Mahāvīra or Mahaviracharya
Mathematician
Mahāvīra was a 9th-century Jain mathematician possibly born in kundalpur, in India. He authored Gaṇitasārasan̄graha or the Compendium on the gist of Mathematics in 850 AD. He was patronised by the Rashtrakuta king Amoghavarsha during (c. 814–878) of the Rashtrakuta dynasty. He separated astrology from mathematics.
Born: About 800 AD , Kundalpur, Mysore,India
Died: 875 AD

Mahavira was of the Jaina religion and was familiar with Jaina mathematics. He worked in Mysore, India where he was a member of a school of mathematics. We have essentially no other biographical details although we can gain just a little of his personality from the acknowledgement he gives in the introduction to his only known work, Ganita Sara Samgraha . However Jain mentions six other works which he credits to Mahavira and he emphasises the need for further research into identifying the complete list of his works.
It is the earliest Indian text entirely devoted to mathematics. He expounded on the same subjects on which Aryabhata and Brahmagupta contended, but he expressed them more clearly. His work is a highly syncopated approach to algebra and the emphasis in much of his text is on developing the techniques necessary to solve algebraic problems. He is highly respected among Indian mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle; rhombus; circle and semicircle. Mahāvīra’s eminence spread throughout South India and his books proved inspirational to other mathematicians in Southern India. It was translated into the Telugu language by Pavuluri Mallana as Saara Sangraha Ganitamu.
He discovered algebraic identities like a3 = a (a + b) (a − b) + b2 (a − b) + b3. He also found out the formula for nCr as
[n (n − 1) (n − 2) … (n − r + 1)] / [r (r − 1) (r − 2) … 2 * 1]. He devised a formula which approximated the area and perimeters of ellipses and found methods to calculate the square of a number and cube roots of a number. He asserted that the square root of a negative number does not exist.

Ganita Sara Samgraha consisted of nine chapters and included all mathematical knowledge of mid-ninth century India. It provides us with the bulk of knowledge which we have of Jaina mathematics and it can be seen as in some sense providing an account of the work of those who developed this mathematics. There were many Indian mathematicians before the time of Mahavira but, perhaps surprisingly, their work on mathematics is always contained in texts which discuss other topics such as astronomy. The Ganita Sara Samgraha Ⓣ by Mahavira is the earliest Indian text which we possess which is devoted entirely to mathematics.
In the introduction to the work Mahavira paid tribute to the mathematicians whose work formed the basis of his book. These mathematicians included Aryabhata I, Bhaskara I, and Brahmagupta. Mahavira writes:-
With the help of the accomplished holy sages, who are worthy to be worshipped by the lords of the world … I glean from the great ocean of the knowledge of numbers a little of its essence, in the manner in which gems are picked from the sea, gold from the stony rock and the pearl from the oyster shell; and I give out according to the power of my intelligence, the Sara Samgraha, a small work on arithmetic, which is however not small in importance.
The nine chapters of the Ganita Sara Samgraha Ⓣ are:
1. Terminology
2. Arithmetical operations
3. Operations involving fractions
4. Miscellaneous operations
5. Operations involving the rule of three
6. Mixed operations
7. Operations relating to the calculations of areas
8. Operations relating to excavations
9. Operations relating to shadows
Throughout the work a place-value system with nine numerals is used or sometimes Sanskrit numeral symbols are used. Many renowned Indian mathematicians such as Aryabhata, Shakuntala Devi, Srinivas Ramanujan, Madhava Sangamagrama enlightened the world with their work, but this book not only provides insights into the history of Indian mathematics, but also a lot about Vedic mathematics.
Major Functions at a Glance
Presented the general formula for the number of permutations and accumulations.
Present the solutions of n-degree equations.
Published several characteristics of a cyclic quadrilateral.
He said that negative numbers cannot have a square root.
Find the sum of the n-terms of the class containing the square of the terms of the A.P.
Presented the empirical formula for the circumference and area of ​​an ellipse.
He was one of the first mathematicians from India to make a contribution to mathematics. He developed formulas for approximating the area and circumference of ellipses and found a method for calculating the number square and the cube root from numbers. His importance extended beyond southern India, and his work proved inspiring to other mathematicians in the region.