# Indian Mathematics - Redressing the balance

### Ian G Pearce

### Keralese mathematics: I. Introduction

The south western tip of India escaped the majority of the political upheaval, which engulfed the rest of the country, allowing a generally peaceful existence to continue. Thus the pursuit of scientific development was able to continue 'uninterrupted'. It has only recently come to light that mathematics (and astronomy) continued to flourish in this area for several hundred years. Kerala mathematics was strongly influenced by astronomy, but this led to the derivation of mathematical results of huge importance. As a result of the recency of these discoveries it is quite probable that there are still further discoveries of 'Kerala mathematics' to be made, and a full analysis has yet to be carried out. However several findings have already been made that show several major concepts of renaissance European mathematics were first developed in India.

Indeed G Joseph quotes:

The works that have so far been analysed are of such a high level that it is though there may be missing links between the "classical period" and the medieval period of Kerala. There is also interest in the claims that European scholars may have had first hand knowledge of some Kerala mathematics, as the area was a focal point for trading with many parts of the world, including Europe. There is also some evidence of a transfer of technology between Europe and Kerala. I will discuss this issue in a little more depth later.

At this point in time only some interest is being paid to the recent discoveries that have been made, highlighting that in many historical 'circles' Indian developments are still not considered important. A further point of interest is that up to the 10

Bhaskara I is also thought to have possibly been a Keralite.

Of the leading mathematicians of Kerala there is quite possibly more to be discovered but currently there are several whose work is of significant interest.

Indeed G Joseph quotes:

...In Kerala, the period between the 14[GJ, P 287]^{th}and 16^{th}centuries marked a high point in the indigenous development of (astronomy) and mathematics.

The works that have so far been analysed are of such a high level that it is though there may be missing links between the "classical period" and the medieval period of Kerala. There is also interest in the claims that European scholars may have had first hand knowledge of some Kerala mathematics, as the area was a focal point for trading with many parts of the world, including Europe. There is also some evidence of a transfer of technology between Europe and Kerala. I will discuss this issue in a little more depth later.

At this point in time only some interest is being paid to the recent discoveries that have been made, highlighting that in many historical 'circles' Indian developments are still not considered important. A further point of interest is that up to the 10

^{th}century there was virtually no mathematical activity of note in the south of India. There are four areas in the south of the country - including Kerala in the south west corner, and with the exception of Mahavira (resident of Karnataka area) there was no mathematical output of significance until the 11^{th}-12^{th}century early Kerala literature. There are however impressions that Aryabhata I was a Keralite, and indeed, if this were true, then in the words of K Rajagopalan:...Kerala would find a prominent place in the mathematical map of "our" country.[KR1, P 81]

Bhaskara I is also thought to have possibly been a Keralite.

Of the leading mathematicians of Kerala there is quite possibly more to be discovered but currently there are several whose work is of significant interest.