Ancient India, mathematics was known by the general name Ganita, which included arithmetic, geometry, algebra, astronomy and astrology. In the field of mathematics ancient Indians made three distinct contributions, the notation system, the decimal system and the use of zero.
The greatest contribution of ancient India to mathematics was the development of notation system. This was done by giving a value for each position in incremental of 10. A notation for powers of 10 up to the power 17 was in existence from the Vedic times. The mathematician Aryabhata (A.D. 476-500) in his book Aryabhatiyam, clearly mentions “sthaanam sthaanam dasha gunam,” meaning from place to place increase 10 times.
The decimal system too was an innovation of ancient India. Indians were the first to use the decimal system. The earliest epigraphic evidence of the use of decimal system is found in the inscriptions of Ashoka in the third century B.C. The famous mathematician Aryabhata was acquainted with it.
Zero was discovered in about the second century B.C. From the very beginning Indian mathematicians considered zero as a separate numeral, and it was used in arithmetic in that sense. The mathematical implications of zero and infinity were fully realized in the field of astronomy.
The earliest inscription regarding the data by a system of nine digits and a zero is dated 595 A.D. It’s evident that the system was known to the mathematicians some centuries before it was employed in the inscriptions. In the second century B.C. Apastemba contributed to practical geometry for the construction of altars on which the kings could offer sacrifices. It describes acute angle, obtuse angle, right angle etc.
Early Indians devised a rudimentary algebra which led to more calculations. Aryabhata gave approximate value of pie. He formulated the rule for finding the area of a triangle. Aryabhatta, gave a new direction to the field of trigonometry. It also led to the evolution of empirical geometry and calculus. The most famous work during his time was Suryasiddanta, a book on Hindu astronomy.
During the Gupta period mathematics developed to greater heights. Brahmagupta in 628 AD wrote the book Brahmasphuta-Siddhantas or rules for numbers. It contained ideas including a good understanding of the mathematical role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series. This book was written completely in verse in Sanskrit.
Indian mathematicians such as Brahmagupta (7th century), Mahavira (9th century) and Bhaskarachary (12th century) made several discoveries. They understood the importance of positive and negative quantities, evolved sound system of extracting squares and cube roots and could solve quadratic and certain types of indeterminate equations.