Concept

Indian mathematics

Overview

The tradition of Indian mathematics flourished in South Asia from circa 1200 BCE until the late 18th century, when it merged into a global discipline. Important contributions were made throughout its history, but especially during its classical period (400 CE to 1200 CE) by scholars such as Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira. 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 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 evidence of their results being transmitted outside Kerala.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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But the altogether momentary act, whose nature is transitory, consists in action itself. I have shown elsewhere that the notion of Entelechy is not altogether to be scorned, and that, being permanent, it carries with it not only a mere faculty for action, but also that which is called 'force', 'effort', 'conatus', from which action itself must follow if nothing prevents it. Faculty is only an _attribute_, or rather…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
States what Indian mathematics is; the author is tied to Indian mathematics in the knowledge graph.
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The moderns, under the influence of Cartesian geometry, have reasserted the universal possibility of numerical measurement, extending arithmetic, partly for that purpose, so as to include what are called "irrational" numbers, which give the ratios of incommensurable lengths. But although irrational numbers have long been used without a qualm, it is only in quite recent years that logically satisfactory definitions…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
States what Indian mathematics is.
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In this employment the algebraic letters are called the ‘arguments’ of the function, or sometimes they are called the ‘variables.’ Then, for instance, if an angle is represented by an algebraical letter, as standing for its numerical measure in terms of a given unit, Trigonometry is absorbed into this new algebra. Algebra thus develops into the general science of analysis in which we consider the properties of…
Alfred North Whitehead, Science and the modern world
States what Indian mathematics is.
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Philosophers who discussed Indian mathematics

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Place in the tradition

Part of History of philosophy in Pakistan.

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