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
*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!
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
Well, if we think about it philosophically, asking "What makes this a better feat than anything TSC had accomplished previously?" TSC had created mathematical dimensions beyond fictional dimensionality, every time that Euler and TSC fought, they turned these dimensions into weaponry and played with definitions of universal logic. "But what does this all equal to feats compared to Goku or Saitama?" Math exists in real life, and these equations can define anything, if TSC can make those definitions into a gigantic beam that almost blew up the void at the end, they used a real life concept as serious action and fighting, that is some serious power.
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.
Animation vs. Math: Basic Explanation 0:07 In the beginning of math, 1 is given as the first number in the math world. 0:13 Equality -- A relationship between numbers and their values, even equations. 0:18 Addition -- The first of the fundamental arithmetic operations. 0:28 Repeated addition of 1s results in omitting them for multiplication. 0:35 The first appearance of 0 in the ones place, it's just a placeholder for numbers that don't have their value. 0:45 Decomposition -- A number which has their expanded form or its equivalent sum inside enclosing with the parentheses symbol in the outside. For example: 2 can be written as (1 + 1). 0:49 Adding numbers that are greater than 1 can also be omitted by just adding 1. 1:10 Simplification -- In some math equations, they can (or can't) simplify their equations. For example: 40 + 68 + 35 = 108 + 35 = 143 1:23 Subtraction -- The second of the fundamental arithmetic operations. 1:31 Any number subtracts itself is always 0. 1:33 If 0 subtracts 1 (or more numbers), a negative number is born (-1). Which is the opposite side of real numbers (negative numbers). 1:39 This is Euler's Identity: -1 = e^(iπ) 1:49 ie^(iπ) is equal to -i and this leads to imaginary realm. 2:12 Subtracting negative numbers gives us even bigger negative numbers. Note: Adding negative numbers gives us even smaller negative numbers. 2:15 Doubling negative gives positive. 2:24 Multiplication -- The third of the fundamental arithmetic operations. 2:26 If a number on the right side has brackets (or parentheses) results in factors of the product. 2:35 Division -- The fourth of the fundamental arithmetic operations. Note: Division symbols can have three types (÷, / and :). The ÷ symbol is (usually) used in math equations, the / symbol is used in fractions. For example: 1/2 = 1 ÷ 2, and the : symbol is often used in ratios. For example: a:b = a/b or a ÷ b. 2:36 This is called long division, that means you have to take the divisor's number and subtract the dividend on how many times that will take you to 0. 2:48 Dividing any number by 0 doesn't make any sense, because when we use "n" and divide by 0 will just be n - 0 - 0 - 0 - 0... It will take you forever but the dividend is still the same. And that's why n÷0 is undefined. 2:57 Any number is equal to (number) - 0. And that's the Basic Explanation. If I did something wrong, tell me in the reply section below!
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.
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.
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 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.
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.
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.
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
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
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
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.
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.
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!
@@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.
Some of my favourite things from this masterpiece I noticed: 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. 4:46 When "+1" and "-1" swords cross they make a "0" effect 4:48 The e^iπ makes a "-4" sword which destroys TSC's "+1" sword making it zero, and as a result e^iπ is now holding "-3". Then the same thing repeats with "-3" and "-2". 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 ∞ 13:34 The golden ratio (φ) when approaching e^iπ takes smaller and smaller steps which shorten according to the golden ratio (each step is about 1.618 shorter than the previous one) 13:46 Aleph (ℵ) represents the size of an infinite set so is presented here as enormously sized number
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.
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.
@@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.
there's something about this i really like, how it's just an endless plane of math with all these interactive mechanism-like systems for all the things in math.
As someone who's been into math since I was 12, this is the best visualization on equations, expressions, symmetry and the true meaning of math as a whole I've ever come accross. This is not just entertainment, this is pure genius. It's brilliant. By the way, I loved how the so called "most beautiful equation" (aka Euler's identity) shows up and basically tries to trick the stickman. That's quite deep. If you know what that equation means, it makes total sense. Also, I loved when they got into the imaginary domain for a brief moment and everything seemed broken, then they came back to the real numbers domain at a different position in space, which also makes perfect sense if you know a bit about operations using imaginary numbers. Every single frame of this video makes perfect sense, really. Not to mention the overal details such as the animation, the plot, the way things build up with math concepts and ideas showing up in a logical order, soundtrack, sound effects... 3blue1brown would be proud. Again, genius.
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
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!
@@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
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.
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)
An animation masterpiece ✅ A cinematic masterpiece ✅ A mathematical masterpiece ✅ A physics masterpiece ✅ Cinematography ✅ Sound design ✅ Everything is so perfect
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.
The function he condensed into f(•) is 9 × (sin(π)/cos(π)). Since sin(π) = 0, the whole equation simplifies down to 0 regardless of what the input is because everything is multiplied together. When he shoots the e^iπ instances with it, they get fed through a function that always returns 0, therefore they become 0.
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
Only Alan Becker can make a video about maths and we’ll all genuinely be invested in it. Edit: GUYS PLEASE STOP COMMENTING ON HOW THERE’S OTHER CHANNELS THAT CAN MAKE MATHS-BASED VIDEOS THIS WAS COMMENTED TWO MONTHS AGO AND I WAS JUST IMPRESSED AT HOW ALAN AND HIS TEAM WERE ABLE TO EXECUTE IT I DON’T WATCH VSAUCE
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.
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
Your animation is more than impressive as always, but the creativity behind the manipulation of mathematics in the animation to create such a story left me in awe.
I love the sound design on this video. I didn’t even know if Scott Buckley was the one behind the music, it sounded so different to his past scores, but it fit perfectly! It did a great job with the “lonely void” vibe without being too overwhelmingly happy or sad. I love the typewriter-clicky sounds throughout the whole thing, along with the digital vibe. Different objects and aspects of math have their own feel. I could watch this video without the visuals and remember what TSC is currently learning about! Really feels like you’re trapped in a Khan Academy video, and it’s perfect!
@@Scrufflyguy101I could see my teacher going frame by frame through the video and explaining each equation to us and the cool unique qualities and random fact about each one
I need to see everymath youtuber react to this! Mathologer, Matt Parker and the Numberphile gang, 3blue1brown in particular, EVERYONE! As a general math enjoyer, I was smiling throughout the entire video at everything! I can't even call anything here "references". Everything was just correct and accurate, with visuals to match. The sound design and musical composition were both excellent! All the sounds fit in ways that were mentally satisfying, and the music built a vibe of intrigue and determination or focus, before it went epic! Alan and co, this was absolutely astonishing!
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 UA-cam after all these years and all the hassles on UA-cam. No Ads, No Sponsors, No Patreon no Merch Plugins, just the art of animation in its purest form. Incredible work, keep it up.
