## What is a Proof?

## Alan Bundy ^{}

### School of Informatics,

University of Edinburgh

To those brought up in a logic-based tradition
there seems to be a simple and clear definition of
proof. But this is largely a 20th century invention;
earlier proofs had a different nature. We will look
particularly at the faulty proof of Euler's Theorem and
Lakatos' rational reconstruction of the history of this
proof. We will ask: how is it possible for the bugs in a
faulty proof to remain undetected for several years --
even when counter-examples to it are known? How is it
possible to have a proof about concepts that are only
partially defined? And can we give a logic-based account
of such phenomena?