Ancient Mathematics with a Unique Style (Part 1)

Unique Ancient Mathematics (Volume 1) is a thematic work by Xiao Feng that systematically introduces the achievements and intellectual trajectory of ancient Chinese mathematics. Rather than a mere chronological list of mathematical history, the book takes "uniqueness" as its entry point, attempting to analyze the differences and distinctive features of ancient Chinese mathematics from Western mathematical traditions in modes of thinking, problem-solving approaches, and theoretical construction. The author, Xiao Feng, has long been devoted to the study of Chinese scientific history; his exposition combines academic rigor with plainness of narration, making specialized content accessible to a wider readership.

This first volume focuses on the development of Chinese mathematics from ancient times through the Song and Yuan dynasties, with emphasis on analyzing the core algorithms and ideas in classic texts such as The Nine Chapters on the Mathematical Art, The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven, and Master Sun's Mathematical Manual. In the editor's view, the value of this book lies in its "problem-oriented" interpretive approach. The author not only introduces specific achievements such as the "method of the celestial unknown" and the "method of increasing multiplication and extraction," but also strives to explain the practical rational spirit, procedural thinking, and the unique mathematical culture shaped by the counting-rod system behind these methods. For example, the analysis of "fangcheng" (the ancient Chinese method for solving systems of linear equations) reveals the ingenuity and mechanized character of its algorithmic construction, enabling readers to go beyond specific knowledge and understand a mathematical development paradigm fundamentally different from the Greek axiomatic system.

For modern readers, this book not only fills in specific knowledge of the brilliant achievements of ancient Chinese science and technology but also offers a perspective of diverse mathematical cultures, prompting reflection on the definition and possibilities of "mathematics" itself. The book's commentary on the work of mathematicians such as Liu Hui, Zu Chongzhi, and Qin Jiushao also presents a vivid picture of how scientific thought grew within specific historical and social contexts. In terms of writing, the author avoids overly abstruse technical symbols and describes algorithmic logic in words as much as possible, lowering the threshold for beginners, though readers still need to maintain a certain focus and reflectiveness. Overall, this is a high-quality introductory work that can effectively guide readers to a deeper understanding of the essence of ancient Chinese mathematics.