The Kerala school of astronomy and mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently created a number of important mathematics concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (c.1500-c.1610), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha.
Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala.
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... to Europe through the trade route from Kerala by traders and Jesuit missionaries ... Kerala was in continuous contact with China and Arabia, and Europe ... Indian work of series was known beyond India, or even outside of Kerala, until the nineteenth century." ...
... The Kerala school of astronomy and mathematics flourished for at least two centuries beyond Madhava ... The group also did much other work in astronomy indeed many more pages are developed to astronomical computations than are for discussing analysis related results ... The Kerala school also contributed much to linguistics (the relation between language and mathematics is an ancient Indian tradition, see Katyayana) ...
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