Born: December 22, 1887
Died: April 26, 1920
Achievements: 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. His most famous work was on the number p(n) of
partitions of an integer n into summands.
Srinivasa Ramanujan was a mathematician par excellence. He is widely
believed to be the greatest mathematician of the 20th Century. Srinivasa
Ramanujan made significant contribution to the analytical theory of
numbers and worked on elliptic functions, continued fractions, and
Srinivasa Aiyangar Ramanujan was born on December 22, 1887 in Erode, Tamil Nadu.
His father worked in Kumbakonam as a clerk in a cloth merchant's shop.
At the of five Ramanujan went to primary school in Kumbakonam. In 1898
at age 10, he entered the Town High School in Kumbakonam. At the age of
eleven he was lent books on advanced trigonometry written by S. L. Loney
by two lodgers at his home who studied at the Government college. He
mastered them by the age of thirteen. Ramanujan was a bright student,
winning academic prizes in high school.
At age of 16 his life took a decisive turn after he obtained a book
titled" A Synopsis of Elementary Results in Pure and Applied
Mathematics". The book was simply a compilation of thousands of
mathematical results, most set down with little or no indication of
proof. The book generated Ramanujan's interest in mathematics and he
worked through the book's results and beyond. By 1904 Ramanujan had
begun to undertake deep research. He investigated the series (1/n) and
calculated Euler's constant to 15 decimal places. He began to study the
Bernoulli numbers, although this was entirely his own independent
discovery. He was given a scholarship to the Government College in
Kumbakonam which he entered in 1904. But he neglected his other subjects
at the cost of mathematics and failed in college examination. He dropped
out of the college.
Ramanujan lived off the charity of friends, filling notebooks with
mathematical discoveries and seeking patrons to support his work. In
1906 Ramanujan went to Madras where he entered Pachaiyappa's College.
His aim was to pass the First Arts examination which would allow him to
be admitted to the University of Madras. Continuing his mathematical
work Ramanujan studied continued fractions and divergent series in 1908.
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.
On 14 July 1909 Ramanujan marry a ten year old girl S Janaki Ammal.
During this period Ramanujan had his first paper published, a 17-page
work on Bernoulli numbers that appeared in 1911 in the Journal of the
Indian Mathematical Society. In 191,1 Ramanujan approached the founder
of the Indian Mathematical Society for advice on a job. He got the job
of clerk at the Madras Port Trust with the help of Indian mathematician
The professor of civil engineering at the Madras Engineering College C
L T Griffith was 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. 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.
Hardy wrote back to Ramanujan and evinced interest in his work.
University of Madras gave Ramanujan a scholarship in May 1913 for two
years and, in 1914, Hardy brought Ramanujan to Trinity College,
Cambridge, to begin an extraordinary collaboration. Right from the start
Ramanujan's collaboration with Hardy led to important results. In a
joint paper with Hardy, Ramanujan gave an asymptotic formula for p(n).
It had the remarkable property that it appeared to give the correct
value of p(n), and this was later proved by Rademacher.
Ramanujan had problems settling in London. He was an orthodox Brahmin
and right from the beginning he had problems with his diet. The outbreak
of World War I made obtaining special items of food harder and it was
not long before Ramanujan had health problems.
On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of
Science by Research. He had been allowed to enrol in June 1914 despite
not having the proper qualifications. Ramanujan's dissertation was on
Highly composite numbers and consisted of seven of his papers published
Ramanujan fell seriously ill in 1917 and his doctors feared that he
would die. He did improve a little by September but spent most of his
time in various nursing homes. On February 18, 1918 Ramanujan was
elected a fellow of the Cambridge Philosophical Society and later he was
also elected as a fellow of the Royal Society of London. By the end of
November 1918 Ramanujan's health had greatly improved.
Ramanujan sailed to India on 27 February 1919 arriving on 13 March.
However his health was very poor and, despite medical treatment, he died
on April 26, 1920.