The most expensive sentence in history was written in a book margin in 1637. "I have a truly marvelous proof, which this margin is too narrow to contain." Nobody found that proof for 358 years.
Fermat's claim was so simple a kid gets it: no three whole numbers solve xⁿ + yⁿ = zⁿ once n passes 2. That one line beat every genius who touched it for three centuries.
Andrew Wiles finally closed it in 1994. But he never attacked Fermat directly. He proved something stranger and much bigger - that two fields nobody thought were related are secretly the same field.
y² = x³ + ax + b
That's an elliptic curve, from number theory. A modular form comes from the opposite end of math - symmetry, complex analysis. For a century the two were studied by separate people who never spoke. Wiles proved they're the same object in two disguises. Fermat just fell off the bridge on the way.
Now the part the documentary skips. Those same elliptic curves guard your bank login, your messages, every Bitcoin wallet alive.
The famous problem was never where the treasure sat.
Wiles on the seven years it took him to see it:
"You enter the first room of the mansion and it's completely dark... after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated."