Editing History of science (section)

===India===
{{Further|History of science and technology in the Indian subcontinent}}

====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>

==== Astronomy ====
{{Main|Indian astronomy|}}
[[File:Page_from_Lilavati,_the_first_volume_of_Siddhānta_Śiromaṇī._Use_of_the_Pythagorean_theorem_in_the_corner.jpg|thumb|Copy of the [[Siddhānta Shiromani|''Siddhānta Śiromaṇī''.]] c. 1650 ]]
The first textual mention of astronomical concepts comes from the [[Veda]]s, religious literature of India.<ref name="Sarma-Ast-Ind">{{cite encyclopedia|last =Sarma|first = K.V.| title=Astronomy in India |date = 2008 |encyclopedia = Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures|editor-last = Selin|editor-first = Helaine|doi= 10.1007/978-1-4020-4425-0_9554|publisher = Springer, Dordrecht|isbn = 978-1-4020-4425-0|pages = 317–321}}</ref> According to Sarma (2008): "One finds in the [[Rigveda]] intelligent speculations about the genesis of the universe from nonexistence, the configuration of the universe, the [[Spherical Earth|spherical self-supporting earth]], and the year of 360 days divided into 12 equal parts of 30 days each with a periodical intercalary month.".<ref name="Sarma-Ast-Ind" />

The first 12 chapters of the ''[[Siddhānta Shiromani|Siddhanta Shiromani]]'', written by [[Bhāskara II|Bhāskara]] in the 12th century, cover topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; syzygies; lunar eclipses; solar eclipses; latitudes of the planets; risings and settings; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; and the patas of the sun and moon. The 13 chapters of the second part cover the nature of the sphere, as well as significant astronomical and trigonometric calculations based on it.

In the ''[[Tantrasangraha]]'' treatise, [[Nilakantha Somayaji]]'s updated the Aryabhatan model for the interior planets, Mercury, and Venus and the equation that he specified for the center of these planets was more accurate than the ones in European or Islamic astronomy until the time of [[Johannes Kepler]] in the 17th century.<ref name="joseph2011j">{{cite book |last=Joseph |first=George G. |title=The Crest of the Peacock: Non-European Roots of Mathematics |date=2011 |publisher=Princeton University Press |isbn=978-0691135267 |edition=3rd |location=New Jersey |pages=418–449 |chapter=A Passage to Infinity: The Kerala Episode}}</ref> [[Jai Singh II]] of [[Kingdom of Amber|Jaipur]] constructed five [[Observatory|observatories]] called [[Jantar Mantar]]s in total, in [[Jantar Mantar, New Delhi|New Delhi]], [[Jantar Mantar (Jaipur)|Jaipur]], [[Jantar Mantar, Ujjain|Ujjain]], [[Mathura, Uttar Pradesh|Mathura]] and [[Jantar Mantar, Varanasi|Varanasi]]; they were completed between 1724 and 1735.<ref>{{Cite web |title=The Observatory Sites |url=http://www.jantarmantar.org/learn/observatories/sites/index.html |access-date=2024-01-29}}</ref>

====Grammar====
Some of the earliest linguistic activities can be found in [[Iron Age India]] (1st millennium BCE) with the analysis of [[Sanskrit]] for the purpose of the correct recitation and interpretation of [[Vedas|Vedic]] texts. The most notable grammarian of Sanskrit was {{IAST|[[Pāṇini]]}} (c. 520–460 BCE), whose grammar formulates close to 4,000 rules for Sanskrit. Inherent in his analytic approach are the concepts of the [[phoneme]], the [[morpheme]] and the [[root]]. The [[Tolkāppiyam]] text, composed in the early centuries of the common era,<ref name= "weiss2009d" >{{cite book | last = Weiss | first = Richard S. | year = 2009 | chapter = The invasion of utopia: The corruption of Siddha medicine by Ayurveda | title = Recipes for Immortality: Healing, Religion, and Community in South India | pages = 79–106 | publisher = Oxford University Press | location = New York, New York | isbn = 978-0195335231}}</ref> is a comprehensive text on Tamil grammar, which includes sutras on orthography, phonology, etymology, morphology, semantics, prosody, sentence structure and the significance of context in language.

====Medicine====
[[File:The_Susruta-Samhita_or_Sahottara-Tantra_(A_Treatise_on_Ayurvedic_Medicine)_LACMA_M.87.271a-g_(1_of_8).jpg|thumb|220x220px|Palm leaves of the ''[[Sushruta Samhita]]'' or ''Sahottara-Tantra'' from [[Nepal]],]]
Findings from [[Neolithic]] graveyards in what is now Pakistan show evidence of proto-dentistry among an early farming culture.<ref>{{cite journal|last1=Coppa|first1=A.|title=Early Neolithic tradition of dentistry: Flint tips were surprisingly effective for drilling tooth enamel in a prehistoric population |journal=Nature |volume=440 |date=6 April 2006 |doi=10.1038/440755a |pages=755–756 |pmid=16598247 |issue=7085 |bibcode=2006Natur.440..755C |s2cid=6787162|display-authors=etal}}</ref> The ancient text [[Sushruta Samhita|Suśrutasamhitā]] of [[Sushruta|Suśruta]] describes procedures on various forms of surgery, including [[rhinoplasty]], the repair of torn ear lobes, perineal [[lithotomy]], cataract surgery, and several other excisions and other surgical procedures.<ref>E. Schultheisz (1981), History of Physiology, Pergamon Press, {{ISBN|978-0080273426}}, page 60-61, Quote: "(...) the Charaka Samhita and the Susruta Samhita, both being recensions of two ancient traditions of the Hindu medicine".</ref><ref>Wendy Doniger (2014), On Hinduism, Oxford University Press, {{ISBN|978-0199360079}}, page 79;

