Lǐ Ruì 李銳
Style name Shàngzhī 尚之, sobriquet Sìxiāng 四香. Native of Yuánhé 元和 (Sūzhōu prefecture, Jiāngsū). Born Qiánlóng 33 (1768); died Jiāqìng 22 (1817). CBDB id 77136 confirms the lifedates.
A self-taught mathematician. Lǐ Ruì never advanced beyond jǔrén status (and indeed, repeatedly failed the metropolitan examination); his scholarly life was spent in Sūzhōu and Yángzhōu in the patronage circle of 阮元 Ruǎn Yuán, working as private mathematical secretary and contributing substantially to Ruǎn Yuán’s biographical compilation Chóurén zhuàn 疇人傳 (the great Qīng-era biographical dictionary of Chinese mathematicians and astronomers, completed 1799). Lǐ Ruì supplied many of the mathematical-historical biographies and the technical-mathematical commentary in the Chóurén zhuàn; his work is the principal documentary basis for Qīng-period historiography of Chinese mathematics.
A polymathic mathematical scholar. His principal independent works are concentrated on the recovery and reconstruction of the indigenous Chinese mathematical tradition, particularly the calendrical-and-astronomical and the equation-theoretical strands. The KR3fc series preserves a substantial run of his works:
(1) KR3fc050 Zhàogào rìmíng kǎo 召誥日名考 — an evidential study of the day-name dating-system in the Shàngshū Zhàogào chapter (one of the foundational chronological-philological problems of QiánJiā scholarship).
(2) KR3fc051 Hàn Sāntǒng shù 漢三統術 — reconstruction of Liú Xīn’s 劉歆 Hàn-period Sāntǒng calendar.
(3) KR3fc052 Hàn Sìfēn shù 漢四分術 — reconstruction of the Hàn-period Sìfēn calendar.
(4) KR3fc053 Hàn Qiánxiàng shù 漢乾象術 — reconstruction of the SānGuó Qiánxiàng calendar of Liú Hóng 劉洪.
(5) KR3fc054 Bǔxiū Sòng Fèngyuán shù 補修宋奉元術 — supplementary reconstruction of the Northern-Sòng Fèngyuán calendar.
(6) KR3fc055 Bǔxiū Sòng Zhàntiān shù 補修宋占天術 — supplementary reconstruction of the Northern-Sòng Zhàntiān calendar.
(7) KR3fc056 Rìfǎ shuòyú qiángruò kǎo 日法朔余強弱考 — evidential study of the lunar-day intercalation residuals.
(8) KR3fc057 Fāngchéng xīnshù cǎo 方程新術草 — new method for solving systems of linear equations (extending the Jiǔzhāng Fāngchéng chapter).
(9) KR3fc058 Gōugǔ suànshù xìcǎo 勾股算術細草 — detailed procedural exposition of right-triangle methods.
(10) KR3fc059 Húshǐ suànshù xìcǎo 弧矢算術細草 — detailed procedural exposition of arc-and-versed-sine methods.
(11) KR3fc060 Kāifāng shuō 開方說 — the equation-theory treatise that is Lǐ Ruì’s most theoretically-original work.
The combination — calendrical reconstruction (1–7), procedural exposition (8–10), and equation-theory (11) — defines Lǐ Ruì’s mathematical identity. He is the principal kǎozhèng mathematician of the Jiāqìng era, applying the methodology of evidential philology to mathematical-and-astronomical content. His Kāifāng shuō in particular — a systematic study of the relations between the coefficients and the roots of polynomial equations — is one of the most theoretically-developed Chinese mathematical works of any pre-modern period.
His mathematical correspondence with 汪萊 Wāng Lái in the years 1800–1813 is the principal documentary record of high-level Jiā-Dào-era Chinese mathematical discussion. After Wāng Lái’s death in 1813, Lǐ Ruì himself died in 1817 — the deaths in quick succession of the two leading theoretical mathematicians of the era effectively ended the Jiā-Dào-era theoretical project, which subsequent generations would not resume until 李善蘭 Lǐ Shànlán’s mid-19th-century work integrated the indigenous tradition with translated European mathematics.
Note: CBDB lists many persons named 李銳 (homonyms); only the entry 77136 with lifedates 1768–1817 matches the mathematician.
Lǐ Ruì 李銳 (Táng, fl. early 8th c.; CBDB id 187219 records a death year of 733). A Jíxián diàn 集賢殿 academician named in the Xīn Táng shū · Yìwén zhì as one of the seven compilers of Xú Jiān’s Chūxué jì 初學記 (KR3k0006) under Táng Xuánzōng’s commission of Kāiyuán 13 (725). No independent biography survives; he is named only in the Chūxué jì preface and in the Yìwén zhì note. Unrelated to the Qīng mathematician above.