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## Animation vs. Math

How much of this math do you know?

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🔹🔶 WRITTEN BY 🔶🔹

Terkoiz

🔹🔶 ANIMATION🔶🔹

Terkoiz

n8ster @n8sterAnimates

Ellis02 @Ellis02Media

Hexal @Hexalhaxel

Oxob @oxob3000

ARC @ARCpersona

SmoilySheep @smoilysheep4670

CoreAdro @CoreAdro

SimpleFox @SimpleFox1

ExcelD

eds! @eds7236

ajanim@ichasedacrow2

Fordz @Fordz

🔹🔶 SOUND DESIGN🔶🔹

Egor / e_soundwork

🔹🔶 EDITOR🔶🔹

Pepper @dan_loeb

🔹🔶 MUSIC🔶🔹

Scott Buckley @ScottBuckley

🔹🔶 PRODUCTION MANAGER🔶🔹

Hatena360 @hatena360

## Пікірлер: 62 000

To be clear, my lead animator is the math nerd behind all this. And as always, watch DJ and I talk about it: kzread.info/dash/bejne/loaelbpweampmrw.html

## @harryalbertsonsevilla9183

## Жыл бұрын

Woah Edit: i was about to say first but i remember i have a brain. Edit 2: Wow many likes anyway here is a recipe for brownies and uh idk just make a brownie here it is: 10 tablespoons (142 grams) unsalted butter 1 cup (200 grams) granulated sugar 1/3 cup (67 grams) packed light brown sugar 3/4 cup plus 2 tablespoons (88 grams) unsweetened cocoa powder, sifted 1/2 teaspoon vanilla extract 2 large eggs plus 1 egg yolk 1 tablespoon corn syrup 2/3 cup (85 grams) all-purpose flour 1 tablespoon cornstarch 1/4 teaspoon salt For the frosting: 1/2 cup heavy cream 1 1/2 cups (255 grams) semisweet chocolate chips Wilton Rainbow Chip Crunch or mini M&M’s, sprinkles, or other candy

## @Emirhanoleo78

## Жыл бұрын

Yoo pogchamp

## @harryalbertsonsevilla9183

## Жыл бұрын

@@Emirhanoleo78hi

## @romanthespeedrunner5020

## Жыл бұрын

hi alan

## @Darkixz-ball

## Жыл бұрын

1 minute lol

Utterly delightful!

## @gagannnnn

## Жыл бұрын

yo legit thought you collabed on this or smthn haha

## @mr.tesseract6854

## Жыл бұрын

Hi there Mr. Pi

## @big_numbers

## Жыл бұрын

Yoooo it's the math guy

## @voidbreak4756

## Жыл бұрын

i KNEW 3b1b would comment

## @donaldputin6390

## Жыл бұрын

Hello

0:07 introduction to numbers 0:11 equations 0:20 addition 1:24 subtraction 1:34 negative numbers 1:40 e^i*pi = -1, euler's identity 2:16 two negatives cancellation 2:24 multiplication 2:29 the commutative property 2:29 equivalent multiplications 2:35 division 2:37 second division symbol 2:49 division by zero is indeterminate 3:05 Indices/Powers 3:39 One of the laws of indices. Radicals introcuced. 3:43 Irrational Number 3:50 Imaginary numbers 3:59 i^2 = -1 4:01 1^3 = -i = i * -1 = ie^-i*pi 4:02 one of euler's formulas, it equals -1 5:18 Introduction to the complex plane 5:36 Every point with a distance of one from the origin on the complex plane 5:40 radians, a unit of measurement for angles in the complex plane 6:39 circumference / diameter = pi 6:49 sine wave 6:56 cosine wave 7:02 sin^2(θ) + cos^2(θ) = 1 7:19 again, euler's formula 7:35 another one of euler's identities 8:25 it just simplifies to 1 + 1/i 8:32 sin (θ) / cos (θ) = tan (θ) 9:29 infinity. 9:59 limit as x goes to infinity 10:00 reduced to an integral 11:27 the imaginary world 13:04 Gamma(x) = (x-1)! 13:36 zeta, delta and phi 13:46 aleph

## @MyBoy69969

## Жыл бұрын

30 likes and no replies let me fixed that😊

## @Barney_Is_your_Friend.

## Жыл бұрын

Yep the pretty much it

## @xvie_z2900

## Жыл бұрын

Man this makes me wanna learn math more

## @RuriYoshinova

## Жыл бұрын

alan should put this in the video. I need to know what types TSC is using

## @Alexa-iv7kr

## Жыл бұрын

@@xvie_z2900fax I wanna understand everything in this video

Love the little detail at 4:20 of TSC flipping his facing direction when hit by the negative sign.

## @geeky_001

## Ай бұрын

Didn't notice at all!

## @aquisaysheanmifelamerot.6606

## Ай бұрын

TSC then does the same to *e* soon after

## @aamirkhan_

## Ай бұрын

It was crucial here 8:03

## @tgcgames123

## Ай бұрын

@@aquisaysheanmifelamerot.6606e eulers identity

## @aznguy.mp4

## Ай бұрын

I laughed too hard at that

I love how you'd need a super-computer brain to be able keep up with what's happening later in the video without pausing

## @thevywern

## 3 күн бұрын

@@CWG2000 just practice and a decent grasp of all math concepts

## @buddy2369

## 17 сағат бұрын

@@thevywern can't I'm too dumb

never in my life would I have ever thought I would see something tactically reload a math formula...

## @janluofficial

## 3 ай бұрын

And then replace the magazine with infinity

## @BACMemesandRoblox

## 2 ай бұрын

And shoot a fricking laserbeam

## @vivi_needssleep

## 2 ай бұрын

I love this comment

## @THEarrasBuddhist

## 2 ай бұрын

Only 3 replies... Let me be da forth

## @smartagent99

## 2 ай бұрын

I burst out laughing at that.

The reason why I love this series so much isn't just because of the animation and choreography, but because rules of how the world works are established and are never broken. Regardless of how absurd fight scenes play out there's a careful balance to ensure that not a single rule is broken.

## @dragoknight589

## Жыл бұрын

Absolutely. The limitations create room for playing around within them. Combat feels just as much of a battle of wits, finding the right application for a tool, as a contest of strength.

## @dr.unventor

## Жыл бұрын

I know! It’s incredible how he can just add world building in and make it so believable

## @captainsprinkles6557

## Жыл бұрын

You clearly haven't seen the Minecraft series yet have you? "Fall damage goes brrrrr"

## @dragoknight589

## Жыл бұрын

@@captainsprinkles6557 Fall damage is present, and it’s relatively consistent. It’s just less severe for rule of cool.

## @captainsprinkles6557

## Жыл бұрын

@@dragoknight589 Less severe? Man they jump off multiple cliffs

13:35 Phi from the next "Animation vs Geometry" short.

