Indian mathematics emerged in the Indian subcontinent[1]

 from 1200 BC [2]

 until the end of the 18th century. In the classical period of Indian mathematics (400

AD to 1200 AD), important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today[3]

 was

first recorded in Indian mathematics.[4]

Indian mathematicians made early contributions to the study of the concept of zero as a number,[5]

 negative numbers,

[6] arithmetic, and algebra.

[7] In addition, trigonometry

[8] was further advanced in India, and, in particular, the modern definitions of sine and cosine were

developed there.[9]

 These mathematical concepts were transmitted to the Middle East,China, and Europe[7]

 and led to further developments that now form the

foundations of many areas of mathematics.

A later landmark in Indian mathematics was the development of the series expansions fortrigonometric functions (sine, cosine, and arc tangent) by mathematicians of the Kerala school in the 15th century CE. Their remarkable work, completed two centuries before the invention of calculus in Europe, provided what is now

considered the first example of a power series (apart from geometric series).[13]

 However, they did not formulate a systematic theory

of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala.[14][15][16][17]

Prehistory

Excavations at Harappa, Mohenjo-daro and other sites of the Indus Valley Civilization have uncovered evidence of the use of "practical mathematics". The people

of the IVC manufactured bricks whose dimensions were in the proportion 4:2:1, considered favorable for the stability of a brick structure. They used a standardized

system of weights based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with the unit weight equaling approximately 28 grams (and

approximately equal to the English ounce or Greek uncia). They mass produced weights in regular geometrical shapes, which included hexahedra, barrels, cones,

and cylinders, thereby demonstrating knowledge of basic geometry.[18]

The inhabitants of Indus civilization also tried to standardize measurement of length to a high degree of accuracy. They designed a ruler—the Mohenjo-daro ruler

—whose unit of length (approximately 1.32 inches or 3.4 centimetres) was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had

dimensions that were integral multiples of this unit of length.[19][20]