As a math major, I think a pretty common experience between all of us is that it's very difficult to talk to anyone about this sorta stuff. It's genuinely pretty heartwarming seeing the discipline as this awesome world, and then to actually have the world itself be rigorous and sound.
You want the world to be rigorous and sound you go be a machine where everything is definite for you. As a human, we want possibilities which means uncertainty and we want everything that we could or could not never ever imagine of to manifest in front of us. I do not want to live in a finite and defined world, I want things that we could never physically figure out and a world that we could never explain.
@@poyenwu O...kay... As a computer scientist, do you honestly not get what OP was trying to say? This could be the start of a typical quickly escalating UA-cam-comment thread, just because of people completely talking past each other within having exchanged two sentences. "I like that they cared enough about the math to not just make it flashy, but also sensible." and "I want freedom, complexity and creativity in my life!", are two statements not compatible within the same conversation. You might as well have entered a conversation about shark skin microstructure analysis by yelling: "I hate bacon!". Put in its own comment outside of this thread, what you expressed would actually fit the video kinda nicely. In here it's poor form.
@@kalimer0968 Not sure what you're talking about. OP is saying how he likes people working on things that focus on the discipline of this world and for us to have a rigorous and sound world. What I was trying to say is that if all you want is a rigorous world which follows some strict disciplines, you do not need to come to this word, you could have just live inside a machine as a program since that alone can meet all your needs already. Being a human in this world, we want the ultimate unlimited possibilities, which means no rule can describe the nature of the world in its entirety (hence not disciplined), and will always have unexpected things happening which you could never (and I mean never) imagine (hence can not be rigorous).
@@kalimer0968 Also, I failed to find the sentences you qouted anywhere in this thread. FYI. I read OP's entire comment and thinks about it before I started to write mine.
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 :)
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.
Achievement obtained 0:12 Welcome to Me- I mean Math (Discover 1) 0:14 Equality (Discover "=") 0:19 No, I'm not used for exorcism (Discover "+") 0:34 Everyone is here (Discover all digit) 0:36 (Secret) What? Do it to your head instead! 0:58 Yay, I counted to 100 (Reach 100) 1:24 Going backward (Discover "-") 1:34 Hey! That's illegal? (Discover negative numbers) 1:40 Unknown identity (Discover Euler's identity) 2:19 You face the same direction (Make a negative number positive) 2:25 What time is it? (Discover Multiplication) 2:28 (Secret) Wait... It's all the same? 2:36 Separated (Discover Division) 2:49 (Secret) Why? 3:05 I feel the POWER (Discover Factorial)
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.
This is one of the most beautiful videos I've ever seen, hands down. The fact that you could so clearly and visually explain some of the hardest concepts in math, from multiplication all the way to trigonometry. The animation is stellar, with every math concept perfected to beauty. As someone who loves math, animation, and Alan Becker, this is a work of art. Keep being awesome!
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!
As a developer for a math learning app, I'm blown away by how math has been visualized here. I've been on a similar path with my project, Animath, which uses animations to explain algebra step by step. It's incredible to see the potential when you bring animation and learning together. If you're curious, I have more about it on my channel. Thanks for sharing this inspiring work, it's truly motivating for creators like me!
@@ahmad-almazeedi you've said at the comment that you were a developer of math learning app and i want to see if the app is published? i would like to take a look.
Timestamps for those who dont know what some of this is 0:01 The Epic One 0:19 Addition 1:10 Simplification 1:19 Subtraction 1:39 Euler's number to the power of imaginary pi 2:23 Multiplication 2:26 Parenthesis 2:34 Division 3:04 Exponents 3:31 Fractions 3:39 Square Roots 3:50 Imaginary 4:01 Imaginary Euler's Number to the power of imaginary pi 4:09 The Chase 4:43 Fighting with Functions 5:16 Back to Math 5:21 Graphs 5:37 Theta 5:52 Radius 6:38 Pi 6:44 sin and cos 6:50 Circumference (I think) 7:09 Imaginary sin 7:19 Euler's Number to the power of imaginary pi (again) 7:26 Another Fight 7:35 Euler's Number to the power of imaginary pi turns into a Sigma Notation 7:39 Sigma Notation Shoots imaginary pi to the power of n, while n is 2 and will stop until it reaches Infinity, so he can shoot an infinite ammount of imaginary pi to the power of n 7:45 TSC multiplies the radian to 4 to have enough to make a circle and multiply the circle and the pi to make the circumference and use it as a sheild 8:24 Euler's Number to the power of imaginary pi is multiplying himself by... dividing... 8:30 not smart enough to understand that but you can see what TSC is trying to do 8:40 TSC with a gun vs Euler's Number to the power of imaginary pi apocalypse 9:46 that doesn't seem fair 9:58 DA GIANT INTEGRAL 10:02 aw he sounds cute 10:17 TSC changing the position of the circle 10:35 TSC just found the most op math function even though he only had 10 minutes to learn it while he have to take years 11:16 TSC launches himself to get Euler's Number to the power of imaginary pi 12:11 Euler's Number to the power of imaginary pi spares TSC him even though his knowledge of math nearly killed him 12:17 TSC learns for Euler's Number to the power of imaginary pi (god im tired of saying Euler's Number to the power of imaginary pi) 13:04 Euler's Number to the power of imaginary pi creates a portal for TSC 13:33 Zeta 13:35 The Golden Ratio, or phi 13:36 Delta 13:39 Thats a BIG aleph 13:49 The + End = The End (I think)
Alan Becker's videos seriously never get old. There's just something about them that just reels you in and you can't stop watching until the very end. The sound effects, the music, the visuals, his videos never lose their touch and on top of that, they are original and are so fun to watch. It felt like Orange was like a pioneer of mathematics or he was trying to fight toward finding the solution to his problem (escaping the place he was trapped in). Looking forward to the next upload!
Part l First number 0:07 Equations 0:13 Addition 0:19 Repeated addition 0:32 Reaching ten 0:34 Adding with two 0:49 Adding with twenty 0:56 Reaching one hundred 0:58 Subtraction 1:24 First negative number 1:34 Part ll i*e^ pops up 1:39 Subtracting negative numbers 2:12 Multiplication 2:25 Division 2:35 The power of __ 3:04 Subtracting the power of __ 3:25 Fractions 3:30 Irrational number 3:43 i^2 pops up 3:50 Adding i^2 3:58 Part lll Multiplying i^2 3:59 e^i* pops up again 4:01 TSC brings the multiplication sign and i^2 4:28 TSC uses the multiplication sign to double his speed 4:33 TSC brings out a sword 4:44 TSC uses a bow and arrows 4:53 Complex plane 5:36 r*theta 5:59 Sine & cosine functions 6:44 Sine wave 6:49 Cosine wave 6:55 Sine & Cosines wave 7:02 Part lV e^i* pops up once again 7:19 e^i* turn into phase two: The aircraft(AKA, e^x with x=i*pi)7:35 TSC is in the complex plane 7:57 e^i* clones himself 8:25 TSC creates a function gun 8:33 TSC grabs the 8 to make the gun stronger 9:30 e^i* is in phase three:The final form 10:01 TSC uses the displacement beam again 10:34 TSC destroyes the mecha suit 11:05 TSC us in the imaginary realm 11:31 Part V TSC tells e^i* hes sorry for trying to destroy him 12:03 How do I get out of here? Says TSC 12:16 e^i* brings down the complex plane 12:56 Get in here. Says e^i* 12:58 TSC finally got out of the mathematical realm 13:28 e^i* meets his family members.Zeta,Phi, and delta 13:36 Bonus: Camo aleph 13:46 The End
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.
