Subbayya Sivasankaranarayana Pillai (5 April 1901 – 31 August 1950) was an Indian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specialising in number theory. His contribution to

Waring's problem In number theory, Waring's problem asks whether each natural number ''k'' has an associated positive integer ''s'' such that every natural number is the sum of at most ''s'' natural numbers raised to the power ''k''. For example, every natural num ...

was described in 1950 by

K. S. Chandrasekharan Komaravolu Chandrasekharan (21 November 1920 – 13 April 2017) was a professor at ETH Zurich and a founding faculty member of School of Mathematics, Tata Institute of Fundamental Research (TIFR). He is known for his work in number theory an ...

as "almost certainly his best piece of work and one of the very best achievements in Indian Mathematics since Ramanujan".

Biography

Subbayya Sivasankaranarayana Pillai was born to parents Subbayya Pillai and Gomati Ammal. His mother died a year after his birth and his father when Pillai was in his last year at school. Pillai did his intermediate course and B.Sc Mathematics in the

Scott Christian College Scott Christian College is an autonomous, co-educational, arts and science college in Nagercoil, Tamil Nadu. Run by the Diocese of Kanyakumari of the Church of South India, the college is graded "''A''" under National Assessment and Accreditat ...

Nagercoil Nagercoil, also spelt as Nagarkovil ("Temple of the Nāgas", or Nagaraja-Temple), is a city and the administrative headquarters of Kanyakumari District in Tamil Nadu state, India. Situated close to the tip of the Indian peninsula, it lies on an ...

and managed to earn a B.A. degree from Maharaja's college, Trivandrum. In 1927, Pillai was awarded a research fellowship at the

University of Madras The University of Madras (informally known as Madras University) is a public university, public State university (India), state university in Chennai, Tamil Nadu, India. Established in 1857, it is one of the oldest and among the most prestigiou ...

to work among professors

K. Ananda Rau K. Ananda Rau (21 September 1893 – 22 January 1966) was an eminent Indian mathematician and a contemporary of Ramanujan. Though Rau was six years junior to Ramanujan, his mathematical trajectory, unlike Ramanujan's, was very much a conventi ...

and

Ramaswamy S. Vaidyanathaswamy Ramaswamy S. Vaidyanathaswamy (1894–1960) was an Indian mathematician who wrote the first textbook of point-set topology in India. Life He was born in India on 24 October 1894. Vaidyanathaswamy studied Mathematics at the University of Edinbu ...

. He was from 1929 to 1941 at

Annamalai University , logo = CampusmapofAU.jpg , image = Annamalai University logo.png , image_size = 225px , motto = "With Courage and Faith" , established = , type ...

where he worked as a lecturer. It was in

Annamalai University , logo = CampusmapofAU.jpg , image = Annamalai University logo.png , image_size = 225px , motto = "With Courage and Faith" , established = , type ...

that he did his major work in

. In 1941 he went to the

University of Travancore University of Kerala, formerly the University of Travancore, is a state-run public university located in Thiruvananthapuram, the state capital of Kerala, India. It was established in 1937 by a promulgation of the Maharajah of Travancore, Chit ...

and a year later to the

University of Calcutta The University of Calcutta (informally known as Calcutta University; CU) is a Public university, public collegiate university, collegiate State university (India), state university in India, located in Kolkata, West Bengal, India. Considered ...

as a lecturer (where he was at the invitation of

Friedrich Wilhelm Levi Friedrich Wilhelm Daniel Levi (February 6, 1888 – January 1, 1966) was a German mathematician known for his work in abstract algebra, especially torsion-free abelian groups. He also worked in geometry, topology, set theory, and analysis. Early ...

Raghavan Narasimhan Raghavan Narasimhan (August 31, 1937 – October 3, 2015) was an Indian mathematician at the University of Chicago who worked on real and complex manifolds and who solved the Levi problem In mathematics, in the theory of several complex variabl ...

The coming of age of mathematics in India, in Michael Atiyah u.a. Miscellanea Mathematica, Springer Verlag 1991, S. 250f For his achievements he was invited in August 1950, for a year to visit the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, Princeton, United States. He was also invited to participate in the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

as a delegate of the

Madras University The University of Madras (informally known as Madras University) is a public state university in Chennai, Tamil Nadu, India. Established in 1857, it is one of the oldest and among the most prestigious universities in India, incorporated by an a ...

but he died during the crash of

TWA Flight 903 TWA Flight 903 was a regularly scheduled flight from Bombay International Airport, India to New York-Idlewild Airport, via Cairo-King Farouk Airport and Rome-Ciampino Airport. Flight ''The Star of Maryland'', a Lockheed L-749A Constellation ...

in Egypt on the way to the conference.

Contributions

He proved the

for

k\ge 6

in 1935 under the further condition of

(3^k + 1)/(2^k - 1)\le .5^k + 1

ahead of

Leonard Eugene Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remem ...

who around the same time proved it for

k\ge 7.

He showed that

g(k) = 2^k + l - 2

where

l

is the largest natural number

\le (3/2)^k

and hence computed the precise value of

g(6) = 73

. The

Pillai sequence The Pillai sequence is the sequence of integers that have a record number of terms in their greedy representations as sums of prime numbers (and one). It is named after Subbayya Sivasankaranarayana Pillai, who first defined it in 1930. It would fo ...

1, 4, 27, 1354, ..., is a quickly growing

integer sequence In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified ''explicitly'' by giving a formula for its ''n''th term, or ''implicitly'' by giving a relationship between its terms. For ...

in which each term is the sum of the previous term and a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

whose following

prime gap A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g'n'' or ''g''(''p'n'') is the difference between the (''n'' + 1)-th and the ''n''-th prime numbers, i.e. :g_n = p_ - p_n.\ W ...

is larger than the previous term. It was studied by Pillai in connection with representing numbers as sums of prime numbers.

References

{{DEFAULTSORT:Pillai, Subbayya Sivasankaranarayana 1901 births 1950 deaths Scientists from Tamil Nadu People from Kanyakumari district 20th-century Indian mathematicians Indian number theorists Academic staff of the University of Calcutta Institute for Advanced Study visiting scholars Academic staff of the University of Madras Academic staff of Annamalai University Victims of aviation accidents or incidents in 1950