Animation vs. Math

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Animation vs. Math
Episode	1
Air date	June 24th, 2023
Written by	Terkoiz
Directed by	Alan Becker
Episode Guide
Next	Animation vs. Physics

Animation vs. Math is the first installment of the Animation vs. Education series. It was first announced on a post, and then a teaser was posted on June 17th. The full animation was released on June 24th on Alan's YouTube channel.

Synopsis

How much of this math do you know?

Plot

The Second Coming wakes up in a black void and is met by the number 1 descending to his level. Curious, he touches it, expanding it into $1=1$ (reflexive property). He then crosses one stroke of the equals sign with the other, turning it into a plus sign and changing the expression into $1+1=2$. Then, by copying and pasting a +1 from the equation, The Second Coming produces $1+1+1=3$, $1+1+1+1=4$ and so on until $1+1+\ldots +1=12$. He copies a 2 from 12, expands it into $(1+1)$ (an equivalent form) briefly, then adds 2 until he reaches 20; then he takes the 20 and adds that until he reaches 100. The Second Coming celebrates this accomplishment, only to feel dejected upon seeing the vast, empty world he's in.

The Second Coming, now realizing the scope of his solitude, sits down hard in sadness, jostling the equals sign and causing a $20+20$ in the equation to simplify into 40. Once again interested, he presses down the equals sign, combining the terms on the left side to $1+99$. He takes a copy of the plus sign for safekeeping, then finishes simplifying into $100=100$. Then, taking only a single line from the equals sign, The Second Coming creates a minus sign, and with a copy of the 1 from the 100 on the right he subtracts by 1, he produces $100-1=99$. He performs further subtraction and finds that $100-1-1-98=0$. Curious, he then takes another -1 and subtracts from the expression again, forming the equation $100-1-1-98-1=-1$.

When The Second Coming goes to inspect the new result, the $-1$ twitches. Knocking on it reveals Euler's identity, $e^{i\pi}$, who kept its distance as The Second Coming approached it. Euler then flees the scene through a white door by putting an i (the imaginary unit, satisfying $i^2=-1$) behind itself. The Second Coming gives chase, but is unable to follow it through the door, and returns to the equation for further experimentation, simplifying it into $-1=-1$.

After failing to summon Euler's identity again, The Second Coming tries adding -1 to itself, producing $-1-1=-2$ and $-1-1-1=-3$, before adding a second negative sign to -3 and watching the negatives cancel out into $1+1+1=3$ ($--3 = 3$ and $-(-1-1-1) = 1+1+1$). He copies another minus sign from the equality for later use. Then, he adds a +3 to the right side of the equation before turning the plus sign 45 degrees. In response, the $1 + 1 + 1$ on the left expands into a three-by-three grid of $+1$s rather than a single line, adding up to $3 \times 3$ (visualising multiplication as repeated addition, and also the area of a rectangle). The Second Coming expands one of the 3's on the right into $(1+1+1)$, adds another +1 into the parentheses, and watches as the grid on the left adjusts to match it. He turns the multiplication sign and the expression shifts into other ways to represent 12 using factor pairs; namely $4 \times 3$, $2 \times 6$, and $6 \times 2$ in order.

Simplifying the expression into $12=6\times2$, The Second Coming wonders what would happen if he tried the same thing with a minus sign rather than a plus sign and changes the equation into $3=6/2$. Turning the slash transforms it into the obelus division sign (÷), and expands the left side into $6-2-2-2$, revealing that the 3 came from counting the number of times 2 can be subtracted from 6. The Second Coming then expands the 2 into $(1+1)$ and adds another 1 to it, creating $2=6/3$ (6 can subtract 3 twice). He exchanges a plus sign for a minus sign (making $(1+1-1)$ and partially cancelling it out to 1), watching as 1 is subtracted from 6, six times. He then subtracts 1 again, creating $6/0$ on the right side of the equation, and The Second Coming watches as an endless stream of 0's are subtracted from 6 (demonstrating that $\frac{n}{0} = undefined$). He shuts it off, converts the slash back into a minus, and simplifies the equation into $6=6$.