Unironically, something like the beginning with all the playing around with numbers and math in an open space would be a sorta cool “Im bored” vr game, seeing how different math works like multiplications and division in a 3D space, and how complex equations could play out just messing with numbers.
I think this just proves TSC is smarter than anyone alive. He just absorbed, learned, and utilized in combat 14 years worth of math learning in just 14 minutes.
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.
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.
I showed this video to the whole class and it was really incredible. It was definitely the best work I have ever seen. I really like the feeling of vividly and visually deducing mathematics, from simple to complex, from small to infinite. As a fan of science and aesthetics, I really hope this series can continue and look forward to the next issue of Animation vs. Physics or Chemistry
I really want to watch vs. physics.Motion,force, heat, light, electricity,atoms to galaxies, stillness to the speed of light, combined with such a plot, it's absolutely amazing
i like how in the beginning, euler’s identity escaped quickly, indicating a lack of fundamental understanding. But as the second coming learns more and more, he becomes more and more capable of keeping up with euler, eventually figuring out how to defeat its dimensional trickery with i, and making peace with it once he understands the prerequisites. very well done animation !!
This is insanely cool. Not only it looks like a cool fight animation, it actually shows the origin of functions and concepts as TSC discover them. To be honest, I only understand the math up to ⅔ of the video, and still it felt very amazing. I can imagine how fascinating this is to people who understands all the math shown here.
I notoriously hated math cuz I was never good at it. But the way Alan makes this stuff look like fun is forever baffling to me. I’m so floored by this, this just further solidifies Alan as my favorite animator ever. Dude just can do anything with his team, props to everyone that helps him and all of that because you guys are always unmatched. I love this channel, still is one of my greatest inspirations to get into animation. And always will be 🙏🏽💖
It’s awesome how it all starts from 1. Then an equal sign appears, and the math begins to slowly evolve through addition, subtraction, multiplication, division, parentheses, exponents, decimals, square roots, fractions, and then into calculus with summation, pi, infinity, etc.; then into geometry with circles, radiuses, sine-, cosine-, and tangent waves. And finally, it ends with an epic battle of e vs. Second Coming. This is legitimately one of the coolest things I’ve ever seen!
I can't even imagine the amount of genius, effort, and elegance dedicated to this work. You're special. Single best math animation story I've ever seen!!
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
I've heard for years now that Euler's Identity was 'the most beautiful formula in mathematics', but I feel like this video represents an actual proof of that. This is a work of absolute genius.
1:02 Green does not exist. Blue does not exist. Red does not exist. Yellow does not exist. *He does not exist.* *He does not exist.* *He does not exist.* *He does not exist.*
I swear Alan is just a machine that takes in ideas and churns out beautiful animation and stupendous sound design! Everyone involved with this project (and others) deserves the best!
This really feels like Alan's old animations, before they became a series. Something exists, it gets explored, big fight, bigger fight, biggest fight, then end. No context, nothing. Except, now the quality of animation is something exceptional.
@@fitzchevalerie6597 Erm... what? Exponential means something that is increasing at an increasing rate. Exceptional on the other hand, means something different, unique; incredible. Just another fancy word, but fits the context and I fancied using it for no reason. Exponential doesn't fit the context?
It fits because we're talking about the quality, it gets better and better each time at an increasing rate, finally, I think exponential is more fiitting and it has a strong bond with maths, wich is the subject of this video, I hope I was clear
@@fitzchevalerie6597 That is a nice viewpoint, but I think you should have worded it more clearly. I thought you were suggesting to just switch the words, when that breaks the sentence completely, but it can be reworded to fit "exponenttial". Other than that, pretty great pun :D
As someone who has taken multiple calculas classes the accuracy and detail in this animation is insane. Well done. Although a great animation is nothing less of what I'd expect of Alan Becker and his team.
Can you explain what that "e" thing is then? The one that is seemingly "sentient" in this math world? What does it mean and why is it the only thing that can create those "portals" to what I assume is a dimension to imaginary numbers.
@@TheEpicGalaxy21e is a very unique number in math. It represents an actual number like pi. For example the derivative of e^x is e^x. e is also used a lot when it comes to interest calculations.
This is a certified banger of a video. It presents maths to all ages in the most cool, accessible and simplistic ways possible, showing hard and abstract concepts in understandable ways that can only be done in animation. It rewards those that have spent their lives on the subject. The pride in knowing every equation, every proof and every little Easter egg, is validation and recognition for their efforts in learning and expanding on the vast sea of knowledge that is mathematics. It helps people that are in the middle of learning math. It motivates the demotivated by displaying how cool maths can be, and guides those that are struggling by presenting concepts in fun and simple ways. Most importantly however, it inspires and draws people to math. Those that never tried math will be inspired and those that dislike math may give it a second chance after seeing how cool maths can be. This is one of the best, if not the best, math videos of time.
To be clear, my lead animator is the math nerd behind all this. And as always, watch DJ and I talk about it: ua-cam.com/video/dRj3X7IFCjY/v-deo.html
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
Yoo pogchamp
@@Emirhanoleo78hi
hi alan
1 minute lol
*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!
hey, are you my teacher?
Nice lore.
I will be waiting for your part 2!
Please continue dude, till end. I confused about the end of the video.
Do everything pls.
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
30 likes and no replies let me fixed that😊
Yep the pretty much it
Man this makes me wanna learn math more
alan should put this in the video.
I need to know what types TSC is using
@@xvie_z2900fax I wanna understand everything in this video
If math lessons were like this, math would for sure be everyone’s favorite subject
Edit: well, this blew up fast. Thanks!
Math is beauty, if not you just not understand it very well
@@naufaljb8204 People have opinions, not saying you're wrong but, People have opinions.
@@naufaljb8204 maybe you're good at math, but you suck at english
@@aliaakari601yeah
@@aliaakari601pople
Gotta love how in 10 minutes this man figured out how to make a weapon of mass destruction
Well, if we think about it philosophically, asking "What makes this a better feat than anything TSC had accomplished previously?" TSC had created mathematical dimensions beyond fictional dimensionality, every time that Euler and TSC fought, they turned these dimensions into weaponry and played with definitions of universal logic. "But what does this all equal to feats compared to Goku or Saitama?" Math exists in real life, and these equations can define anything, if TSC can make those definitions into a gigantic beam that almost blew up the void at the end, they used a real life concept as serious action and fighting, that is some serious power.