## @thekingexe334

## Ай бұрын

I wonder if the other symbols will appear in future animations too

## @RurixGD200

## Ай бұрын

I noticed that too lol

## @chiwyikqi5656

## Ай бұрын

Excuse me,what is the huge symbol at the back calls?

## @thecpg980

## Ай бұрын

@@chiwyikqi5656aleph null, the smallest cardinal infinity

## @gracetonsanthmayor6687

## Ай бұрын

I love how he travels only 1.618 units at a time so he had to take 3 steps there

Returning here not just to rewatch this masterpiece, but also to confirm that Phi has appeared before (believing that Phi had seen TSC before meeting him in Animation vs. Geometry, which is why Phi is friendlier/less defensive when they met than Euler's identity)

So far, this is the best action movie in 2023!

## @pn43279

## Жыл бұрын

Adu anh vfact học toán

## @pn43279

## Жыл бұрын

Video mới là gì thế anh zai

## @GeoN_2605

## Жыл бұрын

I can’t believe Alan is making his own Number lore now… ✊

## @Nerdzel_73450

## Жыл бұрын

Hey, không nghĩ tôi sẽ gặp kênh yêu thích của mình ở đây. Giữ gìn sức khoẻ và nếu có thể thì có thể làm về vũ trụ được không, video này làm tôi có hứng về vũ trụ học.

## @liZa_lIke245

## Жыл бұрын

Yes

If you could turn this format into a video game, you'd have an incredibly powerful tool to teach kids math.

## @Pepplay33

## 10 ай бұрын

imagine

## @jesseweber5318

## 10 ай бұрын

Just to add to this I went and learned eulers identity is after wondering why E to pi I was so crazy

## @ayuballena8217

## 10 ай бұрын

@@jesseweber5318me too, i had no idea

## @rickt.3663

## 10 ай бұрын

Like minecraft?

## @TheGuyWhoComments

## 10 ай бұрын

@@rickt.3663 you mean, Minecraft Education edition?

Watched Animation vs. Geometry. 13:36 was this an anticipation of the next realms?

## @cleandee81thai

## Ай бұрын

It was very cool

## @pqkx_no1fl8i

## Ай бұрын

What's next? The quantum physics?

## @gracetonsanthmayor6687

## Ай бұрын

I love how he travels only 1.618 units at a time so he had to take 3 steps there

## @gracetonsanthmayor6687

## Ай бұрын

According to that theory lets say each symbol has their own domain. Thats why here when e^itt entered imaginary plane, he as rendered lifeless as -1 is not an imaginary number. Similarly in animation v geometry, phi did not had to move only 1.618 units at a time but could even move freely where golden ratio was in use such as the fibonacci spiral or the golden squares. Further expanding, i think that whenever the golden ratio was brought into use or existence, for a short amount of time the phi's powers would be raised to the order of ^1.618 for 1.618 seconds thus allowing him to be much more powerful an construct objects of higher dimensions.......

## @Ilovetulinspower23

## Ай бұрын

I watched AvG before this too!

You don't know how much i want 1 video like this but is like "Animation vs music"

## @Dooooooble-ace

## Ай бұрын

Same bro

## @blockyhour4224

## 28 күн бұрын

Yes I’d LOVE a video like this.

This is actually insane. Having just graduated as a math major and honestly being burnt out by math in general, being able to follow everything going on in this video and seeing how you turn all the visualizations into something epic really made my day. Can’t help but pause every few minutes. GET THIS MAN A WHOLE ASS STUDIO.

## @analt2164

## Жыл бұрын

He has an entire crew working with him

## @acogex

## Жыл бұрын

He does have a WHOLE ASS BUILDING

## @TTVtreekoVr

## Жыл бұрын

Yeah😂

## @pvpcraft2081

## Жыл бұрын

I can only understand a bit.

## @aimonnwood6957

## Жыл бұрын

...and at the end, in comes the zeta function

I love how he goes from learning basic operations to university level maths

## @shariecebrewster5962

## 9 ай бұрын

Evening at home myc myself

## @ferferarry5242

## 8 ай бұрын

We are learning most of this in 9th grade

## @meusauc

## 8 ай бұрын

@@ferferarry5242 key phrase: “most of”

## @idk-lz4nl

## 8 ай бұрын

bruh, you guys think this is uni-level math... damn

## @monstermaker73

## 8 ай бұрын

@idk-lz4nl Most of this is high school level, though the stuff in the last quarter is more common in universities.

Honestly this is one of my favorite KZread videos of all time, I watch it literally every 2 weeks. I am quite a big math nerd in high school, and having so many math concepts ranging from simple operations to advanced calculus… it is really such a treat. Thank you so much to the Alan Becker team for putting this together, I look forward to many more masterpieces in the future!

I didn't understand it fully. Like 40% of it I understood. But man, learning math paid off.

## @user-ht3gg1fx5g

## 17 күн бұрын

did lil bro even go too school

## @ragnar000lothbrok

## 17 күн бұрын

@@user-ht3gg1fx5g What??? Huh?

