mathematics

Aryabhatta was one of ancient India's greatest innovators and mathematicians. Born in 476 AD in Kerala, he studied in Nalanda University near Kusumaputra, now Patna. He gave the value of Pi - 3.1416, arriving at the most accurate value of the mathematical constant. He is also believed to have formulated tables in math, which later came to be called the "Tables of Sine". His method to find solutions for quadratic equations of the sort: ax2 - by2 = c was a ground breaking contribution.

Probably lesser known than Aryabhatta, but standing tall among the greats in this field is Brahmaguptha. With a sound background in astronomy, he set out to understand mathematics better. He devised the rules of operation for 'zero', namely:
   - Addition or subtraction of zero from or to any quantity (either negative or      positive) has no effect.
   - Product of any quantity with zero always gives zero
   - Division of any number (positive or negative) by zero is infinity (He      also claimed that division of 0 by 0 is 0, but this was later proved      incorrect.)
He went on to formulate rules for solving various types of equations such as ax + b = 0 and ax + bx + c = 0 and ways to add up a geometric series. He was the first to identify the difference between algebra and arithmetic and treated them as separate entities.

Bhaskara introduced the world to the concept of infinity (the concept that any term divided by zero is infinity and the sum of any term and infinity is infinity.) He was greatly influenced by Brahmaguptha. One of his most momentous contributions to the branch of algebra was the introduction of Chakrawal or the cyclic method for solving algebraic equations. (Now called the "inverse cyclic" method.) Bhaskara's work focused on important formulae and theorems in trigonometry and permutation and combination. He was also the originator of differential calculus. Concepts such as differential coefficient and the basic idea for the "Rolle's theorem" were touched by him. A renowned astronomer, his concept of Tatkalikagati or instantaneous motion has been applied by astronomers to determine the motion of planets accurately.