Basic Mathematics

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

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as remarked above that for the study of Cosmos and Karma theory, the Jaina scholars had developed mathematics very much. But it is unfortu in spite of some scattered attempts now by some research workers, like Rangáchārya, Smith, Kāpadiyā, Singh, Datta, Saraswati etc., most of the Jaina School mathematics is still unknown to the world, specially to the modern historians. In order to bring out this hidden treasure to light, the author has made a modest attempt. He describes in brief some facts about Ganitasāra-samgraha of Mahāvirācārya (c. 850 A. D.) and also some other texts belonging to Karaṇānuyoga group of the Jainas. It is believed that the number concept based on the set theory was evolved at the hand of Georg Cantor about a hundred years ago but the author, on the basis of researches made by himself and other research workers, states that this concept originated in the Jaina School in the early Christian era and was symbolized to its perfection upto the time of the Jain Scholar Todaramala of the 18th Century A. D. He further remarks that had the Karma system Theory of the Jainas in India with set theoretic approach reached Gauss, Fourier, Bolzano, Galois, Hamilton, Boole etc., the system theories of the biophysical world could have taken a new turn by now.
In Chapter 2, the author gives a synopsis of the world history of mathematics upto the time of Mahāvīrācārya (c. 850 A. D.). He also states, "In what part of the world and when, one thought that number and form could be as much useful as the language for any civilization, is not known. The present structure of mathematics has however been laid down on the basis of number and form. From the number system, were evolved arithmetic and algebra whereas the form study was responsible for the evolution of geometry. By the seventeenth century, the harmonious phases of these both led to the development of mathematical analysis." The author describes in brief the known works on mathematics by some ancient civilizations Sumerian, Babylonian, Egyptian, Chinese, Greek and Indian, the seats of ancient culture, as brought to light by several research workers. These works belong to the period, say, from 3000 B, C. or even earlier to the early centuries of
ne Christian era. A brief description of Indian mathematics from Āryabhata I (5th Century A. D.) to the 16th Century A. D. is also given.
In Chapter 3, the author gives a nice and lucid description of the contents of the famous Jaina mathematical work Tiloyapannatti' by Yati vīşabha of 5th century A. D. This work belongs to the Karaņānuyoga group of the Jaina Prakrit Texts, the other main books belonging to this group being Jambūdiva paņņatti saṁgaho, Lokavibhāga, Trilokasāra, Sūryaprajñapti, Candra-prajñapti, Jambūdvipa-prajñapti etc. This text gives a systematic treatment of basic mathematics as applied to the Jaina Karma
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