New discoveries as a collective effort from folks in the comment. Updated June 29th 13:00 PM. 1. 14:47 phi is clearly the golden ratio. As many people pointed out that its step size decreases when it approaches. I also noticed that delta shakes while moving, indicate the infinitely small difference it often represents. Zeta jumps with a constant step size, which is a clear reference to the Riemann zeta function. 2. Another small mistake I found, if you pause at 8:34, you will see that the term with 9! is already shot, then at 8:35, the running index still starts at 9. Only after firing the 10! term, the running index becomes 10, which is not what summation index is usually used. 3. I made a mistake at 14:23, e^pi is not the volume of all high dimensional unit spheres, but the volume of all even-dimension high dimensional unit spheres. Zach star has a video on this: kzfaq.info/get/bejne/o76gZLmYq73Ge5c.html 4, At 14:36, the running index starts at infinity. The concept of adding volume of spheres from higher of higher infinity is shown in earlier a few seconds but technically at 14:36 the equation no longer holds. In case you want to derive this on your own, be careful. 5. At 9:55, yes TSC has another secret ally that stole the "-" sign at the very left. --- A note on the primary math concepts' discoveries. It is hard to find the exact dates and civilizations of those discoveries. I did my best to do the research. Some people pointed out different opinions. Thank you for sharing, which made the picture more complete. Again, thank you all. It means a LOT for a new channel like this one.

As a pretty amateur programmer I'm liking the idea of making a game like this. Imagine how funny it would be to tell your friend "okay so, stand on top of this number" and then divide it by zero and launch his character to the void out zone and kill him lol

oh boy, cant wait to be able to understand this all this year, the engineering degree calls for it

IS NO ONE GOING TO APPRECIATE THE SOUND DESIGN?! The music feels EXACTLY like how i felt when discovering these concepts while tinkering with math!

"Is it possible to learn that much information in only 15 minutes?" Python: *yes.*

I love that Aleph has no real physical form either. It's so all-encompassing it's just a shimmer in the background. Literally unreachable (no amount of addition, multiplication, potentiation or factorialization of finite numbers will ever reach it). Essentially it is the "stage" upon which all this plays out.

You may have missed one at the very end. Phi (that circle with a vertical line) is used to represent the Golden Ratio, which is related to Fibbonacci. And if you look, as Phi went further in one direction, the steps it took changed in size accordingly.

the fact that TSC knows how to make a bow, machine gun, and orbital strike in the numbers void after under 15 minutes just shows how smart he actually is

hi, this is way better than the analysis I or anyone else has ever done on it. dates, context, everything! this should be way more appreciated and I want you to know that you have smashed it when it comes to analysis. Ty \o/

The animation is absolutely genius. I wonder how much research and math they had to do to make it accurate.

One thing that you missed, which is vital to understand why the 3d space works in the first place on a 2d representation, is because @7:20, when the stickman splits Pi into cos and sin, it's actually "cos(t)" and "sin(t)". He essentially creates the time axis. From 7:26, you can see that as the axis progresses, it has a "t" written on the front the the axis which is basically a time axis. So everytime the stickman bangs the circle with the sin(t) and cos(t) onto the f(●), he basically fires off railgun ammo @11:45 onwards. This is just fucking brilliant. Alan Becker and his team are mind blowing.

The fact that you can find every possible mathematical reference in the animation is amazing

