How do the earliest known mathematical writings highlight the state's management of grains in early imperial China?

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The earliest extant mathematical books from China contain a lot of problems and data about grains. They also betray a close relationship with imperial bureaucracy in this respect. Indeed, these texts quote administrative regulations about grains. For instance, the Book on mathematical procedures 筭數書, found in a tomb sealed ca. 186 BCE, has a section in common with the “regulations on granaries” from the Qin statutes in eighteen domains, known thanks to slips excavated at Shuihudi. Mathematical writings also deal with official vessels used to measure grains. They cast light on statements from, and practices evidenced by, official histories and administrative documents. This article addresses the following issues. Which information about the concrete management of grains can we derive from mathematical writings in relation to administrative documents? Which data can we find in these writings about continuities and changes in the management of grains in the time span between the Qin and Han dynasties? In particular, how can we account for the fact that in a later mathematical text, namely, The Nine Chapters, probably completed in the first century CE, there was a change in the form in which the data about grain equivalences were given, by comparison with the “regulations on granaries”? Finally, what do our conclusions imply with respect to the nature of the earliest extant mathematical writings. In this article, we gather the various types of statement that mathematical writings contain about grains and offer several elements of interpretation for the “regulations on granaries” and the related text in The Nine Chapters. From this perspective, we offer several hypotheses about the management of grain in the Qin and Han dynasties.