# Indian Mathematics - Redressing the balance

### Ian G Pearce

### The Classical period: I. Introduction

Following the Bakhshali manuscript (assuming it was composed no later than 200 AD) Indian mathematics suffered a slump, described by L Gurjar as:

This was in part due to massive communication problems, but also undoubtedly to the huge political upheaval that took place between the 2

During this period however the practice of writing

Following the establishment of the 'Gupta dynasty' a period of political stability arose, which doubtlessly contributed to the ascent of a "galaxy" of mathematician-astronomers, led by Aryabhata. These men were, first and foremost, astronomers, but the mathematical requirements of astronomy (and no doubt further interest) led to them developing many areas of mathematics, as such, I will refer to them just as mathematicians. The vast majority of the works of the 'classical period' were however, in effect, Siddhantas.

...A deep and dire degeneration.[LG, P 78]

This was in part due to massive communication problems, but also undoubtedly to the huge political upheaval that took place between the 2

^{nd}and 4^{th}centuries AD, prior to the capturing of power of most of India by the Imperial Guptas.During this period however the practice of writing

*Siddhantas*(astronomical works), which had started around 500 BC, continued. Of the Siddhantas the*Pitamaha Siddhanta*is the oldest (c. 500 BC) and the*Surya Siddhanta*(c. 400 AD, author unknown, influenced Aryabhata) is the best known. The major contribution of these works was the invention of the sine function. R Gupta comments:...Trigonometry based on sine (instead of chord (as in Greek works)) and related functions is another important gift of India to the world of mathematics.[RG2, P 134]

Following the establishment of the 'Gupta dynasty' a period of political stability arose, which doubtlessly contributed to the ascent of a "galaxy" of mathematician-astronomers, led by Aryabhata. These men were, first and foremost, astronomers, but the mathematical requirements of astronomy (and no doubt further interest) led to them developing many areas of mathematics, as such, I will refer to them just as mathematicians. The vast majority of the works of the 'classical period' were however, in effect, Siddhantas.