There is a strong and growing trend to do mathematics via diagrammatic algebra, which involves constructing and manipulating equations whose elements are diagrams drawn in the plane. The manipulations are diagram rewrites. The diagrams are considered not as figures illustrating a `string of symbols' algebraic expression; instead, they are considered to be algebraic objects in their own rights. An archetypal diagrammatic algebraic theory is the theory of skein modules.

Notation of "algebra as strings of symbols" was pioneered by Al-Qalasadi in the fifteenth century. Previous to Al-Qalasadi, equations were often written as paragraphs of text, as in Al-Khwarizmi's Compendious Book on Calculation by Completion and Balancing.

Question: Who invented diagrammatic algebra? And when?

The first diagrammatic algebraic text I know is Louis Kauffman's 1987 paper State models and the Jones polynomial. It contains passages such as:

A subquestion is: Is this indeed the origin of diagrammatic algebra?