Posted on: 8 February 2015

Digital Rare Book:
The History of the Kerala School of Hindu Astronomy
By K.Venkateswara Sarma
Published by Vishveshvaranand Institute, Hoshiarpur - 1972

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An ancient precursor to India's emerging world dominance in math and science, The Kerala School of Astronomy & Mathematics, a little known school of scholars in southwest India, discovered the ‘infinite series’- one of the basic components of calculus and one of the founding principles of modern mathematics hundreds of years before Newton – in about 1350 according to new research.

Dr George Gheverghese Joseph from The University of Manchester says the ‘Kerala School’ identified the ‘infinite series ’- one of the basic components of calculus - in about 1350.

According to Dr George Gheverghese Joseph of Great Britain's University of Manchester, the discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries.

The team from the Universities of Manchester and Exeter reveal the Kerala School also discovered what amounted to the Pi series and used it to calculate Pi correct to 9, 10 and later 17 decimal places.

And there is strong circumstantial evidence that the Indians passed on their discoveries to Jesuit missionaries who visited India during the fifteenth century. That knowledge, the team argues, may have eventually been passed on to Newton himself.

He said: “The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten.

“The brilliance of Newton’s work at the end of the seventeenth century stands undiminished – especially when it came to the algorithms of calculus. But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus- infinite series.

“There were many reasons why the contribution of the Kerala school has not been acknowledged - a prime reason is neglect of scientific ideas emanating from the Non-European world - a legacy of European colonialism and beyond.

“But there is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written.

He added: “For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.

(Adapted from a University of Manchester study Indians predated Newton 'discovery' by 250 years)

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An artist's impression of Madhava of Sangamagrama.

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The infinite series for π was stated by Madhava of Sangamagrama (c. 1340-1425) and his Kerala school of astronomy and mathematics. He made use of the series expansion of arctanx to obtain an infinite series expression, now known as the Madhava-Gregory series, for π. Their rational approximation of the error for the finite sum of their series are of particular interest. They manipulated the error term to derive a faster converging series for π. They used the improved series to derive a rational expression, 104348 / 33215 for π correct up to nine decimal places, i.e. 3.141592653. Source: