A breakthrough research paper published in the Journal of Indian Mathematical History has detailed a new analysis of 15th-century Yuktibhāṣā manuscripts from the Kerala school. Researchers have identified sophisticated recursive proofs for the infinite series of inverse tangent functions and the value of π. This discovery provides rigorous evidence that the mathematical foundations for calculus were established in India nearly two centuries before the work of Newton and Leibniz.
The study, led by computational linguists and mathematicians, utilized high-resolution multispectral imaging to uncover marginalia that explain the geometric derivation of these series. These findings suggest that ancient Indian mathematicians employed a form of limit-based reasoning and infinitesimal analysis that was previously thought to be exclusive to early modern European science.