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.
