The school flourished between the 14th and 16th centuries and its original discoveries seem to have ended with Narayana Bhattathiri (1559–1632).

In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts.

It does not appear, however, that either Islamic or Indian mathematicians saw the necessity of connecting some of the disparate ideas that we include under the name calculus.

[5][6] The Kerala school has made a number of contributions to the fields of infinite series and calculus.

[1] They used this to discover a semi-rigorous proof of the result: for large n. They applied ideas from (what was to become) differential and integral calculus to obtain (Taylor–Maclaurin) infinite series for

The Kerala school made use of the rectification (computation of length) of the arc of a circle to give a proof of these results.

In 1825 John Warren published a memoir on the division of time in southern India,[10] called the Kala Sankalita, which briefly mentions the discovery of infinite series by Kerala astronomers.

The works of the Kerala school were first written up for the Western world by Englishman C. M. Whish in 1835.

[11] However, Whish's results were almost completely neglected until over a century later, when the discoveries of the Kerala school were investigated again by C. T. Rajagopal and his associates.

[15][16] In 1972 K. V. Sarma published his A History of the Kerala School of Hindu Astronomy which described features of the School such as the continuity of knowledge transmission from the 13th to the 17th century: Govinda Bhattathiri to Parameshvara to Damodara to Nilakantha Somayaji to Jyesthadeva to Acyuta Pisarati.

Transmission from teacher to pupil conserved knowledge in "a practical, demonstrative discipline like astronomy at a time when there was not a proliferation of printed books and public schools."

[17] A. K. Bag suggested in 1979 that knowledge of these results might have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionaries.

[20] According to David Bressoud, "there is no evidence that the Indian work of series was known beyond India, or even outside of Kerala, until the nineteenth century".

[22] Both Indian and Arab scholars made discoveries before the 17th century that are now considered a part of calculus.

[9] According to Katz, they were yet to "combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, and turn calculus into the great problem-solving tool we have today", like Newton and Leibniz.

[9] The intellectual careers of both Newton and Leibniz are well documented and there is no indication of their work not being their own;[9] however, it is not known with certainty whether the immediate predecessors of Newton and Leibniz, "including, in particular, Fermat and Roberval, learned of some of the ideas of the Islamic and Indian mathematicians through sources of which we are not now aware".