*THE MATH LORE* 0:07 The simplest way to start -- 1 is given axiomatically as the first *natural number* (though in some Analysis texts, they state first that 0 is a natural number) 0:13 *Equality* -- First relationship between two objects you learn in a math class. 0:19 *Addition* -- First of the four fundamental arithmetic operations. 0:27 Repeated addition of 1s, which is how we define the rest of the naturals in set theory; also a foreshadowing for multiplication. 0:49 Addition with numbers other than 1, which can be defined using what we know with adding 1s. (proof omitted) 1:23 *Subtraction* -- Second of the four arithmetic operations. 1:34 Our first *negative number!* Which can also be expressed as *e^(i*pi),* a result of extending the domain of the *Taylor series* for e^x (\sum x^n/n!) to the *complex numbers.* 1:49 e^(i*pi) multiplying itself by i, which opens a door to the... imaginary realm? Also alludes to the fact that Orange is actually in the real realm. How can TSC get to the quantity again now? 2:12 Repeated subtraction of 1s, similar to what was done with the naturals. 2:16 Negative times a negative gives positive. 2:24 *Multiplication,* and an interpretation of it by repeated addition or any operation. 2:27 Commutative property of multiplication, and the factors of 12. 2:35 *Division,* the final arithmetic operation; also very nice to show that - and / are as related to each other as + and x! 2:37 Division as counting the number of repeated subtractions to zero. 2:49 Division by zero and why it doesn't make sense. Surprised that TSC didn't create a black hole out of that. 3:04 *Exponentiation* as repeated multiplication. 3:15 How higher exponents corresponds to geometric dimension. 3:29 Anything non-zero to the zeroth power is 1. 3:31 Negative exponents! And how it relates to fractions and division. 3:37 Fractional exponents and *square roots!* We're getting closer now... 3:43 Decimal expansion of *irrational numbers* (like sqrt(2)) is irregular. (I avoid saying "infinite" since technically every real number has an infinite decimal expansion...) 3:49 sqrt(-1) gives the *imaginary number i,* which is first defined by the property i^2 = -1. 3:57 Adding and multiplying complex numbers works according to what we know. 4:00 i^3 is -i, which of course gives us i*e^(i*pi)! 4:14 Refer to 3:49 4:16 *Euler's formula* with x = pi! The formula can be shown by rearranging the Taylor series for e^x. 4:20 Small detail: Getting hit by the negative sign changes TSC's direction, another allusion to the complex plane! 4:22 e^(i*pi) to e^0 corresponds to the motion along the unit circle on the complex plane. 4:44 The +1/-1 "saber" hit each other to give out "0" sparks. 4:49 -4 saber hits +1 saber to change to -3, etc. 4:53 2+2 crossbow fires out 4 arrows. 4:55 4 arrow hits the division sign, aligning with pi to give e^(i*pi/4), propelling it pi/4 radians round the unit circle. 5:06 TSC propelling himself by multiplying i, rotating pi radians around the unit circle. 5:18 TSC's discovery of the *complex plane* (finally!) 5:21 The imaginary axis; 5:28 the real axis. 5:33 The unit circle in its barest form. 5:38 2*pi radians in a circle. 5:46 How the *radian* is defined -- the angle in a unit circle spanning an arc of length 1. 5:58 r*theta -- the formula for the length of an arc with angle theta in a circle with radius r. 6:34 For a unit circle, theta / r is simply the angle. 6:38 Halfway around the circle is exactly pi radians. 6:49 How the *sine and cosine functions* relate to the anticlockwise rotation around the unit circle -- sin(x) equals the y-coordinate, cos(x) equals to the x-coordinate. 7:09 Rotation of sin(x) allows for visualization of the displacement between sin(x) and cos(x). 7:18 Refer to 4:16 7:28 Changing the exponent by multiples of pi to propel itself in various directions. 7:34 A new form!? The Taylor series of e^x with x=i*pi. Now it's got infinite ammo!? Also like that the ammo leaves the decimal expansion of each of the terms as its ballistic markings. 7:49 The volume of a cylinder with area pi r^2 and height 8. 7:53 An exercise for the reader (haha) 8:03 Refer to 4:20 8:25 cos(x) and sin(x) in terms of e^(ix) 8:33 -This part I do not understand, unfortunately...- TSC creating a "function" gun f(x) = 9tan(pi*x), so that shooting at e^(i*pi) results in f(e^(i*pi))= f(-1) = 0. (Thanks to @anerdwithaswitch9686 for the explanation -- it was the only interpretation that made sense to me; still cannot explain the arrow though, but this is probably sufficient enough for this haha) 9:03 Refer to 5:06 9:38 The "function" gun, now "evaluating" at infinity, expands the real space (which is a vector space) by increasing one dimension each time, i.e. the span of the real space expands to R^2, R^3, etc. 9:48 log((1-i)/(1+i)) = -i*pi/2, and multiplying by 2i^2 = -2 gives i*pi again. 9:58 Blocking the "infinity" beam by shortening the intervals and taking the limit, not quite the exact definition of the Riemann integral but close enough for this lol 10:17 Translating the circle by 9i, moving it up the imaginary axis 10:36 The "displacement" beam strikes again! Refer to 7:09 11:26 Now you're in the imaginary realm. 12:16 "How do I get out of here?" 12:28 -Don't quite get this one...- Says "exit" with 't' being just a half-hidden pi (thanks @user-or5yo4gz9r for that) 13:03 n! in the denominator expands to the *gamma function,* a common extension of the factorial function to non-integers. 13:05 Substitution of the iterator from n to 2n, changing the expression of the summands. The summand is the formula for the volume of the *n-dimensional hypersphere* with radius 1. (Thanks @brycethurston3569 for the heads-up; you were close in your description!) 13:32 Zeta (most known as part of the *Zeta function* in Analysis) joins in, along with Phi (the *golden ratio)* and Delta (commonly used to represent a small quantity in Analysis) 13:46 Love it -- Aleph (most known as part of *Aleph-null,* representing the smallest infinity) looming in the background. Welp that's it! In my eyes anyway. Anything I missed? The nth Edit: Thanks to the comment section for your support! It definitely helps being a math major to be able to write this out of passion. Do keep the suggestions coming as I refine the descriptions!

## @ArsakaD1

## Жыл бұрын

hey, are you my teacher?

## @abandonedhhhv

## Жыл бұрын

Nice lore.

## @fishoreo

## Жыл бұрын

I will be waiting for your part 2!

## @rekttt_7374

## Жыл бұрын

Please continue dude, till end. I confused about the end of the video.

## @RaiNBowShine999

## Жыл бұрын

Do everything pls.

It speaks to Alan and his team’s talent on a number of levels that they can even make me feel sympathy for Euler’s number.

## @F2PAlius

## Жыл бұрын

Now all we need is natural logs in minecraft vs animation 😅

## @Shirou230

## Жыл бұрын

He is on another dimension, not on another level anymore

## @possessedpicklejar4762

## Жыл бұрын

Finally, somebody said what it’s called so I can look up what the antagonist actually is.

## @Fletchable

## Жыл бұрын

Ironically enough, this is the first time I’ve utilized my calculus knowledge outside of school hahaha

## @lvlupproductions2480

## Жыл бұрын

@@FletchableEven though I use lot’s of this stuff daily (I’m a programmer) I’d literally never heard it called Euler’s number before this animation lol.

10:57 bro hit the domain expansion: infinite math

## @zian01000

## 29 күн бұрын

Lol

## @dragonx6168

## 27 күн бұрын

Imaginary Technique: Cosin Function

## @bororobo3805

## 26 күн бұрын

@@dragonx6168MathFU Hustle

bro learns math faster than my teacher could teach.

## @zian01000

## 29 күн бұрын

Literally and metaphorically

## @Licker338

## 17 күн бұрын

"I learnt more math in this video then school 🤓" ahh comment

I think the sound design is quite an underrated highlight of this animation. The bleeping and clicking as everything falls into place is so satisfying to listen to.

## @littleyoyo8480

## Жыл бұрын

I completely agree

## @user-dj4ft3en3l

## Жыл бұрын

+

## @Keno5

## Жыл бұрын

Yes, I agree too.

## @joelbobadilla7831

## Жыл бұрын

Egor is too good in sound design and animation

## @FireyDeath4

## Жыл бұрын

Barely anyone talks about sound design in general. Whenever people release an animation or something with great sound design they just take it for granted and continue to laud the animators

This might honestly be the most creative animation ever conceived. And what an epic appearance by the Aleph Number at the end there.

## @Grape7676

## Жыл бұрын

Yeah, but why is א there?

## @rezkreyad833

## Жыл бұрын

@@Grape7676 That is Aleph Nul.

