Computational Discovery in Pure Mathematics

Abstract. We discuss what constitutes knowledge in pure mathematics and how new advances are made and communicated. We describe the impact of computer algebra systems, automated theorem provers, programs designed to generate examples, mathematical databases, and theory formation programs on the body of knowledge in pure mathematics. We discuss to what extent the output from certain programs can be considered a discovery in pure mathematics. This enables us to assess the state of the art with respect to Newell and Simon’s prediction that a computer would discover and prove an important mathematical theorem.

• Type: Conference
• Year: 2007
• Where: DIS
• Authors: Simon Colton
• Keywords: Automated Theorem Provers, DIS 2007, Pure Mathematics, Theory Formation Programs