On 24/03/07, Ray Saintonge saintonge@telus.net wrote:
Not even that. We never know whether we will find the key source in the next place that we look. Fermat's Last Theorem remained unproven for three centuries because nobody could find the killer counterexample.
Um. If they *had* found a counterexample, it'd have been disproven, not proven. And the main reason it wasn't proven for three centuries is that (on current evidence) the mathematical understanding needed to prove it didn't exist before a few decades ago...
I think this may be an unfortunate example to pick on when discussing the nature of proof.