On the Discovery of Mathematical Theorems

Abstract

Graph Theorist, GT, is a system which performs mathematical research in graph theory. This paper focuses upon GTs ability to conjecture and prove mathematical theorems from the definitions in its input knowledge base. Each class of graphs is defined in an algebraic notation with a semantic interpretation that is a stylized algorithm to generate the class correctly and completely. From a knowledge base of such concept definitions, GT is able to conjecture and prove such theorems as The set of acyclic, connected graphs is precisely the set of trees and There is no odd-regular graph on an odd number of vertices. Conjecture and proof are driven both by examples (specific graphs) and by definitional form (algorithms).