## @Grape7676

## Жыл бұрын

@@rezkreyad833 Still didn't understand.

## @jamyangpelsang3099

## Жыл бұрын

@@Grape7676 maybe just a fun cameo that's not meant to be overanalyzed?

## @dfc454

## Жыл бұрын

yeah, lets just think of it that way.

OKAY THIS IS SO AWESOME DAMN IT 9:57 The thing blocking TSC's Infinity function with a limit is just- DAMN. PEAK.

Absolutely incredible animation, I love all the math symbols and equations for detail. Amazing

as an nerd myself, here's the actual math: 0:06 1 as the unit 0:13 equations 0:18 addition, positive integers 0:34 decimal base, 0 as a place holder 0:44 substitution 1:09 simplifying equations, combining terms 1:20 subtraction 1:30 0 as the additive identity 1:34 -1, preview of e^(iπ) = -1 2:10 negative integers 2:16 changing signs 2:20 multiplication 2:28 factors 2:33 division 2:48 division by 0 error 3:03 powers 3:23 x^1 = x , x^0 = 1, x^(-1) = 1/x 3:35 fractional exponents = roots 3:42 √2 is irrational 3:48 √(-1) = i 3:54 complex numbers 4:00 e^(iπ) returns, i*i*i = i*(-1) = i*e^(iπ) 4:15 Euler's formula: e^(iθ) = cosθ + i*sinθ 4:54 e^(iθ) rotates an angle of θ 5:12 complex plane 5:33 unit circle 5:38 full circle = 2π radians 5:55 circle radii 6:36 π 6:41 trigonometry 7:17 Euler's formula again 7:33 Taylor series of e^(iπ) 7:44 circle + cylinder 7:51 (-θ) * e^(iπ) = (-θ) * (-1) = θ 8:22 Euler's formula + complex trigonometry 8:29 sinθ/cosθ = tanθ, function f(x) = 9*tan(πx) 9:01 π radians = half turn 9:57 limits, integrals to handle infinity 10:15 translation 13:01 factorial --> gamma function, n-dimensional spheres 13:31 zeta, phi, delta, aleph (comment by MarcusScience23)

## @Lebanoncontryball

## Жыл бұрын

Someone already did it

## @Lebanoncontryball

## Жыл бұрын

Sorry bro

## @marcusscience23

## Жыл бұрын

@@Lebanoncontryball at least I got likes + replies

## @Lebanoncontryball

## Жыл бұрын

@@marcusscience23 yeah gg

## @Lebanoncontryball

## Жыл бұрын

@@marcusscience23 but he did too

This makes me wish that i could live to be a math nerd like all of the other people who could understand mathematics past the algebra phase. When I get past that part, it's just a little too detailed and surreal to me.

I keep coming back to this video as I learn more math and it just keeps getting better!

The sound design here is simply masterful, and makes the whole thing feel physical and *very* satisfying.

## @CYCLOLCYC2223

## Жыл бұрын

It shows how the stick figure adapt and try to minimize at 1:15

## @MelonMan667

## Жыл бұрын

True

## @Whois_me111

## Жыл бұрын

I don’t understand the last part

## @Leonardo-ht5jk

## Жыл бұрын

It sounds like a movie, its awesome

## @Derpy_Crow

## Жыл бұрын

I’m 699 like

Can we just appreciate how TSC went from basic addition to the far end of Calculus in under twenty minutes. That is a hell of a learning curve.

## @user-eb5bn9xh9w

## Жыл бұрын

15+6=21

## @anicepixelatedbread

## Жыл бұрын

@@user-eb5bn9xh9w 9 + 10 = 21

## @drafezard7315

## Жыл бұрын

@@anicepixelatedbread 2+1 = 21

## @zatx8227

## Жыл бұрын

@@anicepixelatedbread cos(x) = (e^ix + e^-ix)/2

## @8g-26rasyadputraaldora5

## Жыл бұрын

0=ax²+bx+c

This is actually a great way to teach all the math in highschool and how it gets completed Without any filler

## @zian01000

## 29 күн бұрын

True

This should be one of those animated shorts that plays before a movie in theaters

If math lessons were like this, math would for sure be everyone’s favorite subject Edit: well, this blew up fast. Thanks!

## @naufaljb8204

## Жыл бұрын

Math is beauty, if not you just not understand it very well

## @aliaakari601

## Жыл бұрын

@@naufaljb8204 People have opinions, not saying you're wrong but, People have opinions.

## @billcosta

## Жыл бұрын

@@naufaljb8204 maybe you're good at math, but you suck at english

## @_BlackCar251

## Жыл бұрын

@@aliaakari601yeah

## @BernardoFreitas-RM

## Жыл бұрын

@@aliaakari601pople

I love the surprise Euler identity early on when just playing with simple addition and subtraction, because it’s just like when your playing with a simple concept in math and stumble across something bizzare/that you have no clue how to understand yet.

## @quuirrel19_-sz9pj

## 3 ай бұрын

it really so be like that though, our modern basic maths require way more complicated maths we don't even begin to understand until much later on

## @THEarrasBuddhist

## 2 ай бұрын

Euler identity = -1 = e^iπ = cosπ x i(sin)π = (e^iπ + e^-iπ) /2

## @RykerHeldt

## 2 ай бұрын

@@THEarrasBuddhist translate to English is crazy

## @stroopwafelfalafel

## 2 ай бұрын

It reminds me of why I love math. Playing around with a graphing calculator in middle school and discovering beautiful things.

I love the little variables and the big infinity at the end 🥺🥺

Are these animated in 3d space or are some objects just projected?

An animation masterpiece ✅ A cinematic masterpiece ✅ A mathematical masterpiece ✅ A physics masterpiece ✅ Cinematography ✅ Sound design ✅ Everything is so perfect

## @beefchopstick

## Жыл бұрын

@@ultraactiveGDust another bot, ignore him

## @Sentinential38

## Жыл бұрын

how is this physics

## @user-uz1jq5yw4n

## Жыл бұрын

Fr

## @Pixcon

## Жыл бұрын

Worm

this sound design was top notch. The music felt so appropriate for this weird dimension, and the sfx for all the math clinking and plopping felt like it was exactly how math should sound. absolutely stunning.

## @MAXIXPLayer

## Жыл бұрын

Damn yes

the brillance behind is amazing. Well done to say the least, your team has made a masterpiece

9:59 that WAAAAAAAAA was personal😭😭😭

I can see math teachers showing us this video in the future. It's entirely possible. For Grapic Design, our teacher showed us the very first Animator vs. Animation video. And wanted us to see if we could make something similar. That was basically our biggest semester project.

## @JediJess1

## Жыл бұрын

I was always curious about that. My sister did creative tech at uni, and I keep thinking these videos would be brilliant to showcase as examples.

