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	{{short description\|Indian mathematician-astronomer}}		{{short description\|Indian mathematician-astronomer}}
	{{Other uses}}		{{Other uses}}
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	{{Use Indian English\|date=May 2022}}		{{Use Indian English\|date=May 2022}}

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	{{short description\|Indian mathematician-astronomer}}		{{short description\|Indian mathematician-astronomer}}
	{{Other uses}}		{{Other uses}}
	{{pp-vandalism\|small=yes}}		{{pp-vandalism\|small=yes}}{{Use Indian English\|date=May 2022}}

	{{Infobox scholar		{{Infobox scholar
	\| image = 2064 aryabhata-crp.jpg		\| image = 2064 aryabhata-crp.jpg
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	\| influenced = [[Lalla]], [[Bhaskara I]], [[Brahmagupta]], [[Varahamihira]], [[Kerala school of astronomy and mathematics]], [[Astronomy in the medieval Islamic world\|Islamic Astronomy]] and [[Mathematics]]		\| influenced = [[Lalla]], [[Bhaskara I]], [[Brahmagupta]], [[Varahamihira]], [[Kerala school of astronomy and mathematics]], [[Astronomy in the medieval Islamic world\|Islamic Astronomy]] and [[Mathematics]]
	}}		}}
	'''Aryabhata''' (~~{{Lang-sa\|आर्यभट}}~~, [[ISO 15919\|ISO]]: {{transl\|sa\|ISO\|Āryabhaṭa}}) or '''Aryabhata I'''<ref name="Aryabhata the Elder">{{cite web \|last1=O'Connor \|first1=J J \|last2=Robertson \|first2=E F \|title=Aryabhata the Elder \|publisher=www-history.mcs.st-andrews.ac.uk \|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html \|access-date=18 July 2012 \|url-status=live \|archive-url=https://web.archive.org/web/20150711055702/http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html \|archive-date=11 July 2015 }}</ref><ref name="Publishing2010">{{cite book\|author=Britannica Educational Publishing\|title=The Britannica Guide to Numbers and Measurement\|url=https://books.google.com/books?id=cuN7rH6RzikC&pg=PA97\|date=15 August 2010\|publisher=The Rosen Publishing Group\|isbn=978-1-61530-218-5\|pages=97–}}</ref> (476–550 [[Common Era\|CE]])<ref name="Ray2009">{{cite book\|author=Bharati Ray\|title=Different Types of History\|url=https://books.google.com/books?id=9x5FX2RROZgC&pg=PA95\|date=1 September 2009\|publisher=Pearson Education India\|isbn=978-81-317-1818-6\|pages=95–}}</ref><ref name="Yadav2010">{{cite book\|author=B. S. Yadav\|title=Ancient Indian Leaps into Mathematics\|url=https://books.google.com/books?id=nwrw0Lv1vXIC&pg=PA88\|date=28 October 2010\|publisher=Springer\|isbn=978-0-8176-4694-3\|page=88}}</ref> was an ~~[[India]]n~~ mathematician and astronomer of the classical age of [[Indian mathematics]] and [[Indian astronomy]]. He flourished in the [[Gupta era\|Gupta Era]] and produced works such as the ''[[Āryabhaṭīya]]'' (which mentions that in 3600 ''[[Kali Yuga]]'', 499 CE, he was 23 years old)<ref name="Roupp1997">{{cite book\|author=Heidi Roupp\|title=Teaching World History: A Resource Book\|url=https://books.google.com/books?id=-UYag6dzk7YC&pg=PA112\|date=1997\|publisher=M.E. Sharpe\|isbn=978-1-56324-420-9\|pages=112–}}</ref> and the ''Arya-siddhanta.''		[[File:Aryabhatta at Patna Junction.jpg\|thumb\|Aryabhata Photo on Wall of Patna Junction]]
			'''Aryabhata''' (, [[ISO 15919\|ISO]]: {{transl\|sa\|ISO\|Āryabhaṭa}}) or '''Aryabhata I'''<ref name="Aryabhata the Elder">{{cite web \|last1=O'Connor \|first1=J J \|last2=Robertson \|first2=E F \|title=Aryabhata the Elder \|publisher=www-history.mcs.st-andrews.ac.uk \|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html \|access-date=18 July 2012 \|url-status=live \|archive-url=https://web.archive.org/web/20150711055702/http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html \|archive-date=11 July 2015 }}</ref><ref name="Publishing2010">{{cite book\|author=Britannica Educational Publishing\|title=The Britannica Guide to Numbers and Measurement\|url=https://books.google.com/books?id=cuN7rH6RzikC&pg=PA97\|date=15 August 2010\|publisher=The Rosen Publishing Group\|isbn=978-1-61530-218-5\|pages=97–}}</ref> (476–550 [[Common Era\|CE]])<ref name="Ray2009">{{cite book\|author=Bharati Ray\|title=Different Types of History\|url=https://books.google.com/books?id=9x5FX2RROZgC&pg=PA95\|date=1 September 2009\|publisher=Pearson Education India\|isbn=978-81-317-1818-6\|pages=95–}}</ref><ref name="Yadav2010">{{cite book\|author=B. S. Yadav\|title=Ancient Indian Leaps into Mathematics\|url=https://books.google.com/books?id=nwrw0Lv1vXIC&pg=PA88\|date=28 October 2010\|publisher=Springer\|isbn=978-0-8176-4694-3\|page=88}}</ref> was an Indian mathematician and astronomer of the classical age of [[Indian mathematics]] and [[Indian astronomy]]. He flourished in the [[Gupta era\|Gupta Era]] and produced works such as the ''[[Āryabhaṭīya]]'' (which mentions that in 3600 ''[[Kali Yuga]]'', 499 CE, he was 23 years old)<ref name="Roupp1997">{{cite book\|author=Heidi Roupp\|title=Teaching World History: A Resource Book\|url=https://books.google.com/books?id=-UYag6dzk7YC&pg=PA112\|date=1997\|publisher=M.E. Sharpe\|isbn=978-1-56324-420-9\|pages=112–}}</ref> and the ''Arya-siddhanta.''

	Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables. Later commentators such as [[Brahmagupta]] divide his work into ''Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy")''. His pure mathematics discusses topics such as determination of [[Square root\|square]] and [[cube root]]s, geometrical figures with their properties and [[Measurement\|mensuration]], [[Arithmetic progression\|arithmetric progression]] problems on the [[Gnomon\|shadow of the gnomon]], [[quadratic equation]]s, [[Linear equation\|linear]] and [[indeterminate equation]]s. Aryabhata calculated the value of [[pi]] (''π)'' to the fourth decimal digit and was likely aware that [[pi]] (''π)'' is an [[irrational number]], around 1300 years before [[Johann Heinrich Lambert\|Lambert]] proved the same.<ref>{{Cite book\|last=Puttaswamy\|first=T. K.\|url=https://books.google.com/books?id=8oVRSu692qoC~~&newbks=0&printsec=frontcover&hl=en~~\|title=Mathematical Achievements of Pre-modern Indian Mathematicians\|date=2012-09-10\|publisher=Newnes\|isbn=978-0-12-397913-1\|language=en}}</ref> Aryabhata's [[Trigonometric tables\|sine table]] and his work on [[Trigonometry\|trignometry]] were extremely influential on the [[Islamic Golden Age]]; his works were translated into Arabic and influenced [[Muhammad ibn Musa al-Khwarizmi\|Al-Khwarizmi]] and [[Abū Isḥāq Ibrāhīm al-Zarqālī\|Al-Zarqali]].<ref>{{Cite book\|last=Divakaran\|first=P. P.\|url=https://books.google.com/books?id=3XdvDwAAQBAJ&~~newbks=0&printsec=frontcover&dq~~=aryabhata+influence+islamic+golden+age~~&hl=en~~\|title=The Mathematics of India: Concepts, Methods, Connections\|date=2018-09-19\|publisher=Springer\|isbn=978-981-13-1774-3\|language=en}}</ref><ref>{{Cite book\|last=Rashed\|first=R.\|url=https://books.google.com/books?id=Jb3nCAAAQBAJ&~~newbks=0&printsec=frontcover&dq~~=aryabhata+influence+islamic+golden+age~~&hl=en~~\|title=The Development of Arabic Mathematics: Between Arithmetic and Algebra\|date=2013-04-18\|publisher=Springer Science & Business Media\|isbn=978-94-017-3274-1\|language=en}}</ref> In his spherical astronomy, he applied plane trigonometry to spherical geometry and gave calculations on [[Solar eclipse\|solar]], [[lunar eclipse]]s. He discovered that the apparent westward motion of stars is due to the spherical [[Earth's rotation\|Earth's rotation about its own axis]]. Aryabhata also ~~correctly discovered~~ that the [[luminosity]] of the Moon and other planets is due to reflected sunlight.<ref>{{Cite web\|title=Aryabhata {{!}} Achievements, Biography, & Facts {{!}} Britannica\|url=https://www.britannica.com/biography/Aryabhata-I\|access-date=2022-01-24\|website=www.britannica.com\|language=en}}</ref> For his explicit mention of the [[relativity of motion]], he also qualifies as a major early [[physicist]].