Srinivasa Ramanujan
22 Dec 1887 ~ 26 Apr 1920
He was born in Erode, Madras Presidency. By age 11, he exhausted
mathematical knowledge of two college students who were lodgers at his home. By
age 13, he mastered book written by S. L. Loney on advanced trigonometry and
discovered sophisticated theorems on his own.
At 16, he studied A Synopsis of Elementary Results in Pure &
Applied Mathematics, G. S. Carr's collection of 5,000 theorems. The book is
acknowledged as a key element in awakening his genius.
He developed and investigated Bernoulli numbers & calculated
Euler–Mascheroni constant up to 15 decimal places. He received a scholarship to
study but lost it as he neglected other subjects
After marrying in 1909 he began a search for employment & met
Ramachandra Rao who supported his research for a time, but Ramanujan, unwilling
to exist on charity, obtained a clerical post with Madras Port Trust
In 1911 he published papers in Journal of Indian Mathematical Society.
In 1913 he began a correspondence with British mathematician Godfrey H. Hardy
that led to a grant from Trinity College, Cambridge
Overcoming religious objections, he traveled to England in 1914, where
Hardy tutored him & collaborated with him in research.
He worked out Riemann series, elliptic integrals, hypergeometric series,
functional equations of zeta function and his theory of divergent series, in
which he found a value for the sum of such series using a technique that came
to be called Ramanujan summation
He made advances in partition of numbers (the number of ways that a
positive integer can be expressed as the sum of positive integers). His papers
were published in English & European journals and in 1918 he was elected to
Royal Society of London. In 1917 he had contracted tuberculosis & returned
to India in 1919
He died leaving behind 3 notebooks and a sheaf of pages containing many
unpublished results that mathematicians continued to verify long after his
death.
