Jyeṣṭhadeva

Jyeṣṭhadeva ()^[1][2] was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama (). 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.^[3][4] 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.^[5][6] Jyeṣṭhadeva also authored Drk-karana, a treatise on astronomical observations.^[7]

There are a few references to Jyeṣṭhadeva scattered across several old manuscripts. 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". 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. According to K. V. Sarma, the name "Jyeṣṭhadeva" is most probably the Sanskritised form of his personal name in the local language Malayalam.^[8]

Parangngottu, the family house of Jyeṣṭhadeva, still exists in the vicinity of Trikkandiyur and Alathiyur. There are also several legends connected with members of the Parangngottu family.

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 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.

• Kerala School
• Indian mathematics
• Indian mathematicians
• List of astronomers and mathematicians of the Kerala school

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6. ^ 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."
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• Details on the English translation of Yuktibhāṣā by K. V. Sarma: (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:
• For a modern explanation of Jyeṣṭhadeva's proof of the power series expansion of the arctangent function: