History of Mathematics

Mathematics in China

Table of Contents

A brief outline of the history of Chinese mathematics

Primary sources are Mikami's The Development of Mathematics in China and Japan and Li Yan and Du Shiran's Chinese Mathematics, a Concise History. See the bibliography below.

  1. Numerical notation, arithmetical computations, counting rods

  2. Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.)

  3. The Nine Chapters on the Mathematical Art (Jiuzhang Suanshu) (c. 100 B.C.E.-50 C.E.)
    Collects mathematics to beginning of Han dynasty. 246 problems in 9 chapters. Longest surviving and most influential Chinese math book. Many commentaries.

  4. Sun Zi (c. 250? C.E.)
    Wrote his mathematical manual. Includes "Chinese remainder problem" or "problem of the Master Sun": find n so that upon division by 3 you get a remainder of 2, upon division by 5 you get a remainder of 3, and upon division by 7 you get a remainder of 2. His solution: Take 140, 63, 30, add to get 233, subtract 210 to get 23.

  5. Liu Hui (c. 263 C.E.)

  6. Zhang Qiujian (c. 450?)
    Wrote his mathematical manual. Includes formula for summing an arithmetic sequence. Also an undetermined system of two linear equations in three unknowns, the "hundred fowls problem"

  7. Zu Chongzhi (429-500) Astronomer, mathematician, engineer.

  8. Liu Zhuo (544-610) Astronomer
    Introduced quadratic interpolation (second order difference method).

  9. Wang Xiaotong (fl. 625) Mathematician and astronomer.
    Wrote Xugu suanjing (Continuation of Ancient Mathematics) of 22 problems. Solved cubic equations by generalization of algorithm for cube root.

  10. Translations of Indian mathematical works.
    By 600 C.E., 3 works, since lost. Levensita, Indian astronomer working at State Observatory, translated two more texts, one of which described angle measurement (360 degrees) and a table of sines for angles from 0 to 90 degrees in 24 steps (3 3/4 degree) increments.
    Hindu decimal numerals also introduced, but not adopted.

  11. Yi Xing (683-727) tangent table.

  12. Jia Xian (c. 1050)
    Written work lost. Streamlined extraction of square and cube roots, extended method to higher-degree roots using binomial coefficients.

  13. Qin Jiushao (c. 1202 - c. 1261)
    Shiushu jiuzhang (Mathemtaical Treatise in Nine Sections), 81 problems of applied math similar to the Nine Chapters. Solution of some higher-degree (up to 10th) equations. Systematic treatment of indeterminate simultaneous linear congruences (Chinese remainder theorem). Euclidean algorithm for GCD.

  14. Li Chih (a.k.a. Li Yeh) (1192-1279)
    Ceyuan haijing (Sea Mirror of Circle Measurements), 12 chapters, 170 problems on right triangles and circles inscribed within or circumscribed about them. Yigu yanduan (New Steps in Computation), geometric problems solved by algebra.

  15. Yang Hui (fl. c. 1261-1275)
    Wrote sevral books. Explains Jiu Xian's methods for solving higher-degree root extractions. Magic squares of order up through 10.

  16. Guo Shoujing (1231-1316).
    Shou shi li (Works and Days Calendar). Higher-order differences (i.e., higher-order interpolation).

  17. Zhu Shijie (fl. 1280-1303)
    Suan xue qi meng (Introduction to Mathematical Studies), and Siyuan yujian (Precious Mirror of the Four Elements). Solves some higher degree polynomial equations in several unknowns. Sums some finite series including (1) the sum of n^2 and (2) the sum of n(n+1)(n+2)/6. Discusses binomial coefficients. Uses zero digit.
Rest of outline yet to write.

Chronology of Mathematicians and Mathematical Works

Some Selected On-line References


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Maintained by David E. Joyce

Department of Mathematics and Computer Science
Clark University

Initial work December, 1994. Latest update Sept 17, 1995.