Suànxué yuánliú 算學源流
Origins and Currents of Mathematical Learning by 佚名 (anonymous, Sòng)
About the work
A short Sòng-era anonymous historiographical sketch of the development of Chinese mathematical learning, preserved as an appendix to several Yuán and early-Míng mathematical compilations. The catalog gives author “佚名” (anonymous) and dynasty 宋. The work is one of the principal early Chinese sources for the conventional historiography of pre-modern Chinese mathematics — the lineage Huángdì → Jiǔzhāng → Liú Huī → Suànjīng shíshū → SòngYuán algebraists — that would shape later imperial-period accounts of the discipline.
Abstract
The Suànxué yuánliú is most prominently attached as an opening or appendix piece to the Xīnbiān suànxué qǐméng 新編算學啟蒙 (KR3fc020) of 朱世傑 Zhū Shìjié (1299) — where in the Cháoxiǎn / Korean recension transmitted to Japan it forms the principal historiographical introduction. The text is normally less than a juàn in length, structured as a chronological catalog of mathematical predecessors and their works, beginning from the Huángdì legendary period (the Jiǔjiǔ gē 九九歌 multiplication-table tradition) and proceeding through the Zhōulǐ 周禮 Bǎoshì 保氏 Six Arts curriculum, the Jiǔzhāng suànshù, 劉徽 Liú Huī, the Suànjīng shíshū canonized by 李淳風 Lǐ Chúnfēng, and the principal Northern-and-Southern-Sòng mathematicians.
Authorship and dating are uncertain. Three positions are defensible: (a) the work is by Zhū Shìjié himself, composed as part of the Qǐméng’s prefatory apparatus c. 1299; (b) the work is by an earlier Sòng author and was incorporated by Zhū Shìjié; (c) the work is a Yuán-era student’s compilation drawing on Northern-Sòng-Jīn-Yuán bibliographic sources. The catalog placement under Sòng dynasty reflects position (b). Modern Chinese mathematical-historiographers (Qián Bǎocóng, Lǐ Yǎn, Du Shírán) typically follow position (b) or (c) and treat the work as essentially anonymous. NotBefore is conservatively set to the Northern-Sòng period (c. 1100); notAfter to the Qǐméng’s 1299 incorporation date.
The work’s substantive historiographical contribution is the listing of pre-Sòng and Sòng mathematical works no longer extant in any other source. Among the lost works mentioned are Yìngyòng suànfǎ 應用算法 (often cited as the source of certain SòngYuán problem-types), Yáng Sūn suànfǎ 楊鏪算法, and various pre-Yáng-Huī-and-Qín-Jiǔsháo Sòng mathematical primers. For modern scholarship on SòngYuán mathematics — particularly Lam Lay-Yong’s reconstruction of the Sòng mathematical curriculum — the Suànxué yuánliú is the principal documentary source.
Translations and research
- Lam Lay-Yong. 1977. A Critical Study of the Yang Hui Suan Fa: A Thirteenth-Century Chinese Mathematical Treatise. Singapore: Singapore University Press. — Treats the Suàn-xué yuán-liú listing of Sòng mathematical works in the context of the Yáng Huī corpus.
- Hoe, John (Hé Bǐngyù 何丙郁). 1977. Les systèmes d’équations polynomes dans le Siyuan yujian (1303). Paris: Collège de France. — Discusses the Suàn-xué yuán-liú in the context of Zhū Shìjié’s bibliographic awareness.
- Lam Lay-Yong and Ang Tian-Se. 1986. “The Earliest Negative Numbers: How They Emerged from a Solution of Simultaneous Linear Equations.” Archives Internationales d’Histoire des Sciences 37: 222–262.