Fermat's Last Theorem, a 1996 documentary on Andrew Wiles and his proof. Ian Stewart mentions the documentary in his Letters to a Young Mathematician in this passage:

Fermat's Last Theorem... turned out to be very deep and very hard. It is unlikely that Fermat's proof, if it existed, was correct. If it was, no one else has ever thought of it, not even now, when we know Fermat was right. Generations of mathematicians attacked the problem and came away with nothing. A few chipped the odd corner off it; they proved that it couldn't be done with fifth powers, say, or seventh powers. Only in 1994, after a hiatus of 350 years, was the theorem proved by Andrew Wiles; his proof was published the following year. You probably remember a TV documentary about it.

Wiles's methods were revolutionary, and much too difficult for even a university course at undergraduate or introductory graduate level. His proof is very clever and very beautiful, incorporating results and ideas from dozens of other experts. A breakthrough of the highest order.

The TV program was very moving. Many viewers burst into tears.