Star of India - Srinivasa Ramanujan

One of the most remarkable individuals in the history of mathematics must surely be the Indian mathematician Srinivasa Ramanujan, (1887 – 1920) who overcame almost insurmountable difficulties to become one of the great mathematicians of history.

Srinivasa Ramanujan, circa 1915 (Image: Wikipedia Commons – Click to enlarge)

Born into very poor circumstances, Ramanujan was a Brahmin, the highest caste of Indian society, traditionally associated with high academic knowledge and intellectual achievement. 

But lack of available money made it difficult for him to progress to higher education and, as a result, he conducted research into mathematics, his favourite subject, virtually on his own. Using old textbooks, he developed his own style and notation and commenced research into several diverse areas of number theory.

He received a little encouragement when some of his early work was published in the Journal of the Indian Mathematical Society. He also sent several of his papers to prominent mathematicians around the world but with little result. His style of non-standard notation and presentation of results without proof probably counted against him.

But then, in January 1913, he wrote to the prominent English mathematician, G. H. Hardy, who was then resident at Trinity College, Cambridge University. 

G. H. Hardy – prominent English mathematician (Image: Wikipedia Commons – Click to enlarge)

Hardy later recalled that one night after dinner, he and his colleague J. E. Littlewood, sat down to study and try to unravel the jumble of strange formulae that Ramanujan had mailed them.

As Hardy read through the document he became increasingly astounded. He recognised that Ramanujan had derived several results in pure mathematics already known, but using hitherto unheard of techniques. But of even more significance was the fact that there were several results quoted without proof, that were, to Hardy's knowledge, entirely new to mathematics.

Hardy immediately invited Ramanujan to Trinity College, but this created some problems. Brahmins were not supposed to travel across the ocean, but somehow Ramanujan was able to attain a dispensation. He was also a strict vegetarian and this was due to create problems with the typical meat- rich English diet.

Trinity College, Cambridge (Image: Wikipedia Commons – Click to enlarge)

Nevertheless Ramanujan arrived at Cambridge in April 1914, and began a collaboration with Hardy that was to produce some of the great advances in number theory. Hardy’s careful orthodox approach, using rigorous methodology, when combined with the sheer brilliance of Ramanujan, produced a cascade of important results. These included the Ramanujan Prime and the Ramanujan Theta functions, both of which led to major areas of further research by other mathematicians. The Hardy-Ramanujan asymptotic formula was used widely in thermodynamics and atomic physics more than a quarter of a century later. 

Ramanujan was in poor health for much of his life, made worse by the fact that a vegetarian diet was difficult to maintain in early 20^th century England. He spent considerable periods in hospital and it was in one such stay he was visited by Hardy, who later recalled 

“I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Ramanujan had instantly seen that 

1729 = (1x1x1) + (12x12x12) and that also

1729 = (9x9x9) + (10x10x10)

The number 1729 is now known as the Hardy-Ramanujan number.

Recognition of number patterns such as this was Ramanujan's specialty and his skill in this domain has never been surpassed.

Ramanujan went on to produce nearly 4000 important results in number theory, was made a Fellow of the Royal Society and became the first Indian to be elected a Fellow of Trinity College at Cambridge University. Tragically he died at the young age of 34 at Kumbakonam, back in his native India. There is little doubt that he would have contributed even more to mathematics, given an average life span.

Ramanujan's home on Sarangapani Street, Kumbakonam. (image from Wikipedia Commons – click to enlarge)

Hardy, his mentor, later rated him as one of the great mathematicians of history, comparing him to Gauss, Newton and Archimedes. This was made all the more remarkable by the difficult nature of the journey he had to take along the way.

Late in 2011, the Prime Minister of India, Dr. Manmohan Singh, announced that December 22, the anniversary of Ramanujans birthday, would be declared "National Mathematicians Day", and that 2012, the 125th year since Ramanujan's birth, would be known in India as the "National Mathematical Year".

This is a fitting tribute to one of the great mathematicians of both India and human history.