Indian literature on Mathematics during 1400-1800 A.D.

Abstract

The available Indian literature on mathematics during 1400-1800 A.D. can be broadly classified into two main categories. In the first category belong the Sanskrit works, or the works written in scripts of the regional Indian languages. Though the scripts are different, the language of these scripts is mainly Sanskrit and bears Indian tradition both in content and character. The major portion of these works are commentaries on the works of Surya Siddhanta, Aryabhatiya, Lilavati, Bijaganita, Siddhanta Siromani, and some other well-known works of the ancient period, and contribute little to the knowledge of mathematics, The commentators of this period were perhaps content with the preservation and transmission of knowledge from one generation to the other. Their studies gave some impetus to the studies of the scholars like Madhava, Paramesvara, Nilakantha, Sankara, Jyesthadeva, Acyuta Pisarati, etc., for about 500 years starting from fourteenth century A.D. These scholars made some break-through by introducing the idea of series in calculating the value of pi, sine-table, discovery of the sine and cosine series and made many other innovations. The second category of mathematical literature constitute the Persian and Arabic works developed mostly under the patronage of the Mughal rulers. These were mainly written for readers of Persian who know no other language and had no access in standard Sanskrit, Persian and Arabic mathematical works. Many standard mathematical works were brought here from outside India. Some scholars tried to translate or write commentaries on the available works without trying to correlate with the available Indian knowledge. A few scholars like Munisvara, Kamalakara, Jagannath Pandit tried to make a synthesis of the available knowledge but their contribution appears to be negligibly small. The real contribution lies in the effort of Raja Jai Singh who used the observatories at Delhi, Jaipur, Mathura, Banaras and Ujjain to prepare accurate astronomical tables. In the paper, an attempt has been made to make analysis of these two categories of mathematical literature in the period.