Zoomed Vinay Special · First-person editorial
The 'Leibniz' Series for Pi Was Written in a Kerala Verse Two Centuries Before Leibniz. Was It Calculus? Here Is What the Palm Leaves Prove
A Kerala astronomer's verse adds and subtracts one over three, one over five, one over seven, forever, and lands on pi. A Malayalam book of about 1530 proves it by slicing a square into infinitely small pieces. I read the 1834 paper that told London, the 2008 critical edition of the proofs, and Leibniz's own 1682 Latin, and I tell you which part is a fact, which part is a stretch, and which part nobody has been able to prove.
The point of view
Calicut, 1827. A palm-leaf book in Malayalam is being copied; the copy ends up with an Englishman named Charles Whish. Five years later, in London, his paper says infinite series for the circle "originated in Malabar", and that Europe knew them only through Newton's "fluxions". He was right about the series. He was wrong about who wrote them. And he promised a second paper on the proofs that, as far as anyone can find, he never published. I opened his paper, the critical edition of the Yuktibhasa, and Leibniz's 1682 article. Was it calculus? Did the Jesuits carry it to Europe? Here is what the documents prove, and what they don't.
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C. M. Whish, "On the Hindú Quadrature of the Circle, and the infinite Series of the proportion of the circumference to the diameter exhibited in the four S'ástras, the Tantra…
archive.org
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K. V. Sarma (ed., tr.), with explanatory notes by K. Ramasubramanian, M. D. Srinivas and M. S. Sriram, Gaṇita-Yukti-Bhāṣā (Rationales in Mathematical Astronomy) of…
doi.org
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K. V. Sarma, A History of the Kerala School of Hindu Astronomy (in Perspective) (Vishveshvaranand Institute, Hoshiarpur, 1972), pp. 16, 18 and n. 2, 20, 22–23, 25–26, 51,…
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G. W. Leibniz, "De vera proportione circuli ad quadratum circumscriptum in numeris rationalibus expressa", Acta Eruditorum (Leipzig), February 1682, p. 44
archive.org
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G. W. Leibniz, "Nova Methodus pro Maximis et Minimis…", Acta Eruditorum, October 1684, pp. 467, 469
archive.org
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Royal Asiatic Society, Whish Collection catalogue records: Yukti-bhāṣā (raswhishNA-124),; Tantrasaṅgraha-valiyabhāṣā (raswhishNA-120)
archive.org
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Victor J. Katz, "Ideas of Calculus in Islam and India", Mathematics Magazine 68:3 (1995), pp. 163–174
jstor.org
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Dennis F. Almeida and George G. Joseph, "Kerala Mathematics and its Possible Transmission to Europe", Philosophy of Mathematics Education Journal 20 (2007)
exeter.ac.uk
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Kim Plofker, review of G. G. Joseph, A Passage to Infinity (SAGE, 2009), Aestimatio 10 (2013), pp. 56–62
ircps.org
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C. K. Raju, "Teaching mathematics with a different philosophy
arxiv.org
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Bharath Gyan, "Calculus was discovered in India" (22 December 2019)
bharathgyanblog.wordpress.com
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