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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."
Erratum
Since the publication of this news release it has come to the attention of the
University of Manchester that other researchers have made a significant
contribution to knowledge on the transfer of Kerala Mathematics to Europe. The
University would particularly like to recognise the significant body of work
conducted by Professor CK Raju in this area and would have wished to
acknowledge this in the original news release.
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