03:49, 5 செப்டெம்பர் 2009 இல் கடைசித் திருத்தம்
S.Ramanujan - mathematical genius from Tamilnadu
A contribution by Dr.Taher Kagalwala in Nukkad (Fri, 19 Jul 2002)
Srinivasa Ramanujan(22 Dec.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. Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras. When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras.
It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics, but the style of the book was to have a rather unfortunate effect on the way Ramanujan was later to write down mathematics since it provided the only model that he had of written mathematical arguments. The book contained theorems, formulas and short proofs. It also contained an index to papers on pure mathematics which had been published in the European Journals of Learned Societies during the first half of the 19th century. The book, published in 1856, was of course well out of date by the time Ramanujan used it.
By 1904 Ramanujan had begun to undertake deep research. He investigated the series (1/n) and calculated Euler's constant to 15 decimal places. He began to study the Bernoulli numbers, although this was entirely his own independent discovery.
In 1906 Ramanujan went to Madras where he entered Pachaiyappa's College. His aim was to pass the First Arts examination which would allow him to be admitted to the University of Madras. He attended lectures at Pachaiyappa's College but became ill after three months study. He took the First Arts examination after having left the course. He passed in mathematics but failed all his other subjects and therefore failed the examination. This meant that he could not enter the University of Madras. In the following years he worked on mathematics developing his own ideas without any help and without any real idea of the then current research topics other than that provided by Carr's book.
He married on 14 July 1909 when his mother arranged for him to marry a nine year old girl S Janaki Ammal. Ramanujan did not live with his wife, however, until she was twelve years old.
He approach Ramachandra Rao who was a Collector at Nellore. Ramachandra Rao was a founder member of the Indian Mathematical Society who had helped start the mathematics library. He writes :
A short uncouth figure, stout, unshaven, not over clean, with one conspicuous feature-shining eyes-walked in with a frayed notebook under his arm. He was miserably poor. ... He opened his book and began to explain some of his discoveries. I saw quite at once that there was something out of the way; but my knowledge did not permit me to judge whether he talked sense or nonsense. ... I asked him what he wanted. He said he wanted a pittance to live on so that he might pursue his researches.
The University of Madras did give Ramanujan a scholarship in May 1913 for two years and, in 1914, Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration. Setting thisup was not an easy matter. Ramanujan was an orthodox Brahmin and so was a strict vegetarian. His religion should have prevented him from travelling but this difficulty was overcome, partly by the work of E H Neville who was a colleague of Hardy's at Trinity College and who met with Ramanujan while lecturing in India.
Ramanujan sailed from India on 17 March 1914. It was a calm voyage except for three days on which Ramanujan was seasick. He arrived in London on 14 April 1914 and was met by Neville. After four days in London they went to Cambridge and Ramanujan spent a couple of weeks in Neville's home before moving into rooms in Trinity College on 30th April. Right from the beginning, however, he had problems with his diet. The outbreak of World War I made obtaining special items of food harder and it was not long before Ramanujan had health problems.
On 16 March 1916 Ramanujan graduated from Cambridge with a Bachelor of Science by Research (the degree was called a Ph.D. from 1920). He had been allowed to enrol in June 1914 despite not having the proper qualifications. Ramanujan's dissertation was on Highly composite numbers and consisted of seven of his papers published in England.
Ramanujan fell seriously ill in 1917 and his doctors feared that he would die. On 18 February 1918 Ramanujan was elected a fellow of the Cambridge Philosophical Society and then three days later, the greatest honour that he would receive, his name appeared on the list for election as a fellow of the Royal Society of London.
His election as a fellow of the Royal Society was confirmed on 2 May 1918, then on 10 October 1918 he was elected a Fellow of Trinity College Cambridge, the fellowship to run for six years. The honours which were bestowed on Ramanujan seemed to help his health improve a little and he renewed his effors at producing mathematics. By the end of November 1918 Ramanujan's health had greatly improved.
At that time, his mentor, G H Hardy wrote:
I think we may now hope that he has turned to corner, and is on the road to a real recovery. His temperature has ceased to be irregular, and he has gained nearly a stone in weight. ... There has never been any sign of any diminuation in his extraordinary mathematical
talents. He has produced less, naturally, during his illness but the quality has been the same. .... He will return to India with a scientific standing and reputation such as no Indian has enjoyed before, and I am confident that India will regard him as the treasure he is. His natural simplicity and modesty has never been affected in the least by success - indeed all that is wanted is to get him to realise that he really is a success.
