The standard historiography of mathematics holds that two major contributions appeared in mathematical works that were completed in China in the mid-thirteenth century. In modern terms, one of them falls under number theory. We commonly attach to it the name of “Chinese remainder theorem.” The other falls rather under algebra, consisting in the use of polynomials to establish algebraic equations. The purpose of this article is to show that, far from being independent from one another, these two contributions are intimately related and both proceed from an abstract work on mathematical operations, to which they testify. Moreover, I argue that we already have evidence for this type of abstract work much earlier, in what, since at least the seventh century, constituted canonical literature in mathematics. In other words, the two contributions under consideration find their common roots in theoretical practices to which earlier mathematical Chinese works attest. In my view, these theoretical practices indicate a longstanding interest in a mathematical work of an algebraic kind, which I will endeavor to characterize.