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How did The Nine Chapters on the Mathematical Art relate mathematics to government work?
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East Asian mathematics
Counting boards and markers, or counting rods, were used in China to solve systems of linear equations. This is an example from the 1st century ce.
The Nine Chapters on the Mathematical Art (Jiuzhang suanshu) was fundamentally linked to the needs of the Chinese civil administration. It served as a practical manual for officials, providing the mathematical tools necessary to manage the state’s logistical and economic responsibilities.12
The problems presented in the text directly mirror the duties of government work, including:
- Land Management: Surveying fields to determine areas.12
- Taxation: Levying taxes based on different types of grains and proportions.1
- Labor and Infrastructure: Measuring earthworks to calculate labor requirements and assessing granaries to determine storage capacity.1
- Personnel Administration: Determining wages for civil servants based on their specific rank within the hierarchy.1
Because of its practical utility, the work became an official text taught within the Chinese civil examination system. By the 7th century, it was incorporated into the Shibu suanjing ("Ten Classics of Mathematics"), which functioned as the primary training manual for officials in the imperial office of mathematics.1