<ref name="encyclopedia.com">[https://www.encyclopedia.com/international/encyclopedias-almanacs-transcripts-and-maps/aryabhatiya S. Kak, Aryabhatiya. Encyclopedia of India, 2005]</ref>		Aryabhata created a system of phonemic number notation in which numbers were represented by consonant-vowel monosyllables. Later commentators such as [[Brahmagupta]] divide his work into ''Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy")''. His pure mathematics discusses topics such as determination of [[Square root\|square]] and [[cube root]]s, geometrical figures with their properties and [[Measurement\|mensuration]], [[Arithmetic progression\|arithmetric progression]] problems on the [[Gnomon\|shadow of the gnomon]], [[quadratic equation]]s, [[Linear equation\|linear]] and [[indeterminate equation]]s. Aryabhata calculated the value of [[pi]] (''π)'' to the fourth decimal digit and was likely aware that [[pi]] (''π)'' is an [[irrational number]], around 1300 years before [[Johann Heinrich Lambert\|Lambert]] proved the same.<ref>{{Cite book\|last=Puttaswamy\|first=T. K.\|url=https://books.google.com/books?id=8oVRSu692qoC\|title=Mathematical Achievements of Pre-modern Indian Mathematicians\|date=2012-09-10\|publisher=Newnes\|isbn=978-0-12-397913-1\|language=en}}</ref> Aryabhata's [[Trigonometric tables\|sine table]] and his work on [[Trigonometry\|trignometry]] were extremely influential on the [[Islamic Golden Age]]; his works were translated into Arabic and influenced [[Muhammad ibn Musa al-Khwarizmi\|Al-Khwarizmi]] and [[Abū Isḥāq Ibrāhīm al-Zarqālī\|Al-Zarqali]].<ref>{{Cite book\|last=Divakaran\|first=P. P.\|url=https://books.google.com/books?id=3XdvDwAAQBAJ&q=aryabhata+influence+islamic+golden+age\|title=The Mathematics of India: Concepts, Methods, Connections\|date=2018-09-19\|publisher=Springer\|isbn=978-981-13-1774-3\|language=en}}</ref><ref>{{Cite book\|last=Rashed\|first=R.\|url=https://books.google.com/books?id=Jb3nCAAAQBAJ&q=aryabhata+influence+islamic+golden+age\|title=The Development of Arabic Mathematics: Between Arithmetic and Algebra\|date=2013-04-18\|publisher=Springer Science & Business Media\|isbn=978-94-017-3274-1\|language=en}}</ref> In his spherical astronomy, he applied plane trigonometry to spherical geometry and gave calculations on [[Solar eclipse\|solar]], [[lunar eclipse]]s. He discovered that the apparent westward motion of stars is due to the spherical [[Earth's rotation\|Earth's rotation about its own axis]]. Aryabhata also noted that the [[luminosity]] of the Moon and other planets is due to reflected sunlight.<ref>{{Cite web\|title=Aryabhata {{!}} Achievements, Biography, & Facts {{!}} Britannica\|url=https://www.britannica.com/biography/Aryabhata-I\|access-date=2022-01-24\|website=www.britannica.com\|language=en}}</ref>