## @LuffyWantsMeat01

## Жыл бұрын

Can I be in your class bro

## @NateParody

## Жыл бұрын

@themisleadingpath4692 I graduated already, lol. But I can head to my school and put in a good name for you /j

## @FingerMoments

## Жыл бұрын

My math teacher teaches with fun students just don't understand themselves and blame her that her teaching is very poor they always talks (I understand math very well by her)

## @Actual456

## Жыл бұрын

I thought yellow would be in it cause he is a red stone scientist so he would know the simple math😊

This is literally 100/10. The sounds, the effects, the animation, the accurate equations and the story, they all were hella awesome. Thanks Alan.

## @biibs

## Жыл бұрын

100/10 is 10, so it's quite literally 100/10 out of 100/10 :)

## @Aidan751

## Жыл бұрын

The comment sections are so dumb comments💀

## @peakinsert1276

## Жыл бұрын

When a 14 minute KZread video teaches math better than a year of school

## @user-nn7ll5ep6h

## Жыл бұрын

Like

11:06 THIS SCENE LOOKS SO AMAZING!

AMAZING!!! Do "Animation vs. Chemistry" please!

## @matthewhitchens5903

## 5 күн бұрын

If Alan Becker can direct a video like this that actually helps me understand/care about chemistry, he'll have done what three different high school teachers and college professors could not. This is coming from someone with a B.S. in computer science. Chemistry wasn't even in my college curriculum. I took it as an elective just to give myself one last chance to really get it. Barely passed. It's the only fundamental science that I've not ever felt just...click.

To the math nerd that did the equation and to the animator, heavily respected

## @TheGuyThatPlaysKoG

## Жыл бұрын

especially in that mech section

## @elestirmenelestirmen

## Жыл бұрын

pp entry looks pretty accurate lmao

## @happymario3223

## Жыл бұрын

bro both are the same person

## @VitorMaIuquinho

## Жыл бұрын

There is literally a pinned comment saying the lead animator did the math-

## @TheJayTA

## Жыл бұрын

DJ did it all.

Here's my interpretation of each scene as a second-year undergrad: 0:00 Addition 1:23 Subtraction 1:40 Euler's identity (first sighting) 2:25 Multiplication 2:36 Division 2:48 Division by zero 3:05 Positive exponents 3:29 Zero and negative exponents 3:40 Fractional exponents and square roots 3:50 Imaginary unit, square root of negative one 4:00 Euler's identity (second sighting) 4:44 a + -a = 0 5:18 The complex plane 5:34 The unit circle 5:38 Definition of a radian 5:59 Polar coordinates 6:39 Definition of pi 6:51 Trigonometry and relationship with the unit circle 7:12 Phase shift 7:19 Euler's identity (third sighting) 7:35 Taylor series expansion for e^x, x=iπ 7:50 Volume of a cylinder (h = 8) 8:25 Hyperbolic expansion for sine and cosine 8:30 f(x) = tan(x) 9:28 Infinite domain 10:00 Calculus boss fight 11:00 Amplitude = 100 11:30 Imaginary realm? 12:10 TSC befriends Euler's identity (wholesome) 12:38 i^4 = 1 13:05 Taylor series expansion for e^x, x=π 13:06 Gamma function, x! = Γ(x+1) 13:25 Reunion with Zeta function, delta, phi and Aleph Null Definitely my favourite Animator vs. Animation video yet, and I'm not just saying that because I'm a math student. It really says something about Alan's creativity when he can make something like mathematics thrilling and action-packed. Top notch!

## @creepergod3692

## Жыл бұрын

Needs a pin!

## @existing24

## Жыл бұрын

you forgot aleph at the end, it’s really big but sort of hidden in the background for being transparent

## @bananaeclipse3324

## Жыл бұрын

@@existing24As it’s the biggest infinity!

## @Yhp420

## Жыл бұрын

@@bananaeclipse3324 aleph is not the biggest infinity. its a set of cardinal numbers that represent the different types of infinities. Aleph_0 is the number of whole numbers, aleph_1 is the number of real numbers and so on.

## @Travisevilman13-oc4nj

## Жыл бұрын

I dont see the a + -a one

Amazing,bro has described whole math development in just a video from basic addition to quantum computation,,,salute to this skill

These videos are epic this stuff is really incredible I love the use of all theses principles acting through animation this stuff needs to be in schools

This feels like it should win some kind of award. Not even joking this is gonna blow up in the academic sphere. People are gonna show this to their classes from Elementary all the way through college. I don't know if people realize just how powerful of a video you've created. This is incredible. You've literally collected the infinity stones. This is Art at its absolute peak. Bravo.

## @66LordLoss66

## Жыл бұрын

This reminds me that in Geography Class, the teacher showed us Yakko's World Country Song from _Animaniacs._ I guarantee Maths teachers will be showing this to their students for decades to come.

## @CathYeng1

## Жыл бұрын

❤

## @_suzuki1357

## Жыл бұрын

I agree!

## @charlottemabury1164

## Жыл бұрын

That’s exactly what I was thinking

## @SurroGhost

## Жыл бұрын

That’s actually true

I'm studying at the Faculty of Math in university right now and every month i come back to this masterpiece to see what new did i learn. When this animation came out i didnt understand anything besides the begining, now i almost got everything, and everytime it gets more and more interesting to analyse every small detail i notice Thanks for it, it helps he understand that im getting better, smarter, and my efforts arent worthless

## @vlooranthewise7526

## 8 ай бұрын

I showed this to my Precal teacher and she really enjoyed pointing out all the references to stuff like the unit circle and Sin waves. I think she also had that kind of moment!

## @OGSilentMan

## 7 ай бұрын

Man 5 months of progress huh

## @whimsy_vision

## 7 ай бұрын

what were the functions towars the end ?

## @wumi2419

## 7 ай бұрын

@@whimsy_vision phi is probably just generic function, at least I don't remember specific functions that use the name, then there's Riemann zeta function, delta I'm not sure about, might be the delta function, and I don't know which function is in background. Looking at other comments, it's aleph in background. Aleph is "size" of infinite sets. And phi is fibonacchi sequence Delta function is not strictly a function, but physicists like it. What's so weird about it, it has a non-zero integral despite being different from zero in only a single point. It's a part of generalized functions (distributions), which are absolutely amazing, but rarely taught. Then there's weaker version, Sobolev functional spaces, which is used more often, but is less amazing. Imagine, being able to integrate and differentiate (integrate by parts) everything. Delta function appears there as differential of heaviside step (or half of second derivative of modulus). Of course there's a corresponding price to pay

## @jmrabinez9254

## 7 ай бұрын

Why are you studying math?

I could see this being like a video game Kind of like an MMORPG but in order to get stronger you have to understand more complex maths

## @NT-sm5jk

## 11 күн бұрын

@@YourManAl a very very extensive videogame It could be done given 4d games already

IMO this should’ve been the finale to animation vs a random school subject, since math is basically everywhere. It would’ve all lead up to this.

