Editing History of science (section)

====Mathematics====
{{anchor|Indian astronomy|Indian mathematics}}
{{Main|Indian mathematics|}}
[[File:Bakhshali_numerals_2.jpg|thumb|The numerical system of the [[Bakhshali manuscript]]]]
[[File:Brahmaguptra's_theorem.svg|thumb|upright=0.8|[[Brahmagupta's theorem]]]]
The earliest traces of mathematical knowledge in the Indian subcontinent appear with the [[Indus Valley Civilisation]] ({{cx|3300|1300&nbsp;BCE}}). The people of this civilization made bricks whose dimensions were in the proportion 4:2:1, which is favorable for the stability of a brick structure.<ref>{{cite web|url=https://mathshistory.st-andrews.ac.uk/Projects/Pearce/chapter-3/|title=3: Early Indian culture – Indus civilisation|work=st-and.ac.uk}}</ref> They also tried to standardize measurement of length to a high degree of accuracy. They designed a ruler—the ''Mohenjo-daro ruler''—whose length of approximately {{cvt|1.32|inch}} was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length.<ref>{{cite book|last=Bisht |first=R. S.|year=1982|chapter=Excavations at Banawali: 1974–77|editor-last=Possehl |editor-first=Gregory L. |title=Harappan Civilization: A Contemporary Perspective|pages=113–124 |publisher=Oxford and IBH Publishing}}</ref>

The [[Bakhshali manuscript]] contains problems involving [[arithmetic]], [[algebra]] and [[geometry]], including [[Mensuration (mathematics)|mensuration]]. The topics covered include fractions, square roots, [[Arithmetic progression|arithmetic]] and [[geometric progression]]s, solutions of simple equations, [[simultaneous linear equations]], [[quadratic equations]] and [[indeterminate equations]] of the second degree.<ref name="Plofker">{{citation |last=Plofker |first=Kim |title=Mathematics in India |title-link=Mathematics in India (book) |page=158 |year=2009 |publisher=Princeton University Press |isbn=978-0-691-12067-6 |author-link=Kim Plofker}}</ref> In the 3rd century BCE, [[Pingala]] presents the ''Pingala-sutras'',  the earliest known treatise on [[Sanskrit prosody]].<ref>{{cite book |author=Vaman Shivaram Apte |url=https://books.google.com/books?id=4ArxvCxV1l4C&pg=PA648 |title=Sanskrit Prosody and Important Literary and Geographical Names in the Ancient History of India |publisher=Motilal Banarsidass |year=1970 |isbn=978-81-208-0045-8 |pages=648–649}}</ref> He also presents a numerical system by adding one to the sum of [[place value]]s.<ref>B. van Nooten, "Binary Numbers in Indian Antiquity", Journal of Indian Studies, Volume 21, 1993, pp. 31–50</ref> Pingala's work also includes material related to the [[Fibonacci numbers]], called ''{{IAST|mātrāmeru}}''.<ref>{{cite book |author=Susantha Goonatilake |url=https://archive.org/details/towardglobalscie0000goon |title=Toward a Global Science |publisher=Indiana University Press |year=1998 |isbn=978-0-253-33388-9 |page=[https://archive.org/details/towardglobalscie0000goon/page/126 126] |quote=Virahanka Fibonacci. |url-access=registration}}</ref>

Indian astronomer and mathematician [[Aryabhata]] (476–550), in his ''[[Aryabhatiya]]'' (499) introduced the [[sine]] function in [[trigonometry]] and the number 0. In 628, [[Brahmagupta]] suggested that [[gravity]] was a force of attraction.<ref>{{Cite book| last=Pickover| first=Clifford| author-link=Clifford A. Pickover| title=Archimedes to Hawking: laws of science and the great minds behind them| publisher=[[Oxford University Press US]]| year=2008| page=105| url=https://books.google.com/books?id=SQXcpvjcJBUC&pg=PA105| isbn=978-0-19-533611-5| access-date=7 May 2020| archive-date=18 January 2017| archive-url=https://web.archive.org/web/20170118060420/https://books.google.com/books?id=SQXcpvjcJBUC| url-status=live}}</ref><ref>Mainak Kumar Bose, ''Late Classical India'', A. Mukherjee & Co., 1988, p. 277.</ref> He also lucidly explained the use of [[0 (number)|zero]] as both a placeholder and a [[decimal digit]], along with the [[Hindu–Arabic numeral system]] now used universally throughout the world. [[Arabic]] translations of the two astronomers' texts were soon available in the [[Caliph|Islamic world]], introducing what would become [[Arabic numerals]] to the Islamic world by the 9th century.<ref name="ifrah">Ifrah, Georges. 1999. ''The Universal History of Numbers : From Prehistory to the Invention of the Computer'', Wiley. {{ISBN|978-0-471-37568-5}}.</ref><ref name="oconnor">O'Connor, J. J. and E. F. Robertson. 2000. [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Indian_numerals.html 'Indian Numerals'] {{Webarchive|url=https://web.archive.org/web/20070929131009/http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Indian_numerals.html |date=29 September 2007 }}, ''MacTutor History of Mathematics Archive'', School of Mathematics and Statistics, University of St. Andrews, Scotland.</ref>

