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{{Use dmy dates|date=November 2014}}
{{infobox person
| name = Jyeṣṭhadeva
| image =
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| birth_name =
| birth_date = {{circa|1500}} CE
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| death_date = {{circa|1575}} CE
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| nationality = Indian
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| other_names =
| known_for = Authorship of [[Yuktibhāṣā]]
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| notable works = [[Yuktibhāṣā]], Drkkarana
| occupation = Astronomer-mathematician
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| relations = Parangngottu (Sanskritised as Parakroda) family
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| footnotes = Pupil of [[Damodara]], contemporary of [[Nilakantha Somayaji]], teacher of [[Achyuta Pisharati]]
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}}

'''Jyeṣṭhadeva''' ([[Malayalam]]: ജ്യേഷ്ഠദേവൻ) ({{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>http://www-history.mcs.st-andrews.ac.uk/Biographies/Jyesthadeva.html</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 ''[[Yuktibhāṣā]]'', a commentary in [[Malayalam]] of [[Tantrasamgraha]] by [[Nilakantha Somayaji]] (1444–1544). In [[Yuktibhāṣā]], Jyeṣṭhadeva had given complete [[Mathematical proof|proofs]] and rationale of the statements in [[Tantrasamgraha]]. This was unusual for traditional [[Indian mathematicians]] of the time. The [[Yuktibhāṣā]] is now believed to contain the essential elements of the calculus and one of the earliest treatise on the subject.
<ref>
{{cite journal| author1=C. K. Raju | title=Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhāṣā
|url=http://ckraju.net/papers/Hawaii.pdf
| journal=Philosophy East & West
| volume=51
| issue=3
| date=2001
| pages=325–362
| doi=10.1353/pew.2001.0045
| access-date=2020-02-11
}}
</ref><ref>{{cite journal|last=P.P. Divakaran|date=December 2007|title=The First Textbook of Calculus: Yuktibhāṣā|journal=Journal of Indian Philosophy|publisher=[[Springer Netherlands]]|volume=35|issue=5–6|pages=417–443|issn=0022-1791 |doi=10.1007/s10781-007-9029-1|first1=P. P.}}</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 (Sanskrtised as ''Parakroda'') born about the year 1500 CE. He was a pupil of [[Damodara]] and a younger contemporary of [[Nilakantha Somayaji]]. [[Achyuta Pisharati]] was a pupil of Jyeṣṭhadeva. In the concluding verse of his work titled ''Uparagakriyakrama'', completed in 1592, [[Achyuta Pisharati]] has referred to Jyeṣṭhadeva as his ''aged benign teacher''. From a few references in ''Drkkarana'', a work believed to be of Jyeṣṭhadeva, one may conclude that Jyeṣṭhadeva lived up to about 1610 CE.

Parangngottu, the family house of Jyeṣṭhadeva, still exists in the vicinity of Trikkandiyur and Alathiyur.<ref name="Sarma"/> There are also several [[Kottarathil Sankunni|legends]] connected with members of Parangngottu family.

==Mathematical lineage==
Little is known about the mathematical traditions in [[Kerala]] prior to [[Madhava of Sangamagrama]].
[[Paramesvara|Vatasseri Paramesvara]] was a direct disciple of Madhava. [[Damodara]] was a son of [[Paramesvara]]. [[Nilakantha Somayaji]] and Jyeshthadeva were pupils of Damodara. Jyeṣṭhadeva's pupil was [[Achyuta Pisharati]] and [[Melpathur Narayana Bhattathiri]] was [[Achyuta Pisharati]]'s student.

==Jyeshthadeva's works==
{{main|Yuktibhāṣā|Ganita-yukti-bhasa}}

Jyeṣṭhadeva is known to have composed only two works, namely, ''[[Yuktibhāṣā]]'' and ''Drkkarana''.
The former is commentary with rationales of [[Tantrasamgraha]] of [[Nilakantha Somayaji]] and the latter is a treatise on astronomical computations.

Three factors make [[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, again in contrast to the prevailing style of writing even technical manuals in verse. All the other notable works of the [[Kerala school of astronomy and mathematics|Kerala school]] are in verse.
* Most importantly, [[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 [[Nilakantha Somayaji]]. This book is proof enough to establish that the concept of proof was not unknown to Indian mathematical traditions.

==See also==
* [[Kerala school of astronomy and mathematics|Kerala School]]
* [[Indian mathematics]]
* [[Indian mathematicians]]

==References==
{{Reflist}}

==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}}
* {{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|title=Mathematics in India|title-link=Mathematics in India|publisher=Princeton University Press|date=2009|pages=219–254|chapter=7 The school of Madhava in Kerala|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]]|location=2009|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}}

{{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:1500 births]]
[[Category:1575 deaths]]
[[Category:Scientists from Kerala]]
[[Category:People from Malappuram district]]
[[Category:Malayali people]]
[[Category:Kerala school of astronomy and mathematics]]
[[Category:16th-century Indian mathematicians]]
[[Category:Scholars from Kerala]]

Jyeṣṭhadeva - Revision history

>Monkbot at 16:38, 11 January 2021