• DOI:10.1007/978-93-86279-25-5_9
• Corpus ID: 125042994

Proofs in Indian Mathematics

@inproceedings{Srinivas2005ProofsII,
  title={Proofs in Indian Mathematics},
  author={M. D. Srinivas},
  year={2005}
}

• M. Srinivas
• Published 2005
• Mathematics

Contrary to the widespread belief that Indian mathematicians did not present any proofs for their results, it is indeed the case that there is a large body of source-works in the form of commentaries which present detailed demonstrations (referred to as upapatti-s or yukti-s) for the various results enunciated in the major texts of Indian Mathematics and Astronomy. Amongst the published works, the earliest exposition of upapatti-s are to be found in the commentaries of Govindasvāmin (c.800) and Caturveda Pṛthūdakasvāmin (c.860). Then we find very detailed exposition of upapatti-s in the works of Bhaskaracarya II (c.1150). In the medieval period we have the commentaries of Śaṅkara Vāriyar (c.1535), Gaṅeśa Daivajna (c.1545), Kṛṣṅa Daivajna (c.1600) and the famous Malayalam work Yuktibhāṣā of Jyṣṭesthadeva (c.1530), which present detailed upapatti-s. By presenting a few selected examples of upapatti-s, we shall highlight the logical rigour which is characteristic of all the work in Indian Mathematics. We also discuss how the notion of upapatti is perhaps best understood in the larger epistemological perspective provided by Nyāyaśāstra, the Indian School of Logic. This could be of help in explicating some of the important differences between the notion of upapatti and the notion of “proof developed in the Greco-European tradition of Mathematics.