Subbayya Sivasankaranarayana Pillai - Revision history

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	{{Short description\|Indian mathematician}}		{{Short description\|Indian mathematician (1901–1950)}}
	{{Use Indian English\|date=May 2018}}		{{Use Indian English\|date=May 2018}}
	{{Use dmy dates\|date=~~May 2018~~}}		{{Use dmy dates\|date=January 2025}}
	{{Infobox scientist		{{Infobox scientist
	\|name = Subbayya Sivasankaranarayana Pillai		\|name = Subbayya Sivasankaranarayana Pillai
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	\|birth_date = 5 April 1901		\|birth_date = 5 April 1901
	\|birth_place = [[Vallam]], [[British India]]<br/>(now in [[Tamil Nadu]], India)<ref name="The Hindu"/>		\|birth_place = [[Vallam]], [[British India]]<br/>(now in [[Tamil Nadu]], India)<ref name="The Hindu"/>
	\|death_date = {{death-date and age\|31 August 1950\|5 April 1901}}		\|death_date = {{death date and age text\|31 August 1950\|5 April 1901}}
	\|death_place = [[Cairo]], [[Egypt]]		\|death_place = [[Cairo]], Egypt
	\|residence =		\|residence =
	\|citizenship =		\|citizenship =
	~~\|nationality = [[India]]n~~
	\|ethnicity =		\|ethnicity =
	\|field = [[Mathematics]]		\|field = [[Mathematics]]
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	}}		}}

	'''Subbayya Sivasankaranarayana Pillai''' (5 April 1901 – 31 August 1950) was an ~~[[India]]n~~ [[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 [[Srinivasa Ramanujan\|Ramanujan]]".<ref name="The Hindu">{{cite web\|title=An outstanding mathematician\|url=http://thehindujobs.com/thehindu/2001/05/10/stories/08100007.htm\|access-date=14 July 2013\|~~publisher~~=[[The Hindu]]\|url-status=~~dead~~\|archive-url=https://web.archive.org/web/20070928161721/http://thehindujobs.com/thehindu/2001/05/10/stories/08100007.htm\|archive-date=28 September 2007~~\|df=~~}}</ref>		'''Subbayya Sivasankaranarayana Pillai''' (5 April 1901 – 31 August 1950) was an 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 [[Srinivasa Ramanujan\|Ramanujan]]".<ref name="The Hindu">{{cite web\|title=An outstanding mathematician\|url=http://thehindujobs.com/thehindu/2001/05/10/stories/08100007.htm\|access-date=14 July 2013\|work=[[The Hindu]]\|url-status=usurped\|archive-url=https://web.archive.org/web/20070928161721/http://thehindujobs.com/thehindu/2001/05/10/stories/08100007.htm\|archive-date=28 September 2007}}</ref>

	==Biography==		==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.<ref name="The Hindu" />		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.<ref name="The Hindu" />

	Pillai did his intermediate course and B.Sc Mathematics in the [[Scott Christian College]] at [[Nagercoil]]<ref name="The Hindu" /> and managed to earn a B.A. degree from [[University College Trivandrum\|Maharaja's college, Trivandrum]].<ref name="Dasgupta2011">{{cite book\|author=Uma Dasgupta\|title=Science and Modern India: An Institutional History, C. 1784–1947\|url=https://books.google.com/books?id=lrx3wLz4itkC&pg=PA702\|accessdate=14 July 2013\|year=2011\|publisher=Pearson Education India\|isbn=978-81-317-2818-5\|~~pages~~=~~702–~~}}</ref>		Pillai did his intermediate course and B.Sc. Mathematics in the [[Scott Christian College]] at [[Nagercoil]]<ref name="The Hindu" /> and managed to earn a B.A. degree from [[University College Trivandrum\|Maharaja's college, Trivandrum]].<ref name="Dasgupta2011">{{cite book\|author=Uma Dasgupta\|title=Science and Modern India: An Institutional History, C. 1784–1947\|url=https://books.google.com/books?id=lrx3wLz4itkC&pg=PA702\|accessdate=14 July 2013\|year=2011\|publisher=Pearson Education India\|isbn=978-81-317-2818-5\|page=702}}</ref>

	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]].<ref name="Dasgupta2011" /> 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]]).<ref name="Narasimhan">[[Raghavan Narasimhan]] The coming of age of mathematics in India, in Michael Atiyah u.a. Miscellanea Mathematica, Springer Verlag 1991, S. 250f</ref>		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]].<ref name="Dasgupta2011" /> 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]]).<ref name="Narasimhan">[[Raghavan Narasimhan]] The coming of age of mathematics in India, in Michael Atiyah u.a. Miscellanea Mathematica, Springer Verlag 1991, S. 250f</ref>

