Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

Page 23

importance to the historians of Indian Mathematics-the period preceding the fifth century A. D.)9 The study of the analytical methods for comparing infinities led him to opine, “As already pointed out, the method of one-toone correspondence has proved to be the most powerful tool for the study of infinite cardinals, and the discovery and first use of the principle must be ascribed to the Jainas, 20"
Datta and other scholars23 did not have before them detailed commentaries of the Gommatasara, Ksapaņāsāra texts on which two separate chapters on artha samdrsti (symbolic norms) were compiled by Todaramala of Jaipur22 (C+1767), serving as guides to the learners. His predecessors, Keśavavarni (c.+1360) and Nemichandra (c. + 1552), a disciple of Jňānabhūsaņa, had paved the way through Kannada and Sanskrit commentaries wherein one could find two types of mathematical measures : universal and postuniversal. These commentators had before them the Dhavalā texts as well as the Tiloyapannatti, alongwith the summary texts of Nemichandra Sidhāntacakravarti (c.+11th century). The texts are on the mathematical theory of Karmic system. (d) Events :
It is strange to observe, how the western and the eastern parts of the world were deeply absorbed in mathematical manoeuvre. The mathematical world remodelled by Newton was facing the well known crisis in calculus. It was gradually progressing from intuition to absolute rigour. Euler (+1750) made profound changes in analysis and Lagrange (+ 1780) contributed to the theory of numbers, analysis and elliptic functions. It was a dead mathematical world and the number concept based on a set theory was still to evolve at the hand of Georg Cantor after a century, which in the Jaina School originated in the early Christian era and symbolized to its perfection upto the time of Todaramala. Quantum theory was to appear still later, alongwith applications of set theory and functional analysis. Had the Karma system theory of India with its set theoretic approach reached Gauss ( + 1800), Fourier (+1810), Bolzano (+ 1820), Galois ( + 1830), Hamilton ( + 1850) and Boole (+ 1850), the systems theories of the biophysical world could have taken a new turn by now.
19. Cf. Mathematics of Dhavalā, op. cit. 20. Cf. ibid. 21. Vid, the works of the more research workers Kapadia, Misra, Roy, Jain,
Shastri, Saraswati, Volodarsky, Gupta, Vijayaraghavan, Lishk, Sharma, Agrawal, M. Kumar, Sikdar, Zaveri, Bose, Sen, Subbarayappa, Bag and
so on, referred in bibliography 22. Cf. Mathematical contribution, op. cit. bibliography.