What subjects are covered in The Nine Chapters on the Mathematical Art?

The Nine Chapters on the Mathematical Art is a foundational work in Chinese mathematics that organizes various arithmetic, algebraic, and geometric algorithms. Rather than theoretical proofs, the text presents these methods through practical problems related to civil administration, such as surveying land, levying taxes, determining wages, and measuring earthworks and storage capacities.1

The subjects covered include:

• Arithmetic: The text assumes basic knowledge of the four arithmetic operations and utilizes a decimal place-value system facilitated by counting rods.2
• Algebra: It features advanced methods for solving systems of simultaneous linear equations using column reduction, an algorithm known in the West as Gauss elimination. This section also introduces the use of negative numbers, marking a significant milestone in the history of mathematics.3
• Geometry: The work includes algorithms for calculating areas and volumes, essential for tasks like planning construction and managing grain storage.1

The book’s format—providing a problem, a numerical answer, and a general procedure—became the standard for subsequent mathematical literature in East Asia.1