E=MC Hammer

So you see, it's perfectly simple. Any questions, class?

As You Know, some writers didn't exactly do well in math class. So, it seems that, with the passing of time, all their knowledge of math was condensed into a pile of information that they know pasted on every chalkboard in school scenes or written in class notes, regardless of the knowledge necessary to understand those equations.

For example, a first-grade class will sometimes have "pi" (π) written on the board, which would probably only confuse the students who would only be learning arithmetic. Other popular examples are integrals, and their well-known "large S" ( ∫ ) symbol. Very often, however, there won't be any variable of integration. Elementary algebra will be represented as something like "x + y = z", which is entirely meaningless without a description of what the variables represent or how they relate to each other.

Let's not forget about E=mc², the famous equation which has been degraded into nothing but a complex-looking decoration in everything from kids' cartoons to science shows. (E=mc² is actually Albert Einstein's formula for mass-energy equivalence; far more people have heard of it than have any idea of what it actually means).

Also related to relativity,^[1] the Einstein field equations (R_ab - (1/2)g_abR = (8πG/c⁴)T_ab) are rising in prominence as a decorative formula, as E=mc² has started to become a cliché. Loosely, the terms of the left describe the curvature of space-time (which is perceived as gravity) while the terms on the right refer to the distribution of matter.

And then there's the big sigma (∑), the summation symbol. Nothing says smart like a big ol' sigma. There's also big pi (Π) notation (the symbol for a direct product).

Trigonometric relations and the Pythagorean theorem are also popular. But don't ask to see words like "sine", "cosine", and "tangent".

Furthermore, there're only two mathematical mistakes anyone ever makes, no matter how advanced their knowledge of the field; they either "misplaced the decimal point" or "forgot to carry the one". (Sign errors are conveniently absent.)

And math isn't the only subject that gets this treatment. Blackboards full of chemical formulae, sentence diagrams or plot/theme/character diagrams that stretch all over the whiteboard, or genealogies and timelines that look like a tangle of yarn are less common, but serve the same purpose.

This happens for three reasons: First, to ensure that there is some teaching going on, as the show itself thankfully never needs to show the actual classes. Second, to scare the young viewers into believing that they're going to see this stuff when they get older. Third, as a way of showing someone is really smart, often combining it with Room Full of Crazy.

Examples of E=MC Hammer include:

Anime and Manga

A rather infamous example-turned-meme comes from a particular scene in Futari wa Pretty Cure. The original scene is actually intentional, intended to give Honoka an opportunity to show off how smart she is by pointing out the error, but it fails to do anything but make the teacher look stupid.
One scene in Neon Genesis Evangelion has some of this panned through before we see the characters in school. It makes effort to show more than just disjointed numbers, but, as an AMV Hell segment showed, it got several equations horribly wrong.
- (Not really) justified in that the teacher seems to be their history teacher. At least he's never seen talking about anything else than Second Impact...
- Makes sense, since in Japanese high schools the children stay in one room all day while different teachers come in and out, it's quite possible that their math teacher just left without erasing the board.
An episode of Air Gear shows the main character skating on a fence. The camera freezes when he jumps, and it overlays a Cartesian plane (height over time) with a parabola tracing his jump so far. y=x² was written on the bottom. Never mind that the curve was concave down, so the formula should be negated. Never mind that he jumped from under the x-axis to cross the y-axis, which means he leapt from underground into negative time.
Surprisingly averted in an episode of Ouran High School Host Club, where a brief glimpse of Kyoya's homework shows real mathematical notation that actually makes some sense, even if the context in which it is found is unlikely.
In Kore wa Zombie Desu ka?, the protagonist makes the mistake of asking the resident "genius" to explain a math problem from the beginning. A few hours later: "...Spiral galaxies spin like this, kind of like a top. You need a string to spin it, and that's where string theory comes from. Oh, right. I want to touch on super string theory too..."
- Later on, after asking how soup could be used to destroy monsters (it makes sense in context), they are given a lengthy off-screen explanation concluding with "I can't answer any of your questions though. I don't understand the super string theory stuff either."
Some of the math questions that appear on the board in Puella Magi Madoka Magica for an eighth grade math class are taken from, among other places, the entrance exam for Tokyo University. More information here.

