Basic Mathematics

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

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active research work on Jain School of Mathematics started; credit for this goes to authors like Jain (H. L.), Upadhyāya, Smith, Kāpadiya, Singh, Datta, Saraswati, Jaina (L. C.), Guptā, Lishk and Sharmā, Volodarski etc. Even within this short span of time, there have been discovered certain mathematical results and principles which are not only highly interesting but are also considered very important and useful for the study and exposition of ancient Indian Mathematics in general and the Jain mathematics in particular. Dr. A. N. Singh has also remarked that a study of the Jaina canonical works reveals that mathematics was held in high esteem by the Jainas and the knowledge of mathematics and astronomy was considered to be one of the principal accomplishments of the Jaina ascetics and scholars who have written apart from those listed above, works like Sthānānga-sūtra, Tattavārthādhigamasūtra, Sūrya-prajñapti, (Gamitānuyoga), Anuyogadvāra-sūtra, Jambūdvipa-Prajñapti, Lokavibhāga, Bhagavati-sütra, Kalpasūtra, Candraprajñapti, Jyotişa-Karaņdaka etc. Though many of these works are nonmathematical in character but as recognised by Singh also, the knowledge of Jaina mathematics is gleaned very much from them. Most of these works belong to the period much before the 5th century A. D. Āryabhata First (c. 498 A. D.), Brahmgupta (c. 628 A. D.), Mahāvīrācārya (c. 850 A. D.) and Bhāskarācārya (c. 1150 A. D.) are the most eminent known mathematicians of ancient India, though a number of other persons also have worked on mathematics. One of the most important fundamental contributions of ancient Indian mathematicians to the progress of civilisation is the invention of what is called the Decimal system of Numeration including the invention of the number “Zero” and a symbol for it, and the principle of local value which had revolutionised the system of counting and measurement and these were given thousand of years back by Indian mathematicians, their names still being unknown. The importance of the decimal system of numeration can best be appreciated in the words of foreign mathematicians. Laplace (17421827), one of the greatest mathematicians of all times says, “The idea of expressing all quantities by nine digits and a symbol for zero, whereby imparting to them both an absolute value and a positional (local) value, is so simple that this very simplicity is the reason for our not being sufficiently aware how much admiration it deserves." Prof. G. B. Halstead also remarks, "The importance of the creation of the zero mark can never be exaggerated. This giving to airy nothing, not merely a local inhabitation and a name, a picture, a symbol but also a helpful power is the characteristic of the Hindu race whence it sprang up. No single mathematical invention has been more potent for the general on-go of intelligence and power." What a greater tribute can be paid to the genius of the Indian mathematicians ? Prof. Halstead has also proved that the 'zero', existed in India at least at the time
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