Kerala School predated Newton by 250 years.

You can count on Pi

Newton was exceptionally brilliant, especially when it came to the algorithms of calculus.

But ......

Researchers at the University of Manchester report that the 'Kerala School' identified the 'infinite series'- one of the basic components of calculus - in about 1350.

Historians wrongly attribute this and other mathematical breakthroughs to Isaac Newton and Gottfried Leibniz at the end of the seventeenth century.

Other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with Newton as they discovered the other great component of calculus- infinite series.

The Kerala School also discovered what amounted to the Pi series and used it to calculate Pi correctly 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 15th century. This may have eventually been passed on to Newton himself.

Dr Joseph reports this also in his best-selling book 'The Crest of the Peacock: the Non-European Roots of  Mathematics'.

He said: "The beginnings of modern maths are usually seen as a European achievement, but the discoveries in medieval India between the 14th and 16th centuries have been ignored or forgotten.

Two reasons for this. First, the language. Some of the most seminal texts and documentation are in forms such as the 'Yuktibhasa', which is not commonly found nowadays.

Second, a European colonial mindset makes it difficult to acknowledge scientific ideas emanating from the non-European world. It is difficult for the West to abandon a 500-year-old tradition of importing knowledge and books from  India and the Islamic world.

An important path of flow of knowledge from East to West was through European Jesuit priests, who were present in the area at that time. These Jesuits were learned with a strong background in maths and were well-versed in the local languages.

There was also strong motivation and resource support from Pope Gregory XIII himself. He had 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. Large prizes were offered to mathematicians who specialised in astronomy. Kerala mathematicians were hugely skilled in this area.

The lesson of this is that we are often ignorant about ourselves as individuals, groups and as a civilisation. 'One who looks outward may see. The one who looks within awakens.'

Once we awaken, we do not need validation from the outside.

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Acknowledgement: I am grateful to my friend Uday Rao Patwardhan for sharing this information with me.

Interesting Links:

• Indians predated Newton's 'discovery' by 250 years ~ The University of Manchester

• The Crest of the Peacock: the Non-European Roots of  Mathematics ~ George Gheverghese Joseph

• Yukthibhasa And Tantrasangraha Texts ~ Dr K Ramasubramanian (Math Historian)

• You Can Count on Pi ~ Rhett Allain in WIRED

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