A Glimpse Into The Life, Contributions And Expanding Legacy Of Ramanujan

Science, 20 Dec - 2017 ,

A Glimpse Into The Life, Contributions And Expanding Legacy Of Ramanujan
Credit: famousscientists.org

Srinivasa Ramanujan (22nd December, 1887 - 26th April, 1920) is regarded as an all-time great mathematician, like Euler, Gauss and Jacobi, for his unbelievable merit, extraordinary mathematical skill

Srinivasa Ramanujan (22nd December, 1887 - 26th April, 1920) is regarded as an all-time great mathematician, like Euler, Gauss and Jacobi, for his unbelievable merit, extraordinary mathematical skill, unparalleled insight and amazing mathematical contribution. He lived a very short span of life, but his mathematical work of about two decades will have an everlasting effect in the history of science.

During sometime in 1903, Ramanujan obtained a book entitled ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’, written by George Shoobridge Carr. The book contained 4417 mathematical results with very few proofs. It influenced him profoundly andstarted to work for proving the results of the book in his own way through heuristic approach. In proving one result, he discovered many others, and began to compile his famous notebooks. He devoted himself more and more to mathematics neglecting other subjects in the College.  As such he could not obtain F.A. degree.  He had to work under extreme hardship but always preserved mathematics in mind. His remarkable mathematical talents were observed and encouraged by a number of people. With their efforts, he was able to get a job in the Madras Port Trust as a clerk to support the livelihood of his family. With the advice of well-wishers, he wrote on January 16, 1913, a letter to Cambridge Professor G.H. Hardy. This letteris considered as one of the most important and exciting letter ever written, which wasalso filled with mathematical results. In consultation with his colleague J.E. Littlewood, Hardy could decide that the writer of the letter was a man of genius. He felt the necessity to bring Ramanujan to Cambridge for the proper blossom of his mathematical talent. With Hardy’s initiation and involvement of a few important persons, the University of Madras did grant Ramanujan a scholarship for two years to maintain him in Cambridge and his family in Kumbakonam. Ramanujan sailed for England on March 17, 1914 and came to the right place and to the right person (Hardy).For three years, alone and in collaboration with Hardy, Ramanujan produced mathematical papers of highest quality in rapid succession. Then he fell seriously ill. He had to spend quite a lot of time in different nursing homes and sanatoria in England, but he neither ceased his work to produce mathematical marvel nor lost his mathematical agility to surprise others. One day, when Ramanujan was in a nursing home for treatment, Hardy came to see him by riding a cab bearing the number 1729. The number seemed to be dull to Hardy. But hearing the number, Ramanujan’s eyes glittered and said then that the number is a unique one for the fact that 1729 is the least positive integer that can be expressed as the sum of two cubes in two different ways. Indeed, 1729 = 103+93 = 123 + 13.

During his stay in England for five years Ramanujan flourished full-fledged and reached the pinnacle of success. In his entire career, he published 37 research papers, of which seven were jointly with Hardy.Many honours waited for Ramanujan in England. In March, 1916 Ramanujan was awarded B.A. degree ‘by research’ (the degree is called Ph.D. since 1920). He was elected a member of the London Mathematical Society and a Fellow of Cambridge Philosophical Society in 1917. He was the second Indian to be elected Fellow of Royal Society in 1918. He also had the distinction to become the first Indian to be elected as a Fellow of Trinity College, Cambridge in 1918.The honours bestowed on him acted on him positively and it seemed that he improved bodily and mentally. Ramanujan was sent back to India for further improvement of his health. Ramanujan sailed for India and reached on March 27, 1919. But in spite of every care and best possible medical facilities, he died on April 26, 1920 at Chetput of Madras.Regarding his mathematical contribution besides his research papers, Ramanujan left behind 3254 results in his notebooks (edited by Bruce C. Berndt in five parts in about 20 years of research with the help of a number of mathematicians), 58 questions and 5 solutions published in the Journal of the Indian Mathematical Society, 3 progress reports submitted in Madras University and many results in his ‘Lost Notebook’.

Ramanujan made extraordinary contributions to mathematical analysis, theory of numbers enriching the area of continued fractions, infinite series, hyper geometric series, q-series, theory of partition, tau function, elliptic and modular functions, mock-theta functions, etc. He has left behind a great amount of original work, which has greatly influenced the development and growth of some of the best research work not only in mathematics but also in the science of this century. For example, his work on round numbers has given birth to the branch ‘probabilistic number theory’. His formulas for π have been applied in finding approximate of π to a very large number of decimal places; his work on the theory of partitions has application in particle physics, ATM (Automated Teller Machine). Also, his work on Riemann’s Zeta function has been applied to pyrometry and investigation of the temperature of furnaces. Ramanujan’s results on modular forms are finding application in String Theory and Rogers-Ramanujan identities are appearing in solution of Hard Hexagon Model in Statistical Mechanics. Many great mathematicians of his time to the present time have been under the great influence of Ramanujan’s work.

The Man Who Knew Infinity: A Life of the Genius Ramanujan is a biography of Ramanujan, written by Robert Kanigel in 1991 and published by Washington Square Press.Ramanujan’s legacy has also inspired to prepare films on his dramatic life. A documentary film on Ramanujan entitled ‘Letters from an Indian Clerk’ directed by British filmmaker Christopher Sykes was released by the BBC during the birth centenary celebration of Ramanujan. Another film entitled ‘Ramanujan’ in two languages (Tamil and English) directed by GnanaRajasekaran was released in July, 2014. In this film AbhinayVaddi, grandson of Gemini Ganesan, played the role of Ramanujan.  Also ‘The Man Who Knew Infinity’ directed by Matthew Brown is a film on Ramanujan’s life. It was released in September, 2015, and the lead roles were played by Dev Patel (Ramanujan) and Jeremy Irons (Hardy).Ramanujan’s life and work have been inspiring many other people to write different novels, articles, plays, etc.

A stamp picturing Ramanujan was released by the Government of India for the first time in 1962, the 75th anniversary of Ramanujan's birth.It was in recognition of Rumanian’s contribution to mathematics that the Government of India decided to celebrate Rumanujan’s birthday as the National Mathematics Day every year starting with 2012, though the Government of Tripura declared the day as ‘Mathematics Day’ in his centenary year and Government of Tamilnadu declared the day as ‘State IT Day’. SASTRA (Shanmugha Arts, Science, Technology and Research Academy) university purchased the home of Ramanujan in 2003 and created a centre and a museum containing several Ramanujan’s memorabilia. It instituted the annual SASTRA Ramanujan Prize from 2005 for a mathematician, not exceeding the age of 32 for outstanding contribution in areas influenced by Ramanujan. Also ‘Ramanujan Prize’ has been awarded annually to young mathematicians of developing countries by Abdus Salam International Centre for Theoretical Physics and the International Mathematical Union.Several institutions and societies from India and abroad have been celebrating the birthday of Ramanujan every year with various programmes to expand and promote the mathematical legacy of Ramanujan.Ramanujan will continue to be an inspiration for many across the world.

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