Hotel Hilbert

The visitors to a strange hotel (named after David Hilbert, a German mathematician who died in 1943) are met with several paradoxes. For one thing, the hotel has an infinite number of rooms, all of which are full. Yet they manage to accommodate the new guests.

This is an introduction to the idea of infinity and transfinite numbers in mathematics, but aimed at non-mathematicians. As such, it is sometimes seen on UK television in what used to be the Open University slot (BBC2 after midnight). It is told through puzzling conversations between guests and the captivating receptionist, and in discussions between guests themselves.

It is not intended as a film with a plot, so don't expect one (by that yardstick I'd rate it at 3, saved from a lower score by its brevity). However, if you want an inspirational insight into the joys of infinity (and infinity plus one, infinity plus two, ...), then start here, and record it to re-watch later. On that basis, I vote an 8.

Warning: this film could make your brain hurt.