IX.
29. That the most important parts of the works of the Indian mathematicians from Āryabhata to Bhāskara are essentially based upon western knowledge is now established. A somewhat intimate connection between early Chinese and Indian mathematics is also established—but the connection in this direction is not very intimate with respect to those sections that may be termed Greek, e.g., quadratic indeterminates, cyclic quadrilaterals, etc. That the Arabic development of mathematics was practically independent of Indian influence is also proved.
The Arab mathematicians based their work almost wholly upon Greek knowledge; but the earliest of them known to us, M. b. Mūsā, flourished after Brahmagupta so that the Arabs could not have been the intermediaries between the Greeks and Indians. Indeed their chronological position has misled certain writers to the erroneous conclusion that they obtained their elements of mathematics from the Indians.
Other possible paths of communication between the Indians and Greeks are by way of China and by way of Persia. The former is not so improbable as it at first seems. Further information about the early silk trade with China might possibly throw light on the subject. The intellectual communication between India and China at the critical period is well known—there being numerous references to such communication in Chinese literature. If sound translations of the early Chinese mathematical works were available we might be able to draw more definite conclusions, but as the evidence now stands there is nothing that would warrant more than the bare suggestion of a Chinese source.
We have already mentioned the visit of certain Greek mathematicians to the Court of Chosroes I, and there are certain other facts which at least justify the consideration of the Persian route. The Sássánid period, A.D. 229–652, shows a somewhat remarkable parallelism with the age of enlightenment in India that roughly corresponds with the Gupta period. "The real missionaries of culture in the Persian empire at this time were the Syrians, who were connected with the west by their religion and who, in their translations, diffused Greek literature throughout the orient." Mr. Vincent Smith discusses the probability of Sássánian influence on India but states that there is no direct evidence.
Although it may be possible to offer only conjectures as to the actual route by which any particular class of Greek knowledge reached India, the fact remains that during the period under consideration the intellectual influence of Greek on India was considerable. It is evident not only in the mathematical work of the Indians but also in sculpture, architecture, coinage, astronomy, astrology, &c. Mr. Vincent Smith refers "to the cumulative proof that the remarkable intellectual and artistic output of the Gupta period was produced in large measure by reason of the contact between the civilization of India and that of the Roman Empire;" and research is almost daily adding to such proof.
The flourishing state of the Gupta empire, the greatest in India since the days of Asoka, and the wise influence of its principal rulers gave a great impetus to scholarship of all kinds. The numerous embassies to and from foreign countries—which were means of intellectual as well as political communication—no doubt contributed to the same end; and the knowledge of Greek works displayed by Āryabhata, Varāha Mihira, and Brahmagupta was one of the natural results of this renaissance of learning.