Happy Birthday to
Srinivasa Ramanujan, the great Indian mathematician
Today is the birthday of
Srinivasa Ramanujan, the great Indian mathematician who studied number theory,
mastered modular and partition functions, and designed summation formulas.
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 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 33. Today, his home state of Tamil Nadu 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.
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