Ye 😂😂😂😂
bro managed to destroy that red stickman + eiπ guy
If you could turn this format into a video game, you'd have an incredibly powerful tool to teach kids math.
imagine
Just to add to this I went and learned eulers identity is after wondering why E to pi I was so crazy
@@jesseweber5318me too, i had no idea
Like minecraft?
@@rickt.3663 you mean, Minecraft Education edition?
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.
He has an entire crew working with him
He does have a WHOLE ASS BUILDING
Yeah😂
I can only understand a bit.
...and at the end, in comes the zeta function
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)
Someone already did it
Sorry bro
@@Lebanoncontryball at least I got likes + replies
@@marcusscience23 yeah gg
@@marcusscience23 but he did too
Animation vs. Math: Basic Explanation
0:07 In the beginning of math, 1 is given as the first number in the math world.
0:13 Equality -- A relationship between numbers and their values, even equations.
0:18 Addition -- The first of the fundamental arithmetic operations.
0:28 Repeated addition of 1s results in omitting them for multiplication.
0:35 The first appearance of 0 in the ones place, it's just a placeholder for numbers that don't have their value.
0:45 Decomposition -- A number which has their expanded form or its equivalent sum inside enclosing with the parentheses symbol in the outside. For example: 2 can be written as (1 + 1).
0:49 Adding numbers that are greater than 1 can also be omitted by just adding 1.
1:10 Simplification -- In some math equations, they can (or can't) simplify their equations. For example:
40 + 68 + 35 = 108 + 35
= 143
1:23 Subtraction -- The second of the fundamental arithmetic operations.
1:31 Any number subtracts itself is always 0.
1:33 If 0 subtracts 1 (or more numbers), a negative number is born (-1). Which is the opposite side of real numbers (negative numbers).
1:39 This is Euler's Identity: -1 = e^(iπ)
1:49 ie^(iπ) is equal to -i and this leads to imaginary realm.
2:12 Subtracting negative numbers gives us even bigger negative numbers.
Note: Adding negative numbers gives us even smaller negative numbers.
2:15 Doubling negative gives positive.
2:24 Multiplication -- The third of the fundamental arithmetic operations.
2:26 If a number on the right side has brackets (or parentheses) results in factors of the product.
2:35 Division -- The fourth of the fundamental arithmetic operations.
Note: Division symbols can have three types (÷, / and :). The ÷ symbol is (usually) used in math equations, the / symbol is used in fractions. For example: 1/2 = 1 ÷ 2, and the : symbol is often used in ratios. For example: a:b = a/b or a ÷ b.
2:36 This is called long division, that means you have to take the divisor's number and subtract the dividend on how many times that will take you to 0.
2:48 Dividing any number by 0 doesn't make any sense, because when we use "n" and divide by 0 will just be n - 0 - 0 - 0 - 0... It will take you forever but the dividend is still the same. And that's why n÷0 is undefined.
2:57 Any number is equal to (number) - 0.
And that's the Basic Explanation. If I did something wrong, tell me in the reply section below!
WHAT THE HECK?
BRO IS SMART
@@itsme_Shaina Uh, are you okay there?
Thank you for this
Math is cool already, don't get me wrong, but you're gonna open the door to a lot more believers with this one.
yea, open the door alright
. math. ITS NOT REAL
lies
WRONG
MATH IS NOT COOL
@@diogocaetano1REAL a matter of opinion :trollface:
Utterly delightful!
yo legit thought you collabed on this or smthn haha
Hi there Mr. Pi
Yoooo it's the math guy
i KNEW 3b1b would comment
Hello
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.
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.
I know! It’s incredible how he can just add world building in and make it so believable
You clearly haven't seen the Minecraft series yet have you? "Fall damage goes brrrrr"
@@captainsprinkles6557 Fall damage is present, and it’s relatively consistent. It’s just less severe for rule of cool.
@@dragoknight589 Less severe? Man they jump off multiple cliffs
13:22 What do you think happened to him
Probably sent back to alan's PC.
Or if the theory that victim is using hım as a lab rat, he went to animation ve physics or geometry
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.
What is e 😂 seriously I want to know
@@stefanoslouk4183e means exponent
i means imaginary
@@stefanoslouk4183its a
The fifth letter of the alphabet
@@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.
@@stefanoslouk4183Euler's number.
2.718...
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.
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.
❤
I agree!
That’s exactly what I was thinking
That’s actually true
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
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.
Ikr
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
@@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
Incredible truly fantastic the way that you can innovatively come up with this😅
9:54 He's outnumbered.
@@erintyres3609 automath bots roll out 🤖
I love how he goes from learning basic operations to university level maths
Evening at home myc myself
We are learning most of this in 9th grade
@@ferferarry5242 key phrase: “most of”
bruh, you guys think this is uni-level math... damn
@idk-lz4nl Most of this is high school level, though the stuff in the last quarter is more common in universities.
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
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.
i like your funny words magic man
I thought I was wrong when I thought aleph-null for sec there, thanks for confirmation
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.
Main character in this is TSC (the second coming) but neat analasis
TSC is 5’ 5 hmmmmm may be useful information not gonna lie
@@Foxella2010Big brain 200 iq much?
when a stick man is taller than you
TSC is measured in pixels, not meters
Omg they made many people's least favorite subject actually enjoyable to watch
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.
Damn yes
never in my life would I have ever thought I would see something tactically reload a math formula...
And then replace the magazine with infinity
And shoot a fricking laserbeam
I love this comment
Only 3 replies... Let me be da forth
I burst out laughing at that.
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!
Needs a pin!
you forgot aleph at the end, it’s really big but sort of hidden in the background for being transparent
@@existing24As it’s the biggest infinity!
@@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.
I dont see the a + -a one
4:06 that‘s me during my highschool exams fighting these stupid e thingies I don‘t understand 😂
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.
15+6=21
@@ААа-р2м 9 + 10 = 21
@@anicepixelatedbread 2+1 = 21
@@anicepixelatedbread cos(x) = (e^ix + e^-ix)/2
0=ax²+bx+c
Some of my favourite things from this masterpiece I noticed:
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.
4:46 When "+1" and "-1" swords cross they make a "0" effect
4:48 The e^iπ makes a "-4" sword which destroys TSC's "+1" sword making it zero, and as a result e^iπ is now holding "-3". Then the same thing repeats with "-3" and "-2".
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 ∞
13:34 The golden ratio (φ) when approaching e^iπ takes smaller and smaller steps which shorten according to the golden ratio (each step is about 1.618 shorter than the previous one)
13:46 Aleph (ℵ) represents the size of an infinite set so is presented here as enormously sized number
now i respect u too
same, he probably took a long time to write this since it has 26 lines in it, huge respect
@@Exxtreamly and i am doing math homewwork rn , related to circles and R
:D
Amazing
@@plyrocea You know that he copy pasted it right?