Sarah Boslaugh (2007), Encyclopedia of Epidemiology, Volume 1, SAGE Publications, {{ISBN|978-1412928168}}, page 547, '''Quote''': "The Hindu text known as Sushruta Samhita is possibly the earliest effort to classify diseases and injuries"</ref> The ''[[Charaka Samhita]]'' of [[Charaka]] describes ancient theories on human body, [[etiology]], [[Symptom|symptomology]] and [[Pharmacology|therapeutics]] for a wide range of diseases.<ref name="Glucklichtsov141">{{cite book |author=Ariel Glucklich |url=https://archive.org/details/stridesvishnuhin00gluc_414 |title=The Strides of Vishnu: Hindu Culture in Historical Perspective |publisher=Oxford University Press, USA |year=2008 |isbn=978-0-19-531405-2 |pages=[https://archive.org/details/stridesvishnuhin00gluc_414/page/n155 141]–142 |url-access=registration}}</ref> It also includes sections on the importance of diet, hygiene, prevention, medical education, and the teamwork of a physician, nurse and patient necessary for recovery to health.<ref name="Svoboda1992">{{cite book |author=Robert Svoboda |title=Ayurveda: Life, Health and Longevity |publisher=Penguin Books |year=1992 |isbn=978-0140193220 |pages=189–190}}</ref><ref name="valiathan1186">MS Valiathan (2009), An Ayurvedic view of life, Current Science, Volume 96, Issue 9, pages 1186-1192</ref><ref>F.A. Hassler, [https://www.jstor.org/stable/1764939 Caraka Samhita], Science, Vol. 22, No. 545, pages 17-18</ref>

==== Politics and state ====
An ancient Indian treatise on [[Public administration|statecraft]], [[economics|economic]] policy and [[military strategy]] by Kautilya<ref>{{cite journal | first=I.W. | last=Mabbett | date=1 April 1964| title=The Date of the Arthaśāstra | journal=Journal of the American Oriental Society | volume=84 | issue=2 | pages=162–169 | doi=10.2307/597102 | jstor=597102 }}<br />{{cite book | last=Trautmann | first=Thomas R. | author-link=Thomas Trautmann | title={{IAST|Kauṭilya}} and the Arthaśāstra: A Statistical Investigation of the Authorship and Evolution of the Text | year=1971 | publisher=Brill | pages=10 | quote =while in his character as author of an ''arthaśāstra'' he is generally referred to by his ''[[gotra]]'' name, {{IAST|Kauṭilya}}.}}</ref> and {{IAST|Viṣhṇugupta}},<ref>Mabbett 1964<br />Trautmann 1971:5 "the very last verse of the work...is the unique instance of the personal name {{IAST|Viṣṇugupta}} rather than the ''[[gotra]]'' name {{IAST|Kauṭilya}} in the ''Arthaśāstra''.</ref> who are traditionally identified with [[Chanakya|{{IAST|Chāṇakya}}]] (c. 350–283 BCE). In this treatise, the behaviors and relationships of the people, the King, the State, the Government Superintendents, Courtiers, Enemies, Invaders, and Corporations are analyzed and documented. [[Roger Boesche]] describes the ''[[Arthashastra|Arthaśāstra]]'' as "a book of political realism, a book analyzing how the political world does work and not very often stating how it ought to work, a book that frequently discloses to a king what calculating and sometimes brutal measures he must carry out to preserve the state and the common good."<ref>{{cite book| author-link= Roger Boesche | last=Boesche | first=Roger | title=The First Great Political Realist: Kautilya and His Arthashastra | year=2002 | publisher=Lexington Books | isbn=978-0-7391-0401-9 | page=17}}</ref>

==== Logic ====
The development of Indian logic dates back to the Chandahsutra of Pingala and ''[[anviksiki]]'' of Medhatithi Gautama (c. 6th century BCE); the [[Vyākaraṇa|Sanskrit grammar]] rules of [[Pāṇini]] (c. 5th century BCE); the [[Vaisheshika]] school's analysis of [[atomism]] (c. 6th century BCE to 2nd century BCE); the analysis of [[inference]] by [[Nyāya Sūtras|Gotama]] (c. 6th century BCE to 2nd century CE), founder of the [[Nyaya]] school of [[Hindu philosophy]]; and the [[tetralemma]] of [[Nagarjuna]] (c. 2nd century CE).

[[Indian philosophy|Indian]] logic stands as one of the three original traditions of [[logic]], alongside the [[Organon|Greek]] and the [[Chinese logic]]. The Indian tradition continued to develop through early to modern times, in the form of the [[Navya-Nyāya]] school of logic.

In the 2nd century, the [[Buddhist philosophy|Buddhist]] philosopher [[Nagarjuna]] refined the ''Catuskoti'' form of logic. The Catuskoti is also often glossed ''[[Tetralemma]]'' (Greek)  which is the name for a largely comparable, but not equatable, 'four corner argument' within the tradition of [[Classical logic]].

Navya-Nyāya developed a sophisticated language and conceptual scheme that allowed it to raise, analyse, and solve problems in logic and epistemology. It systematised all the Nyāya concepts into four main categories: sense or perception (pratyakşa), inference (anumāna), comparison or similarity ([[upamāna]]), and testimony (sound or word; śabda).