Article ID: CBB202560716

Practices of reasoning: Persuasion and refutation in a seventeenth-century Chinese mathematical treatise of 'linear algebra' (2020)

unapi

This article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.

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Authors & Contributors
Jami, Catherine
Wang, Quanlai
Di, Li
Chang, Ping-Ying
Dauben, Joseph W.
Zhu, Yiwen
Concepts
Mathematics
East Asia, civilization and culture
Algebra
Cross-cultural interaction; cultural influence
Astronomy
Transmission of texts
Time Periods
Qing dynasty (China, 1644-1912)
17th century
18th century
19th century
Ancient
Song Dynasty (China, 960-1279)
Places
China
Japan
Institutions
Jesuits (Society of Jesus)
Astronomical Bureau (China)
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