''Pi'' (stylized as ) is a 1998 American
conceptual psychological thriller
Psychological thriller is a Film genre, genre combining the thriller (genre), thriller and psychological fiction genres. It is commonly used to describe literature or films that deal with psychological narratives in a thriller or thrilling setting ...
film written and directed by
Darren Aronofsky
Darren Aronofsky (born February 12, 1969) is an American Filmmaking, filmmaker. His films are noted for their surreal, dramatic, and often disturbing elements, frequently in the form of psychological realism. His accolades include a Golden Lion ...
(in his
feature directorial debut). ''Pi'' was filmed on high-contrast
black-and-white
Black-and-white (B&W or B/W) images combine black and white to produce a range of achromatic brightnesses of grey. It is also known as greyscale in technical settings.
Media
The history of various visual media began with black and white, ...
reversal film
In photography, reversal film or slide film is a type of photographic film that produces a positive image on a transparent base. Instead of negatives and prints, reversal film is processed to produce transparencies or diapositives (abbrevia ...
. The title refers to the mathematical constant
pi. The story focuses on a mathematician with an obsession to find underlying
complete order in the real world and contrasting two seemingly irreconcilable entities: the imperfect irrationality of humanity and the
rigor
Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as ma ...
and regularity of mathematics, specifically
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
. The film explores themes of religion, mysticism, and the relationship of the universe to mathematics.
The film received positive reviews and earned Aronofsky the
Directing Award at the 1998
Sundance Film Festival
The Sundance Film Festival is an annual film festival organized by the Sundance Institute. It is the largest independent film festival in the United States, with 423,234 combined in-person and online viewership in 2023.
The festival has acted ...
, the
Independent Spirit Award for Best First Screenplay and the
Gotham Open Palm Award.
Plot
Unemployed
number theorist Max Cohen, who lives in a drab apartment in
Chinatown, Manhattan
Manhattan's Chinatown is a Neighborhoods in Manhattan, neighborhood in Lower Manhattan, New York City, bordering the Lower East Side to its east, Little Italy, Manhattan, Little Italy to its north, Civic Center, Manhattan, Civic Center to its s ...
, believes everything in nature can be understood through numbers. He suffers from
cluster headache
Cluster headache is a neurological disorder characterized by recurrent severe headaches on one side of the head, typically around the eye, eye(s). There is often accompanying eye watering, nasal congestion, or swelling around the eye on the aff ...
s, extreme
paranoia
Paranoia is an instinct or thought process that is believed to be heavily influenced by anxiety, suspicion, or fear, often to the point of delusion and irrationality. Paranoid thinking typically includes persecutory beliefs, or beliefs of co ...
,
hallucination
A hallucination is a perception in the absence of an external stimulus that has the compelling sense of reality. They are distinguishable from several related phenomena, such as dreaming ( REM sleep), which does not involve wakefulness; pse ...
s, and
schizoid personality disorder
Schizoid personality disorder (, often abbreviated as SzPD or ScPD) is a personality disorder characterized by a lack of interest in social relationships, a tendency toward a solitary or sheltered lifestyle, secretiveness, emotional coldness, ...
. His only social interactions are with his mathematics mentor, Sol Robeson (now disabled from a stroke), and those who live in his building: Jenna, a little girl fascinated by his ability to perform complex calculations, and Devi, a young woman living next door who sometimes speaks with him.
Max tries to program his computer, named
Euclid
Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...
, to make
stock
Stocks (also capital stock, or sometimes interchangeably, shares) consist of all the Share (finance), shares by which ownership of a corporation or company is divided. A single share of the stock means fractional ownership of the corporatio ...
predictions. Euclid malfunctions, printing out a seemingly random 216-digit number, as well as a single stock 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. He reveals that he came across the same number years ago and urges Max to take a break from his work.
Max meets Lenny Meyer, a
Hasidic Jew who does mathematical research on the
Torah
The Torah ( , "Instruction", "Teaching" or "Law") is the compilation of the first five books of the Hebrew Bible, namely the books of Genesis, Exodus, Leviticus, Numbers and Deuteronomy. The Torah is also known as the Pentateuch () ...
. Lenny demonstrates some simple
Gematria
In numerology, gematria (; or , plural or ) is the practice of assigning a numerical value to a name, word, or phrase by reading it as a number, or sometimes by using an alphanumeric cipher. The letters of the alphabets involved have standar ...
