[[caption-width-right:230: A mad genius at work.]]

-> '''1.''' Mathematics is the language of nature.

-> '''2.''' Everything around us can be represented and understood through numbers.

-> '''3.''' If you graph these numbers, patterns emerge. Therefore: There are patterns everywhere in nature.

-->-- '''Maximillian Cohen'''

A brilliant mathematician and his home-built supercomputer Euclid search for the underlying patterns of the universe.

Max Cohen is a reclusive, paranoid, migraine afflicted genius driven by the unshakable belief that the universe can be explained entirely through math. Chased by agents of a Wall Street firm interested in profiting from his work as well as a sect of Hasidic Jews who want him to help find patterns in the Torah, Max stumbles upon a 216-digit number that seems to hold some universal secret. As he continues his research, his headaches worsen and he begins experiencing vivid hallucinations. Though he pushes on, determined to puzzle out the number's meaning, his mind might not be ready to comprehend it.

Shot in minimalist black and white, the film is mostly atmosphere, with relatively little dialogue. At its core, it's a MindScrew with a GainaxEnding, but an intriguing one indeed. The whole experience is often compared to ''Film/{{Eraserhead}}.''

''π'' is the directorial debut of Creator/DarrenAronofsky, who also wrote the film. It was made for a mere $60,000 and won the 1998 Sundance Film Festival award for Best Director. In his first film-score work, the movie's soundtrack was assembled by Music/ClintMansell of "Lux Aeterna" fame, who contributed the frenetic drum-and-bass theme.

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!! This film provides examples of:

* AffablyEvil:

** Marcy Dawson, who tries to swindle Max to help her stock prediction firm with regular sweet talking, up to her last scene, where she's putting a gun to Max's head to ''force'' him to comply.

** The kabbalistic Jews as well, explaining to Max the reason for their obsession, being genuinely sorry when one of their own punches Max in the face, and letting Max go when he refuses to give them the number (although Max explains it by saying that the group must have already tried all possible 216-digit combinations and haven't gotten the answer they seek, which they acknowledge).

* AmenBreak: Used frequently in Clint Mansell's drum n' bass score.

* AmbiguousDisorder: Max Cohen is never diagnosed, but he suffers from intensive social withdrawal, obsessive compulsiveness, chronic migraines, psychotic episodes, and possesses savant-like abilities in regards to mathematics (performing division on par with a pocket calculator).

* AnimalMotifs: Max finds ants as well as goo infesting his apartment after he loads it into his computer Euclid. A possible interpretation is that the number, [[spoiler: which is the blueprint for all creation,]] causes Euclid to begin creating simple organic matter. The goo and ants also fit into the themes of madness and decay that increasingly plague Max.

* AppliedPhlebotinum: The "Ming Mecca" computer chip that Dawson uses to bait Max, and provides Euclid the processing power to fully realise the number. Max is disbelieving that the firm can even provide it (because they're classified technology), but Dawson simply says [[ScrewTheRulesIHaveConnections that the firm has plenty of connections.]]

* {{Asexual}}: Max isn't interested when his pretty neighbor constantly hits on him and doesn't seem interested in men, either. Due to his anti-social behavior, he is likely asexual. There are hints during one of his last hallucinations that he does yearn for a romantic connection to his neighbor, though.

* BigNo: Max gives one when he comes back from his apparent NearDeathExperience.

* BlankWhiteVoid: In one of his visions, Max finds himself in exactly that setting. It's implied that he's standing on the border of life and death as he calmly starts to recite the universal number, which has previously been noted to possibly be God's true name. [[spoiler:He wakes up from this state, only to realize that he was probably hallucinating.]]

* BodyHorror: Subtle. A small, Hebrew-letter shaped lump appears in Max's head. This, and his headaches getting worse, [[spoiler: and Sol's two strokes,]] all imply that the number can literally mess with your head.

* {{Bookends}}: "When I was a little kid my mother told me not to stare into the sun. So once when I was six, I did" is said at the beginning and end of the film.

* BrownNote: The film is about a number sequence that helps define the universe. However, the process of determining this number is fatally destructive to a computer, be it machine or human.

* ChildHater: Downplayed, then subverted. Max is annoyed when the young neighbor girl tries to constantly test him on his math skills. He warms up to her by the end, it seems.

* CreatorThumbprint: The first of various Aronofsky films with an underlying theme of "obsession leading to destruction."

* CombatPragmatist: Max prefers to run from Marcy Dawson's thugs but at one point, they chase him into a grocery store where he grabs a can of soup and uses it to mass effect.

* CoolOldGuy: Sol, Max's former teacher, mentor, and friend. As well as giving Max sage advice on getting on with life, not becoming obsessed with his work, and coaching him in TabletopGame/Go. [[spoiler: It's all but stated outright that Sol discovered the number long before Max did.]]

* CyberPunk: Max's apartment is taken up by a super computer so every scene at home has a ton of wires and machinery everywhere. The evil stock firm further tips it into this genre.

