Wáng Xiàotōng 王孝通
Tang-period mathematician, active in the Wǔdé and Zhēnguān eras (618–649). The Sìkù 提要 of KR3f0040 Jígǔ suànjīng records his appointment-title as Tōngzhí láng 通直郎 (Court Gentleman for Comprehensive Service) and Tàishǐ chéng 太史丞 (Vice Director of the Bureau of Astronomy). The Tángshū Lǜlì zhì records that under the Wǔdé 9 (626) revision of the Wùyín lì, “the calendrical-checker 校厯人, the Suànlì bóshì (Mathematical-Calendar Erudite) Wáng Xiàotōng” presented memorials. Through his Bureau-of-Astronomy positions and his calendrical-reform work, Wáng Xiàotōng was one of the principal Tang-imperial-academy mathematical specialists of the early Tang.
His sole surviving work is the Jígǔ suànjīng 緝古算經 (KR3f0040) — also known as the Jígǔ suànshù 緝古算術 — in 1 juàn containing 20 problems-with-solutions, presented to the Tang Tàizōng (the yuán biǎo memorial of presentation is preserved). The work is the principal Tang-period independent mathematical text and is one of the Suànjīng shíshū canonized for the Tang Imperial Academy curriculum.
Wáng Xiàotōng’s mathematical contribution centers on cubic equation methods (lìfāng 立方 or kāi sāncìfāng 開三次方): six of the work’s twenty problems treat right-triangle (gōugǔ) configurations whose solution requires the formulation and solution of cubic equations. The work is one of the earliest known systematic treatments of cubic equations in any tradition, predating the Cardano-Tartaglia European cubic-formula discoveries by some 900 years. Wáng Xiàotōng’s method is essentially geometric (formulation-by-volume-relations rather than algebraic-symbolic), but the underlying mathematical content is genuinely cubic.