Qin Jiushao

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Page from the Shushu Jiuzhang, from the edition in the Siku Quanshu Collection from the 1780s

Qin Jiushao (* 1202 in Puzhou ; † 1261 in Meixian ) was a Chinese civil servant, military, writer, inventor and mathematician, known for the introduction of the Chinese remainder of the sentence and as the author of Shùshū Jiǔzhāng (mathematical treatise in nine chapters).


A lot is known about Quin Jiushao in relation to other older Chinese mathematicians, as he held various administrative positions. In his youth he was in a volunteer militia at a command post. In 1224/25 his father was called to the capital of the southern Song dynasty, Hangzhou , and Qin Jiushao, as he wrote in his main work, was able to study at the Office of Astronomy and took mathematics lessons from a secluded scholar. Among other things, he studied Jiu Zhang Suanshu (nine chapters of arithmetic). In 1226 he was in Tongchuan in Sichuan Province with his father . When it was conquered by the Mongols, Qin Jiushao was one of the military defenders. After the conquest (1234) he went south and became sub-prefect in Qizhou , but had to leave after a military revolt directed against him. He became prefect in Hezhou and was responsible for the salt trade. He got rich from the illegal salt trade and went to Huzhou in Zhejiang Province . In 1244 he became a court official in Nanjing , but returned to Huzhou three months later when his mother died. In a three-year mourning period he wrote his major mathematical work, which was finished in 1247. Because of his knowledge of calendar calculations, he was appointed to the imperial court and was allowed to take the exams for the higher administrative career. This did not seem to have been successful since he was a military advisor in Jiankang from 1253 to 1259 . He was then back in his hometown until he was prefect in Qiongzhou in Hainan after a visit by Chancellor Jia Sidao . That ended after a few months on charges of corruption and exploitation. Quin Jiushao went to see his friend Naval Officer Wu Qian in Yin District in Zhejiang and in 1259 became an assistant in the management of the granaries. After his friend Wu Qian fell out of favor in 1260, he too had to leave and he was deported to Meixian (Meizhou).

He developed devices for measuring precipitation and snow, which he deals with in his main mathematical work.

He had a wide range of knowledge and skills (mathematics, poetry, fencing, archery, horse riding, music, architecture), but was also considered aggressive and uncontrolled. In a letter to the emperor, a contemporary described him as violent like a tiger or a wolf and as poisonous as a viper or a scorpion. The latter indicated that he did not shy away from poison attacks.

Shushu Jiuzhang

He completed his main work Mathematical Treatise in nine chapters in 1247. The structure is based on the nine chapters of arithmetic (Jiu Zhang Suanshu), but is more progressive in content. In addition to mathematical topics, military topics and land surveying are also covered. It is noteworthy for the treatment of the Chinese remainder theorem, it contains Heron's theorem and dealt with the numerical solution (determination of the root) of polynomial equations up to the 10th order, with a procedure that corresponds to the Horner scheme . He was also the first to introduce the zero in Chinese mathematical literature, which he represented by a small circle (and noted that a blank space was used in older treatises).

The nine chapters each deal with nine tasks.

  • Chapter 1 covers solving equations with unknowns and the Chinese remainder theorem. A special case was already known to Sun Zi , which is dated from the 3rd to 5th centuries. He presents the sentence in a sophisticated form with a constructive proof. Although he claims to have got it from the calendar experts who taught him in his youth in Hangzhou, he also said they did not understand the method. In the West, a similar understanding was only achieved through Carl Friedrich Gauß .
  • Chapter 2 (Heavenly Phenomena) deals with calendar questions and tasks with rain and snow with volume determinations.
  • Chapter 3 (Field Boundaries) covers surveyor tasks and contains Heron's formula.
  • Chapter 4 (Telemetry) deals with determining the distance to inaccessible points. As in Chapter 3, solutions of polynomial equations of higher degree (this time up to degree 10) are treated.
  • Chapter 5 (Taxes)
  • Chapter 6 (Money and Grain)
  • Chapter 7 (Strongholds and Buildings)
  • Chapter 8 (Military Affairs)
  • Chapter 9 (Trade Matters)

The book was included in the Yongle Dadian Encyclopedia (1421) and in the Siku Quanshu Collection (1787). In 1842 it appeared as a wood print. It became known in the West through the missionary Alexander Wylie (Jottings on the Sciences of Chinese Mathematics, in: North China Herald 1852).


  • Peng Yoke Ho: Ch'in Chiu-shao , in: Dictionary of Scientific Biography , Volume 3, pp. 249-256
  • Ulrich Libbrecht (edited by Andrea Eberhard-Bréard): Qin Jiushao, in: Helaine Selin (ed.): Encyclopaedia of the history of science, technology and medicine in non-western countries, Kluwer 2008, pp. 1854–1855
  • Ulrich Libbrecht: Chinese mathematics in the thirteenth century: the Shu-shu chiu-chang of Ch'in Chiu-shao , MIT Press, Cambridge, Mass., 1973 (= dissertation at the University of Leiden 1971)
  • Jean-Claude Martzloff : A history of chinese mathematics , Springer 1997
  • KS Shen: Historical development of the Chinese remainder theorem , Arch. Hist. Exact Sci., Vol. 38, 1988, pp. 285-305.
  • K. Shen, JN Crossley, AW-C. Lun: The nine chapters on the mathematical art: Companion and commentary , Beijing 1999

Web links

Individual evidence

  1. MacTutor article on Qin Jiushao