Key component of calculus identified two centuries before Newton

1702 Portrait of Newton by Godfrey Kneller

August 16, 2007 New research suggests that a key aspect of the calculus, commonly attributed to Sir Isaac Newton and Gottfried Leibnitz in the late 1600s, may in fact have been discovered more than two centuries earlier by scholars at the Kerala School in southwest India.

One of the basic components of calculus, ‘infinite series’, was actually identified in 1350 according to Dr George Gheverghese Joseph from the University of Manchester. "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" said Dr Joseph.

The team from the University of Manchester in Exeter, UK, made the discovery whilst perusing obscure Indian papers for research for a new book. They also uncovered that the Kerala School had also discovered what amounted to the Pi series and used it to calculate Pi correct to 9, 10 and later 17 decimal places.

The foundations of calculus and Pi are currently attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries. Although he respects Newton as a great mind in mathematics, Dr Joseph says that is incorrect. "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" he said.

There is strong circumstantial evidence to suggest that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century. That knowledge, Dr Joseph argues, may have eventually been passed on to Newton himself but has not be recognized due to "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."

When asked whether he believed the history books will be rewritten, the academic said he found it "hard to imagine that the West would abandon a 500-year-old tradition of importing knowledge and books from India and the Islamic world."

Newton was a renowned physicist, mathematician, astronomer, natural philosopher and alchemist (it sounds strange in the 21st century, but apparently the father of modern physics spent quite a bit of time trying to convert base metals into precious ones). Ironically in the context of undiscovered works, Newton himself reportedly identified calculus as a student and didn't tell anyone about it for some 27 years.

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