Can't wait for all the math channels to do breakdowns of this video. It's incredible how much is packed in here.

## @josuevargas1952

## Жыл бұрын

My school teacher would be good at this until the like, last 25% of the video, then he probably would have gotten nightmares, same as me, can't wait too

## @etakiwarp

## Жыл бұрын

Even in a slowmode /100 i'm not sure you would have time to explain everything 😄

## @wildblack1

## Жыл бұрын

@@etakiwarp I wanted to check the math in the video and I had to use frame advance in some scenes.

## @bettercalldelta

## Жыл бұрын

i came here from a breakdown of the video

TSC discovered the entire realm of calculus in under 15 minutes, seriously one of the coolest parts was when the Euler monster derived from e caught the shot infinity in a limit, and using the 0-∞ integral, that seriously was like a woah moment Another thing i dont see anyone pointing out is aleph null as a behemoth due to it being the smallest infinity, i loved every bit of this, its my third time rewatching

## @HiveEntity001

## Жыл бұрын

It’s a behemoth because even if it’s the smallest infinity, it’s still infinity. Not finite. And that means…. IMPOSSIBLY big. So yeah. Behemoth.

## @andrew_fla

## Жыл бұрын

i like your funny words magic man

## @xkryde

## Жыл бұрын

I thought I was wrong when I thought aleph-null for sec there, thanks for confirmation

The fact that we come back here all the time just shows what a masterpiece this is. This video will remain a legend for years to come if not decades and centuries. Well done Mr. Lead Animator!

This would have been reall good to have on the internet for all those Math, Statistics, and Geometry classes I stressed through.

I didn't understand a good portion of the math, but this is the exact chaotic feeling I get when confronted by math. Only difference is that this animation outs me in awe of math rather than in fear of it. Truly a masterful piece

## @Appl3forPFP

## Жыл бұрын

Mathterful*

## @Officialrobloxbluesky283

## Жыл бұрын

Same I wish I understood all math

## @Officialrobloxbluesky283

## Жыл бұрын

I plan to study hard wish me luck guys!

The graphic design in this episode was nothing short of phenomenal. The way e^iπ and TSC interact with numbers is so smooth and natural, and they use complicated formulas so creatively, too... Too bad it didn't fit in the narrative of AvA's grand story because this was one of the most beautifully animated episodes I've ever seen from your team

## @sargentgullible2794

## Жыл бұрын

I suppose it could, since TSC was last seen in a jail cell, and they could have knocked him out during transfer somewhere else, possibly.

## @A_G0OGLE_user

## Жыл бұрын

Ikr

## @Braga_Rcb

## Жыл бұрын

Are we sure it doesn't fit? I need to rewatch the last chapter, but TSC was captured and in some kind of facility, with the way he woke up in this place he could be in some kind of experiment or simulation

## @harrythetrained5478

## Жыл бұрын

@@Braga_Rcb or mabye this is how TSC learns how to use his power. Math is also a form of code. But thats just a Guess

## @rhodrigomercyf2918

## Жыл бұрын

Incredible truly fantastic the way that you can innovatively come up with this😅

I love coming back to this cause I love math and seeing it used like this is just awesome, but what I like more is the sound used whe. The equations change.

I love these so much. Will there be more? Animation vs Statistics pleeeaaase xxx

As a math nerd, this is like my new favorite thing. I love how you started out with the fundamentals of math, the 1=1 to 1+1=2, and then steadily progressed through different areas until you're dealing with complex functions. There's so much I can say about this, it's so creative. Good job, Alan and the team.

## @stefanoslouk4183

## Жыл бұрын

What is e 😂 seriously I want to know

## @mikayel6175

## Жыл бұрын

@@stefanoslouk4183e means exponent i means imaginary

## @RedoAll

## Жыл бұрын

@@stefanoslouk4183its a The fifth letter of the alphabet

## @ExtremeAce

## Жыл бұрын

@@stefanoslouk4183 e is Euler's number, it's an irrational number and it's value is approximately equal to 2.7. It's useful in many different equations and can express some very complicated logarithms or series.

## @abandonedhhhv

## Жыл бұрын

@@stefanoslouk4183Euler's number. 2.718...

I love this. I can only understand completely a third of the math presented here. But the fact that Alan made entire battles, wars, swords, and weapons out of just numbers and radiuses and equations is insane and SO creative. I cannot stop watching.

## @keithharrissuwignjo2460

## Жыл бұрын

I heard he got rejected by Pixar

## @ThatBillNyeGuy09

## Жыл бұрын

Okay, but how tf did I earn nearly 300 likes within just 30 minutes?

## @abandonedhhhv

## Жыл бұрын

@@ThatBillNyeGuy09I have no idea.

## @mamunrashid6404

## Жыл бұрын

@@keithharrissuwignjo2460 alan becker dont need pixar, pixar needs him.

This and the Phyics Video definitely has a lot of potential of visually teaching math. Someone has to make this into a game.

This is the first time I've understood some of this stuff, and it was explained without a word..

I've never seen anything so mathematically accurate while also entertaining.

## @viniciusdias2330

## Жыл бұрын

now it is explained how the "chosen one" went to this reality

## @sehr.geheim

## Жыл бұрын

No appreciation for proofs?

## @marbot1

## Жыл бұрын

E

## @bvdlio

## Жыл бұрын

3b1b

## @drackflame951

## Жыл бұрын

@@sehr.geheimhe's basically a vector figure, a being made of numbers, to put it in short, he's basically math itself so to speak.

As an engineer this has got to be the coolest animation I've ever seen. Its so fun to watch and 100% acurate all the time

## @AdityaKumar-gv4dj

## Жыл бұрын

π=e=3?

## @rodrigovillegas2263

## Жыл бұрын

As an aspiring engineer I resent my brain for understanding most of it. But yeah, it’s really cool

## @bugg4938

## Жыл бұрын

@@AdityaKumar-gv4dj^2 =g

## @jeremycaswell

## Жыл бұрын

@@bugg4938 wut

## @FEARLESS_FWOG0

## Жыл бұрын

@@jeremycaswellshh were speaking math language

This was brilliantly awesome! ... makes me sad that I never followed my OG plans out of high school to go to Uni for mathematics. Too late to worry about that now, lived a good deal of life since then now that I'm in my 40s.

What a fabulous video!Alan is so creative he makes me wish I remembered more of my high school math.

When I mentioned Alan Becker at the height as an artist I respect, their response was ... "Who?" .... This guy started with a simple animation animator vs animation .. now he makes great crossover stories with his characters and now released , a perfect mathematical spectacle connected to a simple story but so brilliantly done that hats off. I don't care what happened to them, but I will continue to follow his stories, which he permeated in such a way that he creates his own category that he undoubtedly rules. Keep it up.

