SRINIVASA RAMANUJAN

The famous mathematical prodigy Ramanujan was broan and raised in southern India near the city of Madras(now call Chennai).His father was clerk in a cloth shop.His mother contributed to the family income by singing at a local temple.Ramanujan studied at the local English language school,displaying his talent and interest for mathematics.At the age of 13 he mastered a textbook used by college students.When he was 15, a university student lent him a copy of Synopsis of pure mathematics.Ramanujan decided to work out the over 6000 results in this book, stated without proof or explanation, writing on sheets later collected tofrom notebooks.Enrolling in a fine arts curriculum,he neglected subjects other than mathematics and lost his scholarship.He failed to pass examinations at the university four times from 1904 to 1907, doing well only in mathematics.During this time he filled his notebooks with original writings,sometimes rediscovering already published work and at other times making new discoveries.

Without a university degree,it was difficult for find a decent job.To survive, he had to depend on the goodwill of his friends.He tutored students in mathematics,but his unconventional ways of thinking and failure to stick to the syllabus caused problems.He was married in 1909 in an arranged marriage to a young woman nine years his junior.Needing to support himself and his wife,he moved to Madras and sought a job.He showed his notebooks of mathematical writings to his potential employers,but the books bewildered them.However,a professor at the Presidency College recognized his genius and supported him,and in 1912 he found work as an accounts clerk, earing a small salary.

Ramanujan continued his mathematical work during this time and published his first paper in 1910 in an Indian journal.He realized that his work was beyond that of Indian mathematicians and decided to write to leading English mathematicians.The first mathematicians he wrote to turned down his request for help.But in January 1913 he wrote G.H. Hardy,who was inclined to turned Ramanujan down,but mathematical statements in the later,although stated without proof,puzzled Hardy.He decided to examine them closely with the help of colleague and collaborator J.E. Littlewood.The decided,after careful study, that Ramanujan was probably a genius, because his statements "could be written down by a mathematician of the highest class;thy must be true,because if thy were not true,no would have the imaginations to invented them".

Hardy arranged a scholarship for Ramanujan,bringing him to England in 1914.Hardy personally tutored him in mathematical analysis,and they for five five years,proving significant theorems about the number of partitions of integers.During this time,Ramanujan made important contributions to number theory and also worked on continued fractions,infinite series,and elliptic functions.Ramanujan had amazing insight involving certain types of functions and series,but his purported theorems on prime number were often wrong,illustrating his vague idea of what constitutes a correct proof.He was one of the youngest members ever appointed a Fellow of the Royal Society.Unfortunately,in 1917 Ramanujan extremely ill.At the time, it was thought that he had trouble with the English climate and had contracted tuberculosis.It is now thought that he suffered from a vitamin deficiency,brought on by Ramanujan's strict vegetarianism and shortages in wartime England.He returned to India 1919,continuing to do mathematics evenn when confined to his bed.He was religious and thought his mathematical talent came from his family deity,Namagiri.He considered mathematics and religion to be linked.He said that "an equation for me has no meaning unless it expresses a thought of God." His short life came to an end in April 1920,when he was 32 years old.Ramanujan left several notebooks of unpublished results.The writings in these notebooks illustrate Ramanujan's insights but are quite sketchy.Several mathematicians have devoted many years of study to explaining and justifying the results in these notebooks.