# How influential was the Kerala school to European development in Calculus?

Did it influence the work of Newton or Leibniz, i have often heard that Europeans "stole" calculus from the Kerala school, these are views often parroted by Indian nationalists, but how accurate is it?

• This view has no historical support. Geometry derived from Ancient Greece. Algebra in Renaissance Europe wah gratly influenced from Medieval Arabic math. The "merge" of geometry and algebra in Early Modern Europe (Descartes, mainly) was the big step-forward in math before the calculus. – Mauro ALLEGRANZA Jun 1 '18 at 6:52
• A simple argument which refutes these fantasies is that the results of this school were not available in any language that Newton and Leibniz could read. – Alexandre Eremenko Jun 1 '18 at 17:54
• Ah, but Joseph (2000, p. 356) has speculated that the Vatican library contains Jesuit translations of Madhava :-) – Francois Ziegler Jun 1 '18 at 19:02
• The consensus is no. For discussion and references see What was the historical context of the development of Taylor series? – Conifold Jun 1 '18 at 23:17
• Indians predated Newton 'discovery' by 250 years 13 Aug 2007 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....see humanities.manchester.ac.uk/aboutus/news/display/?id=121685 – drvrm Jul 17 '18 at 21:09

In my work with primary sources in such authors as Fermat and Leibniz, I have occasionally come across references to earlier works by Arab mathematicians, but have never seen references to work by the Kerala school. Speculations about Kerala influences are based on the existence of trade routes connecting Europe with India. Apart from this being a highly speculative matter, I have always wondered why the existence of trade routes should be interpreted as evidence in favor of influence of Kerala on Europe rather than influence of Europe of Kerala. After all, the traffic presumably was not a one-way street.

• Madhava worked in late 1300-s, what exactly in the way of influence on his work on power series could Europe offer at the time? – Conifold Jun 9 '18 at 21:25
• The OP spoke of "The Kerala School". This is placed at 14th-16th centuries by wiki. – Mikhail Katz Jun 10 '18 at 10:09
• That school clearly attributed the Gregory-Leibniz series (and 10+ decimal places of $\pi$) to Madhava. “Trade routes” can’t explain that unless either they allowed time travel or it’s all due to Roger Bacon. – Francois Ziegler Aug 4 '18 at 13:01

So I’ll quote Pingree (1992, p. 562) (to which both comment threads led me via Murty (2013)), as it struck me as elucidative in this ugly matter.

Briefly, he says that those making the claim are belittling both Indian and Western math because “Hellenophilia” (~ idea that math cannot exist other than in Greek style) rendered them unable to imagine (p. 563) anything other than plagiarism:

(When) the Indian Mādhava’s demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions (...) was first described in English by Charles Matthew Whish, in the 1830s, it was heralded as the Indians’ discovery of the calculus. (This) resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series without the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava’s mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution.

Other examples of this dangerous tendency abound. For instance, since the 1850s historians ignorant of Mādhava’s work have argued about whether Indian astronomers had the concept of the infinitesimal calculus (...) in a formula for finding the instantaneous velocity of the moon (...) I cannot tell you how that formula was derived, since its author, Varāhamihira, has not told me; but I find it totally implausible that some Indian discovered the calculus — a discovery for which previous developments in Indian mathematics would not at all have prepared him — applied his discovery only to the problem of the instantaneous velocity of the moon, and then threw it away. The idea that he might have discovered the calculus arises only from the Hellenophilic attitude that what is valuable in the past is what we have in the present.

(For exposition and detailed bibliography of the papers on Mādhava see e.g. Roy (2011, Chap. 1, pp. 14-15).)