## @jetstreamnon

## Жыл бұрын

s

## @carmenorozco8833

## Жыл бұрын

wat

## @ccSalman

## Жыл бұрын

I agree!

As a physicist I got to say, this was incredible. I was literally smiling all the way through because of how amazing this was. It captures the math so good and the animations representing the individual math operations, simply astonishing.

## @pitpot2

## Жыл бұрын

almost makes me want to do math

## @michaelregan3345

## Жыл бұрын

yeah same

## @destonmarvelle5627

## Жыл бұрын

Math is like drugs u can be very happy when your right but deppresed when your wrong

13:35 oh look, there's Phi from the latest video "Animation Vs Geometry"!

Marvelous... I can only bow down to the art, knowledge, skill and creativity of this video. As a physicist, I can understand all the math, but to stage it like this is the work of a genius whose mind can grasp, see and imagine more dimensions than probably most of us. Thank you for this enchanting 15 minutes... which I will probably watch many, many times. A jewel.

Love how this is so rewatchable because you can understand the little details in some parts of the video and they're actually mathematically accurate, especially the "imaginary world" bit.

## @Meryemjaja

## Жыл бұрын

ALLAHUAKBARRR!!!!

## @brunopagnoncelli975

## Жыл бұрын

@@Meryemjajawhy tho

## @BIackhole

## Жыл бұрын

The details are amazing in this video

## @puiiralte9038

## Жыл бұрын

@@BIackholeikr

As a mathematician AND a fan of Alan's works, I can't describe how happy I am.

## @eon1311

## Жыл бұрын

Same here bro

## @grandevirtude9830

## Жыл бұрын

Too bad that i understood no shit related to maths after 3:52

## @mogwaisales

## Жыл бұрын

The addition of enjoyment was worth the subtraction of time from my day. I have shown It to multiple people and none are divided on how good this is.

## @snowman3456

## Жыл бұрын

@@grandevirtude9830same

## @noahk6407

## Жыл бұрын

@@grandevirtude9830imagine

This is how i imagine numbers in my head while solving math..absolutely loving thissssssss

Absolutely brilliant!!! So much details in every action!

Some of my favourite things from this masterpiece which I understood: 1:39 e^iπ = -1 1:49 Multiplying by i probably can be represented here as moving to another dimention (of complex numbers) as they're located in a real one 2:37 The division here for a÷b=c is interpreted as "c is how many times you must subtract b from a to get 0" which easily explains later why you can't divide by 0 3:08 The squared number is literally interpreted as a square-shaped sum of single units 4:12 The e^iπ tries to run away to another dimention again by multiplying itself by i but TSC hits it with another i so i×i=-1 returns it back to real numbers 4:16 The e^iπ extends itself according to Euler's formula 4:19 TSC gets hit with minus so he flips 4:22 The reason why e^iπ rides a semicircle comes from visual explaining of e^iπ=-1. e^ix means that you return the value of a particular point in complex plane which you get to through a path of x radians counterclockwise from 1. Therefore e^iπ equals to -1 because π radians is exactly a semicircle. When the e^iπ sets itself to 0 power (e^i0) it returns back to 1 through a semicircle because well 1 is zero radians apart from 1. 4:53 The "2×2=" bow shoots fours 4:55 As I explained above, e^(iπ/4) means you move exaclty π/4 radians (quarter semicircle) counterclockwise 5:06 When you multiply a number by i in complex plane you just actually rotate the position vector of this number 90° counterclockwise, that's where a quarter circle came from 5:39 Each segment here is a radian, a special part of a circle in which the length of the arc coincides with the length of the radius (it's also shown at 5:46); the circle has exactly 2π radians which you can visually see is about 6.283 6:38 Visual explanation of π radians being a semicircle 6:48 Geometric interpretation of sinusoid 7:08 TSC once again multiplies the sine function by i which rotates its graph 90° 7:36 The sum literally shoots its addends so the value of n increases as the lower ones have just been used; you may also notice that every next addend gets the value of n higher and higher as well as extends to its actual full value when explodes 7:45 TSC multiplies the circle by π so he gets the area and can use it as shield 8:04 TSC uses minus on himself so he comes out from another side 8:17 The sinusoid as a laser beam is just priceless 9:02 Multiplying the radius by π here is interpreted as rotating it 180° 9:23 +7i literally means 7 units up in complex plane 9:38 Here is some kind of math pun. TSC shoots with infinity which creates the set of all real numbers (ℝ). With every other shot he creates another set which represents as ℝ², ℝ³ etc. It also means span (vector) in linear algebra and with every other ℝ this vector receives another dimention (x₁, x₂, x₃ etc.). 9:58 The sum monster absorbs infinity (shown as limit) and receives an integral from 0 to ∞ 13:46 Aleph (ℵ) represents the size of an infinite set so is presented here as enormously sized number P.S. Thanks to the people in replies who taught me the name of the orange character (The Second Coming), before that I just called him "the guy" here. P.P.S. Also thank you all for the feedback, I'm glad you appreciated my half hour work.

## @cheeto4604

## Жыл бұрын

Finally someone notices aleph.

## @bicillenium4019

## Жыл бұрын

Where is the aleph

## @shane7534

## Жыл бұрын

@@bicillenium4019it’s colored black with a faint graph texture moving at the end. Might wanna turn up ur brightness 2 see it

## @micahwest3566

## Жыл бұрын

Is the size of an infinite set not just… infinity? This is so typical of math lol

## @guizintheinsect5022

## Жыл бұрын

Hmmmm,interesting,but why the circle is going diagonally at 10:29 (Sorry,i'm still in 9th grade)

As a math enthusiast I will admit that everything in this video was really fun to watch, and everything demonstrated was done creatively and understandably. (most of the time) The different ways math was used in these animations was very cool and I'd love to see more sometime. Good job Alan and team!

## @thatonecabridog

## Жыл бұрын

Could you elaborate on that "most of the time"

## @ferher5139

## Жыл бұрын

@@thatonecabridogi couldn't understand shit past the half second half (prob a skill issue though)

This gives me the same vibes as the old Stick Fight games combined with Captain Bones from Crashbox! I love this so much ❤

4:52, makes a bow out of a 2, an x and another 2, and the arrows it creates are the number 4. I shouldn't love that as much as I do.

Only someone like Alan can turn math into an epic and entertaining battle like this. Props to the animation team because God knows my brain is too smooth to understand a fraction of whatever the hell any of those equations were :)

## @orsonlarter6475

## Жыл бұрын

haha me too

only Alan Becker can turn a math formula into a sub-orbital laser cannon

## @GoodMat66

## Жыл бұрын

134 likes and no replys? Let i fix it

## @GoodMat66

## Жыл бұрын

xD

## @Red_MOON187

## Жыл бұрын

A death star

## @livethefuture2492

## Жыл бұрын

It's a sine and cosine function, which is funny because that's exactly how Lasers actually work in real life as well.