Comic Books

In one Carl Barks comic book, the blackboard in a kindergarten classroom has a slightly illegible, possibly nonsensical mathematical expression written on it, including an integral sign (which, incidentally, does appear to have a variable of integration).
Any Science Hero big brain is prone to this from time to time, but Reed Richards bears noting that he once came up with an equation so ludicrous, it became sentient and had reality warping powers.
- Honestly.
- It wasn't an equation. It was an expression. This was a plot point.
Léonard le Génie does this often. Once he accidentally scribbled part of a long equation on the side of Raoul the cat.

Fan Works

One segment^[2] for AMV Hell focused on a slow crawl across a blackboard covered with math equations in Neon Genesis Evangelion. Halfway through the piece, we hear the Kevin Spacey in Superman Returns "WRONG!", and as the music is swapped out for King Missile's "Equivalencies", all the errors on the board are pointed out with red marker.
- One of the problems is 9ab³x(-2/3* ab²)³ = 9abx(-8/27* a⁶* b³), when it should be 9ab³x(-8/27* a³* b⁶).

Film

The Day the Earth Stood Still:
- The 2008 remake includes a scene where Klaatu et al. visit someone who won Nobel Prize for his work on biological altruism. He has a blackboard covered in maths, which may or may not be correct, including the words "Event Horizon". An event horizon is simply a boundary beyond which no events can be detected with the most commonly referenced one being that which marks the point of no return around a black hole. If there was ever a biological singularity, (evolving into god?), the word could come into play. Also, it sounds dark and foreboding.
- In the 1951 original, Klaatu visits a leading scientist (an Albert Einstein expy), but the man is not home. Klaatu makes an addition to a blackboard-covering equation, then leaves his contact information with the scientist's housekeeper. The addition to the equation was apparently intended to convince the scientist not to write off his unknown caller as a joke.
In School of Rock, Jack Black's character writes E=mc² on the board while pretending to teach the children something. Played with slightly in that he is totally clueless about teaching and this was presumably the only vaguely mathematical formula he could remember, and the school principal doesn't bat an eyelid when she walks into the room, even though the children are preteens.
- When he's actually teaching the class the only subject he knows (rock, of course) he fills the board with a complicated diagram of rock bands.
In the 2000 remake of Bedazzled, according to a blackboard in the background, a schoolteacher (Elizabeth Hurley) has assigned her students to prove Fermat's Last Theorem as homework. Of course, the schoolteacher was actually the devil and all of these scenes in-between wishes were of her intentionally screwing up the lives of other people.
A minor example in Matilda, where the kindergarten students are learning the multiplication tables. Most kindergarten teachers are happy when their students can add one-digit numbers. This is possibly justified due to the Sadist Principal, Miss Trunchbull.
In Good Will Hunting, the protagonist does some Super Epic Hardcore Math that had previously stumped even the professors. Turns out it was one of the more basic proofs from linear algebra.
A Serious Man has a Dream Sequence featuring an implausibly large blackboard covered with enough of the stuff to fill a book.
Pornographic films dealing with teacher/student relationships will often invoke this trope in the background.
E=mc² abuse is played for laughs in Young Einstein, a fictional biography that is deliberately wrong in just about every way. Whenever a character reads it aloud, they pronounce it "emk".
- In one scene, Albert walks in on a class in progress, where the teacher is writing "E=" and an insanely complex mess of scribbles covering the rest of the board. Albert helpfully wipes out a clean space and writes a big "mc²". He's physically thrown out of the room in response.
In Kids in The Hall: Brain Candy, Dr. Cooper is first seen inventing the anti-depression drug by finishing a gigantic equation on the chalkboard with "=HAPPY".
Subverted in Sherlock Holmes: A Game of Shadows. While Moriarty's chalkboard was covered with mathematical symbols and formulas, the writers consulted with actual mathematicians in order to make sure they were scientifically accurate for the time period. According to one of the scholars involved, the original design for the chalkboard would have invoked this trope as explained here.