, the correspondence of the
Hebrew alphabet
The Hebrew alphabet (, ), known variously by scholars as the Ktav Ashuri, Jewish script, square script and block script, is a unicase, unicameral abjad script used in the writing of the Hebrew language and other Jewish languages, most notably ...
to numbers, and explains that some people believe the Torah is a string of numbers forming a code sent by God. Intrigued, Max notes that some of the concepts parallel other mathematical concepts, such as the
Fibonacci sequence
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...
. Agents of a
Wall Street
Wall Street is a street in the Financial District, Manhattan, Financial District of Lower Manhattan in New York City. It runs eight city blocks between Broadway (Manhattan), Broadway in the west and South Street (Manhattan), South Str ...
firm approach Max. One of them, Marcy Dawson, offers him 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 loses consciousness. After waking up, Max appears to become
clairvoyant
Clairvoyance (; ) is the claimed ability to acquire information that would be considered impossible to get through scientifically proven sensations, thus classified as extrasensory perception, or "sixth sense". Any person who is claimed to ...
and visualizes the stock market patterns he sought. 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 the number to manipulate the
stock market
A stock market, equity market, or share market is the aggregation of buyers and sellers of stocks (also called shares), which represent ownership claims on businesses; these may include ''securities'' listed on a public stock exchange a ...
, the firm instead caused the market to
crash. Driving by, Lenny rescues Max, but takes him to his companions at a nearby
synagogue
A synagogue, also called a shul or a temple, is a place of worship for Jews and Samaritans. It is a place for prayer (the main sanctuary and sometimes smaller chapels) where Jews attend religious services or special ceremonies such as wed ...
. They ask Max to give them the 216-digit number, believing it was meant for them to bring about the
Messianic Age
In Abrahamic religions, the Messianic Age () is the future eternal period of time on Earth in which the messiah will reign and bring universal peace and brotherhood, without any evil (through mankind's own terms). Many believe that there will be s ...
, as the number represents the
unspeakable name of God. Max refuses, insisting the number has been revealed to him alone.
Max flees and visits Sol, only to learn from his daughter, Jenny, that he died from another stroke. He 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. Believing the number and the headaches are linked, Max tries to concentrate on the number through his pain. After passing out, Max goes to the bathroom where he stares at himself in the mirror before lighting a match and burning the piece of paper with the number. Max then takes a power drill to his own head,
trepanning
Trepanning, also known as trepanation, trephination, trephining or making a burr hole (the verb ''trepan'' derives from Old French from -4; we might wonder whether there's a point at which it's appropriate to talk of the beginnings of French, ...
himself in an effort to find relief.
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, seemingly at peace.
Cast
*
Sean Gullette as Maximillian "Max" Cohen
*
Mark Margolis
Mark Margolis (, ; November 26, 1939 – August 3, 2023) was an American actor known for his portrayal of the character Hector Salamanca in ''Breaking Bad'' (2009–2011) and '' Better Call Saul'' (2016–2022). His performance in ''Breaking Ba ...
as Sol Robeson
*
Ben Shenkman
Ben Shenkman (born September 26, 1968) is an American actor. He is known for his roles in the comedy-drama series '' Royal Pains'' and the acclaimed HBO miniseries ''Angels in America'', which earned him both Primetime Emmy Award and Golden Globe ...
as Lenny Meyer
*
Samia Shoaib as Devi
* Pamela Hart as Marcy Dawson
*
Stephen Pearlman as Rabbi Cohen
*
Ajay Naidu as Farouq
* Kristyn Mae-Anne Lao as Jenna
* Lauren Fox as Jenny Robeson
*
Clint Mansell as Photographer
Production
Before production, to finance the complex visual sets and shots for the film, producer Eric Watson and director Darren Aronofsky asked every friend, relative, or acquaintance for donations of $100 each. Eventually, they accumulated about $60,000 for their production budget.
The film was shot on an
Aaton XTR Prod Camera, which shoots with 16mm film, with a
Bolex H16 Camera used for most of the handheld shots that the crew broke and had to fix.
A Canon 16mm camera package was also used.
Lenses were from
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.
Pi was produced with a low budget, with the crew being paid $200 a day and actors being paid $75 a day.
