## The Wonders of Ancient Indian Mathematics

### By Aditya Kapur

The famous French mathematician and physicist Pierre Simon Laplace had once said, “It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value. The idea escaped the genius of Archimedes and Apollonius.” This quote is a testimony to the great advances that were made by Indian mathematicians to the development of fundamental mathematical concepts.

Starting from the Vedic ages of approximately 10,000 BCE, Indian mathematicians have contributed to almost all branches of mathematics including arithmetic, algebra, geometry and trigonometry. Bodhayan, in his renown *Shulba Sutras, *discovered what is now known as the Pythagoras Theorem in 800 BC. This means that he discovered the theorem almost 5 centuries before the man who the theorem is named after. Similarly, Pingala discovered the ‘*matrmeru’ *series in the 3rd century BCE, a recursive series that would be called the Fibonacci series 1500 years later.

वर्गः समचतुरश्रः फलं च सदृशद्वयस्य संवर्गः |

सदृशत्रयसंवर्गो घनस्तथा द्वादशाश्रिः स्यात् ||3||

–*Aryabhatiya* by Aryabhatta, 6th century CE

This shook discusses the meaning of two fundamental mathematical function: *varg*(square) and *ghan*(cube). Aryabhatta is most famous for his discovery of the number zero, an arithmetic discovery that revolutionised the working of mathematics and an idea no Western mathematician had ever thought of. In the book *Aryabhatiya*, Aryabhatta also discusses how to find the square root and cube root of numbers, the formula to find the area of a circle, an approximate value of the constant π and a table of sines, the base of trigonometry.

In the 12th century CE, Bhaskara II in his books *Lilavati* and *Bijaganitam *gave an alternate proof for the Pythagoras Theorem, developed the concept of infinity, worked out the

*‘chakravalam’*method to solve Pell’s equation and even developed the fundamental concepts of differential calculus.

These discoveries are true gems in the field of world mathematics, they show the advances in Indian mathematics and ancient wisdom. It is apt to say that these very discoveries form the basics of what we learn today and their impact on all branches of science is profound.