Wanted to chip in with some stuff I noticed. - This is mentioned in another video, but TSC and little monster are both real numbers. That’s why they can interact with the world, why TSC can multiply his speed and change location, same with LM. But more importantly, they’re both real numbers *on the x axis.* They’re not just stick figures, they’re technically the coordinates with the locations (TSC, 0) and (LM, 0), because those are the only types of coordinates that are real in a complex plane. That’s also why when they want to go upwards, they add multiples of i to themselves, but don’t go into a different plane until they multiply themselves by i. Since as real numbers they can add i values and remain in the complex plane, IE change their coordinates to (TSC, 5i) and (LM, i). - When they’re moving, their coordinates (TSC, 0) and (LM,0) are changing, with LM and TSC increasing at a certain rate, the speed they travel (since this is physically what speed is, the rate at which a coordinate changes). So when TSC wants to increase his speed he multiplies himself, making the rate at which he changes faster (or making the initial value being multiplied higher, tho I suspect it’s the former because of the negative trick I, about to get into). - Speaking of, the negative number trick is actually consistent despite being used in two ways. In the chase scene, since LM’s coordinate is changing at a specific rate (its speed)TSC uses a negative to change LM’s velocity. Changing a velocity of a given point to a negative turns the point in the opposite direction (something that shows up again later). However, at another point in the vid, TSC uses a negative to get to the other side of a circle. Inconsistent, right? Wrong. The reason the second negative teleports TSC is because he’s both not moving, and on a *coordinate plane.* His defining characteristic on a static coordinate plane is his position, *not* his velocity. So rather than making his velocity negative, he made his *position* negative. So rather than reverse speed, he teleports to the other side of the circle, since that’s what making a position negative does. To simplify, first time he turned the equation LMm = x into LM(-m) = x, but the second he turned the position (TSC, 0) into (-TSC, 0). - And for my main point: The “blackworld” they were in was *consistently* a complex dimension (minus maybe the parametric bits), that’s why every time he wanted to move upwards, both LM and TSC had to use a multiple of i. Since that changed their positions from, say (TSC, 0) to something like (TSC, 5i), which was represented physically by height in blackworld. But the blackworld is only imaginary on *one* axis, the y axis. But the “other” dimension had *two* imaginary axes, with the x also being imaginary. Now, TSC and LM, as established earlier, are real numbers, but getting into the “other” dimension requires changing the x axis of a point to *also* be a multiple of i, which is why little monster and TSC had to *multiply* themselves by i to get there, otherwise they’re still just real numbers. - The other dimension had square roots of negative numbers throughout it because it’s the *imaginary plane.* Thus numbers that are only represented by i in the blackworld are represented as their “actual” values in the other dimension, IE as square roots of negative numbers. Also the *reason* square roots were spilling out of the cracks because TSC’s cannon was “cracking” the x axis of the imaginary plane…which was as mentioned earlier made up of imaginary numbers (ie square roots of negative numbers). - Also, TSC wanted to get into the imaginary plane because it was another dimension, and he wanted to return to his home dimension. LM had to clarify that multiplying himself by i multiple times would just send TSC back to blackworld, since TSC = real number, i x TSC = imaginary, and i x i x TSC = -TSC = a real number. Hence why he needed a more complicated equation to actually access other dimensions. - Note also, when LM is demonstrating why just multiplying by i won’t access higher dimensions, he, changes positions. Specifically, he’s flipping around the Y axis. Why? Because i x i x LM = -1 x LM. Since LM’s actual value, e^(i(pi)) = -1, is -1, and he’s flipping his value from (LM, 0) to (-LM, 0), he’s going from position (-1, 0) to (1, 0). He’s doing what TSC did earlier with the negative, only in this case he takes a detour to the other dimension first before teleporting to his new position.

"Banish little monster to negative infinity" at 9:13 Is just so stupidly funny without the proper context

I cant stop rewatching this video cause i wouldnt stop until i found an explanation for everything and you have done that. Btw the dimension part near the end is a reference to the imaginary dimension i think Edit: TSC is a real number because the imaginary dimension collapses if you add a real number to any imaginary equation and the imaginary dimension is a dimension of equations made of imaginary numbers Edit 2: TSC is confused when dividing by zero as somehow 6/0 doesnt equal to 6/0 with the other division sign

12:48 i think that's the branch cuts actually. Sqrt(-5) for example has multiple solutions, and just as those are called branch cuts, there is a rift in the world, cracking it apart.

this one is amazing, explains things quickly and is still entertaining

I’m honestly glad this got recommended. I already admired Alan’s style of animation and to understand the meaning behind every sequence as well is probably the best thing I could’ve asked for in recent times. Thank you!

This genuinely deserves alot of attention, You focused on every single bit of detail here and gave a very well splendid explanation, Sure im dumb af, But watching this was very entertaining and made me learn a few things. My hats off to you brother.

I love how expressive Alan animates. For a stick man with no face and a letter, it's pretty easy to tell how they're feeling

13:52 eipi is demonstrating that his "doors" would not help TSC escape, as going through it 4 times would result in the original position (i^4=1)

I'm surprised this only has 1.2k views right now, beautiful art, this is something I always wanted, a sort of show which displays math so I could avoid learning it and kinda take it all in as a form of a show

I'm not an entirely big math nerd, but as I'm glad someone was able to explain some of the bits I wasn't able to get (which I was strangely able to grasp a lot of the concepts). :)

7:35 Would like to note that splitting pi in half also made the halves resemble "t" with sine and cosine on top, equating to sine/cosine over time, and thus creating a graph.

this video made me realize anything can be beautiful as long as you understand whats behind it, how it works down to the core, the meaning of it. what you do with it next stems from passion. thank you a lot for this, i saw the original once but didnt give it a second thought. beautiful.

