History Of Chinese Mathematics Research Articles

Regional Networks in Chinese Mathematics and Astronomy, 311–618 ce

Abstract This article offers a social and geographical network analysis of all attested works, authors, and practitioners in the mathematical sciences in China over the period of disunion and reunification from 311 to 618 ce. Inspired by Karine Chemla’s (2009) efforts to distinguish “different mathematical cultures” within the extant corpus of suan 筭/算 procedure texts, the goal is to explore a viable framework within which to break down the history of Chinese mathematics along different, pluralistic lines. What I find is that this period is home to distinct regional networks working in isolation from one another, and that situating authors within these networks helps explain continuities and discontinuities in their technical writing. This is evidence of plurality, but one that is incommensurable with Chemla’s “mathematical cultures,” so I offer it as an alternative means to the same historiographical ends. In examining what our historical subjects said and did about this plurality of traditions, however, we realize that it was as aberrant to them as the political disunion of which it was a product ‒ something to be rectified by “unification” (tongyi 統一), “integration” (tong 通), and, where necessary, force.

홍정하(洪正夏)의 천원술(天元術)과 증승개방법(增乘開方法)

【Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of $\prod_{k=11}^{n}(x+a_k)$ , Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.】

Should the History of Chinese Mathematics be Rewritten?

More than one and a half decades have elapsed since the Zhangjiashan archaeological findings showed excitingly that a new collection of mathematical texts on bamboo strips were excavated, dating earlier than the then earliest known and most influential Chinese mathematical classic Jiu Zhang Suan Shu. Now that the contents of the findings have finally been made available to the world outside of the group of archaeologists involved, should the history of Chinese mathematics be rewritten? After comparing the new material with the Jiu Zhang Suan Shu I believe that the place of the Jiu Zhang Suan Shu remains an irreplaceable cornerstone in the history of Chinese mathematics; however, the Jiu Zhang Suan Shu can no longer be seen as the earliest sources for the mathematical knowledge therein.

The evolution of transformation media in spherical trigonometry in 17th- and 18th-century China, and its relation to “Western learning”

Problems of spherical trigonometry in 17th- and 18th-century China were often reduced to problems in plane trigonometry and then solved by means of the proportionality of corresponding sides of similar right triangles. Nevertheless, in the literature on the history of Chinese mathematics, there is not much discussion on the transformation and reduction of spherical problems to the plane, and how the techniques utilized for such transformations evolved over time. In this article, I investigate the evolution of the transformation media involved. I will show that in the trigonometric treatises by Mei Wending (1633–1721) and Dai Zhen (1724–1777), the authors’ views on Western learning shaped their choices of transformation media, and conversely their choices of transformation media offered support to their views on trigonometry in the debate of Chinese versus Western methods. Based on my analysis, I also propose a reassessment of Dai’s treatise of trigonometry, which was controversial ever since its publication in the 18th century.

Li Ye and his Yi Gu Yan Duan (old mathematics in expanded sections)

In the history of Chinese mathematics the thirteenth century has been regarded as a period of vigorous growth and brilliant achievements. Among the mathematicians who featured prominently during this epoch was Li Ye [a]. Li Ye, whose literary name was Renjing [b], and whose appellation was Jingzhai [c], was born into a bureaucratic family in 1192. He was originally known as Li Zhi [d] but when he discovered that this name was the same as the Tang emperor whose dynastic title was Tang Kaozong [e], he changed it to Li Ye1. Li Ye's father, Li Yu [p], was a scholar-official serving as a state counsellor in the Jurchen court. To his chagrin, Li Yu found much oppression and corruption within and around the bureaucratic circle and being an upright man himself, he often spoke his mind and was critical of the imperial policy. This incurred the displeasure of his Jurchen superiors and consequently he was edged out of service and forced to lead a life of seclusion. Although the family misfortune left an indelible mark in Li Ye's mind, it did not prevent him from pursuing his education. In 1230 he passed the civil service examination and was offered a post in the government. However, his service was shortlived as the district to which he was assigned fell to the Mongols in 1232. He fled and took refuge in the north. When the Jurchen Kingdom finally collapsed in the face of the Mongol onslaught in 1234, he gave up all hope of

The Historical Role of Confucian Thought in the Formation of the Chinese Nation

The history of Chinese philosophy concerns the history of "China's" or "Chinese" philosophy, not the history of "philosophy in China." If we were to write a book on "The History of Chinese Mathematics," such a work would really be a history of "mathematics in China," or of "the development of mathematics in China" because "mathematics is mathematics" and there is no such thing as "Chinese" mathematics. But philosophy, like literature, is different. There really is a "Chinese" philosophy and a "Chinese" literature, or in general a "Chinese" culture.