Jyesthadeva

Jyesthadeva (* around 1500 in Kerala , † around 1575 in Kerala) was an Indian mathematician and astronomer.

Jyesthadeva belonged to the Kerala school of mathematicians and astronomers, which also included Madhava (1350-1425), Parameshvara (around 1370-1460) and Nilakantha Somayaji (1444-1544), on which he built. Like Nilakantha, he was a disciple of Damodara, the son of Parameshvara. He was among the Nambudiri - Brahmins .

He is known for the astronomical treatise Yutikbhasa (also called Gaṇitanyāyasaṅgraha), which is based in particular on the Tantrasamgraha of Nilakantha (it was completed in 1501). It deals with mathematical astronomy (such as the movement of planets, the sun and moon, eclipses, the rising and setting times of the celestial bodies), in the manner of Tycho Brahe in Europe, and is written in Malayalam , a local language in Kerala. It is dated around 1550.

Of particular importance is the presentation of evidence for mathematical theorems, which is unusual for Indian texts. It was probably written with the intention of recording the evidence for Nilakantha's text, thus showing that the concept of evidence was well known in Indian mathematics.

Of particular interest are series developments for arctangent, sine and cosine (corresponding to Maclaurin's series ), which Madhava was familiar with, but which were only discovered in Europe by James Gregory and Isaac Newton over 250 years after Madhava. Among other things, Madhava achieved precise values ​​for pi and values ​​for sine tables. Because of these infinite series (the first such except the geometric series ), the mathematicians of this school have also been classified among the founders of analysis, and there has been speculation about a possible spread of the results in the West via merchants or Jesuit missionaries. But there is no evidence of this. Even within India, the Kerala school was isolated, partly because of language differences. Sanskrit was traditionally used in other Indian mathematical texts outside the Kerala School. The Yutikbhasa does not use a verse form for the text, contrary to tradition (also in Kerala).

There are also further mathematical advances in the Yutikbhasa such as the first convergence tests (before Augustin-Louis Cauchy ).

The first references to the Yutikbhasa and its importance come from the English administrator and Malayalam specialist Charles Matthew Whish (1794-1833), who published it in 1834 in the Transactions of the Royal Asiatic Society.

One of Jyesthadeva's disciples was Achyuta Pisharati (around 1550-1621).

literature

• KV Sarma Yuktibhāṣā of Jyeṣṭhadeva: A book of rationales in Indin mathematics and astronomy - an analytical appraisal , Indian Journal of History of Science, Volume 26, 1991, 185-207
• KV Sarma, K. Ramasubramanian, MD Srinivas, MS Sriram Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva. Sources and Studies in the History of Mathematics and Physical Sciences , Springer Verlag 2008 (in Malayalam and English with commentary)
  • Previously there was an edition of the text in Malayalam with commentary by Ramavarma Thampuran and Akhileswara Aiyar as early as 1948
• KV Sarma A history of the Kerala school of Hindu astronomy (in perspective) , Vishveshvaranand Indological series 55, Vishveshvaranand Institute of Sanskrit & Indological Studies, Hoshiarpur, Panjab University, 1972
• PP Divakaran The first textbook of calculus: Yutikbhasa , Journal of Indian Philosophy, Volume 35, 2007, pp. 417-443

Web links

• John J. O'Connor, Edmund F. Robertson :  Jyesthadeva. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Whish: 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 , Transactions of the Royal Asiatic Society of Great Britain and Ireland (Royal Asiatic Society of Great Britain and Ireland), Volume 3, 1834, pp. 509-523