Literature

In the Sword Of The Galaxy book series, a simple algebraic expression can be used by the Trakkorians to enter hyperspace. When the author received complaints about this piece of Fridge Logic, he recited the MST3K Mantra.
Played for laughs in The Maelstrom by Roger E. Moore (from Cloakmaster Cycle). Two Words: Tinker Gnomes.
In Men at Arms, Sergeant Detritus gets Locked in a Freezer and his intelligence is boosted to the limit by being frozen nearly to death. His rescuers discover that he has written in the frost an enormous, complicated formula ending in an ominous equal sign, and nothing on the other side.
- His eyes were flashing on and off when they pulled him out, so presumably the cold overcame him just before he could write the answer.
The Maelstrom by Roger E. Moore (Cloakmaster Cycle) has a good parody of the "E=mc² says it all" version.

Live-Action TV

The trope's name comes from a pastiche of E=mc² that appeared in a scene of Farscape: The Peacekeeper Wars where Harvey (who was named after the Not-So-Imaginary Friend of the movie Harvey) writes "E = MC Hammer" on a blackboard of other nonsense. Especially funny in that Crichton, as a physicist and an astronaut, would know exactly what E=mc² actually means, and Harvey is likely just dicking around.
The same exact equation was said aloud by Dina on the Nickelodeon sitcom Salute Your Shorts, during a scene intended to make fun of the "growing and learning" activities going on during her camp experience.
In the NCIS episode "Red Cell", Abby and McGee get into an argument about whether or not a set of equations is homology or cohomology. But the operator symbols are different in these two concepts, and what are subscripts in homology are superscripts in cohomology. No one with sufficient education (as Abby and McGee have) can mistake one for the other.
In the Covert Affairs episode "Walter's Walk", Auggie refers to a sequence of numbers as being a "complex cylic permutation". But a permutation is a rearrangement of things, not a sequence. Moreover cyclic permutations are the simplest of all permutations, and talking about them being complex makes no sense.
In an episode of Torchwood, a integral equation was used to open the rift that led Jack and Tosh into the past. It didn't seem very realistic, though at least it had integration variables.
The Doctor Who episode "The Impossible Planet" has Maxwell's equations of electric and magnetic fields as graffiti on a table in the cafeteria.
- In "The Three Doctors," after coming through the black hole, the physicist Dr. Tyler writes the famous equation in the sand. Justified, too—he's trying to come to grips with the fact that he's just traveled at the speed of light.
In the pilot episode of Sliders, the main character leaves his blackboard covered in equations, not knowing what to write after the equals sign. When he comes back, his double has solved it, and the expression he has written as an infinity symbol on the denominator. That's right. He just needed to divide by infinity.
One of the clips in the Star Trek: Enterprise opener shows a black and white image of a scientist writing complex equations across a blackboard. It looks very fancy until the glaring mathematical error.
- In his original pitch for Star Trek, Gene Roddenberry wanted to use the Drake equation to demonstrate how likely it was we'd encounter aliens. Unfortunately, he couldn't remember the Drake equation, so he just made something up (including two variables being raised to the first power). In the Star Trek: Voyager episode "Future's End" Rain Robinson's work station has both equations on the wall.
- The original series episode "Court-Martial" refers to amplifying the sound of a heartbeat by a factor of "one to the fourth power"... which is one, meaning no amplification (or attenuation) at all.
In Lost Seasons 4 and 5 you get both Daniel Faraday (4) and his mother (5) just constantly writing gibberish on the chalkboard while conducting experiments.
- Terrifyingly, the DVD shows that a real professor of physics wrote that gibberish up for them.
A sketch in series 1 episode 3 of A Bit of Fry and Laurie involves a "hilarious blooper" from a 1970s Open University programme, in which Hugh Laurie's presenter talks us through a blackboard full of nonsensical integral-like equations. What's more, the flub involves the equation giving a "resultant modular quantity" of 0.567395, rather than 0.567359 as Laurie's character states, when the integral in question has no limits and wouldn't have a numerical solution, not to mention that the programme appears to be a physics lecture about wave theory, which wouldn't involve numbers that precise as solutions anyway. ... Hmm, come to think of it, that's a hilarious blooper in itself! I don't believe it! Ha ha ha ha!
In an Imagine Spot, Everybody Hates Chris has a Sadist Teacher demand to know, giving no context whatsoever, "What is a² plus b²?!?". The correct answer is apparently "c²". In other words, the protagonist has internalized the most common expression of the Pythagorean theorem, but with no clue of what it actually means.
Numb3rs gets a lot of credit for having both correct (syntactically) and relevant (in the context of the episode) math equations. Generally, it does—when the equations are displayed in the foreground. Whenever we see one of the fancy animations while Charlie explains something, though, expect at least half of the math in the background to be random and irrelevant. It gets to the point where even people who know nothing about math should be able to figure out that the equations are meaningless, because they appear even when the explanation Charlie is giving is not mathematical in nature (like the infamous IRC explanation, which doubles as being wholly inaccurate itself).
Spoofed in an episode of MythBusters. Grant sketched out a complex but valid mathematical formula on the side of a test vehicle. After Grant finished the calculations and announced the result, this exchange occurred:

