The Proof Is in the Diagram: Liu Yi and the Graphical Writing of Algebraic Equations in Eleventh-Century China

In a specific tradition of dealing with algebraic equations in China, eleventh to thirteenth century writings on the topic combine problems, algorithms, and diagrams of several types. This article focuses on the geometrical diagrams that some of them contain. The argument holds that the captions in these diagrams establish a specific connection with the algorithms in relation to which they are given. Accordingly, I claim that these diagrams constitute the proof of the correctness of the algorithms. Reading the diagrams as assertions is thus in my view essential to capture what is at stake in them. These diagrams disappear from another tradition of dealing with algebraic equations in China, to which writings from the second half of the thirteenth century and the early fourteenth century attest. I suggest that these diagrams are replaced by a form of algebraic proof in an algorithmic context, which is also expressed in specific ways.