Page 10 - Science Focus (Issue 018)

A Hidden Genius:

The Life of Srinivasa Ramanujan

ᒯ˰ෂփjז৵рږ݂ٙԫ

By Sonia Choy 蔡蒨珩

The normal path to becoming a mathematician is a Hardy corresponded with Ramanujan and welcomed
very long one – you would go through close to 10 years the young mathematician to Cambridge with a
of undergraduate and graduate education before scholarship in 1914; Ramanujan graduated in 1916 with
you can begin looking for a full-time research position. what is now a PhD, his thesis being seven papers he
Ramanujan is an exception. With no formal training, he published in England. Hardy and his collaborator, J.
rediscovered many contemporary results in mathematics E. Littlewood, attempted to teach Ramanujan formal
(such as the Bernoulli numbers, a very important set of mathematics, but found it difficult as Ramanujan’s
numbers that occurs frequently in number theory) all by brilliant intuition would often steer the conversation
himself. This makes Ramanujan’s achievements all the sideways. Nevertheless, the five years Ramanujan spent
more remarkable as an untrained mathematician. in Cambridge were fruitful, and his collaboration with
Hardy is still remembered today. For his contributions, he
Ramanujan was born in 1887 in Erode, India, a small was elected a fellow of both Trinity College Cambridge,
village far from the state capital, Madras, and was raised and the Royal Society of London in 1918.
in Kumbakonam, then a small town about 220 km east
of Erode [1]. He first began studying mathematics from Throughout his life, Ramanujan had been plagued
an outdated textbook while he was in high school, by health problems; he contracted smallpox as a child,
and attempted to enter university twice, but in vain and an operation had sent him fearing for his life in
because of sub-par performance in subjects other than 1909. He fell sick again in 1917, but eventually recovered,
mathematics. Instead he studied independently, also and sailed home for India in 1919. However, his health
corresponding with mathematicians in Madras, and deteriorated once he returned to India, and he died the
eventually found a job as a clerk to earn a pittance at following year, aged 32. Even in his last year, he made
the Accountant General's Office in 1912. In his spare time, many discoveries, and wrote them without proof in what
he wrote letters to famous mathematicians in Europe to is known as Ramanujan’s Lost Notebook. Although the
seek advice on his work. notebook was not made available publicly until 1976,
many of the results have since been proved by other
One cannot tell Ramanujan’s story without mathematicians [4]. Still, the world had lost a genius
mentioning G. H. Hardy, his mentor, who was the first far too early – one could only imagine what other
person to recognize Ramanujan’s genius. Hardy was discoveries he could have made, had he lived for a few
an accomplished number theorist himself, and yet he more years.
claimed that his biggest contribution to mathematics
was the discovery of Ramanujan [2], and described Most of Ramanujan’s discoveries are in number
his association with Ramanujan is the theory – the study of numbers themselves. He made
one romantic incident discoveries in elliptic functions, modular forms,
in his life [3]. continued fractions, and a fun little phenomenon
called “taxicab numbers” – the second
taxicab number, 1729, was the number of
the taxi Hardy took to visit Ramanujan
in hospital once, and he remarked to
Hardy on his bed that 1729 could
be expressed as the sum of two
distinct pairs of positive cubes