Question

I vote for 100年の難問はなぜ解けたのか ～天才数学者　失踪の謎 ("Why the difficult 100-year-old conjecture was proven- The mysterious disappearance of the genius mathematician"), about Grigory Perelman, Geometrization, and the proof of the Poincaré Conjecture, as the best mathematical documentary ever. It's non-technical, but it's really very well-made, and gives a good sense of what research mathematics is like, and why some people spend their lives searching for proofs of mathematical conjectures. The mathematics in it is mostly fairly solid. It inspired fashion design house Issey Miyake to design a fashion collection with Bill Thurston inspired by geometrization.