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Indians predated Newton 'discovery' by 250 years
A little known school of scholars in southwest India discovered one of the founding principles of modern mathematics hundreds of years before Newton – 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.
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 mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.
That knowledge, they argue, may have eventually been passed on to Newton himself.
Dr Joseph made the revelations while trawling through obscure Indian papers for a yet to be published third edition of his best selling book ‘The Crest of the Peacock: the Non-European Roots of Mathematics’ by Princeton University Press.
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.
“Certainly it’s hard to imagine that the West would abandon a 500-year-old tradition of importing knowledge and books from India and the Islamic world.
“But we’ve found evidence which goes far beyond that: for example, there was plenty of opportunity to collect the information as European Jesuits were present in the area at that time.
“They were learned with a strong background in maths and were well versed in the local languages.
“And there was strong motivation: Pope Gregory XIII set up a committee to look into modernising the Julian calendar.
“On the committee was the German Jesuit astronomer/mathematician Clavius who repeatedly requested information on how people constructed calendars in other parts of the world. The Kerala School was undoubtedly a leading light in this area.
“Similarly there was a rising need for better navigational methods including keeping accurate time on voyages of exploration and large prizes were offered to mathematicians who specialised in astronomy.
“Again, there were many such requests for information across the world from leading Jesuit researchers in Europe. Kerala mathematicians were hugely skilled in this area.”
Submitted by BJS on Mon, 2007-08-13 08:35.
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More specifics
The article lacks specifics because it is not backed by any recent peer-reviewed publication. The ethics of this is well known. Hence, the focus is on the story, not facts, and don't expect the story to be reliable.
On August 25, 2007, Hindustan Times, New Delhi (p. 2), published a correction to this story dismissing it as incorrect. It pointed out that the Indian infinite series have been known to British scholars since 1832 (at least). It also pointed out that work on transmission of the calculus has already been published in my book, "Cultural Foundations of Mathemamtics: the Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th c. CE"
The correction also mentioned that one of the researchers had been warned in 2004 by Exeter university against plagiarising my work. So, as you can see, this process of suppressing non-European sources is still very much at work, and it should not be presumed that it happened innocently, any more than the suppression of the non-European sources of the calculus happened innocently. The book relates the origins of racist history to theology and the religious fanaticism that prevailed in Europe during the Crusades and Inquisition. So it would be more accurate to replace the term "non-European" by "theologically incorrect".
You are absolutely right that the Indian material was too far ahead of its times from a European perspective to have been understood there. This thesis is discussed in detail in the book, and you can find a quick glimpse of it from the reactions of Descartes and Galileo mentioned in the elementary expository article on the Indian Rope Trick at http://IndianCalculus.info/ropetrick_journal.pdf . (Descartes, in his Geometry, declared it beyond the capacity of the human mind to determine the length of a curved line.) It was due to this lack of understanding that Newton's theory of fluxions had to be eventually abandoned.
The lack of understanding arose because Indian mathematics was practical unlike European mathematics which was spiritual (since Plato) and theological (since Aquinas). This thesis of a "clash of epistemologies" is disccussed in detail in the book, and in supporting papers indicated at the site http://IndianCalculus.info.
Indians predating Newton
This article would be a lot more meaningful if it included some specifics. It is impossible for me or anyone else to have even a remote clue of the actual significance of the mathematics vaguely hinted at here. I would be very interested to hear about what was actually done There were a great many infinite series (and products) that added up to (or multiplied out to) pi and to other numbers as well. I believe that many of them predate Newton considerably, although I would have to look this up.
It appears obvious that the author of this post believes that European racism is behind the fact that non-European scientitst and mathiematicians are not credited with their discoveries. It is not the only factor. In mathematics, credit is often given to the person whose work was followed up, or who took a theorem and used it in a particularly fruitful way. Unfair to the originator no doubt, but common. This unenviable fate has happened to numerous European as well as non-European ones. The Indians themselves clearly never developed this material as was done later in Europe or I expect we would have known about it. They also wrote in a language unlikely to be known in Europe. A final comment is that it is possible that the material was too far ahead of times from a European perspective to have been understood there.
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