Scientific Discovery Processes in Humans and Computers: Theory and Research in Psychology and Artificial Intelligence

By Morton Wagman | Go to book overview

3
Mathematical Discovery

MATHEMATICAL DISCOVERY AND ARTIFICIAL INTELLIGENCE

THE GENERAL LOGIC OF AM

The intelligence of Lenat's Automatic Mathematician (AM) program, guided by mathematical aesthetics, seeks the discovery of new concepts and conjectures in elementary mathematics and set theory. The logic of AM is not directed toward the attainment of preassigned goals such as characterize problem-solving systems. AM does not know what goals it will reach, what concepts it will discover, or how these concepts will be defined and related to other concepts. The general logic of AM's creative acts are motivated and carried along by the type of ideation that characterizes human research mathematicians, namely, ideas of what might be interesting to explore (e.g., converses, maxima, minima, boundary conditions, exceptions, extrema). In this section, AM structures and operations will be described, the mathematical discoveries that it made will be summarized, and an analysis of AM's strengths and limitations will be offered. AM was developed by Lenat ( 1976).


CHARACTERISTICS OF AM

The nature of AM's initial concepts is summarized in Section 2 of Table 3.1. AM discovered over 200 concepts during a run of several

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