History Main / FormulaicMagic

[[caption-width-right:350:Your math textbooks were right: math ''is'' magic!]

** [[UsefulNotes/TheGoldenAgeOfComicBooks Golden Age]] superhero Johnny Quick accessed his superspeed powers by reciting the mathematical formula "3X2(9YZ)4A". More recent materials have [[{{Retcon}} retconned]] this as a mantra that allows him to tap into the mystical Speed Force.

Authors often neglect to establish this link between math and reality, instead treating equations as if they possess a power all on their own.[[note]]Mathematicians make matters worse by routinely referring to certain properties or results as being more or less powerful; this merely means that if such-and-such is true, a great many other useful things are also true.[[\note]] This often manifests in two ways:

Authors often neglect to establish this link between math and reality, instead treating equations as if they possess a power all on their own. This often manifests in two ways:

* Witches in ''Manga/SoulEater'' use "calculation magic" to make their spells more precise.
* It's revealed in the [[AllThereInTheManual supplementary]] [[ComicBookAdaptation manga]] of ''Franchise/LyricalNanoha'' that constructing the InstantRunes needed for magic in that setting requires a very good grasp of math. In fact, one of the reasons why Nanoha and Fate are such powerful mages is because they're both [[TeenGenius math geniuses]]. The [[MagicWand Devices]] aren't just conduits for mana, they're also highly advanced calculators.
* The [[RealityWarper reality warping]] abilities of human interfaces in ''LightNovel/HaruhiSuzumiya'' seem to work like this.

* In ''Anime/YuGiOhGX'', Misawa has a monster called Mathematician, a goofy-looking wizard wearing a mortarboard and academic road. It's attack is called "Battle Curriculum" (or "Number Cruncher" in the dub) and consists of a beam of magical energy full of numbers and mathematical symbols. [[AscendedFanon Konami eventually]] made it into a [[http://yugioh.wikia.com/wiki/Mathematician real card.]]

* The Lovecraft-inspired, ''Literature/TheLaundryFiles'' by Charles Stross shows magic as mathematics, to the point where computers solving certain equations can warp reality as per magical spells. Becomes a bit of a problem when the walls around reality start weakening, to the worst-case scenario of somebody solving equations in their head running the risk of accidentally summoning an EldritchAbomination.
* Jack L. Chalker's ''[[Literature/WellWorld Well of Souls]]'' series: The Great Equation. A couple of supercomputers are capable of [[RealityWarper warping reality]] retroactively (that is, those who didn't see the change actually happen are incapable of realizing that anything actually changed) by "altering" the Equation, which basically ''is'' reality. By moving a few numbers in the equation, the result -- that is, our reality -- changes to suit.
* The ''Literature/HarryPotter'' series has an [[{{Whatevermancy}} Arithmancy]] class. The reader doesn't get to hear much about the subject, though, beyond the fact that Hermione's studying it (and apparently enjoys it).

* In the ''Literature/YoungWizards'' series, all magic is based in math and science, and the kids have quite high-level discussions of these things, because part of magic is being able to completely describe what you want to change.
* In "Career Day", one of the stories in the ''Literature/ChicksInChainmail'' anthology, the protagonist comes from a world where magic is done with mathematical formulas. She brings her daughter's class there on a field trip to observe her in her career as a barbarian swordswoman. When her opponent in a duel cheats by hiring a wizard to help him, the other chaperon on the trip, her daughter's math teacher, counteracts the magic with his knowledge of calculus. ItMakesSenseInContext. Later expanded to a full novel, called ''Mathemagics'' with this entire premise for the magical system.
* ''Literature/TheHitchhikersGuideToTheGalaxy'', in the later books, introduces the field of ''Bistromathics'', math that can be used to warp spacetime for purposes of Faster-than-light travel by taking advantages of the unique properties numbers take on when written down within the confines of an Italian restaurant.

* The premise behind ''Literature/SimonBloom''
* In Literature/MondayBeginsOnSaturday, a book called ''Equations of Mathmagic'' is mentioned.
* In ''Literature/{{Pyramids}}'', You Bastard the camel is a genius mathematician, able to use complex equations to step in and out of pocket dimensions.
* In ''Literature/TheGodEaters'' this appears to be how the very powerful 'Pattern Magic' works.

