The Empty and the Full: Li Ye and the Way of Mathematics

During Song (960 to 1279) and Yuan (1279 to 1368) dynasties, China experienced a peak in high-level algebraic investigation through the works of famous mathematicians such as Qin Jiushao, Zhu Shijie, Yang Hui and Li Ye. Among these is Li Ye's short treatise on a curious ancient geometrical procedure: The Development of Pieces of Areas According to the Collection Augmenting the Ancient Knowledge (Yigu yanduan). The aim of this monography is to contradict traditional scholarship which has long discredited the importance of Li Ye's treatise, considering it a mere popular handbook. The author aims to show that Li Ye's work actually epitomizes a completely new aspect of ancient Chinese mathematics: a crossroad between algebra, geometry, and combinatorics containing elements reminiscent of the Book of Changes (Yi Jing). As well as Li Ye used field measurement as pretext for investigations on quadratic equations and Changes, the present study uses Li Ye's small treatise as pretext for philosophical investigations on link between mathematics and their history. The real topic of the study is the exploration of another expression of proof and generality in Chinese mathematics. This book not only completes the edition of Li Ye's works and presents new features of Chinese mathematics, but also fills a gap in the translation of Chinese mathematics treatises.It is the first book entirely dedicated to the diagrammatic practice of algebra in the history of Chinese mathematics. This practice is more important than expected. While being a monograph, the book is short and detailed enough to be used by students in class. It can also be used as an entry door to the research field of history of Chinese mathematics.Contents: AcknowledgementsConventionsPrefaceIntroduction: General PresentationText, Diagrams and Equation:The Celestial Source ProcedureThe Procedure of the Development of Pieces of Areas: The Example of Problem 1Transformation of Diagrams: The Example of Problem 21Conclusion of Part IOperations on Pieces of Areas:The Six Transformations: The Example of Problem 2Geometric Representation of Negative Coefficient: The Example of Problem 18The Old Procedure: The Example of Problem 5Conclusion to Part IIOrder, Analogy and Reduction:Statement of the Problems: The Example of Problem 3Analogy and Iteration: The Example of Problem 36The Web of Dependencies: The Example of Problem 14Conclusion to Part IIIConclusionAppendices:SupplementsChinese GlossaryChinese NamesBibliographyIndex
Readership: Readers who are interested in the histroy of mathematics, especially the history of Chinese mathematics and the contribution of ancient Chinese mathematicians.History of Mathematics;Algebra;Geometry;China;Song Dynasty0Key Features:The illustrations created with Geogebra makes ancient mathematical practices visibleIt is the first book entirely dedicated to the diagrammatic practice of algebra in history of Chinese mathematics. This practice is more important than expectedWhile being a monograph, the book is short and detailed enough to be used by students is class. It can be used as an entry door to the research field of history of mathematics in China