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The works of the Kerala school were first written up for the Western world by Englishman C. Whish in According to Whish, the Kerala mathematicians had " laid the foundation for a complete system of fluxions " and these works abounded " with fluxional forms and series to be found in no work of foreign countries. However, Whish's results were almost completely neglected, until over a century later, when the discoveries of the Kerala school were investigated again by C.

Rajagopal and his associates.

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The Kerala mathematicians included Narayana Pandit [ dubious — discuss ] c. Narayana is also thought to be the author of an elaborate commentary of Bhaskara II 's Lilavati , titled Karmapradipika or Karma-Paddhati. Madhava of Sangamagrama c. Although it is possible that he wrote Karana Paddhati a work written sometime between and , all we really know of his work comes from works of later scholars.

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Parameshvara c. His Lilavati Bhasya , a commentary on Bhaskara II's Lilavati , contains one of his important discoveries: a version of the mean value theorem. Nilakantha Somayaji — composed the Tantra Samgraha which 'spawned' a later anonymous commentary Tantrasangraha-vyakhya and a further commentary by the name Yuktidipaika , written in He elaborated and extended the contributions of Madhava.

Citrabhanu c. These types are all the possible pairs of equations of the following seven forms:. For each case, Citrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric.

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Jyesthadeva c. Jyesthadeva presented proofs of most mathematical theorems and infinite series earlier discovered by Madhava and other Kerala School mathematicians. It has been suggested that Indian contributions to mathematics have not been given due acknowledgement in modern history and that many discoveries and inventions by Indian mathematicians are presently culturally attributed to their Western counterparts, as a result of Eurocentrism.

According to G. Joseph's take on " Ethnomathematics ":.

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The awareness [of Indian and Arabic mathematics] is all too likely to be tempered with dismissive rejections of their importance compared to Greek mathematics. The contributions from other civilisations — most notably China and India, are perceived either as borrowers from Greek sources or having made only minor contributions to mainstream mathematical development.

An openness to more recent research findings, especially in the case of Indian and Chinese mathematics, is sadly missing" [88].

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The historian of mathematics, Florian Cajori , suggested that he and others "suspect that Diophantus got his first glimpse of algebraic knowledge from India. More recently, as discussed in the above section, the infinite series of calculus for trigonometric functions rediscovered by Gregory, Taylor, and Maclaurin in the late 17th century were described with proofs and formulas for truncation error in India, by mathematicians of the Kerala school , remarkably some two centuries earlier.

Some scholars have recently suggested that knowledge of these results might have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionaries. The existence of communication routes and a suitable chronology certainly make such a transmission a possibility. However, there is no direct evidence by way of relevant manuscripts that such a transmission actually took place. Both Arab and Indian scholars made discoveries before the 17th century that are now considered a part of calculus. This research is being pursued, among other places, at the Centre National de Recherche Scientifique in Paris.

From Wikipedia, the free encyclopedia. See also: Vedanga and Vedas. Main article: Vyakarana. Main article: Kerala school of astronomy and mathematics. This section may lend undue weight to certain ideas, incidents, or controversies. Please help to create a more balanced presentation. Discuss and resolve this issue before removing this message. September Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat.

Introduction to the History of Mathematics

But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own. It must be noted moreover that the conception of zero as a number and not as a simple symbol of separation and its introduction into calculations, also count amongst the original contribution of the Hindus. Leonardo of Pisa wrote that compared to method of the Indians all other methods is a mistake. This method of the Indians is none other than our very simple arithmetic of addition, subtraction, multiplication and division.

Rules for these four simple procedures was first written down by Brahmagupta during 7th century AD. In the following centuries, as there is a diffusion into the West by intermediary of the Arabs of the methods and results of Greek and Hindu mathematics, one becomes more used to the handling of these numbers, and one begins to have other "representation" for them which are geometric or dynamic.

Britannica Concise Encyclopedia. Quote: "A full-fledged decimal, positional system certainly existed in India by the 9th century AD , yet many of its central ideas had been transmitted well before that time to China and the Islamic world. Indian arithmetic, moreover, developed consistent and correct rules for operating with positive and negative numbers and for treating zero like any other number, even in problematic contexts such as division. Several hundred years passed before European mathematicians fully integrated such ideas into the developing discipline of algebra. Greek mathematicians used the full chord and never imagined the half chord that we use today.

Half chord was first used by Aryabhata which made trigonometry much more simple. In fact, the Indian astronomers in the third or fourth century, using a pre-Ptolemaic Greek table of chords, produced tables of sines and versines, from which it was trivial to derive cosines. This new system of trigonometry, produced in India, was transmitted to the Arabs in the late eighth century and by them, in an expanded form, to the Latin West and the Byzantine East in the twelfth century.

Gold and Pingree assert [4] that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use. The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world e.

It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit or Malayalam and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian "discovery of the principle of the differential calculus" somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. When this was first described in English by Charles Matthew Whish , in the s, it was heralded as the Indians' discovery of the calculus.

Islamic scholars nearly developed a general formula for finding integrals of polynomials by A. But, it appears, they were not interested in any polynomial of degree higher than four, at least in any of the material that has come down to us. Indian scholars, on the other hand, were by able to use ibn al-Haytham's sum formula for arbitrary integral powers in calculating power series for the functions in which they were interested. By the same time, they also knew how to calculate the differentials of these functions.

So some of the basic ideas of calculus were known in Egypt and India many centuries before Newton. It does not appear, however, that either Islamic or Indian mathematicians saw the necessity of connecting some of the disparate ideas that we include under the name calculus. They were apparently only interested in specific cases in which these ideas were needed. There is no danger, therefore, that we will have to rewrite the history texts to remove the statement that Newton and Leibniz invented calculus.

They were certainly the ones who were able to combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between them, and turn the calculus into the great problem-solving tool we have today. Rao Marine Archaeology, Vol. Seidenberg, The origin of mathematics. Archive for History of Exact Sciences, vol It is not certain what practical use these arithmetic rules had.

The best conjecture is that they were part of religious ritual.

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A Hindu home was required to have three fires burning at three different altars. The three altars were to be of different shapes, but all three were to have the same area. These conditions led to certain "Diophantine" problems, a particular case of which is the generation of Pythagorean triples, so as to make one square integer equal to the sum of two others.

Among other transformation of area problems the Hindus considered in particular the problem of squaring the circle. The Bodhayana Sutra states the converse problem of constructing a circle equal to a given square. The following approximate construction is given as the solution The authors, however, made no distinction between the two results.

However some scholars have disputed the Pythagorean interpretation of this tablet; see Plimpton for details.

The History of Mathematics: An Introduction

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