Person: Xian, Jia

Jia Xian was a Chinese scholar who wrote some early arithmetic books. He had an early version of Pascal's triangle.

We know that Chu Yan was productive over the years 1022 to 1054 so he must have tutored Jia Xian at some time between these years.
Other evidence would suggest that Chu Yan taught Jia Xian fairly near the beginning of his career.
Jia Xian is known to have written two mathematics books: Huangdi Jiuzhang Suanjing Xicao (The Yellow Emperor's detailed solutions to the Nine Chapters on the Mathematical Art), and Suanfa Xuegu Ji (A collection of ancient mathematical rules).
This is because Yang Hui wrote Xiangjie Jiuzhang Suanfa (A detailed analysis of the mathematical rules in the Nine Chapters) in 1261 with the intention of explaining, and making better known, the work of Jia Xian.
What does Yang Hui tell us of Jia Xian's mathematical contribution?
The algorithm is called the Zeng chang kaifang method by Jia Xian, which means the additive-multiplicative method for root extractions.
After examining earlier Chinese methods given in the Nine Chapters on the Mathematical Art and those by Zhang Qiujian in the fifth century, she concludes that Jia Xian was the first to use the Ruffini-Horner method.
Both Jia Xian and al-Samawal use binomial coefficients, computed with a form of Pascal's triangle, to calculate the denominator of the expression.
The intriguing question of whether al-Samawal discovered the method independently, or whether there was transmission of the Chinese method of Jia Xian into Islamic/Arabic mathematics is left unresolved.

Born about 1010, China. Died about 1070, China.

View full biography at MacTutor

Ancient Chinese, Chinese, Origin China

Epochs: 1

Thank you to the contributors under CC BY-SA 4.0!

O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive