The Man who Knew Infinity - Ramanujan

Yesterday I was watching a movie called - Good Will Hunting. There, a character makes reference to Ramanujan as the Mathematical Genius. I was amazed. Though i had heard of Ramanujan, it wasnt as much as the film refers. I left the movie in between and started googling about Ramanujan and i was startled by what i came to know about him. I have come to a conclusion that Ramanujan is the world's gratest unknown mathematician ! yes, i mean it! I know thats a pretty bold statement for me but i am sure that many of you would feel the same if you read about this legend.

The first thing that sruck me was that Ramanujan died at the age of 32! yes 32! A person who is regarded as the one of the greatest mathematical geniuses of the 20th century, died when he was 32, when he was at the peak of his talent! I know history doesnt believe in If ..then ...But i just wonder what this man could have achieved had he lived for 20 more years ! I dont understand why such things happen. Take the examples of Dnyaneshwara, Vivekanand - They all died at such an early age. Such a loss to the mankind!

Going back to Ramanujan, His passion for mathematics was combined with indifference to other subjects. He failed in most of his other subjects. In January 1913, when he was working as a clerk in Madras, he sent the Cambridge mathematician G.H. Hardy nine pages of closely written mathematical formulae, in a rounded schoolboy script. That letter, now a historic document, was the turning point in his career. At first Hardy thought the author might be a crank; but after studying the theorems he realised that they "could only be written down by a mathematician of the highest class... They must be true because, if they were not true, no one would have the imagination to invent them."

Hardy had developed a scale of mathematical ability on which he could place the mathematicians he knew. He assigned himself a modest 25, and Littlewood a 30. To the eminent David Hilbert(Remember Hilbert Transform?), he assigned an 80 and to Ramanujan, he gave a 100.

Attending his first Cambridge lecture and asked by a professor whether he wanted to add anything, Ramanujan went to the blackboard and wrote results the professor had not yet proved — and which he could not have known before. In one episode, Hardy visited him in a nursing home and commented that the license number of the cab he had come in, 1729, was "rather a dull number." Ramanujan reacted instantly. "No, Hardy. It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways." Wow ! Hats Off !

G. H. Hardy quotes: "The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems... to orders unheard of, whose mastery of continued fractions was... beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta function and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a doubly-periodic function or of Cauchy's theorem, and had indeed but the vaguest idea of what a function of a complex variable was..." Hardy went on to claim that his greatest contribution to mathematics was discovering Ramanujan.

No wonder a film is been made on the life of Ramanujan - Link.
I feel at least that will make people aware about the magical genius the world could see very little of. A good collection of Ramanujan papers, notebooks is available here - link. Even a biographical song has been made on the life of Ramanujan - http://www.archive.org/details/Ramanujan
There are some wonderful books been written on the life of Ramanujan -
The Man who Knew Infinity, Ramanujan, the Man and the Mathematician, Number Theory in the Spirit of Ramanujan etc. A few documentaries have also been made, i tried to search for that torrent but could not find. If any of you ever get that, please let me know.

I still have that question in my mind - what this man would have accomplished had he lived?