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

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).