The Second Coming then turns the equation $6=6$ into $6+6=12$, becoming $2(6) = 12$ (repeating addition twice), and turns $6\times6=36$ into $6^2=36$ (revealing exponentiation as repeated multiplication of the base an exponent number of times), catching his attention. He then adds 2 to the base, becoming $8^2 = 64$. The Second Coming then touches the equals sign to see a large amount of 1's arrange in a square (demonstrating $n^2$ as the area of a square with side length $n$). The Second Coming then turns the plus into a minus, making only $\frac{1}{4}$ of the 1's remain. This is then simplified to $4^2$, and The Second Coming then adds 1 to the exponent, seeing the 1's turn into greater dimensions up to 5. The Second Coming then simplifies the equation $4^5$, evaluating it to 1024. He then repeatedly decrements the exponent, seeing that the result divides by 4 for each time (showing that $a^{b-c} = \frac{a^b}{a^c}$), ending up with $4^1 = 4$. The Second Coming then decrements the exponent, resulting in $4^0 = 1$ (showing that $n^0 = 1$ for all $n$ ≠ 0). He then makes the small number go into the negatives, resulting in a reciprocal of the result as a positive exponent (showing that $a^{-b} = \frac{1}{a^b}$). The Second Coming then interferes with the line, turning it into a division sign, then the alternative division sign. He then simplifies the equation and makes the ^-1 turn into a fraction. He then makes the below fraction turn into 2, making the equation 2.

Shortly after that, The Second Coming obtains the square root radical sign. He then subtracts 2 from the radicand (the number in the square root), creating an irrational number. Through subtraction, he then makes the radicand 1, fixing everything and vanishing the irrational number. He then makes the radicand 0, making the result 0. He then makes the radicand turn into $-1$, creating i. The Second Coming then grabs the i and makes the equation $i+i$. He turns the plus sign to see that the result is $-1$. He then multiplies i again, summoning Euler's identity, multiplied by i. Euler's identity goes away slowly. Once The Second Coming starts moving towards it, Euler's identity growls and starts running away. Euler's identity then opens up a portal, making the i barely miss. This gives Euler's identity a minus sign. The Second Coming opens Euler's identity's mouth, only for it to transform into it's function form, throwing The Second Coming away. Euler's identity then throws the minus sign at The Second Coming, mirroring him. Euler's identity creates a semicircle, allowing it to flee easily. The Second Coming then multiplies his legs, making him faster. Then, he throws the negative sign at Euler's identity, flipping him.

Then, Euler's identity starts a sword fight with the Second Coming. Euler's identity grabs a negative sign using his mouth, while the Second Coming grabs an addition sign. They then grab a 1, and hit each other's swords, thus cancelling the ones by turning them into 0. Euler's identity eventually turns his 1 into 4 and destroys the 1 and subtracting the sword's blade by 1, only for the Second Coming to regenerate his 1. Euler's identity is later thrown away by the Second Coming, who then creates a bow that shoots 4's by rotating the plus by 45 degrees and duplicating his 2. When the Second Coming shoots, Euler's identity divides their π by four, creating an arc that elevates them and enables them to walk on a plane above. The Second Coming continues to shoot his bow after chasing Euler's identity, with the 4 missing every time. Then, he multiplies himself by i, creating an arc that propels him upward, but the 4 still misses Euler's identity. The Second Coming lands on the ground, destroying the equation $=i \times i$ and his bow in the process.

The Second Coming then collects his bow, the multiplication symbol, and an i, and tries to grab the second i before its dot falls to the ground. Curious, the Second Coming gathers most of the i and investigates the dot and throwing it into the air, creating the imaginary axis before he catches the dot and it disappears. He then throws the dot harder and creates a longer line, before it falls into the ground. He then grabs it, making that line disappear. He then throws it in front of him and creates the real number axis. That axis then disappears once he grabs the dot. Then he puts it in front of him, then above him, and traces a perfect unit circle. He then puts it back in the right side of the circle and proceeds to spin it, which makes him discover radians. The Second Coming then grabs a portion of the circle, bending it and turning it into a line. He then puts the line in front of him, discovering that the radius is equal to its length, before the it turns back into a curve. He multiplies the curve, creating two of them before he places the curves back into the circle. He expands the radius, revealing the expression $\text{θ}r=$.

The Second Coming walks towards the equation and pulls r's value out, revealing $r=5$. He adds 2 to 5, making the circle bigger. He then changes the plus sign to a minus sign, making the circle smaller. He simplifies the equation and puts it back into r. He looks at θ and plays around with the symbol. Using θ, he stretches the circle and moves its radial line around. He puts a division sign between θ and r, then turns the radial line 180 degrees to discover π.

After duplicating π, The Second Coming splits his duplicate into cos(τ) and sin(τ). He plays around with the functions like swords, then taps a point on the circle with sin(τ), making the point rotate around the circle and forming a sine wave traveling to the right. He taps the point with cos(τ), stopping the wave. He then taps the point with cos(τ), and it forms a sine wave upwards. He stops the wave again. He taps the point with both functions, and both waves appear again. He multiplies sin(τ) by i, turning the horizontal wave 90 degrees counter-clockwise and forming a ribbon-like pattern. He puts the functions together, adding them and replacing τ with π, and Euler's identity appears again.

