Fermat's last theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. Fermat said that he had a proof of it, but that it was too long to fit in the margin, and it has never been recovered.

It withstood a huge amount of attention from contemporary mathematicians before eventually being proven by Andrew Wiles https://www.dailymotion.com/video/x223gx8 in a complex proof that routed through fields of mathematics that did not exist in Fermat's time.
Given that, it's likely that Fermat did not have a real proof.

But if Fermat really had a proof, if there were really some simpler proof that contemporary mathematicians all somehow missed, this would be jarring and, personally, would assault my metaphysics and make the universe a dimmer place.

Closes yes if a relatively simple medium-length proof that Fermat could have credibly had is found. Closes no if this has not been found by 2050 or by the time very strong AI mathematicians have been made and applied to the problem and fail to find such a proof (could be much sooner than 2050).