We feel that many of these problems can be addressed through
the development
of a rigorous notion of experimental mathematics.
In keeping with the positivist tradition,
mathematics is viewed as the most exact of sciences and
mathematicians have long taken pride in this. But as
mathematics has expanded, many mathematicians have begun to feel constrained
by the bonds placed upon us by our collective notion of proof.
Mathematics has grown explosively during our century
with many of the seminal developments in
highly abstract seemingly non-computational
areas. This was partly from taste and the power of abstraction
but, we would argue, equally much from the lack of an alternative.
Many intrinsically more concrete areas were, by 1900,
explored to the limits of pre-computer mathematics.
Highly computational, even ``brute--force'' methods were of
necessity limited but the computer has changed all that. A re-concretization
is now underway. The
computer--assisted proofs of the four color theorem are a prime example of
computer--dependent methodology
and have been highly controversial despite the fact
that such proofs are much more likely to be error
free than, say, even the revised proof of Fermat's Last Theorem.
Annotation Form Interface