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.
exactly like this or in some way similar?
bro that's cap, no one visualizes math as an epic battle using imaginary numbers
What? As nukes?
@@mebin3059 similar ways. I’m referring to early on in the video.
@@Beagle36 oh cool same 👍
This video just keeps getting better the more I learn about math. For example, graphing trig functions.
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.
s
wat
I agree!
the actual math:
0:06 1
0:13 equations
0:18 addition, positive integers
0:34 base ten, 0 as a place holder
0:44 substitution
1:20 subtraction
1:31 0
1:34 -1, preview of e^(iπ) = -1
2:10 negative integers
2:16 double negative makes a positive
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
3:30 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
8:22 Euler's formula + complex trigonometry
8:29 sinθ/cosθ = tanθ, function f(x) = 9*tan(πx)
9:57 limits, integrals to handle infinity
13:01 factorial --> gamma function
13:04 n-dimensional spheres
13:31 zeta, phi, delta, aleph
That guy really took the time to write all of that a round of applause
copied from me
First day
If may not be provided
cool
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.
Now all we need is natural logs in minecraft vs animation 😅
He is on another dimension, not on another level anymore
Finally, somebody said what it’s called so I can look up what the antagonist actually is.
Ironically enough, this is the first time I’ve utilized my calculus knowledge outside of school hahaha
@@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.
there's something about this i really like, how it's just an endless plane of math with all these interactive mechanism-like systems for all the things in math.
The sound design here is simply masterful, and makes the whole thing feel physical and *very* satisfying.
It shows how the stick figure adapt and try to minimize at 1:15
True
I don’t understand the last part
It sounds like a movie, its awesome
I’m 699 like
As someone who's been into math since I was 12, this is the best visualization on equations, expressions, symmetry and the true meaning of math as a whole I've ever come accross. This is not just entertainment, this is pure genius. It's brilliant.
By the way, I loved how the so called "most beautiful equation" (aka Euler's identity) shows up and basically tries to trick the stickman. That's quite deep. If you know what that equation means, it makes total sense.
Also, I loved when they got into the imaginary domain for a brief moment and everything seemed broken, then they came back to the real numbers domain at a different position in space, which also makes perfect sense if you know a bit about operations using imaginary numbers.
Every single frame of this video makes perfect sense, really.
Not to mention the overal details such as the animation, the plot, the way things build up with math concepts and ideas showing up in a logical order, soundtrack, sound effects...
3blue1brown would be proud.
Again, genius.
As someone who's been into english since I was 12, it's spelled genius.
@@annualdark as a non native English speaker, I want to thank you. Also, I must say you forgot the period, Grammarly.
Como hablante de español XD
@@hi841 Are you referring to me? If yes, I do speak Spanish, but it's not my native language.
@@RateOfChange lmao sorry
As a mathematician AND a fan of Alan's works, I can't describe how happy I am.
Same here bro
Too bad that i understood no shit related to maths after 3:52
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.
@@grandevirtude9830same
@@grandevirtude9830imagine
The little scream at 10:02 gets me every single time.
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
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!
Man 5 months of progress huh
what were the functions towars the end ?
@@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
Why are you studying math?
To the math nerd that did the equation and to the animator, heavily respected
especially in that mech section
pp entry looks pretty accurate lmao
bro both are the same person
There is literally a pinned comment saying the lead animator did the math-
DJ did it all.
10:02 BLEEEEE😂😂😂
?
The letter e 🤣
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.
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.
Can I be in your class bro
@themisleadingpath4692 I graduated already, lol. But I can head to my school and put in a good name for you /j
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)
I thought yellow would be in it cause he is a red stone scientist so he would know the simple math😊
An animation masterpiece ✅
A cinematic masterpiece ✅
A mathematical masterpiece ✅
A physics masterpiece ✅
Cinematography ✅
Sound design ✅
Everything is so perfect
@@ultraactiveGDust another bot, ignore him
how is this physics
Fr
Worm
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.
Hope vsauce sees it
8:50 what math equation did bro use to divide anything into 0💀
The function he condensed into f(•) is 9 × (sin(π)/cos(π)). Since sin(π) = 0, the whole equation simplifies down to 0 regardless of what the input is because everything is multiplied together. When he shoots the e^iπ instances with it, they get fed through a function that always returns 0, therefore they become 0.
@awareqwx thank you!
@@awareqwxbro really paid attention in middle school unlike me
@@gamarkat-officiaI They were teaching trig in radians in your middle school math class? I'm kind of impressed.
You know anything x or ‘/. By 0 is 0
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
Mathterful*
Same I wish I understood all math
I plan to study hard wish me luck guys!
Only Alan Becker can make a video about maths and we’ll all genuinely be invested in it.
Edit: GUYS PLEASE STOP COMMENTING ON HOW THERE’S OTHER CHANNELS THAT CAN MAKE MATHS-BASED VIDEOS THIS WAS COMMENTED TWO MONTHS AGO AND I WAS JUST IMPRESSED AT HOW ALAN AND HIS TEAM WERE ABLE TO EXECUTE IT I DON’T WATCH VSAUCE
Facts
Fr fr
true
Disagreed.
Fr
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.
I completely agree
+
Yes, I agree too.
Egor is too good in sound design and animation
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
12:11 the Euler’s is being nice to TSC in the end
not only did alan somehow make Euler's identity badass, he also made all of its alternate forms even more badass
Euler's formula has been badass for hundreds of years, my guy.
@@RunstarHomer Im impressed that it all made sense too, what a cool animation
He called e the negative one
facts
Your animation is more than impressive as always, but the creativity behind the manipulation of mathematics in the animation to create such a story left me in awe.
he is going to solve world huger in the next years some say he is doing it right now.
Skibidi
I love the sound design on this video. I didn’t even know if Scott Buckley was the one behind the music, it sounded so different to his past scores, but it fit perfectly! It did a great job with the “lonely void” vibe without being too overwhelmingly happy or sad.
I love the typewriter-clicky sounds throughout the whole thing, along with the digital vibe. Different objects and aspects of math have their own feel. I could watch this video without the visuals and remember what TSC is currently learning about! Really feels like you’re trapped in a Khan Academy video, and it’s perfect!
He made an empty void full of curiosity.
What are those huge symbols that appear in dark at 13:38 ?
Aleph
This should legitimately be shown in schools, so much unique intuition for basic concepts in math is shown here
They might need to slow down or break down some parts but yes
No tanto así xd el de la división no entendí
@@FireMageTheSorcererthat's what they should actually do
@@Scrufflyguy101I could see my teacher going frame by frame through the video and explaining each equation to us and the cool unique qualities and random fact about each one
@@Louis_2568teaching limits and the imaginary world would be tricky for non-calculus students 😅
This is literally 100/10. The sounds, the effects, the animation, the accurate equations and the story, they all were hella awesome. Thanks Alan.
