“An equation for me has no meaning unless it expresses a thought of God.”
Ramanujan was born on December 22, 1887, in Erode, a city along the banks of the Cauvery River in the southern state of Tamil Nadu. He enrolled in a local high at the age of 10 but learned more about mathematics from the college students who boarded in his parents' home. According to Robert Kanigel, Ramanujan's biographer and author of The Man Who Knew Infinity, the young mathematician was deeply influenced by two borrowed books: S.L. Loney's Plane Trigonometry and George Shoobridge Carr's Synopsis of Elementary Results in Pure Mathematics. Carr's work, a list of 5000 mathematical formulas, inspired Ramanujan to develop his own proofs for these theorems. By the age of 17, Ramanujan had calculated Euler's constant to 15 decimal places and proposed a new class of numbers. Although his peers "stood in respectful awe of him", said one contemporary, "we, including his teachers, rarely understood him".
Like Albert Einstein,
Srinivasa Ramanujan struggled with school and even failed his high school exams
because of difficulties concentrating. In 1909, the 22-year old college dropout
moved from Erode to Madras and found work as a clerk in the Accountant
General's Office. Ramachandra Rao, an Indian mathematician who helped Ramanujan
obtain the clerkship, encouraged the young man to publish papers and seek
broader support for his work. In 1911, Ramanujan's 17-page paper about
Bernoulli numbers appeared in the Journal of the Indian Mathematical Society.
Two years later, the young mathematician wrote a 10-page letter with over 120
statements of theorems on infinite series, improper integrals, continued
fractions, and number theory. The letter's recipient, a Cambridge mathematician
named G.H. Hardy, had ignored previous communications from Ramanujan, but
shared this latest letter with J.E. Littlewood, a university colleague.
According to Hardy, the English mathematicians concluded that Ramanujan's
results "must be true because, if they were not true, no one would have
the imagination to invent them."
With Hardy's help,
Ramanujan was named a research scholar at the University of Madras, a position
that doubled his clerk's salary and required only the submission of quarterly
reports about his work. In March 1914, Ramanujan boarded a steamship for
England and, upon his arrival at Cambridge University, began a five-year
collaboration with G.H. Hardy. Together, the scholars identified the properties
of highly composite numbers and studied the partition function and its
asymptotics. They also identified the Hardy-Ramanujan number (1729), the
smallest number expressible as the sum of two positive cubes in two different
ways. Individually, Ramanujan made major breakthroughs with gamma functions,
modular forms,
divergent series,
hypergeometric series, and mock theta functions. He also developed closed-form
expressions for non-simple continued fractions (Ramanujan's continued
fractions) and defined a mathematical concept known as the Ramanujan prime.
"I still say to myself when I am depressed, and find myself forced to
listen to pompous and tiresome people," Hardy later wrote, "'Well, I
have done one thing you could never have done, and that is to have collaborated
with both Littlewood and Ramanujan on something like equal terms.'"
Srinivasa Ramanujan
received an honorary bachelor's degree from Cambridge University in 1916 and
was later appointed a Fellow of Trinity and a Fellow of the Royal Society.
Despite his professional accomplishments, Ramanujan suffered from poor health
and was eventually diagnosed with tuberculosis and amoebiasis, a parasitic
infection of the liver. A vegetarian, he also suffered from a severe vitamin
deficiency that may have been due to the shortage of fresh fruits and
vegetables in wartime England. Srinivasa Ramanujan died on April 26, 1920, at
the age of 32. Today, the whole of India celebrates his birthday,
December 22, to memorialize both the man and his achievements.
G. H. Hardy liked to rank
mathematicians on a scale of 1 to 100, and he gave himself 25, Littlewood 30,
David Hilbert 80, and Ramanujan 100, which shows just how great Ramanujan was.
