The high-water mark高水位线、高水平线 of Chinese mathematics occurred in the 13th century during the latter half of the Song dynasty (960–1279), with the development of Chinese algebra. The most important text from that period is the Precious Mirror四元玉鉴？ of the Four Elements by Zhu Shijie (1249–1314), dealing with the solution of simultaneous higher order algebraic equations联立高阶代数方程组 using a method similar to Horner's method. The Precious Mirror also contains a diagram of Pascal's triangle杨辉三角 with coefficients系数 of binomial二项式 expansions through the eighth power八次方的展开, though both appear in Chinese works as early as 1100. The Chinese also made use of the complex combinatorial组合的 diagram known as the magic square and magic circles, described in ancient times and perfected by Yang Hui (AD 1238–1298).
Even after European mathematics began to flourish繁荣 during the Renaissance, European and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline from the 13th century onwards. Jesuit missionaries耶稣会传教士 such as Matteo Ricci利玛窦 carried mathematical ideas back and forth between the two cultures from the 16th to 18th centuries, though at this point far more mathematical ideas were entering China than leaving.
Japanese mathematics, Korean mathematics, and Vietnamese mathematics are traditionally viewed as stemming from Chinese mathematics and belonging to the Confucian-based East Asian cultural sphere. Korean and Japanese mathematics were heavily influenced by the algebraic works produced during China's Song dynasty, whereas Vietnamese mathematics was heavily indebted受恩惠于 to popular works通俗文学作品 of China's Ming dynasty (1368–1644). For instance, although Vietnamese mathematical treatises论著 were written in either Chinese or the native Vietnamese Chữ Nôm script字母字体？, all of them followed the Chinese format of presenting a collection of problems with algorithms for solving them, followed by numerical answers. Mathematics in Vietnam and Korea were mostly associated with the professional court bureaucracy官僚主义 of mathematicians and astronomers, whereas in Japan it was more prevalent流行 in the realm领域 of private schools.