	For his achievements he was invited in August 1950, for a year to visit the [[Institute for Advanced Study]], Princeton, United States. 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.<ref name="Alladi2013">{{cite book\|first=Krishnaswami\|last=Alladi\|authorlink= Krishnaswami Alladi \|title=Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study\|url=https://books.google.com/books?id=XLNJDylP53QC&pg=PA42\|accessdate=14 July 2013\|year=2013\|publisher=Springer\|isbn=978-81-322-0767-2\|~~pages~~=~~42–~~}}</ref>		For his achievements he was invited in August 1950, for a year to visit the [[Institute for Advanced Study]], Princeton, United States. 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.<ref name="Alladi2013">{{cite book\|first=Krishnaswami\|last=Alladi\|authorlink= Krishnaswami Alladi \|title=Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study\|url=https://books.google.com/books?id=XLNJDylP53QC&pg=PA42\|accessdate=14 July 2013\|year=2013\|publisher=Springer\|isbn=978-81-322-0767-2\|page=42}}</ref>

	==Contributions==		==Contributions==
	He proved the [[Waring's problem]] for <math>k\ge 6</math> in 1935<ref name="Thangadurai">{{cite web \|title=S. S. Pillai \|url=http://www.geocities.com/thangadurai_kr/PILLAI.html \|url-status=dead \|archive-url=https://web.archive.org/web/20091019185336/http://geocities.com/thangadurai_kr/PILLAI.html \|archive-date=19 October 2009 ~~\|df=~~ }}</ref> under the further condition of <math>(3^k + 1)/(2^k - 1)\le [1.5^k] + 1</math> ahead of [[Leonard Eugene Dickson]] who around the same time proved it for <math>k\ge 7.</math><ref>{{cite book\|title=Number Theory\|url=https://books.google.com/books?id=BkBSfFjT1BgC&pg=PA95\|accessdate=15 July 2013\|year=2003\|publisher=Universities Press\|isbn=978-81-7371-454-2\|pages=95–}}</ref>		He proved the [[Waring's problem]] for <math>k\ge 6</math> in 1935<ref name="Thangadurai">{{cite web \|title=S. S. Pillai \|url=http://www.geocities.com/thangadurai_kr/PILLAI.html \|url-status=dead \|archive-url=https://web.archive.org/web/20091019185336/http://geocities.com/thangadurai_kr/PILLAI.html \|archive-date=19 October 2009 }}</ref> under the further condition of <math>(3^k + 1)/(2^k - 1)\le [1.5^k] + 1</math> ahead of [[Leonard Eugene Dickson]] who around the same time proved it for <math>k\ge 7.</math><ref>{{cite book\|title=Number Theory\|url=https://books.google.com/books?id=BkBSfFjT1BgC&pg=PA95\|accessdate=15 July 2013\|year=2003\|publisher=Universities Press\|isbn=978-81-7371-454-2\|pages=95–}}</ref>

	He showed that <math>g(k) = 2^k + l - 2</math> where <math>l</math> is the largest natural number <math>\le (3/2)^k</math> and hence computed the precise value of <math>g(6) = 73</math>.<ref name="Thangadurai" />		He showed that <math>g(k) = 2^k + l - 2</math> where <math>l</math> is the largest natural number <math>\le (3/2)^k</math> and hence computed the precise value of <math>g(6) = 73</math>.<ref name="Thangadurai" />
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	[[Category:20th-century Indian mathematicians]]		[[Category:20th-century Indian mathematicians]]
	[[Category:Indian number theorists]]		[[Category:Indian number theorists]]
	[[Category:University of Calcutta ~~faculty~~]]		[[Category:Academic staff of the University of Calcutta]]
	[[Category:Institute for Advanced Study visiting scholars]]		[[Category:Institute for Advanced Study visiting scholars]]
	[[Category:University of Madras ~~faculty~~]]		[[Category:Academic staff of the University of Madras]]
	[[Category:Annamalai University ~~faculty~~]]		[[Category:Academic staff of Annamalai University]]
	[[Category:Victims of aviation accidents or incidents in 1950]]		[[Category:Victims of aviation accidents or incidents in 1950]]
			[[Category:Victims of aviation accidents or incidents in Egypt]]
			[[Category:University of Calcutta alumni]]

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	He showed that <math>g(k) = 2^k + l - 2</math> where <math>l</math> is the largest natural number <math>\le (3/2)^k</math> and hence computed the precise value of <math>g(6) = 73</math>.<ref name="Thangadurai" />		He showed that <math>g(k) = 2^k + l - 2</math> where <math>l</math> is the largest natural number <math>\le (3/2)^k</math> and hence computed the precise value of <math>g(6) = 73</math>.<ref name="Thangadurai" />

	The [[Pillai sequence]] 1, 4, 27, 1354, ..., is a quickly-growing [[integer sequence]] in which each term is the sum of the previous term and a [[prime number]] whose following [[prime gap]] is larger than the previous term. It was studied by Pillai in connection with representing numbers as sums of prime numbers.<ref>{{Cite OEIS\|A066352\|name=Pillai sequence}}</ref>		The [[Pillai sequence]] 1, 4, 27, 1354, ..., is a quickly growing [[integer sequence]] in which each term is the sum of the previous term and a [[prime number]] whose following [[prime gap]] is larger than the previous term. It was studied by Pillai in connection with representing numbers as sums of prime numbers.<ref>{{Cite OEIS\|A066352\|name=Pillai sequence}}</ref>

