This 45 minute TV film made by Simon Singh is about how Andrew Wiles, after seven or eight years of work, cracked the most famous problem in mathematics, proving Fermat's Last Theorem of 1637. It has to be my favorite documentary ever. (It can be viewed online here.)
It helps that the mathematician has a guileless, emotionally transparent face. The opening scene is famous, but the expressions on Wiles's face from 35:15 to 35:40 alone would earn a Hollywood actor an Oscar nomination.