Pi (stylized as π) is a 1998 American psychological thriller film written and directed by Darren Aronofsky in his feature directorial debut. Pi was filmed on high-contrast black-and-white reversal film and earned Aronofsky the Directing Award at the 1998 Sundance Film Festival, the Independent Spirit Award for Best First Screenplay and the Gotham Open Palm Award.

The title refers to the mathematical constant pi. The film explores themes of religion, mysticism, and the relationship of the universe to mathematics.

The story, about a mathematician with an obsession to find underlying complete order in the real world, contrasts two seemingly irreconcilable entities: the imperfect, irrational humanity and the rigor and regularity of mathematics, specifically number theory.

Plot[edit | edit source]

Unemployed and living in a drab apartment in Chinatown, Manhattan, Max Cohen is a number theorist who believes everything in nature can be understood through numbers. Max suffers from cluster headaches, extreme paranoia, hallucinations, and social anxiety disorder. His only social interactions are with Jenna, a young girl fascinated with his ability to perform complex calculations; Devi, a young woman living next door; and Sol Robeson, his mathematics mentor, now an invalid.

Max tries to program his computer, Euclid, to make stock predictions. Euclid malfunctions, printing out a seemingly random 216-digit number, as well as a single pick at one-tenth its current value, then crashes. Disgusted, Max throws away the printout. The next morning, he learns that Euclid's pick was accurate, but cannot find the printout. When Max mentions the number, Sol becomes unnerved and asks if it contained 216 digits, revealing that he came across the same number years ago. He urges Max to take a break from his work.

Max meets Lenny Meyer, a Hasidic Jew who does mathematical research on the Torah. Lenny demonstrates some simple Gematria, the correspondence of the Hebrew alphabet to numbers, and explains that some people believe the Torah is a string of numbers forming a code sent by God. Intrigued, Max notes some of the concepts are similar to other mathematical concepts such as the Fibonacci sequence. Max is approached by agents of a Wall Street firm; agent Marcy Dawson offers Max a classified computer chip called "Ming Mecca" in exchange for the results of his work.

Using the chip, Max has Euclid analyze mathematical patterns in the Torah. Once again, Euclid displays the 216-digit number before crashing. As Max writes down the number, he realizes that he knows the pattern, undergoes an epiphany, and passes out. Waking up, Max appears to become clairvoyant and visualizes the stock market patterns he had searched for. His headaches intensify, and he discovers a vein-like bulge protruding from his right temple. Max has a falling out with Sol after Sol urges him to quit his work.

Dawson and her agents grab Max on the street and try to force him to explain the number, having found the printout Max threw away. Attempting to use it to manipulate the stock market, the firm instead caused the market to crash. Driving by, Lenny rescues Max, but takes him to his companions at a nearby synagogue. They ask Max to give them the 216-digit number, believing it was meant for them to bring about the messianic age, as the number represents the unspeakable name of God. Max refuses, insisting that the number has been revealed to him alone.

Max flees and visits Sol, only to learn that he died from another stroke, and finds a piece of paper with the number in his study. At his own apartment, Max experiences another headache but does not take his painkillers. Driven to the brink of madness, he destroys part of Euclid. Believing the number and the headaches are linked, Max tries to concentrate on the number through his pain. After passing out, Max has a vision of himself standing in a white void and repeating the digits of the number. The vision ends with Max hugging Devi, who turns out to be a hallucination. Standing alone in his trashed apartment, Max burns the paper with the number and blithely performs an impromptu trepanning on himself with an improvised cranial drill.

Sometime later, Jenna approaches Max in a park and asks him to do several calculations, including 748 ÷ 238 (an approximation for pi). Max smiles and says that he does not know the answer. He sits on the bench and watches the trees blowing in the breeze, seemingly at peace.

Cast[edit | edit source]

Production process[edit | edit source]

At the start of production, as a means to finance the extensively visual set pieces and shots for the film, producer, Eric Watson and director, Darren Aronofsky went to every friend, relative or acquaintance and begged them for donations. Through doing this, they managed to accumulate an estimated $60,000 for their production budget.