Tory: You forgot to carry gravity.
(Beat)
Grant: What?!

Rimmer does this to himself in Red Dwarf when he covers his arms and legs in astrophysics equations that are beyond his capacity to understand to cheat on a test he is clearly not qualifies to pass.

Rimmer: Right, they're bound to ask the right thigh, which is 10 per cent. They must ask the left thigh, which is 20 per cent. They've got to ask one of the forearms. Which means I've passed already; anything on the left shin's a bonus! Right. *Looks at one arm* `CUTIE'. Current under tension is ... what's this? Current under tension is equal? Current under tension is expendable? Current under tension is expensive? What does this mean? *Begins to panic* What does any of it mean? I've covered my body in complete and utter and total absolute nonsense gibberish!

In Tattooed Teenage Alien Fighters From Beverly Hills episode "The Spy", Black and Nerdy Swinton ends a joke with a E = MC Hammer.
In That '70s Show, Eric's parents see fit to check that he's not neglecting school, so Red asks him sternly, "What is X?". Eric just stares at him, then very politely explains that it's a variable that can represent a given number. The parents think it sounds right, but neither of them actually know what answer they were expecting.

Music

Mariah Carey went so far as to name her most recent^[when?] album E=MC². She claims it stands for "(E) Emancipation (=) equals (MC) Mariah Carey to the second power." Yeah right.
- See the Quantum Mariah Carey Problem for further discussion.
Subverted and literal: Doctor Steel raps about the Fibonacci Sequence.
E=MC² appears on the Schoolmaster's blackboard in the gatefold art of The Wall.
"Weird Al" Yankovic's video "White and Nerdy". Just to show how smart Alfred is. Ironically, it contains an error.
- Alas, in the song "Pancreas" he gets Newton's equation for the gravitational force between two masses wrong.

Newspaper Comics

An old Sidney Harris cartoon lampshades this one: two scientists are standing in front of a blackboard full of equations. Toward the bottom right of the board, the chaos of integrals, summations, and other mathematical gobbledygook suddenly ends with "and then a miracle occurs" and an answer. The caption reads "You need to be more explicit here in step two."