I fell asleep while watching this video and now I get why I suck at math

I can't believe this masterpiece was 1 year ago... Time really does fly by

I came here thinking this video came out 6 years ago but no it was only 6 hours. I’m sure I could say plenty that others have said but it’s so good to see fun and creative animations like this still existing on KZread after all these years and all the hassles on KZread. No Ads, No Sponsors, No Patreon no Merch Plugins, just the art of animation in its purest form. Incredible work, keep it up.

## @Frog_Plush_THE_ANIMATOR.

## Жыл бұрын

Same, Alan is so good.

## @fdsafdsafdsafdsafd

## Жыл бұрын

You'd see more of it if KZread wasnt doing its best to kill any creator that doesn't toe the line exactly as they want it.

## @TheIrrelevantYT

## Жыл бұрын

KZread is absolutely ruthless to animators. It's just that Alan's content is exactly what KZread likes.

## @singingsun04

## Жыл бұрын

Unrelated note my comment got stolen by a bot and got more likes than me. That’s pretty kooky!

Some Small Details 5:29 this shows The Second Coming is approximately 1.65 units tall. An average adult male is 1.6~1.8 meters tall. It appears the math space is in SI units, m being the SI unit of length. This also shows TSC is about 165cm tall, or 5' 5". 7:45 a circle is represented as x^2 + y^2 = r^2. Inserting a pi turns it into the area of a circle, pi*r^2. Inserting 8 turns it into the volume of a cylinder, 8*pi*r^2. 9:01 since f(x) is 9*tan(x) and tangent turns angle into the steepness of a line, it can latch onto the unit circle. 9:40 f(dot) represents the tangent function at a given point (throughout this video, we can see a dot used as an arbitary number on the number line), and f(inf) represents the tangent function over the entire number line [0, +inf). An entire number line can be seen as a span of an unit vector, thus each shot increases the dimension of the span. This also implies that TSC is a being that is four-dimensional. 9:57 Sigma + limit = integral. If you try to derive the definite integral using the sum of rectangles method, you will eventually transform lim(sigma(f(...)) into integral(g(...)). 10:04 Calculating an integral of a function can be seen as getting the total (polar) area between the function and the number line. Thus the Integral Sword attacks with R2. 11:31 welcome to the imaginary realm. Hope you like it here.

## @therookiegamer2727

## Жыл бұрын

Main character in this is TSC (the second coming) but neat analasis

## @Foxella2010

## Жыл бұрын

TSC is 5’ 5 hmmmmm may be useful information not gonna lie

## @powerstar8862

## Жыл бұрын

@@Foxella2010Big brain 200 iq much?

## @lemonspade3718

## Жыл бұрын

when a stick man is taller than you

## @adt4864

## Жыл бұрын

TSC is measured in pixels, not meters

Aleph at the end is genius 🤩 already saw a couple people talk about this in video game form but I have to say it again. Reminds me of that guy making a game where you fight with music

POV: When Humans Discovered Math

I can’t wait to see math youtubers react to this and explain it all. Here’s hoping the community gets this in front of those creators as soon as possible.

## @user-nr5bt3hd9z

## Жыл бұрын

Hope vsauce sees it

The start was intriguing, the middle was intense, and the end was heartwarming. This isn't just an animation, it's a masterpiece and will be remembered for generations to come.

## @aic8326

## 8 ай бұрын

Lol yet another youtube "masterpiece" comment 😂

## @Sebdet9

## 7 ай бұрын

@@unaval1ble_ I learned imaginary numbers because of this

## @littlemilk973

## 7 ай бұрын

@@Sebdet9 you didn't know imaginary numbers before??

## @Sand_the_Lazy_sand

## 7 ай бұрын

@@aic8326atleast they spent some effort on the comment instead of the jellybean comment (i actually forgot about that)

## @Tenebri_s

## 7 ай бұрын

Yes kids boss fighting with e

I have a feeling we are going to see more of this. Animation vs Set Theory, Animation vs Number Theory, and Animation vs Calculous.

I wish this was a trailer to a math game just like this I would play it all the time if so

not only did alan somehow make Euler's identity badass, he also made all of its alternate forms even more badass

## @RunstarHomer

## Жыл бұрын

Euler's formula has been badass for hundreds of years, my guy.

## @Genisis1082

## Жыл бұрын

@@RunstarHomer Im impressed that it all made sense too, what a cool animation

## @I_killed_that_beard_guy

## Жыл бұрын

Can you explain me why euler identify is running and really hard to catch? Idk

## @allrightformugiwara2656

## Жыл бұрын

He called e the negative one

## @salitroka9661

## Жыл бұрын

facts

As a person who has taken calculus, I can confirm we fight bosses every day in math class.

## @Godzilla_boiS

## Жыл бұрын

😂

## @pantherosgaming1995

## Жыл бұрын

OMG 🤣

## @TWGStorms

## Жыл бұрын

Too true

## @silxm

## Жыл бұрын

i can agree with this ap calculus was scary

## @arda04onuk77

## Жыл бұрын

as a person just started took it and failed and going to take next year nothings changed

In 6:38 , When TSC made the π symbol successfully, its because the number shows "0/r=3.14". The reason it became the symbol π, its because 3.14 is the first 3 digits of pi.

Я боюсь представить какой титанический труд стремящийся к бесконечности был вложен в эту анимацию со всеми просчётами, звуком, раскадровокой, эффектами, музыкой, анимацией и логикой.😮 Опладирую стоя.👏👏👏👏👏👏👏👏👏👏👏👏👏

As a math and sciences major, alongside being a tutor for highschoolers I absolutely LOVE this animation. What amazes me more is this is how some of my students visualize math, and its incredible.

## @mebin3059

## Жыл бұрын

exactly like this or in some way similar?

## @superninja7977

## Жыл бұрын

bro that's cap, no one visualizes math as an epic battle using imaginary numbers

## @_.baited._

## Жыл бұрын

What? As nukes?

## @Beagle36

## Жыл бұрын

@@mebin3059 similar ways. I’m referring to early on in the video.

## @mebin3059

## Жыл бұрын

@@Beagle36 oh cool same 👍

Cancelling Infinity using Limits. That is beyond genius!

## @Herl_Shevin101

## Ай бұрын

Einstein been real quiet since this got exposed

## @krisztiankoblos1948

## Ай бұрын

@@Herl_Shevin101 XD

## @SoftAlexandra3

## Ай бұрын

Not beyond genius, but something high school students in Advanced Mathematics like me gets taught of working with.

## @daysukanbowfive5202

## Ай бұрын

when the video was escalating, and he got to the infinity, I was thinking " oh the next thing that will counter infinity is limit " and it did ! amazing video

can't wait for `Animation vs. Ordinals` where you get to draw infinities of infinities of infinities

Loved the cute little battle cry and uncoordinated woobly circular spin of the giant transformer Euler. 😂