* CyberpunkIsTechno: By Music/ClintMansell (such as the film's theme / LeitMotif for Max) with contributions from other groups like Music/MassiveAttack. Their song "Angel" from ''Music/{{Mezzanine}}'' is used on the soundtrack.

* DeliberatelyMonochrome: And filmed in ultra-high contrast for added creepiness.

* [[DoggedNiceGuy Dogged Nice Girl]]: One of his neighbors is an attractive young woman who obviously has her eye on Max. He seems to realize this to some extent but isn't interested.

* DrivenToSuicide: Not "kill" suicide, but the results of the number on Max's life and body drive him to destroy the part of him that matters to him the most-a symbolic suicide. Before that, there is a lot of "computer melting down" and "self destruct" symbology (such as Euclid's literal self destruction because of the number [[DoesThisRemindYouOfAnything and Max putting his injector gun up to his head (to deliver an injection directly to the lump) while screaming obscenities (to his neighbours having sex next door, which he can hear and is driving him nuts, on top of his migraine's pain)]]).

* EarnYourHappyEnding: The ending leaves you with more questions than answers, but at least Max is happy, one way or another.

* FaceCam: One of the more famous uses of the [=SnorriCam=]. The DVD contains some footage of a test run with Max in a convenience store.

* FadeToWhite: Most notable in the climax.

* {{Foreshadowing}}: If asked why he stopped searching for patterns within the digits of pi, Sol (in most instances) reacts dismissively. After mentioning Euclid's "crash," Max begins to suspect this nonchalance has been [[DarkSecret deliberately misleading:]]

--> Max:

--> Just a long string of digits—

--> Sol:

--> How ''many?''

--> Max:

--> [shrugs] I don't know...

--> Sol (intense):

--> What is it? A hundred and fifty, a thousand? [[{{Beat}} Uh]]—— [[SayingTooMuch Two-hundred and sixteen!?]] How '''''many?'''''

* FormulaicMagic: Max's dogmatic treatment of math as "the language of nature" seems to push past "math is capable of explaining everything in existence" into "math ''determines'' our existence." [[spoiler: The effects of the number point to the latter.]]

* FreezeFrameBonus: The number ''does'' appear in-screen in one scene.

* GainaxEnding: [[spoiler: Max is shown to trepan himself at the end of the movie, voiding himself of his mathematical genius. Whether this is literal or symbolic is left up to the viewer.]]

* {{God}}: The Jewish group believes that the universal number is the true name of God, and that they will come closer to the Messianic Age by invoking it. Max is ambivalent about this notion, but feels that only he is worthy because it was given to him.

* GoMadFromTheRevelation: The entire point of the movie is that this happens when you try to find the ratio that rationalizes pi, predicts the stock market, and is also the true name of God.

* HackerCave: Euclid takes up the majority of Max's apartment. His landlady doesn't much like it.

* HatesBeingTouched: Max winces every time someone touches him or even looks like they are about to touch him.

* HellIsThatNoise: The high-pitched beep that sounds every time Max has a migraine attack.

* {{Hikikomori}}: Max is a shut-in.

* InnerMonologue: Done by Max; train-of-thought stuff such as telling at what time he's doing an action, his MadnessMantra, and remembering factoids that reinforce it.

* ImportantHaircut: Max shaves his head as things start going downhill. [[BodyHorror Of course, there's a reason he does it.]]

* InstantAIJustAddWater: What happens after Max connects the mysterious Ming-Mecca chip to [[CompanionCube Euclid]]: the extravagantly-cheap, lovingly-customized mainframe (threatening to overrun every square centimeter of Max's tiny fortress of an apartment). That is, if one can believe Sol--outwardly rationalistic, yet painfully aware of forbidden mysticism--when the former professor [[HandWave explains]] how the 216-digit number [[ItRunsOnNonsensoleum makes machines "aware of their silicon nature."]]

* IntelligenceEqualsIsolation: Max's quest for the universal number has left him utterly disconnected from the rest of humanity, to the extent that he even fears leaving his apartment if he could run into someone.

* LogicBomb: The universal number [[spoiler:for both computers and people]].

* LuckyCharmsTitle: The title is usually just depicted as the symbol for pi.

* MadMathematician: Max is already neurotic before he starts going insane from the number.

* MadnessMantra: Max "restates his assumptions" several times throughout the film, which includes his various theories as well as the story of how he started getting migraines after looking into the sun too long.

* MadnessMontage: The "hip-hop montages" of surreal imagery.

* MaybeMagicMaybeMundane: Either the number really is connected to God and Max's insanity is due to some supernatural force, or the number is just a really complex equation that Max obsesses over to the point of insanity (and he's just lucky/unlucky enough to meet other people with a similar obsession). The climax counts as well since it could be literal or symbolic.

* MessyHair: Max, the [[MadMathematician reclusive math genius]]. His neighbor tries to adjust it, but he brusques her off.

* MindScrew: ''The A.V. Club'' [[http://www.avclub.com/articles/pi,19384/ called it]] "like ''Film/{{Eraserhead}}'' re-envisioned by {{cyberpunk}} author Creator/WilliamGibson."

