Pramāṇa · Search · About · API

A History of the Kerala School of Hindu Astronomy (in Perspective) c8.s1: 1. The background

A History of the Kerala School of Hindu Astronomy (in Perspective) c8.s1

Language
English

1. The background

c8.s1.1

In the light of the trends that developed in the study and practice in Kerala of the twin sciences of astronomy and mathematics, as indicated in the last chapter, it need not be surprising that some of the significant findings of modern mathematics are found anticipated in the astronomical works produced during the mediaeval times in that region. In their endeavour to make the results obtained by computation accord with observation, the Āryabhaṭan school of astronomers of this corner of India made substantial advancement in their computational skill. Working on the basic principles of algebra, geometry and limiting values, they produced, by dint of shrewd thinking and logical reasoning, coupled with a fund of intuition, significant results on such matters as the reduction to the ecliptic, summations and associated integrations leading up to the value of π etc. Especially, the achievements connected with π were brought to the notice of scholars by Charles M. Whish who presented a paper on the subject before the Royal Asiatic Society in 1832.¹ Among other things, Whish set out in this paper the several formulae enunciated in four Keralite works on astronomy and mathematics, viz., *Tantrasaṅgraha*, *Yuktibhāṣa*, *Karaṇapaddhati* and *Sadratnamālā*, for the circumference of a circle in terms of its diameter and transformations of the infinite series for π associated with the name of Leibnitz.

c8.s1.2

¹ C.M. Whish, ‘On the Hindu quadrature of the circle, and the infinite series of the proportion of the circumference to the diameter exhibited in the four Śāstras, the *Tantrasamgraham*, *Yucti-bhasha*, *Carana Padhati* and *Sadratna-mala*’, *Trans. Royal Asiatic Soc. of Gr. Britain and Ireland*, 3 (1835) 509-23.

c8.s1.3

The significance of the findings of Whish was hardly taken note of by historians of mathematics or of Indian literature, for more than a century. Instead, the view continued to prevail that Indian astronomy and mathematics were mostly borrowed from the West and that, at least since Bhāskara II, little original contribution was made by India to these disciplines.¹ The credit for launching, in the 1940-s, a detailed study of the discoveries of Whish in terms of modern mathematics goes to Prof. C.T. Rajagopal and his students and colleagues, including K. Mukunda Marar, A. Venkataraman, T.V. Vedamurthi Aiyar and K. Balagangadharan. The valuable notes added by Rama Varma Maru Thampuran and A.R. Akhileswara Aiyar to their excellent edition of the First Part of *Yuktibhāṣā*, (Trichur, Kerala, 1948), an expository work in Malayalam, new light on whose date and authorship has recently been thrown,² is another significant contribution in this direction. More recently, some other scholars like T. S. Kuppanna Sastri, T. A. Saraswathi and R.C. Gupta have been making valuable contributions to connected topics. The attempt made herein below to present, in a succinct form, the results of the investigations of the said scholars and those of the present writer which lie scattered in different books and periodicals, will, it is to be hoped, give a bird's-eye view of the significant contributions of Kerala savants to mathematics and astronomy.

c8.s1.4

¹ *Vide*, for instance, G.R. Kaye: "After the time of Bhāskara (born A D. 1114), no Indian mathematical work of historical value or interest is known." (*Indian mathematics*, Calcutta, 1915, p. 24); A. B. Keith: "After Bhāskara, no progress can be recorded in Indian astronomy." (*A history of Indian literature*, Oxford, 1929, p. 523); A. A. Macdonell: "The last eminent Indian astronomer was Bhāskarācārya, born in A.D. 1114." (*A history of Sanskrit literature*, Indian rep., Delhi, 1962, p. 370); D. Arka Somayaji, "Bhāskara is the last name in the field. Barring a number of commentators, no name worthy of mention is there in India subsequent to Bhāskara." (*A critical study of the ancient Hindu astronomy*, Dharwar, 1971, p. 3). Standard historians of mathematics like Cantor, Cajori and D.E. Smith, too, hold the same view. The first Western historian of mathematics to take note of Whish's findings would appear to be A. P. Juschkewitsche in his *Geschichte der Mathematic Mittelalter*, (Leipzig, 1964), as pointed out to C. T. Rajagopal by D. T. Whiteside, the eminent Cambridge authority on Isacc Newton.

c8.s1.5

² K. V. Sarma, 'Jyeṣṭhadeva and his identification as the author of *Yuktibhāṣā*', *Adyar Library Bulletin*, 22 (1958) 35-40.

Linked texts (3)