Algebraic visual symbolism for problem solving: iconic equations from Diophantus to the present

This chapter provides a discussion of mathematical visual symbolism for problem solving based on the algebraic approach. It is formulated as lessons that can be learned from history. The visual formalism is contrasted with text through the history of algebra beginning with Diophantus’ contribution to algebraic symbolism nearly 2000 years ago. Along the same lines, it is shown that the history of art provides valuable lessons. The evident historical success provides a positive indication that similar success can be repeated for modern decision-making and analysis tasks. Thus, this chapter presents the lessons from history tuned to new formalizations in the form of iconic equations and iconic linear programming.

Keywords: Mathematical visual symbolism, problem solving, algebraic symbolism, iconic equations, iconic linear programming, iconic algebraic expressions.