100/10 is 10, so it's quite literally 100/10 out of 100/10 :)
The comment sections are so dumb comments💀
When a 14 minute UA-cam video teaches math better than a year of school
Like
I need to see everymath youtuber react to this! Mathologer, Matt Parker and the Numberphile gang, 3blue1brown in particular, EVERYONE!
As a general math enjoyer, I was smiling throughout the entire video at everything! I can't even call anything here "references". Everything was just correct and accurate, with visuals to match.
The sound design and musical composition were both excellent! All the sounds fit in ways that were mentally satisfying, and the music built a vibe of intrigue and determination or focus, before it went epic!
Alan and co, this was absolutely astonishing!
3b1b already commented on this :D
agreeeeed, yoo! they made a visual representation of a squared number! amazing!
@@mrShift_0044 two minutes before I did. That's awesome!
5:26 bro figured out Nanami's cursed technique 💀
Crazy
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 UA-cam after all these years and all the hassles on UA-cam. No Ads, No Sponsors, No Patreon no Merch Plugins, just the art of animation in its purest form. Incredible work, keep it up.
Same, Alan is so good.
You'd see more of it if UA-cam wasnt doing its best to kill any creator that doesn't toe the line exactly as they want it.
UA-cam is absolutely ruthless to animators. It's just that Alan's content is exactly what UA-cam likes.
Unrelated note my comment got stolen by a bot and got more likes than me. That’s pretty kooky!
I like how Alan didn’t go for a “Brains vs. Brawn” approach, and instead just made a fight to the death with math terms
Hrklo
Hrklo
Hrklo
Hrklo
Hrklo
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
π=e=3?
As an aspiring engineer I resent my brain for understanding most of it. But yeah, it’s really cool
@@AdityaKumar-gv4dj^2 =g
@@bugg4938 wut
@@jeremycaswellshh were speaking math language
1:38 the something i wanna catch it
As a math major, I think a pretty common experience between all of us is that it's very difficult to talk to anyone about this sorta stuff. It's genuinely pretty heartwarming seeing the discipline as this awesome world, and then to actually have the world itself be rigorous and sound.
You want the world to be rigorous and sound you go be a machine where everything is definite for you. As a human, we want possibilities which means uncertainty and we want everything that we could or could not never ever imagine of to manifest in front of us. I do not want to live in a finite and defined world, I want things that we could never physically figure out and a world that we could never explain.
As a computer scientist, so no discrimination to machines
@@poyenwu O...kay... As a computer scientist, do you honestly not get what OP was trying to say? This could be the start of a typical quickly escalating UA-cam-comment thread, just because of people completely talking past each other within having exchanged two sentences.
"I like that they cared enough about the math to not just make it flashy, but also sensible." and "I want freedom, complexity and creativity in my life!", are two statements not compatible within the same conversation. You might as well have entered a conversation about shark skin microstructure analysis by yelling: "I hate bacon!".
Put in its own comment outside of this thread, what you expressed would actually fit the video kinda nicely. In here it's poor form.
@@kalimer0968 Not sure what you're talking about. OP is saying how he likes people working on things that focus on the discipline of this world and for us to have a rigorous and sound world. What I was trying to say is that if all you want is a rigorous world which follows some strict disciplines, you do not need to come to this word, you could have just live inside a machine as a program since that alone can meet all your needs already. Being a human in this world, we want the ultimate unlimited possibilities, which means no rule can describe the nature of the world in its entirety (hence not disciplined), and will always have unexpected things happening which you could never (and I mean never) imagine (hence can not be rigorous).
@@kalimer0968 Also, I failed to find the sentences you qouted anywhere in this thread. FYI. I read OP's entire comment and thinks about it before I started to write mine.
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 :)
haha me too
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.
I heard he got rejected by Pixar
Okay, but how tf did I earn nearly 300 likes within just 30 minutes?
@@ThatBillNyeGuy09I have no idea.
@@keithharrissuwignjo2460 alan becker dont need pixar, pixar needs him.
Achievement obtained
0:12 Welcome to Me- I mean Math (Discover 1)
0:14 Equality (Discover "=")
0:19 No, I'm not used for exorcism (Discover "+")
0:34 Everyone is here (Discover all digit)
0:36 (Secret) What? Do it to your head instead!
0:58 Yay, I counted to 100 (Reach 100)
1:24 Going backward (Discover "-")
1:34 Hey! That's illegal? (Discover negative numbers)
1:40 Unknown identity (Discover Euler's identity)
2:19 You face the same direction (Make a negative number positive)
2:25 What time is it? (Discover Multiplication)
2:28 (Secret) Wait... It's all the same?
2:36 Separated (Discover Division)
2:49 (Secret) Why?
3:05 I feel the POWER (Discover Factorial)
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.
Lol yet another youtube "masterpiece" comment 😂
@@unaval1ble_ I learned imaginary numbers because of this
@@Sebdet9 you didn't know imaginary numbers before??
@@aic8326atleast they spent some effort on the comment instead of the jellybean comment (i actually forgot about that)
Yes kids boss fighting with e
This is one of the most beautiful videos I've ever seen, hands down. The fact that you could so clearly and visually explain some of the hardest concepts in math, from multiplication all the way to trigonometry. The animation is stellar, with every math concept perfected to beauty. As someone who loves math, animation, and Alan Becker, this is a work of art. Keep being awesome!
Complex dirivative antidiravative functions and limits left the chat
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!
Could you elaborate on that "most of the time"
@@thatonecabridogi couldn't understand shit past the half second half (prob a skill issue though)
10:16 that beam is my no.1 tech!
As a developer for a math learning app, I'm blown away by how math has been visualized here. I've been on a similar path with my project, Animath, which uses animations to explain algebra step by step. It's incredible to see the potential when you bring animation and learning together. If you're curious, I have more about it on my channel. Thanks for sharing this inspiring work, it's truly motivating for creators like me!
We are both animators I see
wow new thing created named "Animath"
@@Hur1el Yep! Animath is our take on making math more visual and fun. Glad you noticed!
@@ahmad-almazeedi you've said at the comment that you were a developer of math learning app and i want to see if the app is published? i would like to take a look.
