India is one of the ancient civilizations where high quality mathematics was practised. The decimal number system, we use today, was invented in India, perhaps before the birth of Christ. Zero was invented in India. The earliest example of use of zero in India is in 458 AD when it appeared in a surviving Jain work on cosmology. But indirect evidence indicates that it must have been in use as early as 200 BC. The decimal number system together with zero made the number system easier and popular. The Arabs took it from India and from there it spread to Europe. The Europeans, not knowing its real origin, called it the Arabic Number System. After its original country of birth was known, now it is called Hindu – Arabic Number System.

The famous French mathe- matician Laplace has remarked, “The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple now–a–days that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of antiquity, Archimedes and Apollonius.

Similarly the greatest scientist Einstein has told, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientist discovery could have been made.”

Sulvasutras are Hindu spiritual texts written between 800 BC and 200 BC. The first proof of early Indian mathematics is found here. While describing the construction of altar and fireplaces, it has described areas of rectangles, parallelograms and isosceles trapezoids. It mentions methods to convert squares into circles and vice– versa. From this, value of   ð is found to be 3.088 or 3.004. The most noteworthy mathematics in Sulvasutras is the Pythagoras theorem. It states that in a right–angled triangle the square of diagonal is equal to the sum of the square of the other two sides. History of mathematics says that this theorem was discovered by the Greek mathematician Pythagoras around 500 BC. But nearly two hundred years before him Baudhayan has described this in his Sulvasutras in 800 BC. Some of the Pythagorean triples like (3, 4, 5), (9, 12, 13), (7, 24, 25), (8, 15, 17), (12, 35, 37), (9, 40, 41) etc have been mentioned in his book. The volume of square root of 2 as mentioned in Sulvasutras is astonishing. It gives the value as    which is equal to                                                   1.414213562. Its accurate value is 1.41421356237…..

The Jains used very large numbers unknown in other civilizations. Umaswati (150 BC) wrote texts and started mathematics school at Patliputra. He has discovered the formula for the area of a circle. There are hints of logarithm in a Jain book Anuyog Dwar Sutra written in third century. Amongst the religious works of the Jainas, which are important from the view-point of mathematics are Surya Prajnapti, Jamboo Dwipa Prajnapti, Sthdnanga Sutra, Uttaradhyayana Sutra, Bhagawatl Sutra, and Anuyoga Dwara Sutra. The approximate date of the first two works is about 500 B. C., and the rest may be of about 300 B. C.

In 1881, a seventy page manuscript written on birch bark was unearthed in Bakshali village, about seventy kilometers from Peshawar. It contains mathematical results of high order including quadratic equations, finding square root of numbers which are not perfect squares and arithmetic geometric progression. Its date is uncertain, and has generated considerable debate. Most scholars agree that the physical manuscript is a copy of a more ancient text, so that the dating of that ancient text is possible only based on the content. Recent researchers date it between 300 BC and 200 BC.

Aryabhatta (476 – 550) was the most important mathematician in the classical age. He has written Aryabhatiya in 499  and in it he has described solutions for quadratic equations and integer solutions for linear indeterminate equations. He has given the formula for sum of natural numbers, sum of square of natural numbers and sum of cube of natural numbers. He has given value of ð as 3.1416 and it was the most accurate value at that time. He has given a table of trigonometric sine function. The sine tables are needed to work out the geometrical measurements of positions of stars and planets.

Brahmagupta (598 – 670) has written the famous book Brahma Sphuta Siddhanta, a long work on astronomy with four and half chapters on mathematics. It was translated by Arabs in 770 as Sind – Hind. He has described different operations of zero and negative numbers for the first time. He has solved the indeterminate equation of the type Nx2 + 1 = y2. Not knowing his solution, the European mathematicians rediscovered in the seventeenth century and it is now known as Pell’s equation. He has given the correct formula for the area of cyclic quadrilaterals.

The Jain mathematician Mahavircharya (800 – 870) has written a marvelous mathematics book Ganita Sar Sangraha. He has given general formula for combinations and permutations. He has dealt with problems on unit fractions and has given formula for the area of cyclic quadrilaterals. He is also credited with computing the area of an ellipse.

Bhaskara II (1114 – 1185) has written the famous book on mathematics and astronomy Siddhanta Siromani. It has four parts such as Lilavati (arithmetic), Bijaganita (algebra), Goldayaya (celestial globe) and Graha Ganita (mathematics of the planets). He was the first mathematician to recognize two roots of quadratic equations, even one may be negative. He has discussed operations on surds, zero and negative numbers. He discovered the correct formula for the area and volume of sphere. In trigonometry, he has found the formula for sine of a sum of two angles and double angle formula. He was the first mathematician to describe differential calculus. Nearly five hundred years after him Newton and Leibnitz discovered it in Europe.

In Kerala, mathematics prospered between thirteenth and sixteenth century. Madhava discovered the expansion series for sin (x), cos(x) and arc tan(x) in 1400. About two hundreds years after him these were rediscovered in Europe by Maclaurin and historians, not knowing the contributions of Madhava, credited this to the European mathematicians. A book named Sadaratnamala has been discovered in Kerala. The value of ð given here is astonishingly correct to 17 places.

Unfortunately, Indian contributions to development of mathematics have not been given due credit in modern history. Many theories discovered by Indians have been wrongly attributed to the European mathematicians who have rediscovered these knowing or unknowing the contributions of the Indians.