Euler's identity runs away again, The Second Coming grabs him and then Euler's identity creates a math sword, while The Second Coming grabs a part of circle. Euler's identity and The Second Coming then fight each other, until Euler's identity's math sword evolves, throwing The Second Coming onto the ribbon-like pattern. The Second Coming then grabs out his bow, shooting at Euler's identity. However, Euler's identity evolves into its Taylor's series and shoots a math rocket at The Second Coming, causing The Second Coming to evade. The Second Coming then dodges the rockets. He then makes a shield out of the circle, giving him protection. He then multiplies his shield by 8, turning into a cylinder hitting Euler's identity. They get hit back into the $\frac{\text{θ}}{r}=$, so they then rearrange the symbols and insert themselves into the equation to make $r-\text{θ}e^{i\pi}=r+\text{θ}$. Seeing this, they continually rotate the radius inside of the theta on the left side of the equation to make theta larger, basically making the circle larger. This circle pulls The Second Coming in. The Second Coming, seeing this, divides his cylinder by 8 so it's more portable.

When Euler's identity lunges at The Second Coming, he puts a negative sign on himself, effectively teleporting him to the opposite side of the circle. Euler's identity gets mad, so they evolve into its Taylor's series and starts shooting math rockets at The Second Coming again. He sees the point on the side of the radius. The Second Coming then grabs a part of the circle and multiplies it by 4, so he can reach the point. He then grabs it off and strikes it with the $sin(\tau )$. This generates a sine wave that knocks Euler's identity out of the circle. Euler's identity then devolves into their original form and turns into $\cos(\pi)+i\sin(\pi)$, then transforms into $\frac{e^{i\pi}+e^{i\pi}}{2} + \frac{e^{i\pi}-e^{-i\pi}}{2i}$, which clones Euler's identity by 4. These Euler’s identities devolve into cos(π) and then proceeds to multiply into four again, making sixteen of Euler’s identities. It can be further assumed that these Euler’s identities did this process many more times to make a massive hoard of them. Meanwhile, The Second Coming builds a function gun of $9\times\tan(\text{·})$.

The Second Coming shoots at the horde of Euler's identities which attack him back. During the fight, The Second Coming manages to grab an infinity symbol from an Euler's identity in Taylor's series form and affixes it onto his function gun, dramatically increasing its power and allowing the stick figure to easy eliminate the Euler's identities.

The remaining Euler's identities retreat outside the circle and combine to form a huge entity that absorbs the function gun's blast into an integral. The Second Coming is no match for it and gets knocked back into the circle. The Second Coming moves the circle upward in the imaginary axis and places the function gun at the center of the circle, which he hits with the sine and cosine hammers repeatedly to cause the circle to emit powerful blasts at the huge Euler's identity entity. Finally, after increasing the radius of the circle, The Second Coming destroys much of the Euler's identity entity, and the original Euler's identity attempts to retreat to the imaginary dimension. However, The Second Coming grabs a smaller circle, places some numbers with a multiplication sign, and rolls into Euler's identity into the imaginary dimension.

Upon seeing cracks forming in the dimension, The Second Coming panics and escapes the dimension with Euler's identity. He asks for a truce, and Euler's identity agrees. The Second Coming then asks for a way out of this void. Eventually, using the circle earlier, Euler's identity turns off its beam, decreases its radius, and sends The Second Coming out of the void.

Zeta, Phi, Delta, and Aleph then show up, and they walk away together with Euler's identity.

Characters

Protagonists

• The Second Coming

Antagonists

• Euler's identity (debut/only appearance)
• Euler's identity's Clones † (debut/only appearance)
• Numberzilla † (debut/only appearance)

Other characters

• Zeta (debut/only appearance)
• Phi (debut)
• Delta (debut/only apperance)
• Aleph (debut/only appearance)

Gallery

Gallery
The first teaser. The second teaser, The Second Coming fighting Euler's identity. 1 equals 1. 1 plus 1 equals 2. 1 plus 1 plus 1 equals 3. The Second Coming opening the number 2. The Second Coming's successive addition formula. How formulas work. The Second Coming learning subtraction. How multiplication works. How division works. The Second Coming getting shocked seeing the imaginary unit.

Trivia

• It is the first video of the Animation vs. series to not feature the Fighting Stick Figures nor take place on ALANSPC.
  • It is also the first installment of Animation vs. where Alan Becker is not featured even by a computer mouse since Animation vs. Minecraft, 7 years prior.
• In their AVG commentary, DJ Welch suggested this entire episode takes place in The Second Coming's head while he is imprisoned after the events of "Wanted," but Alan has not confirmed this to be true.
• The font style used for the math symbols is Noto Sans Regular.
• The Second Coming is shown to be storing math symbols similar to storing items in an inventory in Minecraft.