The Integration of Deductive Mathematics and Traditional Chinese Algorithmic Sciences: With a Focus on the Transmission of Euclid's Elements in China

Abstract

This study examines the historical convergence of Western deductive mathematics and traditional Chinese algorithmic science, centered on the transmission and reception of Euclid’s  Elements  in late imperial China. It investigates how  Elements , introduced by Jesuit missionaries like Matteo Ricci and collaboratively translated with Chinese scholars such as Xu Guangqi, catalyzed intellectual dialogue and methodological exchange between these distinct mathematical traditions. Through analysis of key translations, scholarly debates, and mathematical treatises from the Ming-Qing transition, the research demonstrates that Western deductive logic was selectively integrated into Chinese mathematical practice, while indigenous algorithmic approaches persisted and adapted. Case studies comparing  Elements  with classical Chinese texts like  The Nine Chapters on the Mathematical Art  reveal both syntheses and tensions in geometric and algebraic problem-solving. Furthermore, the study highlights practical impacts in astronomy and calendrical science, illustrating how hybrid methods emerged from this cross-cultural encounter. The findings underscore the significance of  Elements  as a vehicle for global knowledge exchange, enriching understandings of the dynamic interplay between local epistemologies and transnational scientific flows in early modern Eurasia.