Shatkhandagama Pustak 04

Author(s): Pushpadant, Bhutbali, Hiralal Jain, Fulchandra Jain Shastri, Devkinandan, A N Upadhye
Publisher: Jain Sahityoddharak Fund Karyalay Amravati

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has been responsible for the invention of the decimal place value notation. It is now established beyond doubt that the place value system of notation was invented in India about the beginning of the Christian Era - the brightest period of Buddhism and Jainism. The new notation was an instrument of great power and accelerated the development of mathematics from the crude Vedic stage - as found in the Sulba sutras to the finished stage of the fifth century-as found in the works of Aryabhata and Varahamihira.
One very significant fact which has escaped the notice of historians of mathematics is the following: whilst the general literature of the Hindus, the Buddhists, and the Jainas is continuous from the third or the fourth century B. C. right up to the middle ages, in the sense that works representing each century are found, there is a gap in the mathematical literature. In fact there is hardly any mathematical text earlier than the Aryabhatiya which was composed in 499 A. D. The only exception is a fragmentary manuscript known as the Bakhshali manuscript, which probably belongs to the second or the third century A. D. This manuscript, however, fails to give us any detailed information regarding the state of mathematical knowledge at the time of its composition for the reason that is not strictly speaking a Mathematical text as the treatises of Aryabhata, Brahmagupta or Sridhara etc. It is of the nature of notes on some selected mathematical problems. All that we can infer from the manuscript is that the piace value numerals as well as the fundamental operations of arithmetic with them were well known, and that some types of problems treated by later mathematicians were also known.
It has already been pointed out that mathematics as found in the Aryabhatiya is highly developed, for we find in it a treatment of the entire elementary arithmetic of today including the rules of proportion, interest, barter and exchange, and of algebra up to the solution of the simple and the quadratic equations, simple. indeterminate equations etc. The question arises: Did Aryabhata borrow from some foreign source or is the material contained in the Aryabhatiya indigenous and of Indian origin? Aryabhata writes:
Having paid reverence to Brahman, the Earth, the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms, Aryabhata sets forth the science which is honoured here at Kusumapura "1 This shows that he did not borrow from a foreign source. The study of the history of mathematics in other countries leads to the same conclusion, for the mathematics of the Aryabhatiya was far in advance of what was known at that time in any other country of the world. The possibility of borrowing from some foreign source having been ruled out, the question arises: How is it that practically no mathematical work anterior to that of Aryabhata is available? The explanation is simple enough. The place value system of notation was invented some time about the beginning of the Christian Era. It must have taken four or five hundred years to come into general use. Aryabhata's work seems to be the first good text book employing the new arithmetic of the place value numerals. Works anterior
1. Aryabhatiya, ii, 1.