Fermat's last theorem is an algebraic statement proposed by Pierre de Fermat.
Following his death, a mathematical formula was found scrawled in the margin of his notes, "xn + yn = zn, where n is greater than 2", which Fermat said had no solution in whole numbers, but he also added a phrase, "remarkable proof."
The above is a direct quote from TNG season 2 episode "Royal." However, the theorem is stated incorrectly in the show. The actual theorem is xn + yn =/= zn, where n > 2.
According to Jean-Luc Picard, people have been trying to find the proof for 800 years, including himself, during his pastime. Picard found it stimulating, and noted that it put things in perspective stating that "in our arrogance, we feel we are so advanced and yet we cannot unravel a simple knot tied by a part-time French mathematician working alone without a computer." (TNG: "The Royale")
Jadzia Dax stated that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." (DS9: "Facets")