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Jinamñnjari, Volume 19, No.1, April 1999
Zero In Place Value System of Jain Mathematics
Dr. L.C. Jain, Professor Emeritus, Jabalpur, India Dr. Padmavathamma, University of Mysore, India
In view of the knowledge derived from Babylonian mathematical cuneiform texts by Neugebauer, Sachs and others, and the claims of Needham and Ling in the "Science and Civilisation in China," various options have been set forth regarding the use of zero and its adoption in the place value system. In India, such volumes as the Dhavalā, the Jayadhavalā, the Fīvatattvapradipikhā Karnātaka and other commentaries as well as the Tiloyapannatti have brought forth rich mathematico-symbolic material. The karma theory points towards the necessity of a place value system in the Purvagata texts - parts of the Agrāyani and the Jñanapravāda - current in the Digambara tradition. They are required to be studied for further opinions and investigation regarding origin of the zero and its use in place value systems. The model for astronomy in India had to do with the geometry of a circle and a straight line and their extension to cosmological details. The study of Jaina karma system as cybernetics in an abstract form is a unified theory of bios and matter with a mutual dynamic interactions, and the Jaina School of algebra and arithmetic was the outcome of the unique experiences and examinations thereof.
Recent INSA project study on the Jaina School of Mathematics has clearly identified two schools: the Digambara and the Svetāmbara. The former held proficiency in the mathematico-symbolic theory of karma whereas the latter seems to tend towards the preservation of religious tenets, astronomy and astrology. The paper highlights this fact that more symbolic details on the use of zero are available in the Digambara School than in the Svetāmbara tradition, contarary to the findings of Datta, Singh and Kapadia.
Introduction
The study of the mathematical cuneiform texts of the old Babylonian period (1600 B. C. E.) has shown their system of numerationis to be based on place-value notation, a sezagesimal scale. Neugebauer opines that it was transmitted to the Greeks and then to the Indians who contributed to the final step by using the place-value
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