Indian mathematics emerged in the Indian subcontinent from
1200 BC 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 was first recorded in Indian mathematics. Indian mathematicians made early
contributions to the study of the concept of zero as a number,negative numbers,arithmetic,
and algebra. In addition, trigonometry was further advanced in India, and, in
particular, the modern definitions of sine and cosine were developed there.
These mathematical concepts were transmitted to the Middle East, China, and Europe
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.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.
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). 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. Read More
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