To save money, various cost-cutting techniques were used, including using only the actors' clothes and thrift store purchases as costumes, and shooting all of the subway and outdoor city scenes illegally to get around paying expensive permits. To get vehicles for the film, Aronofsky says he "probably" rented a station wagon belonging to the film's consulting producer, and claims to have hailed a cab and paid the driver $100 to keep his car there for a scene that was later cut, rather than renting out an additional vehicle.
For the main set, which was Max Cohen's apartment, Scott Vogel secured a section of his fathers's warehouse in
Bushwick, Brooklyn
Bushwick is a neighborhood in the northern part of the New York City borough (New York City), borough of Brooklyn. It is bounded by the neighborhood of Ridgewood, Queens, to the northeast; Williamsburg, Brooklyn, Williamsburg to the northwest; ...
. A back room was cleared out and used as a sound stage,
where Max's Euclid computer was built and the majority of the film was shot.
Finishing the film was more costly than shooting it. The post-budget was $68,183, most of which went into post-production sound, film and lab work, and film editing. Throughout the filming, 53,000 feet of
16mm film
16 mm film is a historically popular and economical Film gauge, gauge of Photographic film, film. 16 mm refers to the width of the film (about inch); other common film gauges include 8 mm film, 8 mm and 35mm movie film, 35 mm. It ...
was shot, amounting to about 23 hours over 28 days.
The film was sent to be developed in Bono Labs in
Arlington, Virginia
Arlington County, or simply Arlington, is a County (United States), county in the U.S. state of Virginia. The county is located in Northern Virginia on the southwestern bank of the Potomac River directly across from Washington, D.C., the nati ...
, which was the only lab capable of developing black and white reversal stock. Consequently, the crew only received dailies a week after sending the footage in.
Raw stock cost $5,414 and developing it cost $18,000. During post-production, most of the budget went toward the negative cut, which was a match back from an
AVID cut list. Clint Mansell created the score on his equipment, for which he was paid a deferred fee.
The production cost was $60,927, with post-production costing an additional $68,183. Along with other expenses, including insurance, the film cost $134,815.
Themes
Mathematics
''Pi'' features multiple references to mathematics and mathematical theories. For instance, Max finds the
golden spiral
In geometry, a golden spiral is a logarithmic spiral whose growth factor is , the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of for every quarter Turn (angle), turn it makes.
Approximations of th ...
occurring everywhere, including the stock market. Max's belief that diverse systems embodying
nonlinear dynamics share a unifying pattern has some similarity to results in
chaos theory
Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...
, which provides a means for describing certain phenomena of
nonlinear systems
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathem ...
, which might be thought of as patterns. During the climactic final scene, a pattern resembling a
bifurcation diagram
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically ( fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the ...
is apparent on Max's shattered mirror.
The game of Go
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
Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.
The term is generally used to c ...
gradually converges toward patterns that can be found.
Gullette and Margolis spent many hours learning the game at the
Brooklyn
Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelv ...
Go Club and received help from Dan Weiner, one of three Go consultants credited to the film.
Barbara Calhoun and Michael Solomon also served as game consultants.
Kabbalah
Early in the film, when Lenny speaks with Max about his work, he asks if Max is familiar with
kabbalah
Kabbalah or Qabalah ( ; , ; ) is an esoteric method, discipline and school of thought in Jewish mysticism. It forms the foundation of Mysticism, mystical religious interpretations within Judaism. A traditional Kabbalist is called a Mekubbal ...
. The numerological interpretation of the Torah and the 216-letter name of God, known as the
Shem HaMephorash, are important concepts in traditional Jewish mysticism.
Quran
Another religious reference comes while Max is at the market looking for that day's newspaper, when a recitation citing
Quran
The Quran, also Romanization, romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a Waḥy, revelation directly from God in Islam, God (''Allah, Allāh''). It is organized in 114 chapters (, ) which ...
2:140 can be heard in the background: "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."
Soundtrack
''Pi'' launched the film scoring career of
Clint Mansell. The soundtrack was released on July 21, 1998, via
Thrive Records. ''
AllMusic
AllMusic (previously known as All-Music Guide and AMG) is an American online database, online music database. It catalogs more than three million album entries and 30 million tracks, as well as information on Musical artist, musicians and Mus ...
'' rated it 4.5 stars out of 5. A music video for "πr²", using an alternative mix of the title track, is available as a special feature on DVD, consisting of footage from the film intercut with stock color reels of ants, referencing one of the film's visual motifs.
