The Life and Work of Srinivasa Ramanujan

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Hardy was so impressed with the theorems, that he wanted Ramanujan to come to Cambridge to do some mathematical research with him. Ramanujan was excited to receive the request to go to England, but at the request of his mother, he declined it. [2] The University of Madras also recognized Ramanujan’s work after the correspondence with Hardy, so in 1913 granted him a special scholarship as a researcher. [2] At the age of 25, Ramanujan accepted the position and resigned from his position at the Madras Port Trust office. During this time, he published two additional papers in the Indian Mathematical Society. He discovered and/or rediscovered a large number of most elegant and beautiful formulas. The results were concerned with Bernoulli’s and Euler’s numbers, hypergeometric series, functional equation for the Riemann zeta function, definite integrals, continued fractions and distribution of primes.

[6] After much persuasion by Hardy, Ramanujan on March 17, 1914 boarded the S.S. Nevasa and set sail for England. He received a scholarship of 250 pounds a year for five years with 100 pounds for the passage by ship to go to England. For his first three years in Cambridge, Ramanujan was very happy. His health, however, had always been rather poor. The winter weather in England, much colder than anything he had ever imagined, made him ill for a time. [2] During this period from 1914 to 1919, Ramanujan worked with Hardy and Littlewood on many Conjectures. The process of working with these great mathematicians helped him learn and create new mathematics. [1] Hardy stated about Ramanujan "The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems... to orders unheard of, whose mastery of continued fractions was... beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta function and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a doubly periodic function or of Cauchy's theorem, and had indeed but the vaguest idea of what a function of a complex variable was." Some of the outcomes of this collaboration was the theory of partitions of numbers, the Rogers-Ramanujan identities, hyper-geometric functions, continued fractions, theory of representations of numbers as sums of squares, Ramanujan’s T-function, elliptic functions and q-series. [5] Ramanujan’s theta function lies at the heart of string theory in Physics.

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The Ramanujan theta function.

Ramanujan in 1916 received a Bachelor of Arts degree from Cambridge University on the basis of his research. During this time Ramanujan contracted tuberculosis and was bed ridden. The change in climate from India to England and a proper vegetarian diet in England were some of the factors for his deteriorating health conditions. The ailment severely weakened him and he was losing weight quickly. Many doctors have tried to diagnose and treat him for the next several years, but was not getting better. Despite his health, he continued to do research and publish 21 papers and 5 of them were collaboration with Dr. Hardy. In May 1918, he was elected a Fellow of the Royal Society. In 1918, he was also elected a Fellow of the Trinity College, Cambridge University. Although he received so many accolades, due to his sickness, Ramanujan wanted to go back to India. Dr. Hardy wrote a letter to Madras University requesting a permanent position for Ramanujan in the university as a researcher. In his letter Hardy stated the following about Ramanujan, [1] “He will return to India with a scientific standing and reputation such as no Indian enjoyed before, and I am confident that India will regard him as the treasure he is.” The university offered him a 250 pounds per year for the five years to be able to do research only and also offered to pay for his travels back to India from England. In 1919, Ramanujan returned back to India, his health showed some improvement and he continued to do research.

[1] Ramanujan travelled several places in India seeking the best health care. Despite this, Ramanujan’s health deteriorated and on April 29, 1920 at the age of 32, surrounded by his wife, parents, brothers, friends and admirers, Ramanujan died. Even in is deathbed, Ramanujan was consumed by math writing down theorems that he said had come to him in his dreams. [5] Ramanujan had published 37 papers in total and in the notebooks that he left contain approximately 4000 claims of which all almost all have been proven and continue to astonish modern mathematicians. [4] Dr. Hardy stated this about Ramanujan’s death “For my part, it is difficult for me to say what I owe to Ramanujan – his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.”

After the death of Ramanujan, his final notebook was sent by University of Madras to G. H. Hardy, who in turn gave it to mathematician G. N. Watson a Professor at the University of Birmingham. After Watson’s death in 1965, Ramanujan’s notebooks were found in his office. [5] George Andrews, an Evan Pugh Professor of Mathematics at Pennsylvania University and Bruce Carl Berndt, a Michio Suzuki Distinguished Research Professor of Mathematics at the University of Illinois, published a series of books in 1987. Berndt said, [5] “The discovery of this ‘Lost Notebook’ caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world.” Many scientists from around the world have testified that they gained inspiration from the life story of Ramanujan.

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References

- Biography.com Editors, available at: http://www.biography.com/people/srinivasa-ramanujan-082515

- Debnath, L., SRINIVASA RAMANUJAN (1887-1920) AND THE THEORY OF PARTITIONS OF NUMBERS AND STATISTICAL MECHANICS A CENTENNIAL TRIBUTE, J. Math. & Math. Sci. Vol. i0 No. 4 (1987) 625-640V

- J. J. O'Connor and E F Robertson, available at: http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ramanujan.html

- Mahabti, Subodh, available at: http://www.vigyanprasar.gov.in/scientists/ramanujan.htm

- The Editors as Famous Scientist, available at: http://www.famousscientists.org/srinivasa-ramanujan/

- The Editors of Encyclopædia Britannica, available at: https://www.britannica.com/biography/Srinivasa-Ramanujan