@@Hur1elit’s not like an anime, it is an anime
Timestamps for those who dont know what some of this is
0:01 The Epic One
0:19 Addition
1:10 Simplification
1:19 Subtraction
1:39 Euler's number to the power of imaginary pi
2:23 Multiplication
2:26 Parenthesis
2:34 Division
3:04 Exponents
3:31 Fractions
3:39 Square Roots
3:50 Imaginary
4:01 Imaginary Euler's Number to the power of imaginary pi
4:09 The Chase
4:43 Fighting with Functions
5:16 Back to Math
5:21 Graphs
5:37 Theta
5:52 Radius
6:38 Pi
6:44 sin and cos
6:50 Circumference (I think)
7:09 Imaginary sin
7:19 Euler's Number to the power of imaginary pi (again)
7:26 Another Fight
7:35 Euler's Number to the power of imaginary pi turns into a Sigma Notation
7:39 Sigma Notation Shoots imaginary pi to the power of n, while n is 2 and will stop until it reaches Infinity, so he can shoot an infinite ammount of imaginary pi to the power of n
7:45 TSC multiplies the radian to 4 to have enough to make a circle and multiply the circle and the pi to make the circumference and use it as a sheild
8:24 Euler's Number to the power of imaginary pi is multiplying himself by... dividing...
8:30 not smart enough to understand that but you can see what TSC is trying to do
8:40 TSC with a gun vs Euler's Number to the power of imaginary pi apocalypse
9:46 that doesn't seem fair
9:58 DA GIANT INTEGRAL
10:02 aw he sounds cute
10:17 TSC changing the position of the circle
10:35 TSC just found the most op math function even though he only had 10 minutes to learn it while he have to take years
11:16 TSC launches himself to get Euler's Number to the power of imaginary pi
12:11 Euler's Number to the power of imaginary pi spares TSC him even though his knowledge of math nearly killed him
12:17 TSC learns for Euler's Number to the power of imaginary pi (god im tired of saying Euler's Number to the power of imaginary pi)
13:04 Euler's Number to the power of imaginary pi creates a portal for TSC
13:33 Zeta
13:35 The Golden Ratio, or phi
13:36 Delta
13:39 Thats a BIG aleph
13:49 The + End = The End (I think)
e^iπ is also called euler's identity
That is, indeed, quite a big aleph.
0÷0 of my braincells understood this.
@@bungercolumbusoh I didn't know that
13:33 that symbol you forgot was zeta
Alan Becker's videos seriously never get old. There's just something about them that just reels you in and you can't stop watching until the very end. The sound effects, the music, the visuals, his videos never lose their touch and on top of that, they are original and are so fun to watch. It felt like Orange was like a pioneer of mathematics or he was trying to fight toward finding the solution to his problem (escaping the place he was trapped in). Looking forward to the next upload!
Apparently according to DJ in AvG Reacts, the place that he was trapped in was his mind while in jail in AvA VI episode 1
@@JustAnotherCommenter That's just his headcanon lol
I see the pun head cannon TSC stuck in his head
Part l
First number 0:07
Equations 0:13
Addition 0:19
Repeated addition 0:32
Reaching ten 0:34
Adding with two 0:49
Adding with twenty 0:56
Reaching one hundred 0:58
Subtraction 1:24
First negative number 1:34
Part ll
i*e^ pops up 1:39
Subtracting negative numbers 2:12
Multiplication 2:25
Division 2:35
The power of __ 3:04
Subtracting the power of __ 3:25
Fractions 3:30
Irrational number 3:43
i^2 pops up 3:50
Adding i^2 3:58
Part lll
Multiplying i^2 3:59
e^i* pops up again 4:01
TSC brings the multiplication sign and i^2 4:28
TSC uses the multiplication sign to double his speed 4:33
TSC brings out a sword 4:44
TSC uses a bow and arrows 4:53
Complex plane 5:36
r*theta 5:59
Sine & cosine functions 6:44
Sine wave 6:49
Cosine wave 6:55
Sine & Cosines wave 7:02
Part lV
e^i* pops up once again 7:19
e^i* turn into phase two: The aircraft(AKA, e^x with x=i*pi)7:35
TSC is in the complex plane 7:57
e^i* clones himself 8:25
TSC creates a function gun 8:33
TSC grabs the 8 to make the gun stronger 9:30
e^i* is in phase three:The final form 10:01
TSC uses the displacement beam again 10:34
TSC destroyes the mecha suit 11:05
TSC us in the imaginary realm 11:31
Part V
TSC tells e^i* hes sorry for trying to destroy him 12:03
How do I get out of here? Says TSC 12:16
e^i* brings down the complex plane 12:56
Get in here. Says e^i* 12:58
TSC finally got out of the mathematical realm 13:28
e^i* meets his family members.Zeta,Phi, and delta 13:36
Bonus: Camo aleph 13:46
The End
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.
almost makes me want to do math
yeah same
Math is like drugs u can be very happy when your right but deppresed when your wrong
I love how TSC is using more and more complicated maths as time goes on. This guy somehow made maths interesting
The difference between the math I enjoy and my teacher's math :3
Unironically, something like the beginning with all the playing around with numbers and math in an open space would be a sorta cool “Im bored” vr game, seeing how different math works like multiplications and division in a 3D space, and how complex equations could play out just messing with numbers.
Playing with the Desmos calculator in VR. I love it.
This is a good idea, maybe you could sell it.
@@AbadracoI would pay for a "game" like that
would especially be cool to see those infinite 0's dropping down
i need this so badly now
please make more animations like this
I think this just proves TSC is smarter than anyone alive. He just absorbed, learned, and utilized in combat 14 years worth of math learning in just 14 minutes.
Bro became Einstein by examining with numbers and stuff
Several hundred years if we're being real here. Math is a culmination of Humanity's Effort.
@@Aku_Cyclone ???????
@@PurpleHeartE54:/
@@Rainbow_anims It's facts though.
So far, this is the best action movie in 2023!
Adu anh vfact học toán
Video mới là gì thế anh zai
I can’t believe Alan is making his own Number lore now… ✊
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.
Yes
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.
ALLAHUAKBARRR!!!!
@@Meryemjajawhy tho
The details are amazing in this video
@@BIackholeikr
13:45 is Aleph-0. It's larger than infinity
I showed this video to the whole class and it was really incredible. It was definitely the best work I have ever seen. I really like the feeling of vividly and visually deducing mathematics, from simple to complex, from small to infinite. As a fan of science and aesthetics, I really hope this series can continue and look forward to the next issue of Animation vs. Physics or Chemistry
I really want to watch vs. physics.Motion,force, heat, light, electricity,atoms to galaxies, stillness to the speed of light, combined with such a plot, it's absolutely amazing
Physics is gonna be crazzy
Guys, I did not understand what those letters were at the end, help me? And, yes
I Russian
And best part is that you can tell your students to just replay the video in slow motion for them to grasp something way better than a book can.
@@Mir_v_takt I recognize only the beta sign so if I had to guess it's probably the Greek alphabet but I'm not sure
i like how in the beginning, euler’s identity escaped quickly, indicating a lack of fundamental understanding. But as the second coming learns more and more, he becomes more and more capable of keeping up with euler, eventually figuring out how to defeat its dimensional trickery with i, and making peace with it once he understands the prerequisites. very well done animation !!
