International Jain Conference 1985 3rd Conference

Author(s): Satish Jain, Kamalchand Sogani
Publisher: Ahimsa International

Page 168

ated by foreign mathematicians. Laplace (1742-1827), 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 giving to airy nothing not mearly 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". What a greater tribute can be paid to the genius of the Indian mathematics? Prof. Halstead has also proved that the 'zero' existed in India at leastat the time of Pingala's work Chanda Sutra-a work on prosody before 200 B.C.
It is said that the concept of infinity in mathematics was conceived for the first time by the Indian mathematician Brahmaguta (628 A.D.) while in the western countries, this credit goes to Bernhard Bolzano of the 19th century A.D. A study of infinity in mathematics as a mature concept was however taken up by Bhaskaracarya (1150 A.D.). He appears to be the first mathematician to have deduced the value of the quotient mathematically, where a is a finite quantity and termed it as Ananta. But the description of infinity as endless or countless can be traced in Rgveda and many other ancient works including those by Jaina and Buddhist scholars An elaborate classification and philosophical explanation of infinity (Ananta) is however found in the Jaina canonical texts as old as 300400 B.C. where infinity of even ten types has been mentioned. In the SthanangaSutra and the Uttaradhyayana-Sutra, the idea of infinity has been combined with that of dimensions, e.g. infinity in one direction, infinity in area, infinity everywhere and infinity perpetual. While in the Dhavala and some other Jaina philosophicsl texts, ten types of infinity have been described e.g. nominal attributed, fluent, numerical, dimensionless, mono, bi, areal, spatial, phase and indestructible (everlasting),
In the Kalpa-Sutra and the Navatattva, infinity is described as a number as great as the number of sand grains on the brinks of all rivers on the earth or the drops of water in all the oceans. The Tilloypannantti, another important Jaina text, deals with infinity under mathematical discipline. The Jaina concept of infinity in mathematics can be explained in modern technology as, 'If the law of variation of a magnitude x is such that it becomes and remains greater than any preassigned magnitude, however large, then x is said to become infinite and this concept is denoted by co.
The Jaina works on mathematics also deal with the rules of operations with numbers, permutations and combinations, solutions of simultaneous equations, indeterminate equations of the first degree, laws of indices, arithmetical and geometrical progressions, the rules for operations with infinity, mensuration formulae for different surfaces and solid bodies and any other topics. Ex-Professor and Head, Department of Mathematics University of Rajasthan, Jaipur (Rajasthan)
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