Apparently, no one is really quite sure how to respond to this film, whose title translates as "Theorem." On its release, religious groups sharply condemned it, chiefly for its sexual content, although one suspects the central ambiguous Christ-like figure and the pious character who appears to perform some minor miraculous acts also had much to do with that. Ironically, the film won a special award at the Venice Film Festival from the International Catholic Film Office, but that was withdrawn after the Vatican loudly protested.

Critics through the years have been equally conflicted. Roger Ebert, in a 1969 review in the Chicago Sun-Times, wrote: "I don't feel ready to write about this mysterious film; perhaps, a week from now, I'll decide it is very bad, a failure. But perhaps it is the most brilliant work yet by that strange director." While offering strong, if ambivalent praise, he went on to admit he didn't think many people would like it and recounted "snorts and giggles" at the screening he attended. Around the same time, Vincent Canby of the New York Times called it "the kind of movie that should be seen at least twice, but I'm afraid that a lot of people will have difficulty sitting through it even once."

The vantage point of distance over time has not occasioned a solid critical consensus. Teorema has been deemed "intolerably silly" (Pauline Kael, The New Yorker), "not a conventional chronicle of bourgeois depravity" but a film that "asks more troubling, cosmic questions" (John Patterson, The Guardian), a "perfect fusion of Marxism and religion...that is both a political allegory and mystical fable" (David Pirie, Time Out) and "basically a film about Terence Stamp's crotch" (Dan Callahan, Slant).

A case could be made that all of the above is true; this is, after all, the sixth film of Italy's most controversial director, Pier Paolo Pasolini, an artist whose towering position in that country's cultural terrain owes as much to his being equally a poet, novelist, journalist and essayist, painter, provocateur, often self-contradictory theorist and boldly vocal Marxist and gay man. From his first film Accattone (1961), a violent story about a pimp in the slums of Rome, through his last, the notorious (and widely banned) Salò, or the 120 Days of Sodom (1975), he constantly ran afoul of Church and State, and his violent murder under still mysterious circumstances (despite the conviction of a young male hustler) was seen as both shocking and somehow inevitable.

Falling right in the middle of Pasolini's cinematic output, Teorema features British star Terence Stamp then at the height of his international success after Billy Budd (1962), The Collector (1965) and Far from the Madding Crowd (1967). He plays a character known only as The Visitor, a mysterious stranger who insinuates himself into the home and lives of a wealthy Milanese family and has erotic encounters with mother, son, daughter, maid and, with less overt sexuality, father. When he just as suddenly departs halfway through the story, each family member unravels and self-destructs in a manner consistent with their darkest desires and doubts and their individual encounters with The Visitor.

The mathematical construction of the plot, the way the second half of the film is virtually a mirror reversal of the first, along with Pasolini's rigorously formal style (what Millicent Marcus in Italian Film in the Light of Neorealism called the "geometric precision" of his camerawork), give the film its title and its purpose as an exercise in cinematic theory beyond the sociopolitical themes foregrounded throughout Pasolini's body of work. In shunning conventional naturalism in favor of this abstract precision, Pasolini makes narrative structure itself the subject of the film.

Formal notions aside, of course, there is also the obvious interpretation of the film as allegory. Pasolini was an atheist but one attracted to myth and religious symbolism (The Gospel According to St. Matthew, 1964; Medea, 1969; The Decameron, 1971). Speaking to this duality in 1966, he said, "I may be an unbeliever, but I am an unbeliever who has a nostalgia for a belief." Stamp's character can be seen as Christ himself (evidenced in his annunciation by an exaggerated angel figure and in the postures in which Pasolini captures him), or as a demonic force that reveals the family members to themselves then abandons them to a destruction brought about by that revelation. Pasolini described the character in a BBC interview as "a generically ultraterrestrial and metaphysical apparition" who could be "the Devil, or a mixture of God and the Devil. The important thing is that he is something authentic and unstoppable."

In its conflation of the spiritual and the sensual, however, Teorema ran afoul of the authorities. The film was banned by the Public Prosecutor of Rome, and Pasolini - not for the first time - was charged with obscenity. As with many of his other legal trials, he ultimately won the case.

More positively, the picture was nominated for the Venice Film Festival's greatest honor, the Golden Lion, and the festival's Best Actress Award went to Laura Betti as Emilia, the servant who becomes a religious figure. Betti was a very close friend of the director and later made a documentary about him, Pier Paolo Pasolini e la ragione di un sogno (2002).

The unsettling soundtrack, with echoes of Mozart's Requiem, is by the prolific film composer Ennio Morricone, best known for his scores for Sergio Leone (The Good, the Bad and the Ugly, 1966), Bernardo Bertolucci (1900, 1976), Quentin Tarantino (The Hateful Eight, 2015), Terrence Malick (Days of Heaven, 1978) and seven other Pasolini releases.

Teorema has had a life beyond the big screen. Pasolini expanded it into a novel of the same title. Giorgio Battistelli composed an opera based on it, and in 2009 the Dutch theater company Toneelgroep Amsterdam adapted it for the stage.

We will let the late Roger Ebert have the last word on the lasting impact of this confounding and controversial film with these lines from his 1969 review: "My guess is that Teorema is a watershed of some kind, a film out of its own time, a film nothing has prepared us for, but a film that in years to come will be seen as a turning point like early Godard."

Director: Pier Paolo Pasolini
Producers: Manolo Bolognini, Franco Rossellini
Screenplay: Pier Paolo Pasolini
Cinematography: Giuseppe Ruzzolini
Editing: Nino Baragli
Production Design: Luciano Puccini
Music: Ennio Morricone
Cast: Silvano Mangano (Lucia, the mother), Terence Stamp (The Visitor), Massimo Girotti (Paolo, the father), Anne Wiazemsky (Odetta, the daughter), Laura Betti (Emilia, the servant), Andrés José Cruz Soublette (Pietro, the son)

By Rob Nixon