A boundary notation for visual mathematics

Instead of traditional mathematical notation, one can describe formal mathematical systems in a visual form. While the traditional notation uses a linear sequence of symbols, visual mathematics uses a boundary notation, which is comprised of objects and boundaries to enclose objects. Boundary notation is abstract, decoupling the underlying mathematics of a system from its visual representation. Once a system is defined in boundary notation, visual designs can be explored that optimize specific features. The authors demonstrate this approach with propositional logic and elementary algebra. Visual mathematics provides a robust foundation for visual languages, much as linear mathematics provides a foundation for programming languages