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."
Source: University of Manchester
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