In 1989, Star Trek: The Next Generation aired The Royale. In this episode, we learn that Captain Picard tries his hand at proving Fermat’s Last Theorem (FLT) in his spare time. The writers must have believed that FLT would still be unresolved in the 24th century. Four years after The Royale, Andrew Wiles announced his proof of FLT. There was a flaw in Wiles’ first proof, but this was patched two years later in 1995.
Richard Feynman also tried his hand at FLT. He wrote a paper (unpublished) in which he gave a pseudo-proof of FLT based on probability. Feynman said that the probability of FLT being false was “certainly less than 10^-200.” The argument was high creative, sketchy, but ultimately nonsensical. Paul Nahin concludes
Feynman’s probabilistic analysis of Fermat’s Last Theorem would have no mathematical interest at all but for the fact it was Feynman who cooked it up.
Source: Number-Crunching by Paul Nahin.