Tobin Dax worked on an alternative proof of the theorem, which he never finished. According to Jadzia Dax, it was the most original approach to the proof since Wiles over three centuries before. (DS9: "Facets")
Wiles' first name was not given in the episode.
"The Royale", which aired several years before Wiles' proof, might be taken to imply that the problem was still not found. However, Wiles used techniques not known to Fermat, meaning that Fermat's own proof is still not known. Picard's dialogue in "The Royale" is consistent with the idea that he was interested in Fermat's original proof.