Ancient Indians were known for their intelligence, innovativeness and enterprise. Especially in the field of Civil engineering, Mathematics, Astronomy, Medicine and Metallurgy, the contribution of ancient Indians is unique and unparalleled. The authors of Saraswathi-Sindhu civilization, which flourished during B.C.2300-1750, were pioneers in various fields. The concept of Town Planning was their innovation. They laid down their town on a gridiron plan with streets running at right angles to each other. There was an extensive drainage system, which collected the sewage from each house. Another remarkable innovation was the technology of waterproofing. The great bath (pool) at Mohenjodaro is a marvel of water proofing engineering skill. To ensure that the bath was water tight, the floor was paved with bricks cemented with gypsum mortar. Similarly, the wall of the pool was coated with bitumen. Another innovation of them was the designing of the corbelled arch, which was used for underground drainage. Well digging technology was another of their contribution, as the earliest wells in the world are to be found in the towns of the Saraswathi-Sindhu civilization.

The uniformity and standardization of the artifacts found in the towns where this civilization flourished show an amazing administrative control over a territory of over half a million square miles and also over production and distribution. The shape and designs of pottery, the types of copper tools, the weights and measures, the standard size of bricks and uniform layout of the towns clearly indicate that they had realized the advantages of standardization.

The most epoch making achievement of ancient Indians in the realm of Arithmetic was the decimal system of notation, based upon the principle of the place value of the first nine numbers and the use of zero. This notation system immensely simplified arithmetical calculation and processes and we can at present hardly imagine that there was a time when our ancestors all over the world were expressing a number like one thousand one hundred and eleven not as 1,111 but by four different and distinct symbols. The last one denoting one, the third one, ten, the second one, hundred and the first one, one thousand. Symbols for ten, twenty, thirty, forty, etc., as well as for hundred, thousand, etc., were all distinct and different. This method of expressing big numbers was very cumbersome, but even Europe was following it down to the 12th Century when it learnt the decimal system of notation from the Arabs. Arab authors like Ibn Washiya, Al Masudi and Alberuni give the credit of the discovery of the new system to Indians. When exactly the Indian Mathematicians made the epoch making discovery is however not known. Nor the name of the discoverer has been preserved. But as the new system of notation is referred by  Aryabhatta (A.D.499) in the Aryabhatiyam and followed by Varahamihira (A.D. 550), it is clear that the new decimal system of notation was well established among Mathematicians in the 5th century and we may therefore place its discovery at least a century or two earlier.

In 1881 a farmer found a manuscript in a fragmentary condition while digging at his village Bakshali near the city of Peshawar. This work ascribed to 3rd century A.D. gives us a fairly comprehensive idea of the state of Mathematics during that period. The Bakshali manuscript not only deals with elementary topics like fractions, square roots, arithmetical and geometric progressions, but also deals with advanced topics like summation of complex series, simultaneous linear equations and indeterminate equations of second degree. It also shows that some work was being done on the theory of numbers in the direction of extracting the square root of a non-square number.

Aryabhatta, born in 476 A.D., in Pataliputra was one of the greatest scientists that India had produced. He was the first to treat Mathematics as a distinct subject and his work Aryabhatiyam dealt with evolution and involution, area and volume, progression and algebraic identities and indeterminate equations of the first degree. In the realm of Geometry, the work describes several properties of the circle, discusses questions connected with projective geometry and give a value for pai, far accurate than any suggested till then. That Trigonometry was also being cultivated at this time will become clear from the use of the sine functions made for solving the problems of astronomy. In the realm of Astronomy, Aryabhatta’s work Surya Siddhanta examines and explains the true causes of the solar and lunar eclipses. He was the first to hold the view that eclipses were caused by the shadow of the earth falling on the moon. His calculation of the size of the earth is very near that figure which is estimated by modern astronomers. He was the first Indian astronomer t discover and declared that the earth rotates round its axis and he was the first to discover sine functions and utilize them in astronomy.

Another famous astronomer and mathematician of ancient India was Brahmagupta. Long before Newton, he declared the Law of Gravity. His works Brahmasiddhanta, Khandakhadya and Dhyanagraha covers arithmetical operations, squares and cube roots, rule of three interest, progressions, geometry, including treatment of the rational right angled triangle and the elements of the circle, elementary mensuration of solids, shadow problems, negative and positive quantities, ciphers, surds, etc.

Varahamihira who flourished in the close of 5th century A.D. was another famous astronomer and mathematician. His work Brihatsamhita is an encyclopedia of useful information in several branches of knowledge such as astronomy, physical geography, botany, architecture, sculpture, movements of heavenly bodies and their effect upon men, etc. Historians will remain ever grateful to him for his Panchasiddhantika, which gives a concise account of the five Siddhantas i.e., astronomical works viz., Paitamaha, Romaka, Paulisa, Vasishta and Surya, that were in use in India during the 3rd and 4th century A.D.

Around the beginning of the 9th century, there lived in Baghdad a great Arab mathematician named Muhammad ibn Musa al Khwarizm who in a celebrated treatise entitled Kitabal Djabrwal Mukabala (Book of Algebra), used the Indian decimal system with full knowledge of its origin and acknowledging it. Around 12th century A.D., the book was translated into Latin by Rudolph Chester and Gerard de Crename and circulated throughout Western Europe. The Arabs called Logarithm, Hindisat, which means the Indian art. It is interesting to note that although Arabic script is written from right to left, its numbers are always written from left to right as they are in Indian texts and inscriptions.

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