Height of the Kerala School (jan 1, 1300 – jan 1, 1500)

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The Kerala School of Astronomy and Mathematics in Kerala, India, flourished between the 14th and 16th centuries. The Kerala school independently created a number of important mathematics concepts. Among their most important results were series expansions for trigonometric functions. The theorems were initially stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided in the 16th & 17th centuries. 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, some sources believe that they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala.The Kerala school was well known in the 15th and 16th centuries, during the period of the first contact with European navigators. This region was a major center for maritime trade, and a number of Jesuit missionaries and traders were active in this region. Given the fame of the Kerala school, and the interest shown by some of the Jesuit groups during this period in local scholarship, some scholars have suggested that the writings of the Kerala school may have also been transmitted to Europe around this time, and may have had an influence on later European developments in analysis and calculus. An 1834 article by Charles Matthew Whish was the first to draw attention to the priority of the Kerala school over Newton in discovering the Fluxion, Newton's name for differentials. Modern scholars have now completed much analysis of the works of the Kerala School.

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