# JAINA MATHEMATICS

The contributions of Jaina mathematics are sidelined not only due to ignorance but also due to the loss of many original works. Amongst the literature available the treatises ** Surya prajnapti**,

**date back to the third or fourth century BCE. But**

*Jambu Dwipa Prajnapti***,**

*Sthananga sutra***,**

*Uttaradhyayana sutra***and**

*Bhagwati sutra***were written much later. Unlike ancient Indian mathematic, which originated due to ritual needs and practical requirements, Jaina mathematics was the outcome of concerns with cosmology and philosophical deliberations. Jaina mathematics emerged after the conclusion of ancient indian mathematics and before the rise of classical age of indian mathematics which was heralded by Aryabhatta.**

*Anuyoga Dwara sutra*__JAINA MATHEMATICIANS__

Among the great Jaina mathematicians the first who needs special mention is **Acharya Virasena **who lived in the 8^{th} century CE. Apart from being a mathematician he was a philosopher and poet. His magnum opus was the treatise ** DHAVALA.** He was the first mathematician who derived an accurate value of

**π (pi)**and developed logarithms to

__base 3__(

*trakacheda*) and

__base 4__(

*caturthacheda*) He also developed a formula for calculating the value of the frustum

**.**

**Mahavira**who was born around 850CE was the author of the book

**. Later there were a host of other illustrious mathematicians like**

*GANITHA SARA SANGRAHA***SRIDHARA**(850 – 950 CE) who wrote

*GANITHA SANGRAHA,***NEMICHANDRA**(980 CE) and

**THAKURA PHERU**(14

^{th}Century CE). Thakura Pheru served the Khilji sultans as a treasurer in the court of the Khiljis. As Islamic architecture became entrenched in India during medieval period, Thakura Pheru in his work

**derived formulas for calculating domes, arches, and tents. Pheru is also credited with providing a formula for constructing magic squares**

*Ganitasarakaumudi*There were in ancient India various schools of mathematics, one of which was in Kusumapura, Bihar. The renowned Jain saint **BHADRABAHU** lived here and wrote his scholarly treatise ** Suryaprajnapti**and

*In SURYAPRAJNAPATI the value of piwas calculated to a fair degree of accuracy and was known as the*

**Bhadrabahavi-samhita**.

__Jain value__*.*The other important school of mathematics was in Mysore and Mahaviracarya who lived there made many valuable contributions to Jaina mathematics.

__CONTRIBUTIONS OF JAINA MATHEMATICS__

**Permutation and combination** Jain mathematicians were greatly interested in this and the treatise *Bhagawati sutra *contains rules to perform this. The Jain mathematician **Silanka** developed three rules pertaining to it.

**Arithmetic of large numbers** and categorization of infinity was another area of interest. Jain mathematicians were the first to conceive the idea of transfinite numbers and they classified numbers into three categories viz; * enumerable*,

*and*

__innumerable__*apart from odd and even numbers*

__infinite__*.*According to Jain mathematicians there are five different kinds of infinity. There was the

__infinite in one and two__directions,

__infinite in area__,

__infinite everywhere__and

__infinite perpetually__. This was a very novel idea developed by them, which was far ahead of their time. The Jains were also familiar with the laws of indices (though it was not clearly spelt out) and anticipated the concept of logarithm.

Their other areas of contributions were in the Geometry of the circle, Operations with fractions, Simple equations. Cubic equations and magic numbers. The potential for research in Jaina mathematics and its popularization is still great and needs to be looked into.