Encyclopedia of India–China Cultural Contacts v1.c6.38

v1.c6.38

Both Ancient India and China possessed excellent advanced knowledge of mathematics. The Vedas are a repository of the most ancient Indian mathematics. *Sheng fa jing* (*Sulba Sutra* or *Śulbasūtra*) is the most important classic on mathematics in India. This includes geometric contents, questions in algebraic calculus in architecture as well as approximation of circumference ratio. There is a symbol representing the number zero on a 9ᵗʰ century stone tablet in Gwalior, India. The external spread of Indian numerical codes via Arabia is also one of the important contributions in the history of mathematics in the world. Liu Ping, the scholar who participated in the translations of sutras in Dharmagupta's translation institute in the Sui Dynasty was proficient in mathematics and compiled one volume on *Nei wai bang tong bi jiao shu fa* [*Internal-external Mastery and Comparison with Mathematics* (or *External-internal Mastery and Comparison with Mathematics*)]. This sums up mathematical names and calculation methods in sutras translated into Chinese and compares them with the corresponding Chinese units and numbers ie "adopted mathematical methods in sutras to compare with the Eastern Xia" so that Indian mathematical terms and numbers in the process of sutra translation could be standardised. This book can be regarded as the first work related to the study on comparison of India-China algorithm. The Indian calendar calculation works, which were introduced in China before the Tang Dynasty, included three volumes of *Po luo men sun fa* (*Brahman Algorithm*), one volume of *Po luo men yin yang suan li* (*Brahman Yin-yang Calculation Calendar*) and three volumes of *Po luo men suan jing* (*Brahman Calculation Sutra*), which were recorded in *Sui Shu: Jing ji zhi* (*Book of the Sui Dynasty: Records on Sutras*). During the Tang Dynasty, an Indian astronomer based in China, Gautama Siddhartha, compiled 120 volumes of *Kai yuan zhan jing* (*Classic of Astrology in the Kaiyuan Period*) and part of Jiu zhi li (*Jiuzhi Calendar*) (ie Volume 104 Algorithm) recorded nine numerical codes in Indian algorithm and decimal null/invalid point symbols. Gautama Siddhartha also introduced the Indian mathematical knowledge of taking measurements with an arc and sine function table at the interval of 3°45′. This was a significant contribution in the history of exchanges between India and China in mathematics. Commenting on Indian astronomical algorithms, the *Xin tang shu* (*New Book of the Tang Dynasty*) in its Volume XXVIII, writes that "calculation was written in characters (written calculation) rather than in a planned manner. Algorithm was so complicated, the accurate number may be obtained through luck, but it cannot be regarded as proper standard method. Astronomical algorithms were so confused that they could not be explained on first sight." These derogatory words showed that ancient Chinese scholars could not understand the Indian astronomical algorithms profoundly.