RAMANUJAM

"An equation for me has no meaning unless it expresses a thought of God."- RAMANUJAM

Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series. His most famous work was on the number p(n) of partitions of an integer n into summands.

By age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book on Advanced Trigonometry written by S. L. Loney. He completely mastered this book by the age of 13 and discovered sophisticated theorems on his own.

When he was 16, Ramanujan came across the book "A Synopsis of Elementary Results in Pure and Applied Mathematics"  by George S. Carr. This book was a collection of 5000 theorems, and it introduced Ramanujan to the world of mathematics. The next year, he had independently developed and investigated the Bernoulli numbers and had calculated Euler's constant up to 15 decimal places.

Ramanujan, with the help of Ramaswami Iyer(founder member of the Indian Mathematical Society) , had his work published in the Journal of Indian Mathematical Society.

In January 1913 Ramanujan wrote to G .H. Hardy having seen a copy of his  book Orders of infinity. Hardy, together with Littlewood, studied the long list of unproved theorems which Ramanujan enclosed with his letter.

Hardy wrote back to Ramanujan and in 1914, Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration.

On 6 December 1917, he was elected to the London Mathematical Society. 

In 1918, he became a Fellow of the Royal Society , and he was the youngest Fellow in the entire history of the Royal Society.

On 13 October 1918, he became the first Indian to be elected a Fellow of Trinity College, Cambridge.


TAXICAB NUMBER:
The number derives its name from the following story:
G. H. Hardy told about Ramanujan. I remember once going to see him when he was ill . I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather dull one, and that I hoped it was not an unfavorable 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."
1729 is the second taxicab number (the first is 2= 1^3 + 1^3). The number was also found in one of Ramanujan's notebooks dated years before the incident.

Every positive integer is one of Ramanujan's personal friends" - John Littlewood, on hearing of the taxicab incident

Ramanujan had problems settling in London. He was an orthodox Brahmin and right from the beginning he had problems with his diet. Ramanujan sailed to India on 27 February 1919 arriving on 13 March. However his health was very poor and, despite medical treatment, he died on April 6, 1920.