	==Biography==		==Biography==
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	===Education===		===Education===
	It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.<ref>{{cite book\|last=Cooke\|author-link=Roger Cooke (mathematician)\|title=History of Mathematics: A Brief Course \|url=https://archive.org/details/historyofmathema0000cook\|url-access=registration\|date=1997\|chapter=''The Mathematics of the Hindus''\|page=[https://archive.org/details/historyofmathema0000cook/page/204 204]\|quote=Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late 5th and the early 6th centuries at [[Kusumapura]] ([[Pataliutra]], a village near the city of Patna) and wrote a book called ''Aryabhatiya''.}}</ref> Both Hindu and Buddhist tradition, as well as [[Bhāskara I]] (CE 629), identify Kusumapura as [[Pāṭaliputra]], modern [[Patna]].<ref name=sarma/> A verse mentions that Aryabhata was the head of an institution (''{{IAST\|kulapa}}'')<!--NOT "kulapati", see source--> at Kusumapura, and, because the university of [[Nalanda]] was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.<ref name=sarma/> Aryabhata is also reputed to have set up an observatory at the Sun temple in [[Taregana]], Bihar.<ref>{{cite web\|url=http://ncsm.gov.in/docs/Get%20ready%20for%20Solar%20eclipse.pdf \|title=Get ready for solar eclipse \|publisher=National Council of Science Museums, Ministry of Culture, Government of India \|access-date=9 December 2009 \|url-status=dead \|archive-url=https://web.archive.org/web/20110721162632/http://ncsm.gov.in/docs/Get%20ready%20for%20Solar%20eclipse.pdf \|archive-date=21 July 2011 }}</ref>		It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.<ref>{{cite book\|last=Cooke\|author-link=Roger Cooke (mathematician)\|title=History of Mathematics: A Brief Course \|url=https://archive.org/details/historyofmathema0000cook\|url-access=registration\|date=1997\|chapter=''The Mathematics of the Hindus''\|page=[https://archive.org/details/historyofmathema0000cook/page/204 204]\|quote=Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late 5th and the early 6th centuries at [[Kusumapura]] ([[Pataliutra]], a village near the city of Patna) and wrote a book called ''Aryabhatiya''.}}</ref> Both Hindu and Buddhist tradition, as well as [[Bhāskara I]] (CE 629), identify Kusumapura as [[Pāṭaliputra]], modern [[Patna]].<ref name=sarma/> A verse mentions that Aryabhata was the head of an institution (''{{IAST\|kulapa}}'')<!--NOT "kulapati", see source--> at Kusumapura, and, because the university of [[Nalanda]] was near Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.<ref name=sarma/> Aryabhata is also reputed to have set up an observatory at the Sun temple in [[Taregana]], Bihar.<ref>{{cite web\|url=http://ncsm.gov.in/docs/Get%20ready%20for%20Solar%20eclipse.pdf \|title=Get ready for solar eclipse \|publisher=National Council of Science Museums, Ministry of Culture, Government of India \|access-date=9 December 2009 \|url-status=dead \|archive-url=https://web.archive.org/web/20110721162632/http://ncsm.gov.in/docs/Get%20ready%20for%20Solar%20eclipse.pdf \|archive-date=21 July 2011 }}</ref>

