The history and historiography of the discovery of calculus in India

Abstract

Weaving through the emergence and convergence of various mathematical ideas that led towards the discovery of calculus in India provides an enthralling experience for aficionados of mathematics and its diverse history. This article attempts to briefly capture some of the milestones in the journey made by Indian mathematicians through two eras that paved the way for the discovery of infinite series for $\pi$ and some of the trigonometric functions in India around the middle of the 14th century. In the first part we shall discuss the developments during what may be called the classical period, starting with the work of Āryabhaṭa (c. 499 CE) and extending up to the work Nārāyaṇa Paṇḍita (c. 1350). The work of the Kerala School starting with Mādhava of Saṅgamagrāma (c. 1340), which has a more direct bearing on calculus, will be dealt with in the second part. The third part recounts the story of the 19th century European discovery of infinite series in India which seems to have struck a wrong note among the targeted audience in Europe with a serious cascading effect.