	==References==		==References==

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{{Short description|Indian mathematician}}
{{Use Indian English|date=May 2018}}
{{Use dmy dates|date=May 2018}}
{{Infobox scientist
|name = Subbayya Sivasankaranarayana Pillai
|image = S.S. Pillai.jpg
|image_size =
|caption =
|birth_date = 5 April 1901
|birth_place = [[Vallam]], [[British India]]<br/>(now in [[Tamil Nadu]], India)<ref name="The Hindu"/>
|death_date = {{death-date and age|31 August 1950|5 April 1901}}
|death_place = [[Cairo]], [[Egypt]]
|residence =
|citizenship =
|nationality = [[India]]n
|ethnicity =
|field = [[Mathematics]]
|work_institutions =
|alma_mater = [[Scott Christian College]], [[Nagercoil]]
|doctoral_advisor =
|doctoral_students =
|known_for = {{plainlist|1=
*[[Pillai's conjecture]]
*[[Pillai's arithmetical function]]
*[[Pillai prime]]
*[[Pillai sequence]]
}}
|author_abbrev_bot =
|author_abbrev_zoo =
|influences =
|influenced =
|prizes =
|religion =
|footnotes =
|signature =
}}

'''Subbayya Sivasankaranarayana Pillai''' (5 April 1901 – 31 August 1950) was an [[India]]n [[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 [[Srinivasa Ramanujan|Ramanujan]]".<ref name="The Hindu">{{cite web|title=An outstanding mathematician|url=http://thehindujobs.com/thehindu/2001/05/10/stories/08100007.htm|access-date=14 July 2013|publisher=[[The Hindu]]|url-status=dead|archive-url=https://web.archive.org/web/20070928161721/http://thehindujobs.com/thehindu/2001/05/10/stories/08100007.htm|archive-date=28 September 2007|df=}}</ref>

==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.<ref name="The Hindu" />

Pillai did his intermediate course and B.Sc Mathematics in the [[Scott Christian College]] at [[Nagercoil]]<ref name="The Hindu" /> and managed to earn a B.A. degree from [[University College Trivandrum|Maharaja's college, Trivandrum]].<ref name="Dasgupta2011">{{cite book|author=Uma Dasgupta|title=Science and Modern India: An Institutional History, C. 1784–1947|url=https://books.google.com/books?id=lrx3wLz4itkC&pg=PA702|accessdate=14 July 2013|year=2011|publisher=Pearson Education India|isbn=978-81-317-2818-5|pages=702–}}</ref>

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]].<ref name="Dasgupta2011" /> 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]]).<ref name="Narasimhan">[[Raghavan Narasimhan]] The coming of age of mathematics in India, in Michael Atiyah u.a. Miscellanea Mathematica, Springer Verlag 1991, S. 250f</ref>

For his achievements he was invited in August 1950, for a year to visit the [[Institute for Advanced Study]], Princeton, United States. 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.<ref name="Alladi2013">{{cite book|first=Krishnaswami|last=Alladi|authorlink= Krishnaswami Alladi |title=Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study|url=https://books.google.com/books?id=XLNJDylP53QC&pg=PA42|accessdate=14 July 2013|year=2013|publisher=Springer|isbn=978-81-322-0767-2|pages=42–}}</ref>

==Contributions==
He proved the [[Waring's problem]] for <math>k\ge 6</math> in 1935<ref name="Thangadurai">{{cite web |title=S. S. Pillai |url=http://www.geocities.com/thangadurai_kr/PILLAI.html |url-status=dead |archive-url=https://web.archive.org/web/20091019185336/http://geocities.com/thangadurai_kr/PILLAI.html |archive-date=19 October 2009 |df= }}</ref> under the further condition of <math>(3^k + 1)/(2^k - 1)\le [1.5^k] + 1</math> ahead of [[Leonard Eugene Dickson]] who around the same time proved it for <math>k\ge 7.</math><ref>{{cite book|title=Number Theory|url=https://books.google.com/books?id=BkBSfFjT1BgC&pg=PA95|accessdate=15 July 2013|year=2003|publisher=Universities Press|isbn=978-81-7371-454-2|pages=95–}}</ref>

He showed that <math>g(k) = 2^k + l - 2</math> where <math>l</math> is the largest natural number <math>\le (3/2)^k</math> and hence computed the precise value of <math>g(6) = 73</math>.<ref name="Thangadurai" />

The [[Pillai sequence]] 1, 4, 27, 1354, ..., is a quickly-growing [[integer sequence]] in which each term is the sum of the previous term and a [[prime number]] whose following [[prime gap]] is larger than the previous term. It was studied by Pillai in connection with representing numbers as sums of prime numbers.<ref>{{Cite OEIS|A066352|name=Pillai sequence}}</ref>

==References==
{{Reflist}}

{{Authority control}}

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