Basic Mathematics

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

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start from Diophantus, but quite earlier from Mesopotamia (c.-2000), and as such the Pythagorean arithmetica deserves to be Babylonian arithmetica. Thus Waerden124 has tried to prove : 1. Thales and Pythagoras started with Babylonian mathematics and gave it
a special character, quite different from it. 2. Mathematics was developed in advanced forms in the Pythagorean schools and outside, and began to satisfy the problems of logic.
He has also supported the following hypothesis in astronomy125, "Freudenthal's hypothesis reduces therefore to the following : Before becoming subject to the Greek influence, the Hindus had a versified positional system, arranged decimally and starting with the lowest units. They had the digits 1-9 and similar symbols for 10, 20,...... Along with Greek astronomy, the Hindus became acquainted with the sexagesimal system and the zero. They amalgamated this positional system with their own; to their own Brahmin digits 1-9, they adjoined the Greek 0 and they adopted the Greek Babylonian order."
Regarding the Buddhist's use of large numbers, he remarks, 126
“It is clear that these numerals were never used for actual counting or calculations. They are pure fantasies which like Indian towers, were constructed in stages to dazzling heights."
The attention of above scholars may be attracted towards the source material of Prakrit texts like the Satkhaņdagama and the Tiloyapannatti, as also the Svetambara texts, wherein the motivation to use the very large numbers is evident. Therein the basis of space and time measures is principle-theoretic and not construction--theoretic as in Greek works of B.C. The exposition of the Jaina Karma theory needed the infinities in space and time, apart from the innumerables and numerables, 127 It also needed various types of set-thoretic measures in simile (equivalence), based on relations between sets themselves, and as such apart from their other discoveries, necessity might have led them to formation of place value systems elaborated earlier.
The following facts are also important to relate : 1. In the Tiloyapannatti, a formula about the chord belongs to
Babylon, recorded at -2600 . The formula for the arc is,
124. Cf. p. 5, op. cit. 125. Cf. ibid., pp. 56-57. 126. Cf. ibid., p. 52. 127. Cf. research paper of Jain, op. cit.
Cf. also, T.P.G.
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