Nine Chapters on the Mathematical Art
九章算術 (Jiuzhang Suanshu)
Mathematics should be organized around the practical problems a Han administrator actually faces, land area, tax proportion, engineering, and surveying, and solved by generalizable step-by-step procedures rather than by abstract proof for its own sake.
- problem-based rather than proof-based mathematics
- earliest systematic treatment of negative numbers
- matrix method equivalent to Gaussian elimination
- transmitted chiefly through Liu Hui's 3rd century commentary
The foundational text of the Chinese mathematical tradition, organized into nine chapters of worked problems covering land surveying, proportional distribution of grain and tax, engineering volumes, and equation solving, including the earliest known systematic treatment of negative numbers and a matrix-based method for solving simultaneous linear equations equivalent to Gaussian elimination, developed some 1,500 years before Gauss. Anonymous and compiled in stages across the Qin and Han from earlier administrative mathematics, it survives essentially through the extensive 3rd century AD commentary of Liu Hui, who supplied proofs and derivations the terse original problems lack. It shaped Chinese, and through it East Asian, mathematics for the next thousand years.
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