The 17th-century mathematical conjecture left without its proof by Pierre de Fermat, which Picard works at for relaxation in The Royale and which Deep Space Nine later noted had long been solved.
Fermat's last theorem is a real problem in number theory, stating that a certain simple equation has no whole-number solutions for powers above two. Fermat claimed in a margin note to have a proof but never wrote it down.
In The Next Generation episode The Royale in 2365, Picard is found puzzling over it in his ready room. He tells Riker that the theorem has resisted solution for eight hundred years and that he finds it humbling that a part-time French mathematician working without a computer could pose something 24th-century science cannot answer. The theme of an old riddle echoes the mystery of the casino on Theta VIII.
The theorem was in fact proved by Andrew Wiles in the 1990s, after the episode was made. Deep Space Nine quietly corrected the record in Facets in 2371, where Jadzia Dax remarks that her earlier host Tobin produced the most original approach to the proof since Wiles.