Yang Hui
c. 1238-c. 1298
Chinese Mathematician
Though he did not invent the Pascal triangle, Yang Hui did provide an early discussion concerning its use. He also wrote several texts, at least one of which proved influential in East Asian mathematics for centuries to come. Some scholars consider Yang Hui's career the apex of Chinese algebraic studies in the medieval period.
Almost nothing is known about the life of Yang Hui, except for the fact that he served as an official under the southern Sung. The Sung Dynasty, established in 960, had controlled all of China until 1127, when an attack by "barbarian" peoples from the north forced them to move their government southward. Yang Hui's contemporary and fellow mathematician Li Yeh (1192-1279), for instance, lived in northern China, which was controlled first by Juchen nomads and later by Mongols.
During this same time, southern China flourished, and despite the humiliating retreat that had forced the Sung to vacate, the Southern Sung period proved to be one of the cultural high points of Chinese history. With a population of 1.5 million, the capital city of Hangchow was probably the largest city in the world, and its size is particularly remarkable considering the fact that only the largest European urban centers had even as many as 100,000 inhabitants.
Throughout Sung China, the arts and sciences flourished, and though the Sung would lose their power to the Mongols during Yang Hui's lifetime, even the invaders did their best to permit the southern Chinese to go on as before. As for Yang Hui, he had served as a government official under the Sung, and it is quite possible that he continued to do so with their usurpers. (Unless, like many Chinese, he left government service as a means of protesting his country's invasion by foreigners whom the Chinese considered their inferiors.)
Yang Hui is credited with mathematical studies that appeared in 1261, 1275, and 1299. The first of these applied decimal fractions—centuries before these would be adopted in the West—and made use of the triangular configuration of binomial equations usually known today as Pascal's triangle. In many parts of East Asia, the latter is known as Yang Hui's triangle, though in fact it seems to have been in use long before Yang Hui, with Chinese references to it dating as far back as c. 1100.
The 1275 book was Cheng chu tong bian ben mo, (The beginning and end of variations in multiplication and division). The latter is particularly valuable for the insights it provides historians of mathematics regarding the curriculum used by Chinese mathematical students at that time. Furthermore, Yang Hui's syllabus, included in the book, shows him to have been a highly competent teacher who emphasized genuine learning rather than memorization—not always the case in medieval schools, East or West.
Another volume, Suan-hsiao chi-meng, appeared after Yang Hui's death in about 1298. The book was destined to be well-received in Japan, where it served as an impetus to mathematical inquiry for half a millennium.
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