The second coming
The Second Coming, not The Chosen One :)
It's like the story of very much people who decides to learn maths
That sounded like a beautiful literature analysis of a math animation. I like it!
This is insanely cool. Not only it looks like a cool fight animation, it actually shows the origin of functions and concepts as TSC discover them. To be honest, I only understand the math up to ⅔ of the video, and still it felt very amazing. I can imagine how fascinating this is to people who understands all the math shown here.
YES!!!!¡¡¡!!!!¡! I really wanted to say THIS THANK YOU
What is TSC?
@@PrinceShehzad name of the orange stickman with the hollow head
@@8609pp Oh ok.
What does TSC mean? Is it an acronym?
@@PrinceShehzadIt stands for “The Second Coming” (orange guy’s name)
WE BE FIGURING OUT HOW TO PASS MATH CLASS WITH THIS ONE🗣️🔥🔥🔥🔥🔥
I notoriously hated math cuz I was never good at it. But the way Alan makes this stuff look like fun is forever baffling to me. I’m so floored by this, this just further solidifies Alan as my favorite animator ever. Dude just can do anything with his team, props to everyone that helps him and all of that because you guys are always unmatched. I love this channel, still is one of my greatest inspirations to get into animation. And always will be 🙏🏽💖
If only the animations could be done in an instant
it's specifically helpful with the 3d part of it (the enoumous amount of 1's), cause calculators never explain whats going on.
You deserve more likes
Same (i need to learn more cuz i'm too bad at it ;-;)
It’s awesome how it all starts from 1. Then an equal sign appears, and the math begins to slowly evolve through addition, subtraction, multiplication, division, parentheses, exponents, decimals, square roots, fractions, and then into calculus with summation, pi, infinity, etc.; then into geometry with circles, radiuses, sine-, cosine-, and tangent waves. And finally, it ends with an epic battle of e vs. Second Coming. This is legitimately one of the coolest things I’ve ever seen!
Second coming?!
You forgot the "The" in The Second Coming
Th second comingis in a whole different animation
You mean e v orangs
@@Twilight_upon_12_cycles both names works
@@orangeheartguy a
I can't even imagine the amount of genius, effort, and elegance dedicated to this work. You're special. Single best math animation story I've ever seen!!
Math lore
It's not just him bro there is a team behind it
its garbage i can do better
The only math animation story you’ve ever seen
Ishan Awasthi from taare zameen par guys
It says exit or is it just me 12:29
yeah ..he wants to return to his home.. where his friends and alan are
@ Oh
The whole time I never noticed
@ I thought it was just me
Can't wait for all the math channels to do breakdowns of this video. It's incredible how much is packed in here.
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
Even in a slowmode /100 i'm not sure you would have time to explain everything 😄
@@etakiwarp I wanted to check the math in the video and I had to use frame advance in some scenes.
i came here from a breakdown of the video
Can we all take a minute and appreciate the sound design here? It makes the action and visuals so much more enjoyable than they already are!
yeah man, sound design is the most impressive here, also how he signifies actions
fr
Yes
What but I can't hear any sounds is it a problem on my end or is this a joke?
@@asafapowell4813turn up ur volume, restart ur device, wear earphones. The sounds are really cool /srs
I've heard for years now that Euler's Identity was 'the most beautiful formula in mathematics', but I feel like this video represents an actual proof of that. This is a work of absolute genius.
where's the proof
@@ericsombody8912the number is more smarter than the normal things
@@ericsombody8912in the video
The finał equation if prolly the proof (via induction i believe)
1:02
Green does not exist.
Blue does not exist.
Red does not exist.
Yellow does not exist.
*He does not exist.*
*He does not exist.*
*He does not exist.*
*He does not exist.*
I swear Alan is just a machine that takes in ideas and churns out beautiful animation and stupendous sound design! Everyone involved with this project (and others) deserves the best!
Skynet but it's into art xD
Did the second coming just break the entire concept of math literally
This really feels like Alan's old animations, before they became a series. Something exists, it gets explored, big fight, bigger fight, biggest fight, then end. No context, nothing.
Except, now the quality of animation is something exceptional.
even before the quality was great tbh
not exceptional, exponential
@@fitzchevalerie6597 Erm... what? Exponential means something that is increasing at an increasing rate. Exceptional on the other hand, means something different, unique; incredible. Just another fancy word, but fits the context and I fancied using it for no reason. Exponential doesn't fit the context?
It fits because we're talking about the quality, it gets better and better each time at an increasing rate, finally, I think exponential is more fiitting and it has a strong bond with maths, wich is the subject of this video, I hope I was clear
@@fitzchevalerie6597 That is a nice viewpoint, but I think you should have worded it more clearly. I thought you were suggesting to just switch the words, when that breaks the sentence completely, but it can be reworded to fit "exponenttial".
Other than that, pretty great pun :D
10:03 goofy ahhh scream
Only a person that 'understands' maths well could make a animation this beautiful.
E
*math
So anyone
@@fetch300meth
Cool
As someone who has taken multiple calculas classes the accuracy and detail in this animation is insane. Well done. Although a great animation is nothing less of what I'd expect of Alan Becker and his team.
Indeed
Can you explain what that "e" thing is then? The one that is seemingly "sentient" in this math world? What does it mean and why is it the only thing that can create those "portals" to what I assume is a dimension to imaginary numbers.
why is the funniest letter have the funniest role
@@TheEpicGalaxy21e is a very unique number in math. It represents an actual number like pi. For example the derivative of e^x is e^x. e is also used a lot when it comes to interest calculations.
this*
This is a certified banger of a video.
It presents maths to all ages in the most cool, accessible and simplistic ways possible, showing hard and abstract concepts in understandable ways that can only be done in animation.
It rewards those that have spent their lives on the subject. The pride in knowing every equation, every proof and every little Easter egg, is validation and recognition for their efforts in learning and expanding on the vast sea of knowledge that is mathematics.
It helps people that are in the middle of learning math. It motivates the demotivated by displaying how cool maths can be, and guides those that are struggling by presenting concepts in fun and simple ways.
Most importantly however, it inspires and draws people to math. Those that never tried math will be inspired and those that dislike math may give it a second chance after seeing how cool maths can be.
This is one of the best, if not the best, math videos of time.
I agree tbh
😢
Top Ten Most Emotional Essays of All Time
Well said,well said
cool yeah, simplistic IDK man, seemed like Nolan stuff to me
The music is terrifying with the void stuff which is creepy but This is one of my favorite parts of you Alan! I Just Keep watching it, Its to good!
This man just gave the sentence “imagine maths are a videogame” a whole new meaning
There is a math game called Baldi’s basics
And the sentence of "imagine math is weaponized"
...You could pick up the sword, the bow, or the arrow...
Obscure reference :)
@@autumn_sunday Gumball reference moment
Video games are made through math.