* MinimalisticCoverArt: Some posters (and covers of a few DVD versions) of the Darren Aronofsky film ''Film/{{Pi}}'' were this. All it showed is the ratio's mathematical symbol.

* MouthfulOfPi: Not strictly pi, but Max can do rather complicated arithmetic in his head. The opening credits do show Pi itself counted out to thousands of numbers, but only the first 8 digits after the decimal point are correct.

* NearDeathExperience: In the climax, Max experiences his greatest migraine attack so far. As he goes mad from the pain, he suddenly finds himself in a white void and recites the numerical designation of God's name which [[TheseAreThingsManWasNotMeantToKnow he was never supposed to discover]]. His neighbor begs him to come back and comforts him in her arms when he is resuscitated. [[spoiler:Then it turns out that he was hallucinating all of it and is truly alone.]]

* NonindicativeName: Neither the actual number π, nor what it represents (the ratio of the circumference of a circle to its diameter), is important to the plot of this film at all.

* TheProfessor: Sol, Max's mentor and one of the few people Max actually talks to.

* RageAgainstTheReflection: The climax involves Max [[spoiler: drilling a hole through his head while looking into his bathroom mirror.]]

* ReligionIsMagic: Played straight and subverted in equal measure. The Kabbalistic Jews know about the universal number, and it is related to the Torah, but they are unable to discover it themselves. In the end, they are no closer to it than a stockbroking firm.

* RightThroughTheWall: Max can hear his neighbor having sex with her boyfriend right through the wall of his apartment. Not played for laughs however; at the same time Max is obsessively working on his computer to pursue the universal number, emphasizing how detached he is from everyday life.

* RuleOfSymbolism: Ants (as in "buggy" computers and decay), the slime (Euclid's decay, same as Max), numbers (especially the Golden Ratio-[[MadMathematician duh]]), brains (hallucinations leading to insanity [[spoiler: and self-trepanation]]), God (like the stock prediction firm's slogan [[BlasphemousBoast of "Only God is Perfect" to reflect their 80% accuracy]], the group of Jews looking for God's true name by working numerology on the Torah, some of Max's breakdowns looking like religious experiences).

* ScaryBlackMan: {{Gender Flip}}ped with Marcy Dawson, the stockbroker who hounds Max for the universal number.

* SciFiWritersHaveNoSenseOfScale: Examining all possible numbers with 216 decimal digits, one per second, would take a time that's unconceivably larger than the estimated age of the Universe.

* SharpshooterFallacy: Sol warns Max against obsessing over the 216-digit number (and overworking in general) because if he does so he will stop being a mathematician and turn into a "numerologist", starting to look for any way to shove a meaning to the number, even thinking that regular events he performs add up to 216 (amount of steps he takes to get somewhere, amount of seconds in an elevator, etc). Dawson and the Jews [[MaybeMagicMaybeMundane appear to]] showcase this devolving, thinking that Max's number is the key to manipulate the stock market (not "predict", ''manipulate'') and that it's God's name, respectively.

* SmartPeoplePlayChess: Max and his mentor play Go, which factors into several mathematical and visual motifs.

* SniffSniffNom: Max tastes a suspicious melted computer part.

* TechnologyPorn: Averted for most of the film with Max's supercomputer "Euclid"; it's quite obviously home-made, and looks it. Played straight when Marcy Dawson offers him a "Ming Mecca" chip as payment and Max is utterly incredulous that she could get her hands on anything so powerful.

* TheseAreThingsManWasNotMeantToKnow: [[spoiler:The 216-digit number repeatedly crashes Euclid and drives Max insane. It's also implied that [[SignificantName Sol]]'s second stroke came about because he started researching the number again. Just a ''partial'' number brings along an epic stock market crash. It's repeatedly linked with the sun, which fried Max's optic nerves when he gazed at it and killed Icarus when he flew too close to it.]]

* ThroughTheEyesOfMadness: There is ''one'' scene which is clearly a hallucination:[[spoiler: Max finding an human brain in the subway]]. The rest? Who knows?

* VideoFullOfFilmClips: A music video for the soundtrack's "πr^2" is included on the DVD, with shots from the film interspersed with random color footage of ants (a major recurring motif).

* VillainousRescue: [[spoiler: The Jews save Max from Dawson and her goons' strong-arming attempt, because they have need of Max's knowledge of the number]].

* WeaponsGradeVocabulary: Knowing THE number, among other things, is a true name of God, so knowing it has bad effects on body and sanity. Heck, a computer calculating it created slime and ants as side-effect. Pretty large effect for a mere 216 digit number.

* WritersCannotDoMath:

** Several mathematical facts get mixed up (for example, the golden ratio is usually phi, not theta), but it doesn't detract too much from the plot.

** Max guesses that the Jews have already "intoned" every possible name of God, which the rabbi does not deny. This would be completely impossible if each name were a 216 digit number. However, earlier Lenny shows that words in Hebrew have numeric values based on the sum of the values of their letters, so the Jews might actually be looking for a word that adds up to 216. Barring some unmentioned grammatical limitations, it would probably still be impossible to intone every single possible permutation.

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