As a math and physics student, I was so impressed and excited. I've always loved interpreting math concepts in a creative way, the idea of ​​merging math and "art" is smart, it helps to better visualize concepts (and understand their usefulness) Shout out to the 2x2 bow, the design is so cool !

9:52 There's actually a third, on the left you an see a Little Monster facing the other way holding a negative sign. If you look back you can also see it moving away from TSC

This is one of the greatest videos ever produced by humanity. PhD level knowledge of mathematics storyboarding,the music the animation the concept and execution is mind blowing

This is bonkers brilliant. I have always believed mathematics should be taught in a more playful and engaging manner. We all know the intricacies behind mathematics and not everyone can handle the deep abyss of the field. But what I am saying is that I want more people to think mathematics as something else other than stressed moments in their life filled with souless homework and tests. Alan Becker did an amazing job, and you Python with Prosper did an astounding job on taking the time to go through all the details in the video along with bits of history that just makes the video more flavourful. Thank you for putting in the effort for this video. I wish you success. Also Imagine if Brian Cox for narration, that would be insane.

12:36 Notice the 90 degree rotation

3:12 Since the / sign is more commonly used in programming I'mthink that bit's a reference to how division by zero won't compile into usable code and for TSC doesn't have an output, not that there is no answer ;) Amazing video, love watching this type of breakdown!

I can't believe that these characters, who don't speak, have better character development and a more satisfying arc in 10 minutes than some some characters from big budget studios are able to have in entire seasons (looking at you "Rings of Power"). What's brilliant about this video is how it's sort of a pseudo history of math, but done in the most creative way possible. Alan Becker is an actual mad man for making millions of people in love with characters who are literal numbers and letters, it's like Alphabet lore all over again.

this kind of analysis is great because i learn a lot more about the history of math and some concepts like the complex plane

This came out just in time I have been helping some relatives with summer tutoring in math and the kid is brilliant but unmotivated, I showed him this video and his response was absolutely golden: "WHY DID NOBODY TELL ME THAT MATH COULD BE THAT COOL!!"

There's an easter egg mentioned by another from Bilibili at 2:11, we know the formula's answer is -1, which means TSC is "-1" as well when he stands behind the equal mark.

i think the imaginary door that TSC wants to go thru is actually gonna be to rewrite flash in pure math.... which would be Animation vs. Code (Animation vs. Math part II)

I love how Alan was able to make an entertaining video while also teaching us math! He’s a legend!

0:09 “God created the natural numbers; all the rest is the work of man.” - Leopold Kronecker

This deserves a million views, dude! This is amazing! Alan Becker should see this!

This is really more detailed than other explanations out there Nice job man

When I reached the animation character adding ones and you mentioned induction I knew that this video is going to be the most accurate analysis I will watch. I thought it was an obvious reference but others missed it.

Wow! This was amazing! I got a lot of it while watching but this showed so many things i still missed! This is probably the best break down video I've seen and it is SO GOOD and the references are ON POINT! Great Work!

Very in-depth explanations, educational, and humorous! Massively underrated.

A true masterpiece by Alan This video taught me so much about the lore of math, some math breaking stuff, and other cool stuff All of this is amazing

Honestly, dude, you did a very good job explaining this. Props to Alan Becker and his team for making this masterpiece. I'm currently looking forward to becoming a programmer. Best of luck on everyone's dream. o7

thank you for deciphering this masterpiece! I feel like I learned more than I ever had.

I have learned more about the foundational uses of mathematics here than I EVER DID in school. I have been studying this second by second since I first saw it, and my understanding of math has only gotten stronger from this. Thanks for making this video. I already loved mathematics as a whole, but this just gave me an even greater appreciation of it.

honestly i was never really interested in math due to how boring the classes were and i just didnt find the fun in learning math and then this shit drops and im like "WHAT"

As someone who really struggled with math this video is just as great as the original with explanation of how things work in a basic sense. Also infinity is scary AF, constantly reappearing

You are the one who caught the minute details(like using x to gain speed, the bow made of 2x2 shooting 4), that every other channels missed. Thank you for that.

