The mathematical genius Srinivasa Ramanujan
(22 December 1887 – 26 April 1920)
R. Ramanujam, The Institute of Mathematical Sciences, Chennai

December 22, 2012 is the 125th birth anniversary of the mathematical genius Srinivasa Ramanujan. This year has been celebrated as the Year of Mathematics
in India in memory of Ramanujan.
If there is one mathematician that we should keep reminding ourselves about at every opportunity, that would be Ramanujan. Thinking about him makes us wonder what is humanly possible, how much the mind is capable of.
Ramanujan lived in dire poverty, had the bare necessities of life, and could not even get enough paper to do lengthy calculations on. He did all his work on slate so that he could erase and re-use, writing down only conclusions in notebooks, thereby economizing on paper. He failed to get a college degree, or any scholarships that could support him, or a well paying job. All this depressed him, but never affected his confidence or attitude towards mathematics. Such unwavering commitment and depth of thought is truly rare. In a very short life, working until his dying moments, Ramanujan left behind a rich treasury of mathematics for future generations.
The English mathematician G.H. Hardy, who invited Ramanujan to Cambridge University and collaborated with him, compared Ramanujan with great European mathematicians like Carl Gustav Jacob Jacobi and Leonhard Euler. He often mentioned that he had never met Ramanujan's equal at any time.
It is understandable that the common people revere a romantic figure like Ramanujan ? But why do mathematicians, even a century later, consider Ramanujan to be among the great mathematicians of all time ?
The answer is simple: because Ramanujan's work opened up new vistas, gave new techniques that helped to make progress on many old and hard problems, and raised new questions that kept people thinking and working for a long time. His work had tremendous depth.
It is difficult to explain Ramanujan's mathematics in simple terms, without referring to a great deal of other mathematics.  Briefly, the letters Ramanujan wrote to Hardy in 1913 already contained many fascinating results. He had worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function. He had independently discovered results of Johann Carl Friedrich Gauss, Ernst Eduard Kummer and others on hypergeometric series. 
Ramanujan's own work on partial sums and products of hypergeometric series have led to major developments in the topic. Perhaps his most famous work was on the number of partitions p(n) of an integer n, which is to say, the number of distinct ways of representing n as a sum of natural numbers (with order irrelevant). Percy Alexander MacMahon had produced tables of the value of p(n) for small numbers n, and Ramanujan used this numerical data to conjecture (infer or guess) some remarkable properties some of which he proved using elliptic functions. Others were only proved after Ramanujan's death.
In a joint paper with Hardy, Ramanujan gave an asymptotic formula for p(n) (asymptotic means that it is approximately correct and the accuracy will improve for larger values of n, becoming exact as n goes to infinity). It had the remarkable property that it appeared to give the correct value of p(n), and this was later proved by Rademacher.  Ramanujan left a number of unpublished notebooks filled with theorems that mathematicians have continued to study. 
Let us celebrate the memory of Ramanujan, and while we do so, pause to think of how far preoccupations with mathematical discovery can take us, whatever be the circumstances.