Thursday, October 11, 2007

pioneer: Plethora of evidence - Kerala School

oct 11th, 2007

k v sarma was an awesome person. i met him just before he died in jan 2005.

i am from kerala, and i am definitely happy that the kerala school of mathematics more or less invented the calculus.

---------- Forwarded message ----------
From: Sushama

Plethora of evidence – Kerala School

Op ed - October 11, 2007


Who says 'Kerala School' is not present in the annals, asks Jatindernath Joshi


This is with reference to a sweeping statement by KL Jhingan, based solely upon Jawaharlal Nehru's Discovery of India and AL Basham's Wonder that was India, in the article, "Kerala school missing in annals" (October 8). The writer asserts that no original work in mathematics was carried out in India after 12th century AD. That's not true.


There is vast literature in Sanskrit and regional languages to prove that significant original work in mathematics was carried out even after 12th century AD. Kerala's palm-leaf' records in Malayalam, available in the Oriental Institute Baroda, is one such source of reference.


One may refer to Indian Science through the Ages, Part II, by the publisher Vivekananda Kendra Patrika, Volume 12, No 2, (1983), in which Mr KV Sarma writes on "Astronomy and Mathematics in Medieval India". He describes the development of maths in India after the 12th century AD. Just a few examples are given as under.


Reduction to the Ecliptic by Tyco Brahe (1546-1601), enunciated by Achyut Pisarati (1550-1621) in his Sphutanirnaya (4.2) and simplified formula in his later(1583) work Uparagakriyakrama, is a glorious example.


As for Irrationality of Pi by Lambert (1671), the value of pi, approximately 62832/20000 = 3.1416, correct to four rounded-off decimal places was offered by commentator Nilakantha Somayaji, (Kerala School, 15th century). He argued that this is not only an approximation, but also that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, for the irrationality of pi was proved in Europe only in 1761 by Lambert.


Next comes Gottfried Leibnitz's Power series for Pi. The Kerala school of astronomy and mathematics was founded by Madhava of Sangamagrama in Kerala. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559-1632).


In attempting to solve astronomical problems, the Kerala school independently created a number of important mathematics concepts. Their most important results - series expansion for trigonometric functions - were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work, Yuktibhasa (c.1500-c.1610), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha. 


Their discovery of these three important series expansions of calculus - several centuries before calculus was developed in Europe by Leibniz and Isaac Newton-was a landmark achievement in mathematics.


I am no Keralite. But I can assert that the "Kerala School" is very much present in the annals.



Harish said...
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