[nurettin]

Whether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.

[EGreg]

Well, it could have been like Kempe's chains... they finally realized there is a problem, and then it took like 100 years before Appel and Haken made what is probably the first computer-aided proof. And who can say it's really a "proof" if it doesn't explain "why" it's true.