Mahaviracharya: 9th Century Mathematician

Prof. Yashwant Maliya

The Jains have always been very interested in mathematics. One distinguished Jain mathematician monk was Mahaviracharya who wrote "Ganita-sara-samgraha" in 850 AD during the reign of the great Rashtrakuta king Amoghavarsha. Amoghavarsha had become a Jain monk in the later part of his life. His capital was in Manyakheta in modern Karnataka.

Some of the interesting things in Ganita-sara-samgraha are:

A naming scheme for numbers from 10 up to 10^24, which are eka, dasha, ... mahakshobha.
Formulas for obtaining cubes of sums.

He was the first person to mention that no real square roots of negative numbers can exist. The imaginary numbers were not identified until 1847 by Cauchy in Europe!

He gave techniques for least common denominators. It was used in Europe not before the 15th century.

He gave techniques for Combinations (n choose r). It was later invented in Europe in 1634.
He discussed techniques for solving linear, quadratic as well higher order equations.
He studied several arithmatic and geometric series.

He gave techniques for calculating areas and volumes. No personal information about Mahaviracharya is available.

This is based on an article recently published in Vishva Viveka (a Hindi Quarterly published from New Orleans, LA, USA) by Prof. S.C. Agrawal and Dr. Anupam Jain. As you will recall, Dr. Anupam Jain is the editor of a Jain research journal "Arhata Vachan".

There is an annotated Hindi translation on Ganita-Sara-Samgraha by Prof. L.C. Jain.

Yashwant K. Malaiya