[[Narayana Pandita (mathematician)|Narayana Pandita]] (1340–1400<ref>{{Cite web |title=Narayana - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Narayana/ |access-date=2022-10-03 |website=Maths History |language=en}}</ref>) was an Indian [[mathematician]]. [[Kim Plofker|Plofker]] writes that his texts were the most significant Sanskrit mathematics treatises after those of [[Bhaskara II]], other than the [[Kerala school of astronomy and mathematics|Kerala school]].<ref>{{citation | author=[[Kim Plofker]] | title=Mathematics in India: 500 BCE–1800 CE | title-link= Mathematics in India (book) | year=2009 | publisher=Princeton University Press | isbn= 978-0-691-12067-6}}</ref>{{rp|52}} He wrote the ''[[Ganita Kaumudi]]'' (lit. "Moonlight of mathematics") in 1356 about mathematical operations.<ref>{{citation | last=Kusuba|first=Takanori | contribution=Indian Rules for the Decomposition of Fractions | year=2004 | title=Studies in the History of the Exact Sciences in Honour of [[David Pingree]] | publisher=[[Brill Publishers|Brill]] | isbn=9004132023 | issn=0169-8729 | editor1=Charles Burnett | editor2=Jan P. Hogendijk | editor3=Kim Plofker |display-editors = 3 | editor4=Michio Yano | page = 497}}</ref> The work anticipated many developments in [[combinatorics]].

Between the 14th and 16th centuries, the [[Kerala school of astronomy and mathematics]] made significant advances in astronomy and especially mathematics, including fields such as trigonometry and analysis. In particular, [[Madhava of Sangamagrama]] led advancement in [[mathematical analysis|analysis]] by providing the infinite and taylor series expansion of some trigonometric functions and pi approximation.<ref name=katz>{{Cite journal|last=Katz |first=Victor J. |author-link=Victor J. Katz |date=June 1995 |title=Ideas of Calculus in Islam and India |url=https://www.tandfonline.com/doi/full/10.1080/0025570X.1995.11996307 |journal=[[Mathematics Magazine]] |language=en |volume=68 |issue=3 |pages=163–174 |doi=10.1080/0025570X.1995.11996307 |issn=0025-570X |jstor=2691411}}</ref>  [[Parameshvara]] (1380–1460), presents a case of the Mean Value theorem in his commentaries on [[Govindasvāmi]] and [[Bhāskara II]].<ref>J. J. O'Connor and E. F. Robertson (2000). [https://mathshistory.st-andrews.ac.uk/Biographies/Paramesvara/ Paramesvara], ''[[MacTutor History of Mathematics archive]]''.</ref> The ''[[Yuktibhāṣā]]''  was written by [[Jyeshtadeva]] in 1530.<ref name="gybrima">{{cite book |last=Sarma |first=K. V. |author-link=K. V. Sarma |url=https://www.springer.com/math/history+of+mathematics/book/978-1-84882-072-2 |title=Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva |last2=Ramasubramanian |first2=K. |last3=Srinivas |first3=M. D. |last4=Sriram |first4=M. S. |date=2008 |publisher=Springer (jointly with Hindustan Book Agency, New Delhi) |isbn=978-1-84882-072-2 |edition=1st |series=Sources and Studies in the History of Mathematics and Physical Sciences |volume=I-II |pages=LXVIII, 1084 |bibcode=2008rma..book.....S |access-date=17 December 2009}}</ref>