Video Games

The first few levels of Super Paper Mario feature "joke" equations in the background, made up of random numbers and mathematical symbols combined with famous Mario icons such as the Fire Flower and mushrooms.
In EarthBound, Doctor Andonuts has a big chalkboard in his lab with nothing written on it but a big "E=mc²".
Half-Life has a number of blackboards adorned with Newton's equation for gravity. That's like Ernest Hemingway trying to come to grips with "Hop On Pop".
- This is lampshaded and blasted to bits in Freeman's Mind.
In Portal 2, there are posters around that list paradoxes in the event of a rogue AI. One of the listed paradoxes is "Does a set of all sets contain itself?" ^[3]
- Knowing the dev team's sense of humor, it might be deliberate.
While chalkboards in Team Fortress 2 do sport real equations (including the ridiculously complicated equation they use for rendering rim lights), it also boasts "equations" like "FIRE = QQ".
The World Ends With You's Mad Mathematician Sho Minamimoto not only SPEAKS in Math, he uses it as his Formulaic Magic and the Incantation of a Level i Flare.

Web Comics

This xkcd strip includes an integral without a variable of integration, as part of a clearly erroneous equation—but in this case the error is integral (sorry) to the punchline.
- The variable of integration is obvious, since there's only one variable; the bigger issue is somehow getting a constant out of an indefinite integral (this would only happen if you nonsensically integrated zero, and even then you wouldn't get a specific constant because the derivative of any constant is zero). But this is also part of the joke, and the Alt Text takes it further: "It's pi plus C, of course."
A more elaborate variant appears in this cartoon by Tom Tomorrow. Instead of meaningless numerical symbols, it's an invalid proof that involves dividing by zero, perhaps to complement the scientist's fallacious reasoning.
- The invalidity of the proof is probably intentional, but it still appears to be copied from an online source by someone who doesn't understand mathematical notation. It writes "a^2" instead of "a²" (the former notation is a substitute that is only ever used when technical constrains make it impossible to write the latter, which is not the case for blackboards).
In Two Lumps, Eben is occasionally shown contemplating equations right before Snooch interrupts with his latest insanity. In at least one instance readers have submitted corrections for the math displayed.
Although Saturday Morning Breakfast Cereal is usually quite good about this sort of thing, this strip features a justified example - the designers are snowing their audience.

Web Original

The title card for The Angry Video Game Nerd video Chronologically Confused features the Nerd in front of a board filled with nonsensical equations and formulae, including at points a Triforce and a drawing of Mario.
E equals MC Hawking.
This FailBlog entry tries to show Einstein's equation but, well, fails.
Fan Art for the Whateley Universe: Hot Scientist Bugs, who is a genius deviser with a fascination with egg shapes: here.
Episode 1 of Echo Chamber has Tom and Dana (and possibly Zack) trying to figure out how to "show a Show Within a Show" and covering an entire blackboard with ideas, including nonsensical chemical and mathematical formulae that have little to do with...anything they are trying to discuss.
The blog Blackboards in Porn is devoted to pointing out examples of this trope in pornography.

