Computational discovery in pure mathematics

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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.

Original languageEnglish
Title of host publicationComputational Discovery of Scientific Knowledge - Introduction, Techniques, and Applications in Environmental and Life Sciences
EditorsSaso Dzeroski, Ljupco Todorovski
Pages175-201
Number of pages27
Publication statusPublished - 1 Dec 2007
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4660 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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