The development of the classical Chinese algebra of polynomials: From the Nine Chapters and Liu Hui through Wang Xiaotong, Li Ye and Zhu Shijie

Donald B. Wagner

doi:10.1177/20966083261418725

March 25, 2026Cultures of ScienceOpen Access

The development of the classical Chinese algebra of polynomials: From the Nine Chapters and Liu Hui through Wang Xiaotong, Li Ye and Zhu Shijie

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Key Points

The aim is to explore the historical development of polynomial algebra in classical Chinese mathematics.
Reviewed historical texts including the Nine Chapters and works by Liu Hui, Wang Xiaotong, Li Ye, and Zhu Shijie.
Analyzed examples of polynomial equations and methods presented in these texts.
Compared techniques across different periods to highlight the evolution of algebraic thought.
Identified key advancements in polynomial methods from the Han to Yuan periods.
Showed how concepts from the Nine Chapters influenced later mathematicians.
Established a continuous thread of development in Chinese algebra leading to Zhu Shijie's contributions.

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Implication

This article traces the evolution of polynomial algebra in Chinese mathematics, showing its historical progress and significance.

Abstract

The remarkable algebra of polynomials used by mathematicians in the Song and Yuan periods was the product of a development that started in the Han period or before. This article traces that development through examples from four important books.

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Donald B. Wagner (2026) studied this question.

synapsesocial.com/papers/69c6206115a0a509bde18d16 https://doi.org/10.1177/20966083261418725

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The development of the classical Chinese algebra of polynomials: From the Nine Chapters and Liu Hui through Wang Xiaotong, Li Ye and Zhu Shijie

Key Points

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Abstract

Discussion

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The development of the classical Chinese algebra of polynomials: From the Nine Chapters and Liu Hui through Wang Xiaotong, Li Ye and Zhu Shijie

Key Points

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Implication

Abstract

Discussion

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