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Mathematics in Ancient India

The first appearance of evidence of the use of mathematics in the Indian subcontinent was in the Indus Valley Civilization, which dates back to around 3300 BC. Excavations at Harappa, Mohenjo-daro and the surrounding area of the Indus River, have uncovered much evidence of the use of basic mathematics. The mathematics used by this early Harappan civilization was very much for practical means, and was primarily concerned with weights and measuring scales.

By 1800 BC, Indian mathematicians were discussing the idea of infinity, pointing out that "if you remove a part from infinity or add a part to infinity, what remains is still infinity." By about 400 BC, Indian mathematicians were doing more work on the idea of infinity. The Surya Prajinapti defines five kinds of infinity: an infinite line beginning from an endpoint, an infinite line going directions, an infinite plane, an infinite universe, and the infinity of time.

Lot of progress was made in geometry as a result of interest in astronomy, and by 1300 BC the Indian astronomer Lagadha used geometry to write a book of rules for the apparent movement of the sun and moon.

Around 300 BC, Indian mathematicians began working on the mathematical idea of combinations. This is the study of how many combinations you can make out of the same group of things. They were working on how you could figure that out, and published their ideas in a book called the Bhagabati Sutra. Around the same time, Indian mathematicians worked out the first beginnings of our modern number system. By 100 AD, people in India were writing the numbers.

Indian mathematician’s biggest invention was the use of zero as a placeholder, to make it easier to add and multiply numbers. Our word "zero" comes from the Sanskrit word meaning "nothing." In 458 AD, Indian mathematicians wrote a book, the Lokavibhaaga, that uses zero in this way. In 628 AD, Brahmagupta wrote a book explaining how zero worked, with rules like "The sum of zero and zero is zero" and "The sum of a positive and a negative is their difference; or, if they are equal, zero.”

Algebraic theories, as also other mathematical concepts, which were in circulation in ancient India, were collected and further developed by Aryabhatta, an Indian mathematician, who lived in the 5th century. He has referred to Algebra as Bijaganitam in his treatise on mathematics named Aryabhattiya, composed in A.D. 499. He was first to treat Mathematics as a distinct subject and he dealt with evolution and involution, area and volume, progressions and algebraic identities, and intermediate equations of the first degree. He also arrived at a remarkably accurate value of PI ( 3.1416). Aryabhatta was also the first to hold that the earth was a sphere and rotated on its axis. He says, to a person traveling in a boat trees on the shore appear to move in opposite direction, similarly because earth is rotating on its axis towards east it appears to us as if the sun moves from east to west. He also explained that the eclipses were caused by the shadow of the earth falling on the moon. One of the most important features of Aryabhatta's mathematical system is his unique system of notation. It is based on the decimal place value system, now in use throughout the civilized world.

Another mathematician of the 12th century, Bhaskaracharya also authored several treatises on the subject ­ one of them, named Siddantha Shiromani has a chapter on algebra. He is known to have given a basic idea of the Rolle's theorum and was the first to conceive of differential calculus Bhaskaracharya's Leelavati translated to English in 1816 by James Taylor.

The 14th century Indian mathematician Madhava of Sangamagrama along with other mathematician’s of the Kerala School studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala School wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus repeated only in seventeenth century Europe.

The credit for fine-tuning and internationalizing these mathematical concepts originated in India ­ goes to the Arabs and Persians. Al-Khawarizmi, a Persian mathematician, developed a technique of calculation that became known as "algorism." This was the seed from which modern arithmetic algorithms have developed. Al-Khwarizmi¹s work was translated into Latin under the title Algoritmi de numero Indorum, meaning The System of Indian Numerals. A mathematician in Arabic is called Hindsa which means from India. With the formation of the Islamic in 16 the century, the use of Indian Mathematics spread quickly from India to West Asia and Africa (by the 800's), and then more slowly to Christian Europe.

Will Durant, American historian, said that India was the mother of our philosophy of much of our mathematics. A. L. Basham, an Australian, writes in his book, "The Wonder That was India" says the world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. Albert Einstein says, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.”