The film was shot on an Aaton XTR Prod Camera, which shoots with 16mm film and a Bolex H16 Camera, used for most of the handheld shots, and the lens manufacturer used was Angenieux. The film was shot on black and white reversal film stock, Aronofsky aimed for high-contrast shots to give Pi a more "technically raw and spontaneous" look.

While a "no-budget film" is challenging it allows for a more authentic display of creativity. Within Pi, stunts were replaced with ideas, action sequences with allegorical montages and special effects with a haunting redefinition of New York City. For the main set which was Max Cohen’s apartment, Scott Franklin's father lent the production his warehouse out in Bushwick, a neighborhood in Brooklyn, NY. They cleared out a backroom and used it as a sound stage. There, they built Euclid, Max Cohen's super computer and shot the majority of the film there. New York was chosen for this film due to Darren Aronofsky's upbringing and all that he was surrounded with growing up. The film gives a greater multicultural view of the city which is the way Darren Aronofsky personally viewed New York. That being said, to shoot on location the production usually needs to obtain permits. This costs money and as a low budget film, permits weren't on the top of Aronofsky's list. For that reason, a lot of the film was technically shot illegally with all of the subway and New York City scenes shot without permits.

It cost more to finish the film than it did to shoot it. The post budget was $68,183 which mostly went to post-production sound, post-production film and lab work, and film editing. Throughout the entirety of shooting Pi, they shot fifty-three thousand feet of 16mm film, which amounts to about 23 hours over a 28 day period.

Budget breakdown[edit | edit source]

Pi was produced under the SAG Limited Exhibition Agreement and actors were paid $75 a day. Under this agreement the film was only allowed to be shown in limited art venues. If or when the film was to be sold for broader distribution, it would be required for actors to receive an increased payment. As for set operations which includes but is not limited to catering, different location expenses, and the grip department, Aronofsky stated that “Every member of the crew was on deferment for $200 a day. These deferred personnel also split 45 profit points. But, we couldn't find a grip or gaffer to do it for free, so we paid those guys $50 a day.”

Wardrobe mainly consisted of actors wearing their own clothing with the exception of Sean Gullete. Most of his wardrobe was thrifted. There was a standard kit fee for make-up and hair dressing which amounts to around $25 per day.

The producers managed to get a free lighting package. All of the money within the electric department was then shifted toward the gaffer and expendables. The Bolex H16 Camera was borrowed, but the crew ended up breaking this camera. Money came out of the budget to fix it. They also got an Aanton 16mm camera package.

Vehicles used within the film included a cab and a station wagon. In order to obtain a cab for that specific shot, Aronofsky stated that they hailed a cab and paid the driver $100 in order for him to keep his car there. They also paid their consulting producer for his station wagon.

Pi was shot on 16mm black and white reversal stock. They sent the film to be developed in Bono Labs in Arlington, Virginia. According to Aronofsky, this particular lab was the only one that could develop this type of stock, thus resulting in the crew only receiving dailies after a week of sending the footage in. Raw stock cost $5,414 and developing it cost $18,000. While the crew got to shoot the film in a warehouse for free, they did have to pay for the electricity bill, which increased dramatically during filming.

During post-production, most of the budget went toward the negative cut which was a matchback from an AVID cut-list. The score was created by Clint Mansell on his own equipment and was paid a deferred fee. The rest of the money for music went toward rights for festival entries. There was a separate budget for film and lab for post production for the blow up release print, which cost roughly $25,571. Another $3,000 went to the 35mm optical soundtrack.

The production cost a total of $60,927, and post-production costs amounted to $68,183. Along with other expenses, including insurance, the film cost a total of $134,815.

Themes[edit | edit source]

Mathematics[edit | edit source]

Pi features multiple references to mathematics and mathematical theories. For instance, Max finds the golden spiral occurring everywhere, including the stock market. Max's belief that diverse systems embodying highly nonlinear dynamics share a unifying pattern bears much similarity to results in chaos theory, which provides machinery for describing certain phenomena of nonlinear systems, which might be thought of as patterns. During the climactic drill scene, a pattern resembling a bifurcation diagram is apparent on Max's shattered mirror.

The game of Go[edit | edit source]

In the film, Max periodically plays Go with his mentor, Sol. This game has historically stimulated the study of mathematics and features a simple set of rules that results in a complex game strategy. Each character uses the game as a model for their view of the universe; Sol says that the game is a microcosm of an extremely complex and chaotic world, while Max asserts its complexity gradually converges toward patterns that can be found.

Both Gullette and Margolis spent many hours learning the game at the Brooklyn Go Club, and had the help of a Go consultant, Dan Weiner, for the film. The film credits list Barbara Calhoun, Michael Solomon, and Dan Wiener as Go consultants.

Kabbalah[edit | edit source]

Early in the film, when Lenny begins talking with Max about his work, he asks if Max is familiar with kabbalah. The numerological interpretation of the Torah and the 216-letter name of God, known as the Shem HaMeforash, are important concepts in traditional Jewish mysticism.

Quran[edit | edit source]

Another religious reference is when Max is in the market looking for today's newspaper, there is a recitation from Quran, in the background, citing Quran 2:140: "Or do you say that Abraham and Ishmael and Isaac and Jacob and the Descendants were Jews or Christians? Say, 'Are you more knowing or is Allah?' And who is more unjust than one who conceals a testimony he has from Allah? And Allah is not unaware of what you do."

Schizophrenia[edit | edit source]

The film strongly suggests that the main character Max Cohen is actually a paranoid schizophrenic.[15] The soundtrack uses screeching and disturbing tones that are thematic of auditory hallucinations experienced by such patients. The character of Devi, the old man in the metro, people of large corporations stalking him, visions of a human brain infested with ants in his sink could be interpreted as visual hallucinations. He sees patterns everywhere, especially the logarithmic spiral, which can be attributed to such a phenomenon.

Soundtrack[edit | edit source]

Pi launched the film scoring career of Clint Mansell. The soundtrack was released on July 21, 1998, via Thrive Records. AllMusic rated it 4.5 stars out of five. A music video for "πr²", using an alternative mix of the title track, is available as a special feature on the π DVD, consisting of footage from the film intercut with stock color reels of ants, harking back to one of the film's visual motifs.

Release[edit | edit source]

Produced on a budget of $134,815 (including $60,927 for production and $68,183 for post-production), the film was financially successful at the box office, grossing $3,221,152 in the United States despite only a limited theatrical release. It has sold steadily on DVD. Pi was the first ever film to legally be made available for download on the Internet.

Critical reception[edit | edit source]

The film was well received. On Rotten Tomatoes, the film has an 88% approval rating based on 56 reviews with an average rating of 7.3/10. The website's critical consensus reads: "Dramatically gripping and frighteningly smart, this Lynchian thriller does wonders with its unlikely subject and shoestring budget." On Metacritic, the film has a rating of 72 out of 100 based on 23 reviews, indicating "generally favorable reviews". Roger Ebert gave the film three and a half stars out of four, writing:

  • Pi is a thriller. I am not very thrilled these days by whether the bad guys will get shot or the chase scene will end one way instead of another. You have to make a movie like that pretty skillfully before I care. But I am thrilled when a man risks his mind in the pursuit of a dangerous obsession.

James Berardinelli gave the film three out of four stars, writing:

[Pi] transports us to a world that is like yet unlike our own, and, in its mysterious familiarity, is eerie, intense, and compelling. Reality is a fragile commodity, but, because the script is well-written and the central character is strongly developed, it's not hard to suspend disbelief....It probably deserves 3.1416 stars, but since my scale doesn't support that, I'll round it off to three.

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