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Automated Theory Formation in Pure Mathematics

  • Simon Colton

Part of the Distinguished Dissertations book series (DISTDISS)

Table of contents

  1. Front Matter
    Pages iii-xvi
  2. Simon Colton
    Pages 1-8
  3. Simon Colton
    Pages 9-28
  4. Simon Colton
    Pages 29-43
  5. Simon Colton
    Pages 45-58
  6. Simon Colton
    Pages 59-67
  7. Simon Colton
    Pages 69-100
  8. Simon Colton
    Pages 101-120
  9. Simon Colton
    Pages 121-140
  10. Simon Colton
    Pages 141-163
  11. Simon Colton
    Pages 165-179
  12. Simon Colton
    Pages 181-223
  13. Simon Colton
    Pages 225-245
  14. Simon Colton
    Pages 247-279
  15. Simon Colton
    Pages 281-293
  16. Simon Colton
    Pages 295-301
  17. Back Matter
    Pages 303-380

About this book

Introduction

In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.

Keywords

Addition Automated Theory Computational Creativity Computer Equivalence Machine Learning Pure Mathematics artificial intelligence calculus classification database intelligence number theory proving

Authors and affiliations

  • Simon Colton
    • 1
  1. 1.University of EdinburghEdinburghUK

Bibliographic information