Jyeṣṭhadeva

{{Short description|Indian scientist and astronomer-mathematician (1500–1575)}} {{Use British English|date=May 2020}} {{Use dmy dates|date=April 2026}} {{Infobox person | name = Jyeṣṭhadeva | image = | alt = | caption = | birth_name = | birth_date = {{circa|1500}} | birth_place = | death_date = {{circa}} {{Death year and age|1575|1500}} | death_place = | body_discovered = | death_cause = | resting_place = | resting_place_coordinates =  | citizenship = | other_names = | known_for = Authorship of Yuktibhāṣā | education = | alma_mater = | employer = | notable_works = Yuktibhāṣā, Drkkarana | occupation = Astronomer-mathematician | years_active = | height = | title = | term = | predecessor = | successor = | political_party = | opponents = | boards = | spouse = | partner = | children = | parents = | relatives = Parangngottu (Sanskritised as Parakroda) family | callsign = | awards = | signature = | signature_alt = | website = | footnotes = Pupil of Damodara, contemporary of Nilakantha Somayaji, teacher of Achyuta Pisharati }}

'''Jyeṣṭhadeva''' ({{circa|1500}}{{snd}}{{circa|1575}})<ref name="Sarma">{{cite journal|last=K.V. Sarma|author-link=K.V. Sarma|date=1991 |title=Yuktibhāṣā of Jyeṣṭhadeva: A book of rationales in Indin mathematics and astronomy – an analytical appraisal |journal=Indian Journal of History of Science |volume=26 |issue=2 |pages=185–207 |url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005ac0_185.pdf |access-date=28 January 2010 |url-status=dead |archive-url=https://web.archive.org/web/20140912165846/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005ac0_185.pdf |archive-date=12 September 2014 }}</ref><ref>{{Cite web|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Jyesthadeva.html|title = Jyesthadeva - Biography}}</ref> was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama ({{circa|1350}}{{snd}}{{circa|1425}}). He is best known as the author of the ''Yuktibhāṣā'', a commentary in Malayalam of the treatise ''Tantrasamgraha'' by Nilakantha Somayaji. In the ''Yuktibhāṣā'', Jyeṣṭhadeva gave complete proofs and rationales for the statements in ''Tantrasamgraha'', which was unusual for traditional Indian mathematicians of the time. The ''Yuktibhāṣā'' is now believed to contain derivations of Taylor and infinite series expansions for certain trigonometric functions.<ref>{{Cite web |title=Madhava - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ |access-date=2025-02-18 |website=Maths History |language=en}}</ref><ref name="charles">{{Citation | author =Charles Whish | author-link =C.M. Whish | date = 1834 | title = On the Hindu Quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, the Tantra Sahgraham, Yucti Bhasha, Carana Padhati and Sadratnamala | journal = Transactions of the Royal Asiatic Society of Great Britain and Ireland | doi=10.1017/S0950473700001221 | volume=3 | issue=3 | pages=509–523 | jstor=25581775 | url =https://zenodo.org/record/2223599 | doi-access =free }}</ref> However, it did not combine several ideas under the unifying concepts of the derivative and the integral, show the connection between the two, or turn calculus into the powerful problem-solving tool we have today.<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|url-access=subscription }}</ref><ref>{{Harv|Bressoud|2002|p=12}} Quote: "There is no evidence that the Indian work on series was known beyond India, or even outside Kerala, until the nineteenth century. Gold and Pingree assert that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use."</ref> Jyeṣṭhadeva also authored ''Drk-karana,'' a treatise on astronomical observations.<ref>{{cite web|url=http://www-history.mcs.st-and.ac.uk/Biographies/Jyesthadeva.html|title=Jyesthadeva |author1=J J O'Connor |author2=E F Robertson |date=November 2000 |publisher=School of Mathematics and Statistics University of St Andrews, Scotland |access-date=28 January 2010}}</ref>

==Life period of Jyeṣṭhadeva== There are a few references to Jyeṣṭhadeva scattered across several old manuscripts.<ref name="Sarma"/> From these manuscripts, one can deduce a few bare facts about the life of Jyeṣṭhadeva. He was a Nambudiri belonging to the Parangngottu family (Sanskritised as ''Parakroda'') born about the year 1500 CE. He was a pupil of Damodara and a younger contemporary of Nilakantha Somayaji. Acyuta Piṣāraṭi was a pupil of Jyeṣṭhadeva. In the concluding verse of his work ''Uparagakriyakrama'', completed in 1592, Piṣāraṭi referred to Jyeṣṭhadeva as his "aged benign teacher".{{Citation needed|date=March 2026}} From a few references in ''Drk-karana'', a work believed to be of Jyeṣṭhadeva, one may conclude that Jyeṣṭhadeva lived up to about 1610 CE.{{Inconsistent|date=March 2026}} According to K. V. Sarma, the name "Jyeṣṭhadeva" is most probably the Sanskritised form of his personal name in the local language Malayalam.<ref>{{cite book |last1=K. V. Sarma |title=A history of the Kerala school of Hindu astronomy (in perspective) |date=1972 |publisher=Vishveshvaranand Institute of Sanskrit & Indological Studies |location=Hoshiarpur, Panjab University |page=59|bibcode=1972hksh.book.....S }}</ref>

Parangngottu, the family house of Jyeṣṭhadeva, still exists in the vicinity of Trikkandiyur and Alathiyur.<ref name="Sarma"/> There are also several legends connected with members of the Parangngottu family.{{Example needed|date=March 2026}}

==Mathematical lineage== Little is known about the mathematical traditions in Kerala prior to Madhava of Sangamagrama. Madhava taught Parameshvara Nambudiri, who taught Damodara. Damodara taught Nilakantha Somayaji and Jyeṣṭhadeva. Jyeṣṭhadeva taught Acyuta Piṣāraṭi, who taught Melpathur Narayana Bhattathiri.

