Emergence of a New Era in the History of Indian Mathematics

It is now well established that the school of astronomy and mathematics, founded by Mādhava in Kerala in the 14th century, came up with two of the major discoveries, namely calculus and non-geocentric planetary models, a couple of centuries before they were to become the hallmarks of the modern European scientific revolution. The seminal discovery of the Kerala school, of the infinite series for \piπ was brought to the notice of modern scholarship for the first time in the book Kālasa\dot{n}n˙kalita of John Warren, published from Madras in 1825. This was soon followed by the detailed account presented in the pioneering articles of Charles Whish, which were published during 1827–1834. However, the work of the Kerala school was totally ignored by modern scholarship for over a hundred years. This was because Whish’s paper and the Kerala work on infinite series were denigrated and suppressed by the British academic establishment so much so that even reputed Indologists such as Albrecht Weber, and George Thibaut, and renowned historians of mathematics such as David Smith chose not to say anything about the work of the Kerala school even when they referred to the articles of Whish in their scholarly writings.

The work of the Kerala school was resurrected by the pioneering article on the “Hindu values of \piπ” by Bibhutibhushan Datta in 1926. This was followed by the article “On the use of series in Hindu Mathematics” by Datta’s colleague, Avadhesh Narayan Singh, which was published in the first issue of Osiris in 1936. During 1940–1952, C.T. Rajagopal and his collaborators wrote a series of important articles explaining, in modern mathematical terms, all the important demonstrations for the infinite series for \piπ, and the sine and the cosine functions, as given in the Malayalam text Yuktibhāṣā. Equally significant was the publication in 1948 of the mathematics part of this classic text, which was edited along with detailed notes in Malayalam, by Rama Varma Tampuran and Akhileswaraiyer. When the contents of these important publications were taken note of in the 1950s and 1960s, by some of the well-known historians of mathematics such as J.E. Hoffmann (1953), C.N. Srinivasiengar (1958, 1967), A.P. Yushkevich (1961, 1964), D.T. Whiteside (1961, 1968), H.L.L. Busard (1962), T.A. Sarasvati Amma (1963, 1979), A.K. Bag (1966, 1979) and M.E. Baron (1969), one could clearly see the emergence of a new era in the historiography of Indian mathematics.

Starting from the publication of Bhaṭadīpikā commentary of Parameśvara on Āryabhaṭīya by H. Kern in 1874, around fifteen source-texts of the Kerala school were published in the next eighty years. Still, there remained several gaps in our understanding of the history and achievements of the Kerala school. It is the monumental work of K.V. Sarma, whose prolific writings have contributed substantially to our present understanding of the history and contributions of the Kerala school. Starting from 1953, Sarma edited and published about twenty very important works of the leading savants of the Kerala school. Sarma also brought out a comprehensive history and bibliography of Kerala works on Astronomy and Mathematics in 1972, where he listed around 400 works. It was Sarma’s relentless efforts to bring out works which present yuktis, or demonstrations, which led to the publication of the Sanskrit commentaries, Kriyākramakarī and Yuktidīpikā of Śa\dot{n}n˙kara, the compilation Gaṇitayuktayaḥ (containing 27 small tracts of yuktis), and the critical edition of Yuktibhāṣā of Jyeṣṭhadeva, along with English translation and explanations. Sarma’s publication of the seminal works of Nīlkaṇṭha such as Golasāra, Siddhāntadarpaṇa and Grahasphuṭānayane Vikṣepavāsanā, led to a clearer understanding of the revised planetary model that was proposed by Nīlkaṇṭha in his Tantrasa\dot{n}n˙graha and Āryabhaṭīyabhāṣya. One of Sarma’s landmark publications has been the Jyotirmīmāṃsā of Nīlkaṇṭha, which discusses the crucial role of continuous parīkṣā, or examination of the theories by observation, and the consequent process of revision and preparation of newer and more accurate karaṇas or computational manuals.

Currently, there are still many important source-works of the Kerala school–-including works composed by legendary figures such as Mādhava, Parameśvara, Putumana Somayājī, Śa\dot{n}n˙kara and Acyuta–-which are yet to be edited and published. Further, among the fifty major source-works (and about thirty small tracts) which have been published, only about a dozen have been translated; and even among them, there are only perhaps half a dozen works which have been studied in depth to explicate their full technical content. It will be befitting to the legacy of K.V. Sarma, and his illustrious predecessors such as Datta and Singh, Rama Varma Tampuran, C.T. Rajagopal and others, that our young scholars imbibe their great dedication and respect for our tradition, and carry forward their mission to ensure that the entire corpus of works of the Kerala school is rigorously and comprehensively studied and brought to light.

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