Jesus Christ the sound design underneath the animations is soooo well done, love the use of some classic fm and the plucky pitch attacks for asmr clicks

This scratches a brain itch I didn't know I had..

Love when “naturally extends into a hypercube” is a throwaway line. That’s how you know a graph theory video is gonna be good.

WHY IS THE QUALITY SO DAMN HIGH. MY INFERIOR EYES WERE NOT MEANT FOR THIS

hyper advanced math with ungodly editing gotta be my favourite movie genre

I love that you can classify how "hard" a game is by how easy it is to traverse from one cluster to another. I wonder how well other games and their "moves"/"degrees of freedom" can be broken down and visualized, like sudoku or the ball sort puzzle. Seems very interesting for generating levels and classifying their difficulty.

Completely alien editing work man, insane

I'm a physicist and genuinely don't think I've seen an explanation of state space this good anywhere. This is one of the best videos I've watched in a long time!

4:46 "let's take a tour around this graph" *proceeds to send me to another world with the most beautiful melody i've ever heard* then I'm hit with the melody at 6:31

at 6:17 I legit felt like I was discovering an alien spaceship

Everyone's rightly gaga over the visuals and sound, but as a math sometime-YouTuber, I want to call out the excellent choice of topic. Everyone's familiar with sliding block puzzles, but not with moduli spaces, and this is a really friendly example. EDIT: It occurred to me that instead of making a graph as he does, where the vertices have real meaning but the points along the edges don't individually, he could consider all real positions of the sliding block puzzle, where blocks are allowed to slide non-integer amounts. This would have the effect, for example, of replacing the semi-triangular grid at 2:12 with an actual solid triangle. It would then be interesting to figure out what homotopy types are achievable as the moduli spaces of positions of a sliding block puzzle (in various dimensions!).

gosh, so this is why my math teach kept saying "math is beautiful", I'm starting to feel it

not only is the math/logic of this incredible, but the way you presented it is just art at its finest

i feel like a flatlander who has been sucked into the 12th dimension

Math PhD here. I subscribed today and watched some of your recent videos. The visuals, sound design, and the choice of math topics fits so incredibly well. Kudos!

I watched the whole video, learned everything, understood nothing, remembered a little, forgot how to breath, remembered my death, saw the color of infamy, and fell awake

This is what you feel when an eldritch being shows you the complexity behind something you think is extremely simple

sorry babe i can´t make it to our wedding today, 2swap just uploaded and i need to watch it

Your channel is incredible. I genuinely don’t even think I’d know where to begin to make something like this.

Absolutely gorgeous visuals! I wouldve never thought such a simple puzzle can create such complex and beautiful structures and similarities!