It is shown here that Peirce's ten trichotomies, specifically art as discussed in , provides a structure for presenting a mathematical conjecture and provide a heuristic for going about attempting a mathematical proof of the conjecture. The mathematics is presented through the work of the mathematical proof theorists George Polya and Daniel Solow. Here a geometric conjecture is shown to be true using a ten trichotomy context for a proof. Thus through the structure of mathematical proof the ten trichotomy structure validates itself.