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算學啟蒙

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Text ID
KR3fc016
Date
1299–1299
Dynasty
元

Suànxué qǐméng 算學啟蒙

Introduction to Mathematical Studies by 朱世傑 (撰)

About the work

朱世傑 Zhū Shìjié’s introductory pedagogical primer in 3 juàn, dated Dàdé 3 (1299) by its preface. The catalog gives “extent: ‘1299’” — interpretable as the preface-year used as the dating reference rather than a juàn-count.

Abstract

The Suànxué qǐméng is the elementary companion to Zhū Shìjié’s advanced Sìyuán yùjiàn (KR3fc017, 1303). Where the latter expounds the four-variable algebraic-equation method (the sìyuán shù 四元術) for advanced students, the Qǐméng covers the elementary mathematical curriculum: integer and fraction arithmetic, the standard rules of three and false position, area-and-volume calculations, root extraction, and an introduction to the tiānyuányī 立天元一 algebraic-equation method (one variable only). The work contains 259 problems organized into 20 chapters in 3 juàn.

The work is notable for two reasons. First, it is the principal elementary mathematical primer of the Yuán period and one of the most widely-transmitted pre-modern Chinese mathematical texts: lost in China from the late Míng (its early-Yuán transmission was overtaken by the practical-mathematical primers of Dīng Jù KR3fc013 and Ān Zhǐzhāi KR3fc014), it survived in Korea where it became one of the principal texts of the Chosŏn-state mathematical curriculum, and was re-imported to China in the 1660 Cháoxiǎn imprint (see KR3fc020). Second, its opening sections include some of the most famous expository passages in the Chinese mathematical tradition — the systematic jiǔjiǔ gē 九九歌 (Multiplication-Table Song), the qiúyī 求一 (multiplication-division shortcut formulas), and the dàshù 大數 (Great Numbers) name-list giving Chinese terminology for powers of ten up to 10⁸⁴.

The work’s preservation history makes it a key text for the comparative history of East-Asian mathematics. The Korean Chosŏn recension (1660 imprint) preserves a text-form slightly different from the Chinese Yuán original, and is the principal source for the Japanese Edo-period wasan 和算 reception of SòngYuán mathematics — Seki Takakazu’s 関孝和 mathematical work begins from direct study of the Suànxué qǐméng. The work’s substantive influence on Korean and Japanese mathematics is far greater than its influence on late-Míng / Qīng Chinese mathematics, where it was rediscovered only in the Dào-guāng-era recovery led by 羅士琳 Luó Shìlín.

Dating: 1299 per Zhū Shìjié’s own preface. NotBefore and notAfter both fixed accordingly. See KR3fc020 for the 1660 Korean / 1839 Luó Shìlín commentary recension.

Translations and research

  • Lam Lay-Yong. 1979. “Chu Shih-Chieh’s Suan-hsüeh ch’i-meng 算學啟蒙 (Introduction to Mathematical Studies).” Archive for History of Exact Sciences 21: 1–31. — The standard English-language scholarly treatment.
  • Hé Bǐngyù 何丙郁 (John Hoe). 1977. Les systèmes d’équations polynomes dans le Siyuan yujian (1303). Paris: Collège de France. — Treats the Qǐ-méng as the pedagogical preliminary to the Sì-yuán yù-jiàn.
  • Horiuchi Annick. 1994. Les mathématiques japonaises à l’époque d’Edo (1600–1868). Paris: Vrin. — Discusses the Japanese reception of the Qǐ-méng.
  • Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer.

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