For those in the UK, BBC iPlayer has an old Horizon doc on this made shortly after the theorem was fixed currently. It's pretty good, and even has the old "lingering shot until the subject starts crying," except the subject is Wiles, getting emotional about his proof, and it's quite moving
I presume that you're referring to Wiles' statement to the effect that, "Proving Fermat's Last Theorem is probably the biggest thing that I'll ever do." As a young student, it made a big impression. Eighteen years later, as a professional scientist, it's even more poignant.
Found it in a NOVA transcript [1]:
"At the beginning of September, I was sitting here at this desk, when suddenly, totally unexpectedly, I had this incredible revelation. It was the most—the most important moment of my working life. Nothing I ever do again will. . . I'm sorry."
