You wrote
> The famous 4-colour problem took more or less a hundred years to
> be "solved" after several intelligent and creative attempts.
> However, the "proof" required the helping hand of the computer.
> I once heard the question "How are we to prove the correctness of
> the program?"
We can't prove its correctness, but think of Wiles's proof of Fermat's Last
Theorem:
How can we prove its correctness?
We've had fine number theorists go over it with a metaphorical fine-toothed
comb.
With the 4 color program, perhaps the most effective way is to have a new
team of programmers under the direction of mathematicians re-program it
from scratch to try to obtain the same result.
Best wishes,
Sam Kutler