I've been working through "Seven Sketches in Composability" [1], posted here a few weeks ago, and thinking about how much math relies in diagrams which are somewhere between drawing and writing. In research meetings, I often see people reasoning with diagrams and mathematical notation. In the vein of this article, I wonder whether it would also be possible to formalize mathematical pictographs to the point where they could be computable--a not-strictly-textual programming language. iPython notebooks often toggle between symbolic expressions and their implementation in code.
One thing that might be missing is context. Diagrams are indexical (pointing to contextual meaning) even more than text, often illustrating a problem that has previously been defined. This feels to me like potentially-fruitful design problem.