Lǐ Yě 李冶 (also written 李治 Lǐ Zhì in some sources)
Style name Rénqīng 仁卿, sobriquet Jìngzhāi 敬齋. Native of Luánchéng 欒城 (in modern Héběi). Born Mìngchāng 3 of the Jīn (1192); died Zhìyuán 16 of the Yuán (1279) at age 87.
The personal name appears in the Sìkù-recorded form as 李冶 (the catalog meta gives 李治, the alternative form). Both forms appear in different sources; the Sìkù 提要 of KR3f0042 uses Yě 冶. Modern scholarship generally prefers Yě. The character variation is conventional; the same person.
The greatest mathematician of the JīnYuán transition period and one of the great SòngYuán mathematicians. Jìnshì of the late Jīn (Zhèngdà 7, 1230); served as Magistrate of Jūnzhōu under the Jīn. After the Mongol conquest of the Jīn (1234), Lǐ Yě withdrew from official service and lived in retirement in the Lùntái 龍臺 area, devoting himself to mathematical-and-classical scholarship. Refused service in the early Yuán despite repeated invitations from Khubilai Khan — eventually accepted appointment as Hànlín xuéshì (Academician) but resigned almost immediately, returning to his retirement until his death.
His two principal mathematical works are both Sìkù-preserved:
(1) The Cèyuán hǎijìng 測圓海鏡 (KR3f0042) in 12 juàn (170 problems) — composed Mìngchāng 5 (1248), his magnum opus. The work systematizes the geometry of right-triangles inscribed in circles (gōugǔ róngyuán 勾股容圓), using the lì tiānyuányī 立天元一 (algebraic-equation) method developed by 秦九韶 Qín Jiǔsháo. Lǐ Yě’s elaboration of tiānyuányī methodology is the most thoroughgoing in the SòngYuán mathematical tradition.
(2) The Yìgǔ yǎnduàn 益古演段 (KR3f0044) in 3 juàn — Lǐ Yě’s elementary-pedagogical work designed to make the tiānyuányī method accessible to beginners, by re-working a now-lost earlier work (Yìgǔ jí 益古集 by an unknown earlier author) into 64 problems with explicit cǎo (procedural-elaboration), tiáoduàn (sectional-decomposition), tú (diagrams), and yì (meaning-explanations).
Through Lǐ Yě’s two works the lì tiānyuányī method became the foundational algebraic methodology of the SòngYuán mathematical tradition; without his works (and Qín Jiǔsháo’s KR3f0041 Shùshū jiǔzhāng), the method would probably not have survived into the late-imperial period.
The Sìkù 提要 of KR3f0042 makes a famous historical observation: by the late Míng, the tiānyuányī method had been forgotten — Tang Shùnzhī 唐順之 wrote to Gù Yìngxiáng 顧應祥 (顧應祥) saying lì tiānyuányī “means absolutely nothing to me” (màn bù shěng wéi hé yǔ 漫不省為何語). Gù Yìngxiáng’s KR3f0043 Cèyuán hǎijìng fēnlèi shìshù attempted to expound Lǐ Yě’s work but had to remove the tiānyuányī sections because Gù could not understand them. Only with the Kāngxī-period transmission of European algebra (jiègēnfāng 借根方) was the tiānyuányī method recovered: Méi Juéchéng 梅㲄成 (Méi Wéndǐng’s grandson, working at the Méngyǎng zhāi) recognized that the European algebra was equivalent to the lost LǐYě method, providing a methodological key by which the SòngYuán algebra could be re-understood. The European jiègēnfāng itself was named Āěrrèbālā 阿爾熱巴拉 (Algebra) in Méi Juéchéng’s account, with explicit etymology Dōnglái fǎ 東來法 (Eastern-Coming Method) — implying the European algebra had originally come from the East. This is the foundational Chinese statement of the Xīfǎ Zhōngyuán 西法中源 thesis applied to algebra.
Lǐ Yě also composed substantial classical-philological works: the Jìngzhāi gǔjīn dù 敬齋古今黈 (50 juàn, his collected miscellany on classical-textual matters), the Jìngzhāi shīcǎo 敬齋詩草 (collected poems), and others.
name: 李冶 pinyinName: Lǐ Yě alternateNames: [季蘭, Jìlán] dynasty: 唐 birthDate: 730 deathDate: 784 cbdbId: created: 2026-05-13 updated: 2026-05-13
Lǐ Yě 李冶 (midTáng, ca. 730–784) — Daoist priestess and poet
Zì Jìlán 季蘭, of Wūchéng 鳥程 (in modern Húzhōu, Zhèjiāng). The leading Táng-dynasty female poet of the Dàlì generation, a Daoist priestess (nǚ dàoshì) whose verses circulated widely under the patronage of Liú Chángqīng 劉長卿 and Liú Yǔxī 劉禹錫. The Sìkù 提要 to the Xuē Tāo Lǐ Yě shī jí KR4h0017 places her career at Cháng’ān in the Tiānbǎo and post-rebellion years; she is reported to have died ca. Xīngyuán 1 (784), executed by Dézōng for having submitted verses praising the rebel general Zhū Cǐ 朱泚. The SKQS tíyào judges her five-character verse “indistinguishable in style from the Dàlì shí cáizǐ” and “in rank above Xuē Tāo.” Of her work only fourteen poems were recoverable by the Sìkù compilers.