The Telegraph
Since 1st March, 1999
Email This Page
Unsung Newtons of India
- Researchers trace calculus roots to wizards of Kerala

New Delhi, Aug. 13: Isaac Newton may have developed one of the most elegant and useful tools of mathematics using ideas that had originated in Kerala more than 200 years before his time, new research suggests.

Science historians have long attributed the origins of calculus — a bedrock of mathematics, physics and even economics — to Newton and other 17th-century European mathematicians.

But researchers in Britain have gathered evidence that a basic component of calculus, developed by mathematicians in Kerala during the 14th and 15th centuries, was passed on to Jesuit scholars who may have carried it to Europe.

George Gheverghese Joseph at the University of Manchester and Dennis Almeida at the University of Exeter analysed mathematical contributions of Madhava, Nilakantha and other mathematicians who lived in Kerala between 1340 and 1540. They also searched through obscure Jesuit documents scattered in archives in Italy, Portugal, Spain and the Netherlands.

“We have strong circumstantial evidence that mathematics from the Kerala school influenced the development of modern mathematics in Europe centuries later,” Joseph told The Telegraph.

Their research suggests Jesuit scholars had visited Kerala at the time, and one of their tasks was to gain some understanding of Indian mathematics. “There is evidence of motivation and evidence of opportunity. There was also a corridor of communication… we also know that the Jesuit scholars were in touch with leading European mathematicians of their time,” Joseph said.

“The brilliance of Newton’s work at the end of the 17th century stands undiminished, especially when it came to the algorithms of calculus. But Madhava and Nilakantha should stand shoulder to shoulder with him,” Joseph said.

Madhava and Nilakantha developed a basic component of calculus called “infinite series”. The Kerala school also discovered the pi series, and had used it to compute pi up to 17 decimal places. The two UK researchers argue that knowledge carried by the Jesuit scholars and passed on to contemporary mathematicians may have eventually reached Newton.

The great English physicist is himself known to have acknowledged his debt to past thinkers, saying: “If I have seen farther, it is by standing on the shoulders of giants.”

The research, funded by the UK Arts and Humanities Research Council, was part of an effort by Joseph to gather new evidence for the possibility of transmission of knowledge from India to Europe. He was seeking fresh information for incorporation into a yet-to-be-published third edition of his book, The Crest of the Peacock: the Non-European Roots of Mathematics.

While the beginnings of modern mathematics are usually viewed as a European achievement, the discoveries in medieval Kerala between the 14th and 15th centuries have either been ignored or forgotten, Joseph said.

One of the first references to the contribution of the Kerala school was published in a paper in the Journal of the Royal Asiatic Society in 1935. During the 1970s and 1980s, another journal had highlighted medieval Kerala mathematics.

Email This Page