;Credits
*Design – Jeremy Dawson, Sneak Attack
*Executive-Producer – Eric Watson, Ricardo Vinas, Sioux Zimmerman
*Mastered By – Mark Fellows
*Written-By
oiceover– Darren Aronofsky, Sean Gullette
Release
More than a decade after its theatrical release, the rights to the film reverted from
Lionsgate Lions Gate, Lion Gate or similar terms may refer to:
Gates
*Lion Gate at Mycenae in Greece
*Lion Gate, one of the entrances to the ancient Hittite city of Hattusa, now in Turkey
*Lion Gate, one of the entrances to the gardens of Hampton Court Pala ...
(owner of Summit Entertainment and the Artisan library) back to Aronofsky, who sold it to
A24 in 2023. The
8K and
Atmos restoration version was released on
March 14
Events Pre-1600
* 1074 – Battle of Mogyoród: Dukes Géza and Ladislaus defeat their cousin Solomon, King of Hungary, forcing him to flee to Hungary's western borderland.
* 1590 – Battle of Ivry: Henry of Navarre and the H ...
by A24 in the
IMAX
IMAX is a proprietary system of High-definition video, high-resolution cameras, film formats, film projectors, and movie theater, theaters known for having very large screens with a tall aspect ratio (image), aspect ratio (approximately ei ...
format, to commemorate its 25th anniversary.
Box office
Produced on a budget of $134,815,
the film was financially successful at the box office, grossing $3,221,152 in the United States
despite only a
limited theatrical release
__FORCETOC__
Limited theatrical release is a film distribution strategy of releasing a new film in a few cinemas across a country, typically art house theaters in major metropolitan markets. Since 1994, a limited theatrical release in the Unite ...
. It sold steadily on
DVD
The DVD (common abbreviation for digital video disc or digital versatile disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any ki ...
, and was the first film ever to be sold as a
download
In computer networks, download means to ''receive'' data from a remote system, typically a server such as a web server, an FTP server, an email server, or other similar systems. This contrasts with uploading, where data is ''sent to'' a remote ...
on the
Internet
The Internet (or internet) is the Global network, global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a internetworking, network of networks ...
. Through the website
Sightsound.com, the film was available for
streaming
Streaming media refers to multimedia delivered through a network for playback using a media player. Media is transferred in a ''stream'' of packets from a server to a client and is rendered in real-time; this contrasts with file downl ...
in a
pay-per-view
Pay-per-view (PPV) is a type of pay television or webcast service that enables a viewer to pay to watch individual events via private telecast.
Events can be purchased through a multichannel television platform using their electronic program ...
window.
Critical response
''Pi'' was received well by critics upon release. On
Rotten Tomatoes
Rotten Tomatoes is an American review aggregator, review-aggregation website for film and television. The company was launched in August 1998 by three undergraduate students at the University of California, Berkeley: Senh Duong, Patrick Y. Lee ...
, the film has an 88% approval rating based on 59 reviews with an average rating of 7.4/10. 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
Roger Joseph Ebert ( ; June 18, 1942 – April 4, 2013) was an American Film criticism, film critic, film historian, journalist, essayist, screenwriter and author. He wrote for the ''Chicago Sun-Times'' from 1967 until his death in 2013. Eber ...
gave the film three and a half out of four stars, 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."
See also
*
List of cult films
*
List of films about mathematicians
*
List of films featuring surveillance
Notes
References
External links
*
*
*
*
Pi: Faith in Numbers - Brows Held High on YouTube
{{DEFAULTSORT:Pi
1998 films
1998 directorial debut films
1998 independent films
1990s avant-garde and experimental films
1990s English-language films
1998 psychological thriller films
American avant-garde and experimental films
American black-and-white films
American independent films
American psychological thriller films
American neo-noir films
Artisan Entertainment films
Fiction with unreliable narrators
Films about Jews and Judaism
Films about mathematics
Films directed by Darren Aronofsky
Films scored by Clint Mansell
Films set in Manhattan
Films shot in New York City
Films with screenplays by Darren Aronofsky
Hebrew-language films
Names of God in literature and fiction
A24 (company) films
Protozoa Pictures films
Sundance Film Festival award–winning films
Films shot in 16 mm film
IMAX films
Pi
1990s American films
English-language independent films
English-language thriller films