Yang Hui

Timeline

1. c. 1250–1260Qiantang · QiantangYang Hui was a native of Qiantang; his early years are not recorded in the official histories. Judging from the familiarity with the Nine Chapters on the Mathematical Art and everyday multiplication and division shown in his later works, he had received systematic mathematical training in the Lin'an area and had access to earlier mathematical texts by Jia Xian, Liu Yi, and others.
2. 1261Qiantang · QiantangIn the second year of Jingding, Yang Hui completed the Detailed Commentary on the Nine Chapters Algorithms, providing detailed explanations, diagrams, and exercises organized by the categories of the Nine Chapters, and including the 'Origin of the Root-Extraction Method' diagram. He explicitly stated that this diagram came from Jia Xian; later generations commonly call it Yang Hui's triangle, but it is in fact a preservation and transcription of Northern Song mathematics.
3. 1274Qiantang · QiantangIn the tenth year of Xianchun, Yang Hui wrote the Fundamentals of Variations in Multiplication and Division and the Shortcut Methods of Multiplication and Division by Comparison for Fields, explaining practical shortcut methods of multiplication and division, field areas, and analogical algorithms, aimed at practical computation and teaching, reflecting the demands of commerce and land surveying on mathematics in the late Southern Song.
4. 1275Qiantang · QiantangIn the eleventh year of Xianchun, Yang Hui wrote the Continued Collection of Curious Algorithms from Antiquity, compiling magic squares, stacked-heap series, and mathematical problems from earlier ages. Together with the works of the preceding years, later generations collectively called them Yang Hui's Algorithms, making them a key text transmitted from Song-Yuan mathematics. His year of death remains unverifiable.