Ramanujan sailed to India on 27 February 1919 arriving on 13 March. However his health was very poor and, despite medical treatment, he died there the following year.
I did a Comet Search for Ramanujan, and got the above details. To visit the page , go to this url, where his picture, and more details are published.
After reading this, I am really feeling humbled, friends. What a short life..and yet..so tragic..! -Taher
References for Srinivasa Ramanujan
Biography in Dictionary of Scientific Biography (New York 1970-1990).
Biography in Encyclopaedia Britannica.
Books:
B C Berndt and R A Rankin, Ramanujan : Letters and commentary (Providence, Rhode Island, 1995).
G H Hardy, Ramanujan (Cambridge, 1940).
R Kanigel, The man who knew infinity : A life of the genius Ramanujan (New York, 1991).
J N Kapur (ed.), Some eminent Indian mathematicians of the twentieth century (Kapur, 1989).
S Ram, Srinivasa Ramanujan (New Delhi, 1979).
S Ramanujan, Collected Papers (Cambridge, 1927).
S R Ranganathan, Ramanujan : the man and the mathematician (London, 1967).
P K Srinivasan, Ramanujan : Am inspiration 2 Vols. (Madras, 1968).
Articles:
P V Seshu Aiyar, The late Mr S Ramanujan, B.A., F.R.S., J. Indian Math. Soc. 12 (1920), 81-86.
G E Andrews, An introduction to Ramanujan's 'lost' notebook, Amer. Math. Monthly 86 (1979), 89-108.
B Berndt, Srinivasa Ramanujan, The American Scholar 58 (1989), 234-244.
B Berndt and S Bhargava, Ramanujan - For lowbrows, Amer. Math. Monthly 100 (1993), 644-656.
B Bollobas, Ramanujan - a glimpse of his life and his mathematics, The
Cambridge Review (1988), 76-80.
B Bollobas, Ramanujan - a glimpse of his life and his mathematics, Eureka 48 (1988), 81-98.
J M Borwein and P B Borwein, Ramanujan and pi, Scientific American 258 (2) (1988), 66-73.
S Chandrasekhar, On Ramanujan, in Ramanujan Revisited (Boston, 1988), 1-6.
L Debnath, Srinivasa Ramanujan (1887-1920) : a centennial tribute,
International journal of mathematical education in science and technology 18 (1987), 821-861.
G H Hardy, The Indian mathematician Ramanujan, Amer. Math. Monthly 44 (3) (1937), 137-155.
G H Hardy, Srinivasa Ramanujan, Proc. London Math, Soc. 19 (1921), xl-lviii.
E H Neville, Srinivasa Ramanujan, Nature 149 (1942), 292-294.
C T Rajagopal, Stray thoughts on Srinivasa Ramanujan, Math. Teacher (India) 11A (1975), 119-122, and 12 (1976), 138-139.
K Ramachandra, Srinivasa Ramanujan (the inventor of the circle method), J. Math. Phys. Sci. 21 (1987), 545-564.
K Ramachandra, Srinivasa Ramanujan (the inventor of the circle method), Hardy-Ramanujan J. 10 (1987), 9-24.
R A Rankin, Ramanujan's manuscripts and notebooks, Bull. London Math. Soc. 14 (1982), 81-97.
R A Rankin, Ramanujan's manuscripts and notebooks II, Bull. London Math. Soc. 21 (1989), 351-365.
R A Rankin, Srinivasa Ramanujan (1887- 1920), International journal of mathematical education in science and technology 18 (1987), 861-.
R A Rankin, Ramanujan as a patient, Proc. Indian Ac. Sci. 93 (1984), 79-100.
R Ramachandra Rao, In memoriam S Ramanujan, B.A., F.R.S., J. Indian Math. Soc. 12 (1920), 87-90.
E Shils, Reflections on tradition, centre and periphery and the universal
validity of science : the significance of the life of S Ramanujan, Minerva 29 (1991), 393-419.
D A B Young, Ramanujan's illness, Notes and Records of the Royal Society of London 48 (1994), 107-119.
JOC/EFR June 1998 School of Mathematics and Statistics University of St Andrews, Scotland