Theorem is an enigma, a beautiful enigma that deserves to be considered carefully and analyzed for its many rich subtexts. On the surface level, it is a fantasy of eroticism in which an otherworldly being visits and summarily seduces each member of a bourgeois Italian family. However, in keeping with Pasolini's lifelong preoccupation with Marxist criticisms of consumer culture, it is also an examination of the means through which those trapped within the system of capitalism can be elevated above the restraints and repressions foisted upon them.
Visually, this film is stunning. The director uses a sort of magical realist system of representation in which documentarian portrayals of the family's every day life are combined with brief splashes of the super natural. The set pieces are intricate and detailed with Pasolini preferring to shoot on location to capture a sense of realism. And the performances of the actors are astonishing due to the psychological depth possessed by each characterization.
Those looking for a film which can be easily explained with few ambiguities should look elsewhere. The film provides few narrative details with which to make sense of the events depicted. Nevertheless, Theorem is so rich with ideas and visual references that even those who find its political and social commentary befuddling will surely find something to latch on to.