Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction: a role for history
- PART I HUMAN AND ARTIFICIAL MATHEMATICIANS
- 2 Communicating with automated theorem provers
- 3 Automated conjecture formation
- 4 The role of analogy in mathematics
- PART II PLAUSIBILITY, UNCERTAINTY AND PROBABILITY
- PART III THE GROWTH OF MATHEMATICS
- PART IV THE INTERPRETATION OF MATHEMATICS
- Appendix
- Bibliography
- Index
2 - Communicating with automated theorem provers
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction: a role for history
- PART I HUMAN AND ARTIFICIAL MATHEMATICIANS
- 2 Communicating with automated theorem provers
- 3 Automated conjecture formation
- 4 The role of analogy in mathematics
- PART II PLAUSIBILITY, UNCERTAINTY AND PROBABILITY
- PART III THE GROWTH OF MATHEMATICS
- PART IV THE INTERPRETATION OF MATHEMATICS
- Appendix
- Bibliography
- Index
Summary
it is only the very unsophisticated outsider who imagines that mathematicians make discoveries by turning the handle of some miraculous machine.
(Hardy, A Mathematician's Apology)INTRODUCTION
Had you subscribed to the New York Times back on December 10, 1996, you might well have noticed the following headline:
Computer Math Proof Shows Reasoning Power
By Gina Kolata
Computers are whizzes when it comes to the grunt work of mathematics. But for creative and elegant solutions to hard mathematical problems, nothing has been able to beat the human mind. That is, perhaps, until now …
The article announced that a computer had solved a famous mathematical problem – The Robbins Problem – sixty years after it had been posed. Noted mathematicians had tried but all had failed. Even the great logician Alfred Tarski had spent time on it to no avail.
To date computers have had little impact on the process of deriving mathematical proofs, or, at least, very much slighter an impact than one might casually have reckoned on from the way mathematics was represented in much of the philosophical literature of the twentieth century. To give a couple of examples briefly, where Pierre Duhem spoke of the role of bons sens and finesse in the field of physics, he contrasted these to géométrie, the automatic mode of thought to which the mathematician is restricted (cf. Crowe 1990).
- Type
- Chapter
- Information
- Towards a Philosophy of Real Mathematics , pp. 37 - 56Publisher: Cambridge University PressPrint publication year: 2003