Ramanujan was a mathematician with almost no formal training in pure mathematics. He found thousands of results in number theory, infinite series and continued fractions. Mathematicians use his work today in number theory and physics.

Life and work

In 1913 Ramanujan sent a letter with his results to G. H. Hardy at Cambridge. Hardy saw that the results were new and important. In 1914 Ramanujan went to Cambridge to work with Hardy. He became ill in England and went back to India in 1919. He died one year later, at the age of 32.

Publications

Ramanujan published 37 papers. These are three of the most important. You can read all of them in the online archive of his papers.

Notebooks

Mysteries

The lost notebook

After Ramanujan died, his wife gave his papers to the University of Madras. In 1923 the university sent many of the papers to Hardy in Cambridge. Some of the papers then went to the mathematician G. N. Watson. Watson died in 1965. His papers covered the floor of a room and were almost burned.

J. M. Whittaker found Ramanujan's notes in these papers. In 1968 he and R. A. Rankin sent them to the Wren Library at Trinity College. The notes stayed in a box there. In 1976 the mathematician George Andrews found them. The "notebook" is more than 100 loose pages with more than 600 formulas and no proofs. (Source)

The mock theta functions

On 12 January 1920 Ramanujan wrote his last letter to Hardy. The letter gave 17 new functions with the name "mock theta functions". Ramanujan did not give a definition of these functions. For more than 80 years, mathematicians did not know what these functions really were.

In 2002 Sander Zwegers gave the answer in his doctoral thesis. The functions are parts of a larger family, the mock modular forms. In 2006 Kathrin Bringmann and Ken Ono used this result to prove a conjecture about one of Ramanujan's functions.

How did he find his results?

Ramanujan wrote down thousands of results, but he gave almost no proofs. He said that the goddess Namagiri of Namakkal gave him ideas. Mathematicians do not know the methods that he used. George Andrews and Bruce Berndt needed five books, from 2005 to 2018, to prove the formulas of the lost notebook. (Part I)

Known associates

Awards

  • Fellow of the Royal Society (1918). He was one of the youngest Fellows in the history of the Society. (List of Fellows, 1918)
  • Fellow of Trinity College, Cambridge (1918), the first Indian to get this fellowship. (MacTutor)

Sources