== Jyeṣṭhadeva's works == {{main|Yuktibhāṣā|Ganita-yukti-bhasa}} thumb|420x420px|Pages from the ''Yuktibhasa'' c.1530 Jyeṣṭhadeva is only known to have composed two works, namely the ''Yuktibhāṣā'' and ''Drk-karana''. The former is commentary on ''Tantrasamgraha'' by Nilakantha Somayaji and the latter is a treatise on astronomical computations.

Three factors make the ''Yuktibhāṣā'' unique in the history of the development of mathematical thinking in the Indian subcontinent: * It is composed in the spoken language of the local people, namely, the Malayalam language. This is in contrast to the centuries-old Indian tradition of composing scholarly works in the Sanskrit language, which was the language of the learned. * The work is in prose, also in contrast to the prevailing style of writing even technical manuals in verse. All the other notable works of the Kerala school are in verse. * Most importantly, the ''Yuktibhāṣā'' was composed intentionally as a manual of proofs. The very purpose of writing the book was to record in full detail the rationales of the various results discovered by mathematicians-astronomers of the Kerala school, especially of Somayaji. This book therefore demonstrates that the concept of proof was known to at least some Indian mathematical traditions.

==References== {{Reflist}}

==Sources== *{{Citation | last=Bressoud | first=David | author-link=David Bressoud | title=Was Calculus Invented in India? | journal=The College Mathematics Journal | volume=33 | issue=1 | year=2002 | pages=2–13 | doi=10.2307/1558972 | jstor=1558972 }}

==Further references== * Details on the English translation of Yuktibhāṣā by K. V. Sarma: {{cite book|last=Sarma, K.V., Ramasubramanian, K., Srinivas, M.D., Sriram, M.S. |title=Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyeṣṭhadeva: Volume I: Mathematics, Volume II: Astronomy|publisher=Springer jointly with Hindustan Book Agency, New Delhi, India|date=2008|series=Sources and Studies in the History of Mathematics and Physical Sciences |isbn=978-1-84882-072-2|url=https://www.springer.com/math/history+of+mathematics/book/978-1-84882-072-2}} (This is a critical translation of the original Malayalam text by K.V. Sarma with explanatory notes by K. Ramasubramanian, M.D. Srinivas and M.S. Sriram.) * For a review of the English translation of Yuktibhāṣā: {{cite journal|last=Homer S. White|date=17 July 2009|title=Ganita-Yukti-Bhāsā (Rationales in Mathematical Astronomy) of Jyesthadeva|journal=MAA Reviews|publisher=The Mathematical Association of America |url=http://www.maa.org/maa%20reviews/7302.html|access-date=30 January 2010}} {{Dead link|date=October 2010|bot=H3llBot}} * {{cite journal|last=R.C. Gupta|date=1973|title=Addition and subtraction theorems for the sine and the cosine functions in medieval india|journal=Indian Journal of History of Science|volume=9|issue=2|pages=164–177|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b61_164.pdf|url-status=dead|archive-url=https://web.archive.org/web/20141129080011/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b61_164.pdf|archive-date=29 November 2014|df=dmy-all}} * {{cite book|last=K. V. Sarma|author-link=K. V. Sarma|title= A history of the Kerala school of Hindu astronomy (in perspective)|publisher=Vishveshvaranand Institute of Sanskrit & Indological Studies, Hoshiarpur, Panjab University|date=1972|series=Vishveshvaranand Indological series|volume=55|bibcode=1972hksh.book.....S}} * {{cite journal|last=K.V. Sarma|author-link=K.V. Sarma|title=Tradition of Aryabhatiya in Kerala : Revision of planetary parameters|journal=Indian Journal of History of Science|volume=12|issue=2|pages=194–199|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af8_194.pdf|access-date=30 January 2010|url-status=dead|archive-url=https://web.archive.org/web/20141129075805/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af8_194.pdf|archive-date=29 November 2014|df=dmy-all}} * {{cite book|last=George Gheverghese Joseph|title=The Crest of the Peacock: The Non-European Roots of Mathematics|publisher=Princeton University Press|date=2000|pages=[https://archive.org/details/crestofpeacockno00jose/page/416 416]|isbn=978-0-691-00659-8|url=https://archive.org/details/crestofpeacockno00jose/page/416|df=dmy-all|url-access=registration}} * {{cite book|last=Plofker|first=Kim|author-link=Kim Plofker|title=Mathematics in India|title-link=Mathematics in India (book)|publisher=Princeton University Press|date=2009|pages=219–254|chapter=7 The school of Madhava in Kerala|isbn=9780691120676|chapter-url=http://press.princeton.edu/titles/8835.html}} * For a modern explanation of Jyeṣṭhadeva's proof of the power series expansion of the arctangent function: {{cite book|last=Victor J. Katz|title=A history of mathematics: An introduction|publisher=Addison Wesley|edition=3|pages=450–455|chapter=12|year=2009|isbn=978-0-321-38700-4|chapter-url=http://www.maa.org/maa%20reviews/11111.html}}

{{Kerala School}} {{Indian mathematics}} {{Scientific Research in Kerala |state=collapsed}} {{Malayalam Literature |state=collapsed}} {{Authority control}}

{{DEFAULTSORT:Jyesthadeva}} Category:Indian Hindus Category:16th-century Indian astronomers Category:1500s births Category:1575 deaths Category:People from Malappuram district Category:Malayali people Category:Scientists of the Kerala school of astronomy and mathematics Category:16th-century Indian mathematicians