Prime Minister declared that 22 December will be National Mathematics Day.
It is the birthday of Sreenivasa Ramanujam, a mathematics genius of India.
Srinivasa Ramanujan - Biography
Srinivasa Ramanujan (22 December 1887 – 26 April 1920) was a mathematician, who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions.
Ramanujan independently compiled nearly 3900 results (mostly identities and equations).
Ramanujan went to Cambridge in 1914. Hardy, his collaborator at Cambridge said Ramanujan could have become an outstanding mathematician if his skills had been recognized earlier. It was said about his talents of continued fractions and hypergeometric series that, “he was unquestionably one of the great masters.” It was due to his sharp memory, calculative mind, patience and insight that he was a great formalist of his days.
He got elected as the fellow in 1918 at the Trinity College at Cambridge and the Royal Society. He departed from this world on April 26, 1920.
In 1918, Hardy and Ramanujan studied the partition function P(n) extensively and gave a non-convergent asymptotic series that permits exact computation of the number of partitions of an integer. Hans Rademacher, in 1937, was able to refine their formula to find an exact convergent series solution to this problem. Ramanujan and Hardy's work in this area gave rise to a powerful new method for finding asymptotic formulae, called the circle method.
He discovered mock theta functions in the last year of his life.For many years these functions were a mystery, but they are now known to be the holomorphic parts of harmonic weak Maass forms.
The Ramanujan conjecture
Ramanujam has many conjectures to his credit
One conjecture has connection with conjectures of André Weil in algebraic geometry that opened up new areas of research. Ramanujan conjecture is an assertion on the size of the tau-function, which has as generating function the discriminant modular form Δ(q), a typical cusp form in the theory of modular forms. It was finally proven in 1973, as a consequence of Pierre Deligne's proof of the Weil conjectures. The reduction step involved is complicated. Deligne won a Fields Medal in 1978 for his work on Weil conjectures.
Hardy-Ramanujan number 1729
The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy In Hardy's words:
|“||I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."||”|
The two different ways are
- 1729 = 13 + 123 = 93 + 103.
Some Books on publications by Ramanujan
Srinivasa Ramanujan, G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson, Bruce C. Berndt (2000). Collected Papers of Srinivasa Ramanujan. AMS. ISBN 0-8218-2076-1.
It contains the 37 papers published in professional journals by Ramanujan during his lifetime.
S. Ramanujan (1957). Notebooks (2 Volumes). Bombay: Tata Institute of Fundamental Research.
S. Ramanujan (1988). The Lost Notebook and Other Unpublished Papers. New Delhi: Narosa. ISBN 3-540-18726-X.
This book contains photo copies of the pages of the "Lost Notebook".
Problems posed by Ramanujan, Journal of the Indian Mathematical Society.
S. Ramanujan (2012). Notebooks (2 Volumes). Bombay: Tata Institute of Fundamental Research.