[[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 ClintMansell of "Lux Aeterna" fame, who contributed the frenetic drum-and-bass theme.
!!This film provides examples of:

* AllThereIsToKnowAboutTheCryingGame: The infamous "drill" scene.
* 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.
* {{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.
* BigNo: Max gives one when he comes back from his apparent NearDeathExperience.
* 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.
* 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.
* 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.
* 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.
* 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.
* 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.
* 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.]]
* HackerCave: Euclid takes up the majority of Max's apartment. His landlady doesn't much like it.
* HatesBeingTouched: Max winces everytime someone touches him or even looks like they are about to touch him.
* {{Hikikomori}}: Max is a shut-in.
* 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. The climax counts as well since it could be literal or symbolic.
* MindScrew: ''The A.V. Club'' [[http://www.avclub.com/articles/pi,19384/ called it]] "like ''Film/{{Eraserhead}}'' re-envisioned by {{cyberpunk}} author Creator/WilliamGibson."
* MouthfulOfPi: Not strictly pi, but Max can do rather complicated arithmetic in his head.
* 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.]]
* NoBudget: It was made on the cheap but rarely shows.
* 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.
* ScaryBlackMan: {{Gender Flip}}ped with Marcy Dawson, the stockbroker who hounds Max for the universal number.
* SmartPeoplePlayChess: Max and his mentor play Go, which factors into several mathematical and visual motifs.
* 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. 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).
* WhiteVoidRoom: In one of his visions, Max finds himself in exactly that setting.
* 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.