Mathematics, East Asian

East Asian mathematics, the discipline of mathematics as it developed in China and Japan.

When speaking of mathematics in East Asia, it is necessary to take into account China, Japan, Korea, and Vietnam as a whole. At a very early time in their histories, Japan, Korea, and Vietnam all adopted the Chinese writing system, in addition to other cultural institutions. As a result, books produced in any one of these countries could, and actually did, circulate in scholarly circles throughout the region. Scholars versed in mathematics in Japan, Korea, and Vietnam learned at first from Chinese sources, but in time books produced in Japan and Korea found their way to China. (Scholars have not determined the extent of any original mathematical developments made in Korea and Vietnam, and whether such advancements made it back to China.) It may be more appropriate, therefore, to speak not so much of “Chinese mathematics” as of “mathematics in Chinese characters.”

The following discussion of the evolution of mathematical subjects within the Chinese tradition emphasizes several common characteristics: an interest in general algorithms and the importance given to “position” (a place-value notation involving rods or counters), a specific part devoted to configurations of numbers, and the parallelisms between procedures. It covers the history of mathematics in East Asia from ancient times through the region’s direct interaction with the European world in the 17th and 18th centuries—previously, East Asian contact with the West was indirect through ongoing interactions with India and the Islamic world. After this period, mathematics in the East was under the deep influence of mathematics imported from Europe, which Chinese mathematicians tried to synthesize with traditional Chinese mathematics. This paved the way to the adoption, at the end of the 19th century, of mathematics as it was practiced in the West. Thus, for later mathematical developments in the East, see mathematics: Mathematics in the 19th and 20th centuries.