Forms of proofs for algebraic equations in medieval China

How can diagrams account for the correctness of algorithms? Writings composed in China between the 11th and the 13th centuries and devoted to algebraic equations illustrate an unexpected answer to this question. They contain geometrical diagrams whose captions establish a specific connection between the diagrams and the algorithms in relation to which they are given. The talk will analyze the context in which these diagrams, in and of themselves, formulate an argument. It will further examine the form of algebraic proof in an algorithmic context that replaces these diagrams when later on, they disappear from writings devoted to algebraic equations.