I'm a fifth grader, when I grow up, I'm going to study math at college, and then I'll watch this video again, and I think I'll understand almost everything.

I believe the imaginary world cracking is simply due to the energy being released by the huge circle. At 13:04 you can clearly see that the black/cracked region follows the energy ray with pretty much the same angle/inclination, as if it were an extension of it. At 13:18 you can see the cracks on the floor caused by the energy, and at 14:02 they "heal" when e^(iπ) stops the circle and brings it back.

Thanks for the run down! I was able to pick up on more stuff from the video thanks to this!

This is the best interpretation of the "Animation vs Math" video! Learned few information regarding Math's history. Very nice indeed. Thank you. Btw, I love the original video background music. It's a thrilling one but encouraging.

NICE Its probably better than the other one I watched

This video is pure gold for math addicts !

I love this version of explanation because you point out all of the history references.

this is actually amazing, good job on this analysis!

9:40 damn, the allies are so cute

This video started to make me love math. I mean what Alan did and that's it. :)

This one is one of the best explanations of Alan's that video. Marvelous!

Best analysis I've watched so far!!!!!

Finally, math becomes fun for once, now i can learn even better

11:43 *"It's over Anakin... I have the high ground."* *death ray*

Thats one of the most coolest thing I've ever seen. Great job.

both the idea and making of animation took an immense effort and time

11:14 “WAAAAAH” Edit: Alan Becker did the animation but not just thank him, than one of the people working for him who is a complete math wiz B)

13:45 Makes sense, because iiii = 1 and 1 * e^ipi = e^ipi

bro you put a lot of effort to explain each thing....appreciate it mate

God, this was so much more interesting than the others I have seen. Great job

I think at 14:50 phi is Euler's Constant (0.57721). It would make sense that they're friends! :)

as a middle schooler. I don't feel so bad only being able to barely comprehend the information up to around 6:00

I am so happy to see this, the music , the creativity, everything just looks fantastic

Thank you for the explanations in this vid!

Do you want to mention that (sometime during or after 6:42) that the letter r here is the variable for the radius of a circle? r = 5 when The Second Coming first looks at the variable's value, but then he adds 2 to increase the radius to 7, and then subtracts 5 by 2 (by flipping the expression) to make it equal to 3.

I thought that TSC gets more speed from multiplication because he multiplied his own velocity

This single 15 minute video made me learn more math then 9 years of boring 40 minute lectures about it. Thank you!

This is the best analysis i could find! Great job!

I believe you should be tanking Terkoiz as well. He's the one with the idea for this and the lead animator for this I think.

9:28 Why is it perfect

The 2nd analyses of this video I've seen... both have given me deeper and deeper appreciation for the video as a math smooth brain.

This is so cool! Thank you for explaining all of the complicated functions and math show in Alan's video... I never realised he wrote "exit" lmao.

i was like 'i understand this' :) and then at 11:00 I just lost it bro wtf is happening anymore

12:42 Imaginary number crisis ?

Genuinely a superr impressive analysis!!! Great video!!!

Beautifully done.

someone needs to make a full on series on this like come on. I would love to watch mathematics like this more come on you can do science you could do chemistry with this

At 2:03 you mention TSC, what is TSC?

This taught me things. Thank you, and the original animator!

this is my favorite one out of all the analysis videos

I understand everything up until the unit circle and complex plane, I am now scared for pre calculus next year

0:43 my guy 0 didn't appear casually in mesopotamia. 0 was invented by Hindu/Indian mathematician Aryabhata. Have some respect to those that we have today so advanced in maths

hella underrated man, you deserve more subs

"math is a gift from above?" nah, math is a curse from hell

Thanks for the reference showing.

Yessssss finally was looking for someone to explain this

Is it normal if I teared up watching this? 😂 So beautiful and the explanation makes it even more glorious, even though I know nothing about it

this is an amazing explanation of that video, thank you for making this, amazing job

This video is really showing the beauty of fundamental math nature. Brilliant.

Wow, really great video; both the original and your explanations. I did the German finals this year and had to do math orally. What confused me was that the questions weren't this typical "here is a formula and here some numbers now deal with it" but rather seeing if you can grasp the complexity of the topic and the logical connections. An guess what- that was so much easier for me! So yeah, math can be fun and interesting 😄