This Mahavira is a mathematician

An Indian he shares his name with one of the greatest men of all times. His fame rests on the fundamental mathematical calculations that he arrived at more than thousand two hundred years ago.

He was also among the first to separate astronomy from mathematics. He expounded several mathematical calculations more clearly than either Aryabhata or Brahmagupta. Yet, his name is not as familiar in India and abroad as the two former mathematicians.

He shares his name with the founder or rather pioneer of one of the oldest religions in the world. The name is Mahavira, who is considered to be one of the Theerthankaras of Jainism.

Jain Mahavira’s namesake, Mahavira of Gulbarga, was a mathematical genius of the ninth century and he was patronised by the Rashtrakurta Emperor Amoghavarsha (815-874).

Very few today care to remember that it is Mahavira or Mahaviracharya (817-875), the mathematician of Gulbarga, who asserted that the square root of a negative number did not exist. He then proceeded to give the sum of a series whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse.

Mahavira was the author of Ganit Saar Sangraha. This book has nine chapters and it is an important text as it includes all known mathematical concepts in India then.

The Sangraha is one of the best books on Jain mathematics. Here, Mahavira concentrated only on mathematics and there is no elaboration on astronomy. Thus this is the earliest exclusive text on mathematics in India.

An extremely modest man, Mahavira pays tributes to mathematicians who predated him such as Aryabhata, Bhaskara and Brahmagupta. He acknowledges the role they have played in helping him writing the book.

The nine chapters of the Sangraha are contained in 1100 slokas. The chapters deal with arithmetic, algebra, geometry and mensuration. The nine chapters are: Terminology, Arithmetic operations, Fractions, Miscellaneous operations, Operations involving the rule of three, Mixed operations, Operations relating to the calculations of areas, Operations relating to excavations and Operations relating to shadows. This book can be dated to around 850 AD.

The book omits any mention of decimals.  

He is also a pioneer in firmly establishing terms such as equilateral, rhombus, isosceles triangle, circle and semi circle. He also solved higher order equations of n degree of the forms.

He also expounded on the same subjects on which Aryabhata and Brahmagupta worked, but his expressions were more clear and lucid.

Mahavira also established equations for the sides and diagonal of Cyclic Quadrilateral.

If sides of Cyclic Quadrilateral are a, b, c and d and its diagonals are x and y while

and

then,

His mathematical genius was acknowledged in south India and he proved to be an inspiration to other mathematicians from south India.

Mahavira also came up with rules for operations with zero, although he thought that division by zero left a number unchanged.

He was born in Gulbarga and he was one of the gems patronised by Emperor Amoghavarsha.

He asserted that the square root of a negative number did not exist. He gave the sum of a series whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse.

His work on arithmetic was on garland numbers.  He gave examples of garland numbers-they give the same results, whether read from right to left or from right to left. For example the number, 1111.

In algebra, he worked on finding the cube of a natural number. He also worked on unit fractions. In geometry, he worked on an inscribed circle in a triangle.

To put it in layman’s terms, Mahavira came up with a naming scheme for numbers from 10 up to 10^24, which are eka, dasha, ... mahakshobha.

He also devised formulas for obtaining cubes of sums and he was  first to come up with the notion that no real square roots of negative numbers can exist. The imaginary numbers were not identified until 1847 by Cauchy in Europe.

He also gave us techniques for least common denominators. This concept came to Europe in the 15th century. He also discovered techniques for Combinations (n choose r). It was later reinvented in Europe in 1634.

He discussed techniques for solving linear, quadratic as well higher order equations and he also studied several arithmatic and geometric series.

Mahavira also came up with techniques for calculating areas and volumes.

Mahavira expounded on the same subjects on which Aryabhata and Brahmagupta contended, but he expressed them more clearly. 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. Mahavira's eminence spread in all South India and his books proved inspirational to other Mathematicians in Southern India.

What have we done to Mahavira. We blindly follow western form of mathematics and term our own as Vedic or Hindu mathematics. Do we still need to ape the West when our own forefathers strode the mathematical scene and gave us much of the information that the West has copied.