** ''Literature/{{Ra}}'', by the same author, is about actual magic, which is a poorly-understood branch of physics. Magic is accessed by reciting specific incantations while performing mental exercises stated to be not dissimilar to solving differential equations. More generally, spells also require a lot of math to design, and resemble computer programs (right down to concepts like modularity, recursion, and writing interpreters to parse gestures as incantations).

* ''VideoGame/TheWorldEndsWithYou'': Minamimoto summons a nuke by initializing the Level ''i'' Flare, which consists of [[MouthfulOfPi reciting pi to 150 digits]]. Of course, there are a lot of people capable of reciting pi to 150 digits, but they aren't Minamimoto, and they don't have a [[ItMakesSenseInContext graffiti covered dead end alleyway and eldritch tattoos]]. [[labelnote: Fun bit of math[=/=]''FinalFantasy'' info here.]] "Level x Flare" is a type of spell that casts Flare (one of the most powerful attack spells) on everything with a level divisible by whatever number x is. ''i'' is a mathematical term referring to the square root of -1, the consummate imaginary number. In addition to that, as the root of -''1'', that also makes it a possible factor in every number, real ''or'' imaginary. It would affect ''everything'', across all possible realities. Useful when your target can travel through dimensions.[[/labelnote]]
* The ''VideoGame/FinalFantasyTactics'' series has a Calculator class that uses various magical effects, such as casting spells that hit every target whose level is a prime number. How their abilities work from an in-universe perspective is not specified.
** According to the remake for the PSP's tutorial, Calculators are attuned enough to the flow of mist that they can manipulate it in unique and bizarre ways which other classes just can't pull off. In other words: SE knew it made absolutely no sense and handwaved it.
* ''VideoGame/FinalFantasyVII'' has an interesting example: When [[OneWingedAngel Safer Sephiroth]] casts [[OverlyLongFightingAnimation Super Nova]], four equations fly by the screen. They are, roughly, the potential attractive force between the sun and the planet, the Earth's potential attractive force, and... the area of a circle. Still, 75% good scientific formulae being used in a magic spell is better than average.
** FridgeLogic (or EpilepticTrees, depending on who you talk to): the area of a circle can be used calculate the distribution of impact force over a target area, so could theoretically useful. Its also possible to use a derived equation, √(A/π)=R to calculate a radius based on a given cross sectional area- for example, exactly how big the nova's blast would have to be to stretch to reach the battlefield and stop exactly as it does.
** This is echoed in ''VideoGame/{{Dissidia|FinalFantasy}}'': When doing Supernova as his [[LimitBreak EX Burst]], Sephiroth will begin chanting the equations, which briefly appear on-screen.
* Rita's non-spell special attacks in ''VideoGame/TalesOfVesperia'' take the form of mathematical equations.

[[folder:Visual Novel]]

* ''VisualNovel/ChaosHead'': fun[[superscript:10]] × int[[superscript:40]] = [=Ir2=], [[spoiler:the equation Takumi discovered in elementary school and the basis of the Noah Project]].

* The Khert in ''Webcomic/{{Unsounded}}'' is a BackgroundMagicField that oversees the setting's reality and powers its magic system, [[SufficientlyAnalyzedMagic pymary]]. The [[MagicalIncantation incantations]] for spells are a very precise shorthand spoken in the LanguageOfMagic describing which materials and physical properties are to be manipulated and how. Logic errors, on the other hand, get messy: when someone tried to liquefy a material that turned out to be saturated with water already, the Khert glitched and melted his casting hand instead.

* ''WesternAnimation/LooneyTunes'' has Egghead Junior, who can [[AwesomenessByAnalysis accomplish anything]], even to the point of bending reality, so long as he has a few seconds to write down an appropriate equation for doing so.

* There's a DonaldDuck cartoon called "Donald Duck's Adventures In Mathemagic Land," which is Donald exploring (with the Narrator) the history of mathematics, and math's contribution to things such as music, games, and the natural world.

