Fermat definitely couldn't have understood Wiles' proof in terms of the mathematics of his time, since it relies on a lot of theory that wasn't available then.

Fermat definitely couldn't have understood Wiles' proof in terms of the mathematics of his time, since it relies on a lot of theory that wasn't available then. It's technically possible that there's a proof that only requires the mathematics of that period, but since no one has found it yet it seems unlikely.