HR - Automatic Concept Formation in Finite Algebras

Abstract

We are investigating how and why mathematicians invent new concepts while developing a theory, and im-plementing our ideas into the HR system, which auto-matically produces, assesses and displays concepts in finite algebras, such as finite group theory. We fit’st determined a reason for HI ~ to produce concepts- to classify a given set of groups up to isomorphism. Doing so would involve inventing concepts which help describe groups, so a classification can occur, and inventing con-cepts which help generate new examples of groups, so that improvements to the classification are necessitated, perpetuating the process. Next, we developed measures to tell us how interesting the concepts produced were (see Colton 1997). This helped us determine the kinds of concepts HR. should produce and with this in mind,