# Subbayya Sivasankaranarayana Pillai

Subbayya Sivasankaranarayana Pillai
Born April 5, 1901
Nagercoil, Kingdom of Travancore (in present day Tamil Nadu)
Died 31 August 1950
Cairo, Egypt
Nationality Indian
Fields Mathematics
Known for Pillai's conjecture
Pillai's arithmetical function
Pillai prime

Subbayya Sivasankaranarayana Pillai (1901–1950) was an Nagercoil native Indian mathematician specialising in number theory. His contribution to Waring's problem was described in 1950 by K. S. Chandrasekharan as "almost certainly his best piece of work and one of the very best achievements in Indian Mathematics since Ramanujan".[1]

## Biography

Subbayya Sivasankaranarayana Pillai was born to parents Subbayya Pillai and Gomati Ammal who were natives of Nagercoil. His mother died a year after his birth and his father when Pillai was in his last year at school.[1]

Pillai did his Intermediate course in the Scott Christian College at Nagercoil[1] and managed to earn a B.A. degree from Maharaja's college, Trivandrum.[2]

In 1927, Pillai was awarded a research fellowship at the University of Madras to work among professors K. Ananda Rau and Ramaswamy S. Vaidyanathaswamy. He was from 1929 to 1941 at Annamalai University where he worked as a lecturer. It was in Annamalai University that he did his major work in Waring's problem.[2] In 1941 he went to the University of Travancore and a year later to the University of Calcutta as a lecturer (where he was at the invitation of Friedrich Wilhelm Levi).[3]

For his achievements he was invited in August 1950, for a year to visit the Institute for Advanced Study, Princeton, USA. He was also invited to participate in the International Congress of Mathematicians at Harvard University as a delegate of the Madras University but he died during the crash of TWA Flight 903 in Egypt on the way to the conference.[4]

## Contributions

He proved the Waring's problem for ${\displaystyle k\geq 6}$ in 1935[5] under the further condition of ${\displaystyle (3^{k}+1)/(2^{k}-1)\leq [1.5^{k}]+1}$ ahead of Leonard Eugene Dickson who around the same time proved it for ${\displaystyle k\geq 7.}$[6]

He showed that ${\displaystyle g(k)=2^{k}+l-2}$ where ${\displaystyle l}$ is the largest natural number ${\displaystyle \leq (3/2)^{k}}$ and hence computed the precise value of ${\displaystyle g(6)=73}$.[5]

## References

1. ^ a b c "An outstanding mathematician". The Hindu. Retrieved 14 July 2013.
2. ^ a b Uma Dasgupta (2011). Science and Modern India: An Institutional History, C. 1784-1947. Pearson Education India. pp. 702–. ISBN 978-81-317-2818-5. Retrieved 14 July 2013.
3. ^ Raghavan Narasimhan The coming of age of mathematics in India, in Michael Atiyah u.a. Miscellanea Mathematica, Springer Verlag 1991, S. 250f
4. ^ Alladi, Krishnaswami (2013). Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study. Springer. pp. 42–. ISBN 978-81-322-0767-2. Retrieved 14 July 2013.
5. ^ a b "S. S. Pillai". Archived from the original on October 26, 2009.
6. ^ Number Theory. Universities Press. 2003. pp. 95–. ISBN 978-81-7371-454-2. Retrieved 15 July 2013.