Little is known about his life, but two of his mathematical works have survived. Introduction to Mathematical Studies (《算學啟蒙》), written in 1299, is an elementary textbook on mathematics. Zhu included about 260 problems to explain operations in arithmetic and algebra. This book also showed how to measure different twodimensional shapes and threedimensional solids. The Introduction had an important influence on the development of mathematics in Japan. The book was once lost in China until a copy of the book was made from a Korean source in 1839.
Zhu's second book, Precious Mirror of the Four Elements (《四元玉鑒》1303), is his most important work. With this book, Zhu brought Chinese algebra to its highest level. It includes an explanation of his method of the four elements, which are used to signify four unknown quantities in a single algebraic equation. Zhu also explained how to find square roots and added to the understanding of series and progressions. The preface of the book describes how Zhu traveled around China for 20 years as a teacher of mathematics.
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