Pierre de Fermat scrawled a claim in the margin of a book around 1637: no whole numbers x, y, and z can satisfy x^n + y^n = z^n for any n greater than 2, and he had a proof too long for the margin to hold. That proof never surfaced, and the theorem sat unsolved for 358 years while mathematicians built careers trying to crack it. The film follows Andrew Wiles, who first read about the problem as a ten-year-old in a library book and later worked on it in secret for seven years in his Princeton attic, telling no one but his family. His route runs through the Taniyama-Shimura Conjecture, a bridge he found in 1986 linking elliptic curves to modular forms, and his 1993 Cambridge lecture announcing the solution. The story does not end there: colleague Nick Katz finds a gap in the argument during peer review, and Wiles spends another year, with mathematician Richard Taylor, repairing it before the proof stands. Interviews with Wiles and the mathematicians around him carry the account of how the fix finally came.