# HISTORY OF Indian mathematics

**Indian mathematics** emerged in the __Indian subcontinent____[1]__ from 1200 BCE__[2]__ until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like __Aryabhata__, __Brahmagupta__, __Bhaskara II__, and __Varāhamihira__. 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.

Ancient and medieval Indian mathematical works, all composed in __Sanskrit__, usually consisted of a section of * sutras* in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved.

__[1]__

__[10]__All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form. The oldest extant mathematical

*document*produced on the Indian subcontinent is the birch bark

__Bakhshali Manuscript__, discovered in 1881 in the village of

__Bakhshali__, near

__Peshawar__(modern day

__Pakistan__) and is likely from the 7th century CE.

__[11]__

__[12]__

A later landmark in Indian mathematics was the development of the __series__ expansions for __trigonometric 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]__