* In ''Franchise/TheElderScrolls'' series, the [[OurElvesAreBetter Altmeri (High Elven)]] Clan Direnni, who once ruled nearly 1/3 of Tamriel's land mass as the Direnni Hegemony in the 1st Era, were known to use "hidden magic" in the form of signs and runes in their ''financial reports'' in order to keep them out of the hands of their competitors. "Sorcerous precautions" were required on the part of the reader, lest these magic numbers prove fatal. Per one text on the subject:

* The Khert in ''Webcomic/{{Unsounded}}'' is a BackgroundMagicField that oversees the setting's reality and powers its magic system, [[SufficientlyAnalyzedMagic pymary]]. The [[MagicalIncantation incantations]] for spells are a very precise shorthand describing which materials and physical properties are to be manipulated and how. Logic errors, on the other hand, get messy: when someone tried to liquefy a material that turned out to be saturated with water already, the Khert glitched and melted his casting hand instead.

* During the 19th century, 4th dimensional mathematics was seen by occultists as the key to understanding ghosts and the spirit world: if people could just teach themselves how to think and move in four dimensions rather than the normal three, they could become like ghosts themselves, {{teleport|ation}}ing}} and becoming {{intangible|Man}} at will. While that's technically true (if oversimplified), today it's believed that, if higher spatial dimensions such as hyperspace exist, they're curled up far too small for human beings to move through, and/or necessitate immense amounts of energy in order to access.

* During the 19th century, 4th dimensional mathematics was seen by occultists as the key to understanding ghosts and the spirit world: if people could just teach themselves how to think and move in four dimensions rather than the normal three, they could become like ghosts themselves, [[TeleportersAndTransporters teleporting]] and becoming [[IntangibleMan intangible]] at will. While that's technically true (if oversimplified), today it's believed that, if higher spatial dimensions such as hyperspace exist, they're curled up far too small for human beings to move through, and/or necessitate immense amounts of energy in order to access.

* In ''Discworld/{{Pyramids}}'', You Bastard the camel is a genius mathematician, able to use complex equations to step in and out of pocket dimensions.

[[folder:VideoGames]]

* ''Webcomic/{{Erfworld}}'' has Mathamancy, which involves "analyzing probabilities," "predicting outcomes," and "the raw calculations thereof." It should be noted, however, that Mathamancy in Erfworld (or at least [[{{Protagonist}} Parson]]'s Mathamancy Bracer) seems to be more than merely math from the real world: for example, Parson has a magical deal to give [[ChessMaster Charlie]] twelve Mathamancy calculations whenever he wants. At one point, when negotiating whether to give up the deal in exchange for information, Charlie asked Parson to calculate whether the information was worth the nine calculations remaining. The answer was that there was a probability of 4% that it was worth the exchange, something that should not be possible to calculate.

* ''Literature/FineStructure'' uses science, not magic. In later stories, scientists fluent in [[https://tvtropes.org/pmwiki/pmwiki.php/Main/LanguageOfMagic Eka]] can unlock the "The simple knowledge of an equation is powerful in itself" kind of formulaic magic. [[spoiler:It's also revealed that the universe, or more accurately the imprisoning god, doesn't like anyone messing around with Eka.]]
** ''Literature/{{Ra}}'', by the same author, is about actual magic, which is a poorly-understood branch of physics. Magic is accessed by reciting specific incantations while performing mental exercises stated to be not dissimilar to solving differential equations. More generally, spells also require a lot of math to design, and resemble computer programs (right down to concepts like modularity, recursion, and writing interpreters to parse gestures as incantations).

* In ''Anime/YuGiOhGX'', Misawa has a monster called Mathematician, a goofy-looking wizard wearing a mortarboard and academic road. It's attack is called "Battle Curriculum" (or "Number Cruncher" in the dub) and consists of a beam of magical energy full of numbers and mathematical symbols. [[SureWhyNot Konami eventually]] made it into a [[http://yugioh.wikia.com/wiki/Mathematician real card.]]

* ''VideoGame/TheWorldEndsWithYou'': Minamimoto summons a nuke by initializing the Level ''i'' Flare, which consists of [[MouthfulOfPi reciting pi to 150 digits]]. Of course, there are a lot of people capable of reciting pi to 150 digits, but they aren't Minamimoto, and they don't have a [[ItMakesSenseInContext graffiti covered dead end alleyway and eldritch tattoos]]. [[note:Fun bit of math[=/=]''Franchise/FinalFantasy'' info here. "Level x Flare" is a type of spell that casts Flare (one of the most powerful attack spells) on everything with a level divisible by whatever number x is. ''i'' is a mathematical term referring to the square root of -1, the consummate imaginary number. In addition to that, as the root of -''1'', that also makes it a possible factor in every number, real ''or'' imaginary. It would affect ''everything'', across all possible realities. Useful when your target can travel through dimensions.

