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Yuktibhāṣā (Malayalam: യുക്തിഭാഷ, lit. 'Rationale'), also known as Gaṇita-yukti-bhāṣā:xxi and Gaṇitanyāyasaṅgraha (Compendium of Astronomical Rationale), is a major treatise on mathematics and astronomy, written by the India n astronomer Jyesthadeva of the Kerala school of mathematics around 1530. The treatise, written in Malayalam, is a consolidation of the discoveries by Madhava of Sangamagrama, Nilakantha Somayaji, Parameshvara, Jyeshtadeva, Achyuta Pisharati, and other astronomer-mathematicians of the Kerala school. It also exists in a Sanskrit version, with unclear author and date, composed as a rough translation of the Malayalam original. The work contains proofs and derivations of the theorems that it presents. Modern historians used to assert, based on the works of Indian mathematics that first became available, that early Indian scholars in astronomy and computation lacked in proofs, but Yuktibhāṣā demonstrates otherwise. Some of its important topics include the infinite series expansions of functions; power series, including of π and π/4; trigonometric series of sine, cosine, and arctangent; Taylor series, including second and third order approximations of sine and cosine; radii, diameters and circumferences; and tests of convergence. Yuktibhāṣā mainly gives rationale for the results in Nilakantha's Tantra Samgraha. It is considered an early text on the ideas of calculus, predating Newton and Leibniz by centuries. The treatise was largely unnoticed outside India, as it was written in the local language of Malayalam. In modern times, due to wider international cooperation in mathematics, the wider world has taken notice of the work. For example, both Oxford University and the Royal Society of Great Britain have given attribution to pioneering mathematical theorems of Indian origin that predate their Western counterparts.
References
- K V Sarma; S Hariharan (1991). "Yuktibhāṣā of Jyeṣṭhadeva: A book on rationales in Indian Mathematics and Astronomy: An analytic appraisal". Indian Journal of History of Science 26 (2). http://www.new.dli.ernet.in/insa/INSA_1/20005ac0_185.pdf. Retrieved 9 July 2006.
- Sarma, K.V.; Ramasubramanian, K.; Srinivas, M.D.; Sriram, M.S. (2008). Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva. Sources and Studies in the History of Mathematics and Physical Sciences. I-II (1st ed.). Springer (jointly with Hindustan Book Agency, New Delhi). pp. LXVIII, 1084. ISBN 978-1-84882-072-2. Bibcode: 2008rma..book.....S. https://www.springer.com/math/history+of+mathematics/book/978-1-84882-072-2. Retrieved 17 December 2009.
- For more details on contents see Kinokuniya DataBase: "Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva". http://bookwebpro.kinokuniya.co.jp/booksea.cgi?ISBN=1848820720http://www.buscalibros.cl/libro.php?libro=2104208.
- "The Yuktibhasa Calculus Text". The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala. Dr Sarada Rajeev. http://www.canisius.edu/topos/archives/rajeev2.pdf.
- "The Kerala School, European Mathematics and Navigation". Indian Mathemematics. D.P. Agrawal – Infinity Foundation. http://www.infinityfoundation.com/mandala/t_es/t_es_agraw_kerala.htm.
- "Science and technology in free India". Government of Kerala – Kerala Call, September 2004. Prof.C.G.Ramachandran Nair. http://www.kerala.gov.in/keralcallsep04/p22-24.pdf.
- "Science and Mathematics in India". South Asian History. India Resources. http://india_resource.tripod.com/mathematics.htm.
- Divakaran, P. P. (2007). "The First Textbook of Calculus: "Yuktibhāṣā"". Journal of Indian Philosophy 35 (5/6): 417–443. doi:10.1007/s10781-007-9029-1. ISSN 0022-1791. https://dx.doi.org/10.1007%2Fs10781-007-9029-1
- Yuktibhâsâ, Part I (ed) with notes by Ramavarma (Maru) Thampuran and A. R. Akhileswara Aiyer, Magalodayam Ltd., Trichur, Kerala, 1123 Malayalam Era, 1948 CE.
- See publishers's (Springer's) web page on the book: Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva. ISBN 9781848820722. https://www.springer.com/mathematics/history+of+mathematics/book/978-1-84882-072-2. Retrieved 29 April 2010.
- Sarma, K.V. (2009) (in ml, en). Ganita Yuktibhasa. III. Indian Institute of Advanced Study, Shimla, India. ISBN 978-81-7986-052-6. http://www.iias.org/p_ganita_yuktibhasa_volume-III.html. Retrieved 16 December 2009.
- K.V. Sarma (2004). Ganita Yuktibhasa (Volume III). Shimla: Indian Institute of Advanced Study. ISBN 81-7986-052-3.
- Publisher's (Indian Institute of Advanced Study) web page on the book:"Ganita Yuktibhasa by K.V. Sarma". http://www.iias.org/p_ganita_yuktibhasa_volume-III.html.
- For a review of Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva by Mathematical Association of America see : Homer S. White (2009-07-17). "Ganita-Yukti-Bhāsā (Rationales in Mathematical Astronomy) of Jyesthadeva". The Mathematical Association of America. https://www.maa.org/press/maa-reviews/ganita-yukti-bh-s-rationales-in-mathematical-astronomy-of-jyesthadeva.
- Sayahna Foundation (2020-11-20). "Yukthibhasha digital edition". https://books.sayahna.org/ml/pdf/yukthibhasha.pdf.
