.
CONTRIBUTIONS
●Ramanujan gave his contibutions to the analytical theory of numbers, elliptic functions, continued fractions, infinite series and summed geometric andarithmetic series.
●He discovered an incredible number of beautiful and original formulae in the field of number theory. He was well known as a self-taught mathematical genius from South India. He investigated the series(1/n) and calculated Euler's constant to 15 decimal places.
●He worked on hypogeometric series and investigated relations between integrals and series .
●Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of Indian Mathematical Society.
●He worked out the Riemann series ,the elliptic integrals, hypergeometric series and functional equations of the zeta function. In the other hand he had only a vague idea of what constitutes a mathematical proof. Despite many brilliant results, some of his theorems on prime numbers were completely wrong.
●He independently discovered results of Gauss, Kummer, hyper-geometric series He also worked on partial sums and products of hyper-geometric series.
●In a joint paper with Hardy, Ramanujan gave an asymptotic formula for p(n) .This was later proved by Rademacher Ramanujan,
●He discovered a number of rermarkable identitis that imply divisibility propertis of the partition function.
●He worked on divergent series. He sent 120 theorems on divergent series to Hardy in 1913.
●He gave a meaning to Eulerian Second Integral for all values of n (negative,positive and fractional). He proved that the integral of x ^n-1.e^-i= γ( gamma) is true for all values of gamma.
●Goldbach's conjecture is one of the important iustrations of Ramanujan contribution towards the proof of the conjecture. The statement is every even integer greater than two is the sum of two primes,that is，numbers having no divisions. Ramanujan and his associates had shown that every large intege can be written as the sum of at most four primes (eg. 43=2＋5＋17+19)
●Ramanujan studied composite numbers, their structure, distributifon and special forms.
● he worked on fermat theorem which states that a prime number of the form4m+1 is the sum of two squares.
●Ramanujan had an amazing gift when it came to numbers. Once when Hardy visited Ramanujan while he was sick in hospital, he mentioned that the taxi he had just taken had an unremarkable number i.e. 1729. Ramanujan immediately replied that it was infact a very interesting number. So, 1729 is a famousRamanujan number.It is the smallest number which can be expressed as the sum of two cubes in two different ways.
i.e.1729=1^3+12^3=9^3+10^3
●He also produced a number of results in definite integrals in the form of general formulae.
Besides his published work, Ramanujan lef behind several notebooks flled with theorems that mathematicians have continued to study. The English mathematician GN. Watson, from 1918to1951,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. In 1997 the Ramanujan journal was launched to publish work "in areas of mathematics influenced by Ramanujan."