Western Animation

SpongeBob SquarePants usually has Sandy show SpongeBob some equations.
The Fairly OddParents has done this as well.
Abused by Dexter's Laboratory.
Professor Utonium's lab in The Powerpuff Girls.
- And Pokey Oaks Kindergarten. In one episode, Ms Keane starts out with "1 + 1 = 2", then proceeds to give a theoretical description of time travel.
Fillmore! has an episode set around a maths test. When the teacher gives her class an assignment, it reads: 2+ x=5, x-y= 16, -2x-y=-14, 2x+ 4y=12, -2x+ 5y=5. She asks them to solve both x and y, and tells them to spend the rest of the lesson doing so. This amount of time would make sense, as it's actually impossible—the value of x and y changes in those equations from one example to the next.
- And what is worse, the moral of the story is that "the value of x remains constant". Arghh!
The intro to Pinky and The Brain has a scene where Brain is writing his "theory of everything" on a chalkboard, which is basically a bunch of pseudo-mathematical mumbo-jumbo, including "THX=1138".
- Spoofed in another episode which has Brain reveal that his latest plan to take over the world was hinged on an equation he had just uncovered. Pinky askes him if it is something complicated like E=mc², and Brain replies that it is in fact even simpler, just E.
Monkey Dust has a chalkboard full of geometry in a class teaching cottaging! (For non-UK readers, that's anonymous gay sex in public bathrooms). True to the title of this trope, the board also contains "run=dmc".
The Simpsons is fond of this one. When Homer has a bright idea, the camera would occasionally do a close-up of his head, revealing two chimpanzees in graduation gowns and mortarboards writing E=mc² on a chalkboard. Otherwise, the chimps would be grooming each other and eating the lice.
- Parodied when Homer is an inventor. During a montage, he's shown writing equations on a blackboard. After he's done, the camera moves to shot of the house—where there's a massive explosion. Cut back to Homer: who examines his equation and crosses out the offending section, a drawing of a stick of dynamite, which he then replaces with something else. This results in another, bigger explosion.
  - Also done in Phineas and Ferb. The boys finally solved it by replacing the bomb with a smiley face.
- And subverted in another episode: Homer puts on some Nerd Glasses he finds in the power plant's toilets and immediately recites what he seems to think is the Pythagorean Theorem (he's actually quoting The Wizard of Oz movie):

Homer: The sum of the square roots of any two sides of an isoceles triangle is equal to the square root of the remaining side!
Co-worker in a stall: That's a right triangle, y'idiot!
Homer: D'oh!

- - Note that the co-worker's correction is nowhere near complete, becase the formula refers to the squares, nor the square roots, and "the remaining side" has to be the hypotenuse. But that wouldn't be as funny.
- Variation, in the episode in which the Simpsons discover the third dimension, "P=NP" can be read in the 3d-CGI world.
- Also parodied in "Moneybart":

Nelson: Lisa's a genius! She can do the kind of math that has letters! Watch: what does X equal, Lisa?
Lisa: Well, that depends...
Nelson: She could do it yesterday, I swear!

The board in Arthur‍'‍s class would often be filled with formulas like the Pythagorean theorem or simple derivatives, even though the characters are respectively three and six years too young for them. Apparently, this is part of Mr. Ratburn's Sadist Teacher reputation.
In Rocko's Modern Life in an episode where Rocko keeps being late for work. While he gets berated for it by his boss, there's a flipchart in the background that contains, amongst other things, a clipart of a clock followed by a plus-minus sign and a square root containing "MC" and a clipart of a hammer.
In Code Lyoko, the same board (y=ax+b) is used for every science course. Including one about parthenogenesis.
In Robot Chicken, they parody this trope in a sketch. Where two scientists are laughing their heads off to a bizarre problem on the board, only for one of them to stop, erase a symbol, add another, and then both burst out laughing again.
One episode of The New Adventures of Winnie-the-Pooh centered on Gopher's "equation for the ultimate tunnel." How and why the layout for a tunnel took the form of a chalkboard full of mathematical-looking scrawlings was never explained.

Real Life

Even children's math workbooks have this problem. Some of them that go from K-12 will have the same picture with pi, percents, and algebra symbols on every book regardless of if it is a 11th grade (age 16-17) or 3rd grade (age 8-9) book.
- This extends even to the university level. The cover of late-undergraduate/early-graduate level "Introduction to Lie Algebras" from the Springer series is adorned with many generic calculus and linear algebra equations not particularly related to the topic at hand. Subverted in that the equations, while complicated and arguably "pretty", should not be mysterious to anyone capable of understanding the contents of the book.
Speaking about Truth in Television - imagine what goes on when TV people come and ask for "some formulas" as a background for an interview with someone related to maths/physics education (and their request is granted just to please them).

Exceptions

General

Clausius-Clapeyron and the derivation via the Maxwell relations is extremely common, usually as Mad Science. It's easy to copy verbatim, and looks scary because it's an important equation in Thermodynamics and requires high level chemistry, physics and mathematics to understand.