Ramanujan

Srinivasa Aiyangar Ramanujan

Born: 22 Dec 1887 in Erode, Tamil Nadu state, India
Died: 26 April 1920 in Kumbakonam, Tamil Nadu state, India

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Ramanujan 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, although self-taught in mathematics, was given a fellowship to the University of Madras in 1903 but the following year he lost it because he devoted all his time to mathematics and neglected his other subjects. He married in 1909.

After publication of a brilliant research paper on Jacob Bernoulli's numbers in 1911 in the Journal of the Indian Mathematical Society his gained recognition for his work.

After his papers were sent to several English mathematicians his genius was recognised immediately by G H Hardy. In 1914 Hardy brought Ramanujan to Trinity College, Cambridge, to begin an extraordinary collaboration. He sailed from India on 17 March 1914.

Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function. On the other hand he had only a vague idea of what constitutes a mathematical proof. Despite many brilliant results, some of his theorems on prime numbers were completely wrong.

Ramanujan independently discovered results of Gauss, Kummer and others on hypergeometric series. Ramanujan's own work on partial sums and products of hypergeometric series have led to major development in the topic.

He fell ill in 1917 and spent some time in nursing homes. After a slight improvement in his health, he sailed to India on 27 February 1919 but he died there the following year.

Ramanujan left a number of unpublished notebooks filled with theorems that mathematicians have continued to study. G N Watson, Mason Professor of Pure Mathematics at Birmingham from 1918 to 1951 published 14 papers under the general title Theorems stated by Ramanujan and in all he published nearly 30 papers which were inspired by Ramanujan's work. Hardy passed on to Watson the large number of manuscripts of Ramanujan that he had, both written before 1914 and some written in Ramanujan's last year in India before his death.

The picture above is taken from a stamp issued by the Indian Post Office to celebrate the 75th anniversary of his birth.

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. G H Hardy, Ramanujan (Cambridge, 1940).
  4. R A Rankin, Ramanujan's manuscripts and notebooks, Bull. London Math. Soc. 14 (1982), 81-97.
  5. R A Rankin, Ramanujan's manuscripts and notebooks II, Bull. London Math. Soc. 21 (1989), 351-365.
  6. R Kanigel, The man who knew infinity : A life of the genius Ramanujan (New York, 1991).
  7. B Berndt, Srinivasa Ramanujan, The American Scholar 58 (1989), 234-244.
  8. B Berndt and S Bhargava, Ramanujan - For lowbrows, Amer. Math. Monthly 100 (1993), 644-656.
  9. J M Borwein and P B Borwein, Ramanujan and pi, Scientific American 258 (2) (1988), 66-73.
  10. S R Ranganathan, Ramanujan : the man and the mathematician (London, 1967).
  11. S Ram, Srinivasa Ramanujan (New Delhi, 1979).
  12. L Debnath, Srinivasa Ramanujan (1887-1920) : a centennial tribute, International journal of mathematical education in science and technology 18 (1987), 821-861.
  13. R A Rankin, Srinivasa Ramanujan (1887- 1920), International journal of mathematical education in science and technology 18 (1987), 861- . 
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