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.
