A life extraordinaire; touching new heights and creating new wonders: that was the story of Srinivasa Ramanujan. This was the man who knew infinity and beyond, a genius in his own right. Armed with an extraordinary intellect and a thrust to follow his passions; he set the world of mathematics buzzing with a new light.
Ramanujan was a man decades, even centuries ahead of his time. He had independently compiled nearly 3,900 results (mostly identities and equations) and nearly all his claims have now been proven correct, although some were already known. He was the first to determine the infinite series of π (pie). He had an uncanny ability to recognise the inherent properties of numbers; the Hardy-Ramanujan numbers bearing a fine testimony to it.
The famous British mathematician G.H. Hardy had once arrived in a taxi cab numbered 1729 and remarked that it seemed a very dull number. Ramanujan had at once disagreed and pointed out that it was ‘the smallest number expressible as the sum of two cubes in two different ways’.
1729 = 1^3 + 12^3 = 9^3 + 10^3
This had led to Hardy’s comment that ‘every positive integer was his personal friend’.
Hailing from a humble background, Ramanujan started his life’s journey in the temple town of Kumbakonam. He was a child prodigy who never stopped questioning all that was ambiguous. He had later moved to Madras (now Chennai) for the intermediate (higher secondary) studies and faced failure. This proved a big hurdle in his dream of pursuing a professional career in Mathematics. But being the determined and hard working person that he was, he overcame this difficulty to become one of the most celebrated mathematicians of all times.
He had faced such a time when he had no money to buy himself two square meals, leave alone notebooks and ink. He used to work out his theorems on a slate, such was his financial crisis. But he persevered over all these hardships to become the man that we know today.
He was a self-taught genius; with almost no formal education in higher level Mathematics. He made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. His was a knowledge of startling profundity: discovering identities and equations of orders unheard of, while being completely clueless of Cauchy’s theorem or a function of complex variable.
Most of Ramanujan’s theorems were merely stated as fact, with no formal proof accompanying them. It was almost as if the young Indian had plucked the results readymade from some abstract realm of mathematical forms and relationships. Contemporaries and future mathematicians had speculated that it was not mere guesses; rather his economic hurdles had compelled him to only note the results, without the proofs.
Although Ramanujan was a self taught genius, his major break-through came when his letter to G.H. Hardy was recognised by the later. Such was his incredibility that Hardy had concluded that Ramanujan’s ‘results must be true because if they were not true, no one would have the imagination to invent them’.
It is very sad that his life burned short; short but bright. His untimely death at the age of 32 was a great loss. By then, he had developed the mock theta functions which find their use in the string theory. Such was his genius that he could look decades into the future (string theory had not been developed during Ramanujan’s time).
His mathematical brilliance speaks for itself in terms of his achievement. Quite aptly, December 22 (Ramanujan’s birthday) has been declared as the National Mathematics Day in honour of the brilliant mathematician.
Ramanujan is a legend, and an inspiration for us all to learn from. You can also read about Elon Musk – a legend in the making – here.