The Ten Mathematical Classics: The Mathematics and Mathematical Education of Pre-Modern China

Abstract

The Ten Mathematical Classics were the only imperially prescribed mathematics textbooks in pre-modern China. They were used during the Sui (581 – 618), Tang (618 – 906), and Northern Song (960 – 1127) dynasties at the imperial academy to structure the mathematical training of students. This dissertation explores the contents as well as information about the writers and commentators of these texts in order to arrive at a better understanding of Chinese mathematics and mathematical writers. It also analyzes how mathematical education actually took place, presenting a new perspective on why state-run mathematical education only existed at specific times. Lastly, this dissertation examines the circulation and transmission of the Ten Mathematical Classics. My thesis consists of three central points. Firstly, the history of Chinese mathematics should take into serious account the entire corpus of knowledge and endeavours, such as divination, that historical actors associated indivisibly with what we would consider pure mathematical knowledge. Secondly, the known writers, commentators, and readers of the Ten Mathematical Classics were all highly educated, many of whom were also government officials, so it is over-simplistic to attribute the lack of long-term state-run mathematical education to a general disdain among the Chinese literati for technical subjects. Thirdly, I argue that the state’s decisions to institute or drop mathematical education should be understood within the broader context of the state’s needs at the time, and were directly related to the availability of suitable mathematically skilled candidates who could be recruited into the bureaucracy.