1620392Indian Mathematics — IntroductionGeorge Rusby Kaye

I.

1. The orientalists who exploited Indian history and literature about a century ago were not always perfect in their methods of investigation and consequently promulgated many errors. Gradually, however, sounder methods have obtained and we are now able to see the facts in more correct perspective. In particular the early chronology has been largely revised and the revision in some instances has important bearings on the history of mathematics and allied subjects. According to orthodox Hindu tradition the Sūrya Siddhānta, the most important Indian astronomical work, was composed over two million years ago! Bailly, towards the end of the eighteenth century, considered that Indian astronomy had been founded on accurate observations made thousands of years before the Christian era. Laplace, basing his arguments on figures given by Bailly considered that some 3,000 years B.C. the Indian astronomers had recorded actual observations of the planets correct to one second; Playfair eloquently supported Bailly's views; Sir William Jones argued that correct observations must have been made at least as early as 1181 B.C.; and so on; but with the researches of Colebrooke, Whitney, Weber, Thibaut, and others more correct views were introduced and it was proved that the records used by Bailly were quite modern and that the actual period of the composition of the original Sūrya Siddhānta was not earliar than A.D. 400.

It may, indeed, be generally stated that the tendency of the early orientalists was towards antedating and this tendency is exhibited in discussions connected with two notable works, the Śulvasūtras and the Bakhshālī arithmetic, the dates of which are not even yet definitely fixed.

2. In the 16th century, A.D., Hindu tradition ascribes the invention of the nine figures with the device of places to make them suffice for all numbers 'to the beneficent Creator of the universe'; and this was accepted as evidence of the very great antiquity of the system! This is a particular illustration of an attitude that was quite general, for early Indian works claim either to be directly revealed or of divine origin. One consequence of this attitude is that we find absolutely no references to foreign origins or foreign influence.[1] We have, however, a great deal of direct evidence that proves conclusively that foreign influence was very real indeed—Greek and Roman coins, coins with Greek and Indian inscriptions, Greek technical terms, etc., etc.; and the implication of considerable foreign influence occurs in certain classes of literature and also in the archæological remains of the north-west of India. One of the few references to foreigners is given by Vahrāha Mihira who acknowledged that the Greeks knew something of astrology; but although he gives accounts of the Romaka and the Pauliśa siddhāntas he never makes any direct acknowledgment of western influence.


  1. It may be noted that beyond the vague pseudo-prophetic references in the Purānas, no early Indian writer mentions the invasion of Alexander the Great.