cit., p. 282; George Joseph, The Crest of the Peacock:: Non-European Roots of Mathematics, Princeton, Princeton University Press, 2000, pp. He developed infinite series approximations for a range of trigonometric functions, including π, sine, etc. In conclusion, it is worth noting that we have focused so far on evidence of direct transmis¬sions of Kerala ideas to Europe. Carana Padhati, and Sadratnamala”, Transactions, 3 (1835): 509-523, p. 521. But opting out of some of these cookies may have an effect on your browsing experience. The achievements of the Kerala School and their chronological priority over similar developments in Europe were now being aired in several Western publications [20]. Van der Waerden concludes his work on the Greek origins of these works of Aryabhata and Bhaskara work by stating that scientific discoveries are, in general, dependent on earlier prototypical works [33]. The school flourished in the 14th-16th centuries. Here he states that “the original common source of the Hindu authors was a Greek treatise in which the whole method was explained.”, [33] B. van der Waerden, “Pell’s equation in Greek and Hindu mathematics”, Russ. Kerala Mathematics Vararuchi to Purushothaman Namboothiri Overview Kerala school of astronomy and mathematics Katapayadi system Jyā, koti-jyā and utkrama-jyā An Important Source Book by K. V. Sarma A History of the Kerala School of Hindu Astronomy Vararuchi Vararuchi Chandravakyas Paramesvara Parameshvara Parahita Drigganita Sangamagrama Madhava What we see from these paradigms is that a case for claiming the transmission of knowledge from one region to another does not necessarily rest on documentary evidence.
The object of this forgery was to throw Varaha Mihira, who lived about the time of Akber, back into antiquity… Thus we see how Brahma Gupta, a person who lived long before Aryabhata and Varaha Mihira, is made to quote them, for the purpose of throwing them back into antiquity….
[54] Josef Wicki 1948-. [62] Isaia Iannccone, Johann Schreck, op. Whatever the nature of the profit, intellectual or material, the motivation may have been sufficient for the learned Jesuits to have acquired the relevant manuscripts containing the Kerala mathematics.
This transmission was not just westwards for there is documentary evidence of Indian mathematical manuscripts being found and translated in China, Thailand, Indonesia and other south-east Asian regions from the 7th century onwards [28]. The Origins of the Infinitesimal Calculus. The last two names belong to the amazing Kerala school of mathematics and astronomy. This is attested by [68] and Srinivasiengar [69] who state that the author of the Sadratnamala is Sankara Varma, the younger brother of Raja of Cadattanada near Tellicherry and further states that the Raja is a very acute mathematician.
Ricci’s arrival in Goa was significant in respect of Jesuit acquisition of local knowledge. A prominent early Jesuit de Nobili, for instance, in 1615, wrote a critical paper on the Varamihira’s Vedanga Jyotisa [56]. He is a faculty in the Department of Humanities and Social Sciences at the Indian Institute of Technology (IIT)-Mumbai. However, it needs to be pointed out that this acknowledgement is not necessarily universal. XV, p. 667. [53] Ugo Baldini, Studi su filosofia, op. Neugebauer uses his paradigm to establish his conjecture about the Greek origins of the astronomy contained in the Siddhantas. Srinivasiengar [70] further refers to the Malyalam History of Sanskrit Literature in Kerala which identifies the King of Cochin, Raja Vanna, as being aware of the chronology of the Karana-Paddhati. [14] L. Fiegenbaum, 1986. [69] C N Srinivasiengar, The History of Ancient Indian Mathematics, op. XIV, p. 425 and vol. [38] Marin Mersenne, Correspondance, op. He has also published detailed explanatory notes in two volumes on ganita-yuktibhasa, a seminal work of the Kerala School of Mathematics (Springer 2009). This website uses cookies to improve your experience while you navigate through the website. This suggests that the former royal family in Cochin, which was in possession of a large number of MSS, had not only a scholarly tradition, but also a tradition of helping other scholars. Van der Waerden makes a similar claim about Bhaskara’s work on Diophantine equations and, whilst offering an argument based on methodological similarities, he is sufficiently convinced about the existence of an unknown Greek manuscript which was available to Bhaskara and his students [32]. p. 151. cit., p. 169. cit., vol. An earlier version of this paper came out in 2007 online in Philosophy of Mathematics Education Journal (No. The rationale for learning the vernacular languages was to aid their work in converting the local populace to Jesuit Catholicism by understanding their science, culture and customs. They were able to appreciate this knowledge by their learning of the vernacular languages such as Malayalam and Tamil [55]. The earliest known urban Indian culture was first identified in 1921 at Harappa in the Punjab and then, one year later, at Mohenjo-daro, near the Indus River in the Sindh. This may explain the absence of documentary evidence in Jesuit communications. At some point in their stay in India these Jesuits went to the Malabar region including the city of Cochin, the epicentre of developments in the infinitesimal calculus [52]. He asserted: “I can only compare their mathematical and astronomical literature, as far as I know it, to a mixture of pear shells and sour dates, or of pearls and dung, or of costly crystals and common pebbles [8].”. [45] Claude Brezinski, History of Continued Fractions, op. The famous Matteo Ricci was in the first batch of Jesuits trained in the new mathematics curriculum introduced in the Collegio Romano by Clavius. [4] For example, Margaret Baron, Origins of Calculus, op. 214-215. [19] For example, C. T. Rajagopal and T. V. Vedamurthi 1952: “On the Hindu proof of Gregory’s series,” Scripta Mathematica, 18, 65-74, C. T. Rajagopal and M. S. Rangachari 1978: “On an Untapped Source of Medieval Kerala Mathematics,” Archive for the History of Exact Sciences, 18, 89-102. Similarly van der Warden uses the ‘hypothesis of a common origin’ to claim that Aryabhata’s trigonometry [31] was borrowed from the Greeks. New York, Springer Verlag, p. 30. Figure 5a-b: Palm leaf manuscript from Kerala. All this is circumstantial – to make our case for the transmission of Kerala mathematics we will use stronger criteria.
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[13] F.F. In the next section all these aspects will be discussed. 2, p. 395.
[52] See for example Isaia Iannaccone 1998.
[41] Victor Katz,”Ideas of calculus in Islam and India”, Math Magazine, op. These developments first occurred in the works of the Kerala mathematician Madhava and were subsequently elaborated on by his followers Nilakantha Somayaji, Jyesthadeva, Sankara Variyar and others between the 14th and 16th centuries [3]. However, this work was overshadowed by the rise of Indian mathematical research and mathematical societies on the lines of Western models. Even after the colonial policy of basing “native education” on an English curriculum was established in the 19th century, some scholars continued to recast foreign mathematics in the form of traditional Sanskrit verse treatises.
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