* ''VideoGame/TheWorldEndsWithYou'': Minamimoto summons a nuke by initializing the Level ''i'' Flare, which consists of [[MouthfulOfPi reciting pi to 150 digits]]. Of course, there are a lot of people capable of reciting pi to 150 digits, but [[CrazyAwesome they aren't Minamimoto]], and they don't have a [[ItMakesSenseInContext graffiti covered dead end alleyway and eldritch tattoos]].
** Fun bit of math[=/=]''Franchise/FinalFantasy'' info here. "Level x Flare" is a type of spell that casts Flare on everything with a level divisible by whatever number x is. ''i'' is a mathematical term referring to the square root of -1, the consummate imaginary number. In addition to that, as the root of -''1'', that also makes it a possible factor in every number, real ''or'' imaginary. ''Nothing'' escapes Level ''i'' Flare.
*** That said, ''1'' holds that same property as well, because as the multiplicative identity, it is a factor of ''every number ever''.
*** The beauty of Level ''i'' Flare is that it's a factor of every number, not just real numbers, meaning it would affect ''everything'', across all possible realities. Useful when your target can travel through dimensions.

* The ''Literature/HarryPotter'' series has an [[{{Whatevermancy}} Arithmancy]] class, whose name would imply divination through arithmetic. (Ironic, because Hermione actively loathes Divination ''itself''.) The reader doesn't get to hear much about the subject, though, beyond the fact that Hermione's studying it (and apparently enjoys it).
** In {{Fanon}}, Arithmancy is a common choice for [[PeggySue Intelligent!Harry]] stories. In these stories, its usually presented as discussing (and learning) the rules that govern magic itself. For instance, Arithmancy masters can cast wandlessly more easily, because they understand the way the magic flows and can create shortcuts, similar to simplifying a complicated equation. Its usually also implied that math in the magic world is dreadfully behind that of {{Muggles}}, with Trig being 'the last lesson before Mastery'. Cue Harry [[ShipToShipCombat (and Hermione, more often than not)]], [[MarySue learning Calc]].

* Connected to the above, ''Literature/TheLaundrySeries'' by Charles Stross also shows magic as mathematics, to the point where computers solving certain equations can warp reality as per magical spells. Becomes a bit of a problem when the walls around reality start weakening, to the worst-case scenario of somebody solving equations in their head running the risk of accidentally summoning an EldritchAbomination.

* ''FineStructure'' uses science, not magic. In later stories, scientists fluent in [[http://tvtropes.org/pmwiki/pmwiki.php/Main/LanguageOfMagic Eka]] can unlock the "The simple knowledge of an equation is powerful in itself" kind of formulaic magic. [[spoiler:It's also revealed that the universe, or more accurately the imprisoning god, doesn't like anyone messing around with Eka.]]

* The ''VideoGame/FinalFantasyTactics'' series has a Calculator class that uses various magical effects. How their abilities work from an in-universe perspective is not specified.

* The last panel of ''{{Webcomic/xkcd}}'' [[http://xkcd.com/804/ #804]] treats the (very counter-intuitive) [[https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox Banach-Tarski paradox]] as a result you can get in real life if you take the axiom of choice.

* Magic in Creator/HPLovecraft's mythos is often related to mathematics, and it makes sense considering his preference for AlienGeometries. In ''Dreams in the Witch House'', for instance, the protagonist is a mathematician who discovers an equation that would allow him to travel outside angled space (basically, to create wormholes). If you can understand the true nature of the universe, you can use that knowledge to do things that seem physically impossible to us. Provided you don't first GoMadFromTheRevelation or attract the attention of some EldritchAbomination, of course.

* Witches in ''Manga/SoulEater'' use "calculation magic" to make their spells more effective.

* Part 7 of ''Manga/JojosBizarreAdventure'' takes geometry very seriously. A short 2 page lesson on the golden ratio gives the protagonist the power to create miniature wormholes.

* The UltimateMarvel version of the Scarlet Witch needs to work out the statistical probability of her hexes before she casts them for desired effects.