	==Works==		==Works==
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	The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (''Bhashya'', c. 600 CE) and by [[Nilakantha Somayaji]] in his ''Aryabhatiya Bhasya,'' (1465 CE).		The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (''Bhashya'', c. 600 CE) and by [[Nilakantha Somayaji]] in his ''Aryabhatiya Bhasya,'' (1465 CE).

	The Aryabhatiya is also remarkable for its description of relativity of motion. He expressed this relativity thus: "Just as a man in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so are the stationary stars seen by the people on earth as moving exactly towards the west."<ref name="encyclopedia.com"/>

	==Mathematics==		==Mathematics==
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	A problem of great interest to [[Indian mathematicians]] since ancient times has been to find integer solutions to [[Diophantine equations]] that have the form ax + by = c. (This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the [[Chinese remainder theorem]].) This is an example from [[Bhāskara I\|Bhāskara]]'s commentary on Aryabhatiya:		A problem of great interest to [[Indian mathematicians]] since ancient times has been to find integer solutions to [[Diophantine equations]] that have the form ax + by = c. (This problem was also studied in ancient Chinese mathematics, and its solution is usually referred to as the [[Chinese remainder theorem]].) This is an example from [[Bhāskara I\|Bhāskara]]'s commentary on Aryabhatiya:
	: Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7		: Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
	That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text [[Sulba Sutras]], whose more ancient parts might date to 800 BCE. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621 CE, is called the ''{{IAST\|kuṭṭaka}}'' (कुट्टक) method. ''[[Kuṭṭaka]]'' means "~~pulverizing~~" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole subject of algebra was called ''kuṭṭaka-gaṇita'' or simply ''kuṭṭaka''.<ref>		That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text [[Sulba Sutras]], whose more ancient parts might date to 800 BCE. Aryabhata's method of solving such problems, elaborated by Bhaskara in 621 CE, is called the ''{{IAST\|kuṭṭaka}}'' (कुट्टक) method. ''[[Kuṭṭaka]]'' means "pulverising" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the whole subject of algebra was called ''kuṭṭaka-gaṇita'' or simply ''kuṭṭaka''.<ref>
	Amartya K Dutta, [http://www.ias.ac.in/resonance/Volumes/07/10/0006-0022.pdf "Diophantine equations: The Kuttaka"] {{webarchive\|url=https://web.archive.org/web/20141102224109/http://www.ias.ac.in/resonance/Volumes/07/10/0006-0022.pdf \| date = 2 November 2014}}, ''Resonance'', October 2002. Also see earlier overview: [http://www.ias.ac.in/resonance/Volumes/07/04/0004-0019.pdf ''Mathematics in Ancient India''] {{webarchive\|url=https://web.archive.org/web/20141102223752/http://www.ias.ac.in/resonance/Volumes/07/04/0004-0019.pdf \|date=2 November 2014 }}.</ref>		Amartya K Dutta, [http://www.ias.ac.in/resonance/Volumes/07/10/0006-0022.pdf "Diophantine equations: The Kuttaka"] {{webarchive\|url=https://web.archive.org/web/20141102224109/http://www.ias.ac.in/resonance/Volumes/07/10/0006-0022.pdf \| date = 2 November 2014}}, ''Resonance'', October 2002. Also see earlier overview: [http://www.ias.ac.in/resonance/Volumes/07/04/0004-0019.pdf ''Mathematics in Ancient India''] {{webarchive\|url=https://web.archive.org/web/20141102223752/http://www.ias.ac.in/resonance/Volumes/07/04/0004-0019.pdf \|date=2 November 2014 }}.</ref>

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	\| url=https://archive.org/details/The_Aryabhatiya_of_Aryabhata_Clark_1930		\| url=https://archive.org/details/The_Aryabhatiya_of_Aryabhata_Clark_1930
	}}		}}
	* [[Subhash Kak\|Kak, Subhash C.]] (2000). 'Birth and Early Development of Indian Astronomy'. In {{Cite encyclopedia
	~~\| editor-last= Selin~~
	~~\| editor-first = Helaine~~
	~~\| editor-link = Helaine Selin~~
	~~\| date = 2000~~
	~~\| title = Astronomy Across Cultures: The History of Non-Western Astronomy~~
	~~\| publisher = Boston: Kluwer~~
	~~\| isbn = 0-7923-6363-9~~
	}}
	* Shukla, Kripa Shankar. ''Aryabhata: Indian Mathematician and Astronomer.'' New Delhi: Indian National Science Academy, 1976.		* Shukla, Kripa Shankar. ''Aryabhata: Indian Mathematician and Astronomer.'' New Delhi: Indian National Science Academy, 1976.
	* {{Cite book		* {{Cite book

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2022-01-25T18:49:45Z