Ramanujan and Mathematics

Srinivasa Ramanujan

"An equation means nothing to me unless it expresses a thought of God."
-Srinivasa Ramanujan

"Every positive integer is one of Ramanujan's personal friends."
-John Littlewood

"He could remember the idiosyncrasies of numbers in an almost uncanny way. It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. 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 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." 
-G.H. Hardy

G.H. Hardy

     Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was an Indian mathematician who had a natural born talent for mathematics. Having no formal training of mathematics, Ramanujan taught himself  through textbooks starting at the age of 10. The house he lived in as a child was also a place for lodgers to stay. As a result, he bonded with individuals staying and received textbooks from them and Ramanujan studied them.  As his school career progressed, he was awarded many merits and certificates due to his outstanding performance in mathematics. He was awarded a scholarship to the best school in India but after focusing on math and not his other subjects, he would fail. It would be after dropping out of two colleges in India that he would begin to search for a job. After receiving a job as a clerk in Madras, India, making 30 rupees a month, Ramanujan began correspodence with British mathematicians.

     In 1913, his secondary school headmaster would contact three mathematicians from the University College of London to look at Ramanujan's conjectures and theorems scribbled in his notebook. Having been looked down upon by two claiming that his mathematical ability was there, but not fully developed and there were gaps in his argument, it would be G.H. Hardy that would take him under his wing. Hardy recognized that Ramanujan was a very gifted individual and brought him to Cambridge University where the two would work together.

     Ramanujan's contribution to mathematics is quite large in areas of composite numbers, the partition function, gamma functions, modular forms, divergent series, hyper geometric series, and prime number theory. Ramanujan also looked at infinite series for the calculation of pi. These series that he looked at would be responsible for creating algorithms today that calculate pi with accuracy up to 5 trillion decimal places.

     Both Hardy and Ramanujan shared an unfortunate time in their lives where both tried to commit suicide. Both men were very involved in their work and shared extreme depression. The collaboration between the two was looking at the Riemann Hypothesis and other parts of it. Some say now it has a curse.

     It would be in 1920 that Ramanujan would pass away at 32 years of age. There is a lot of speculation as to what caused his death. Some claim it was the stress of being in a new country and that during the first World War there was no vegetarian food around for him to consume. He was diagnosed with Tuberculosis and extreme vitamin deficiencies. It would be G.H. Hardy that was quoted later in his life talking about his research and collaboration with Ramanujan saying it was  "the one romantic incident in my life".

The documentary that made me want to learn more about Ramanujan and Hardy:

https://www.youtube.com/watch?v=OARGZ1xXCxs











Sources:

http://www.storyofmathematics.com/20th_hardy.html

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ramanujan.html

https://www.youtube.com/watch?v=OARGZ1xXCxs