The Math Theorem that just SHOULDN'T work

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Tools used to create this video:
- Affinity Designer (icons and graphics)
- Powerpoint (animations)
- DaVinci Resolve (video edits)

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Music credit:
"MAGIC TAVERN" by Alexander Nakarada

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Keywords:
matrix tree theorem, Kirchoff theorem, Gustav Kirchhoff, graph theory, linear algebra, spanning tree

[keeperofthelight]

Imagine you hit a tavern but they discuss mathematical adventures there

[jumpydino]

came for the math. did not understand 80 percent of it. stayed for the celtic music

[BoBoNUto]

at first I thought the music choice is odd, but it fits so well and conveys the feeling of exploration in math, great video!

[nestorrente]

As someone who has a small background on graphs and matrices (I studied a computer science degree), I understood the explanation perfectly. It's true that the video doesn't explain how to calculate the determinant, which may be confusing for those who doesn't know how to do it, but the rest is very well explained.

Very interesting tho! This relationship between the determinant of the submatrix and the amount of trees is like magic 🤯

[andersbahrami]

I thought this was perfectly paced for my level, I didn’t have to pause or skip forward a single time the whole video and I was left a bit of room to think! I haven’t taken a linear algebra course but have seen matrices and the determinant used frequently and this level of explanation felt perfect. The relaxing vibe was the cherry on top!

[yuwumi]

Interesting video and nice visuals. One small critique, when first transforming from graph to matrix, consider labeling the nodes. Obviously still a neat little video but something small like this could help people in the future

[LordoftheFleas]

The transition from graph to the matrix using the edges as ones is so beautiful!

[suseJattackIsBack]

Super cool video! Long time no see the Consolas typeface being used this effectively! Going to check the blogpost!!🎉

[therealpancake]

This is such a good explanation. I can honestly see a problem like this popping up in a competitive programming competitive, and if I ever see it now I'll know exactly how to solve it. The bit about the determinant left me curious for more so I'll definitely be checking out the blog post as well! Grateful that the yt algorithm showed me this, it's a very interesting video and a perfect explanation

[Ruktiet]

Great video with nice visualization!

To be honest, I had problems understanding this connection between these seemingly completely unrelated structures when I first learned about them, but realizing these possible graphs and their matrix maps are simply a subset of all the possible square matrices (that is, functions from [n]x[n] to a real number, or even integer in this case of laplacians) without considering linear algebra just yet, demystified everything for me. This subset has properties in it’s rows and columns which translate to the original graph. Even though matrices are used, they are at this point still unrelated to linear algebr and are nothing more than a quantified rectangular distillation of the original graph.

But given that almost anyone ever sees matrices of numbers in the context of linear maps such as seen in linear algebra, it is only human to try out if any of the tools from linear algebra lead to any useful results, and apparently, it does, which led to the fruitful field of algebraic graph theory.

[zakariaabderrahmanesadelao]

What a video man. 0 words spoken but conveyed all necessary informarion. Brief and concise yet very precise. The music is a plus and the animations were very much appreciated. Thank you and subbed.

[Red-Brick-Dream]

Graph theory is the most humbling thing I ever encountered in my undergrad. I always felt like I was being tickled by the leaves of some great tree that I could never fully explore. A structure that seems so simple up close, but whose true breadth always slipped through my fingers.

Great video. Thank you for this little walk through the forest.

[migyah]

When you invent a formula at an exam to get the right answer

[noahlibra]

That was the perfect pace for somebody unacquainted with graph theory. 🙏🏻. I’ll read the blogpost later as I’m more interested in why the determinant “counts” the combinations.

[rmt]

I mostly tuned out because there were no verbal audio, but the music was pretty.

[tomahawk]

I'm not even interested in the maths anymore. Put me in a dnd world with this music

[tcaDNAp]

At first I was puzzled by the music replacing a voiceover, but I realized it's the perfect video to leave on the TV at a party! I'll show the paper to people I catch watching 😛

[ezikbro]

At first I thought that this music video has a really strange name for the song

[mipasabiyanavril]

I hope more math videos has an epic enchanted celtic bgm like this

[jacobsiehler]

Beautiful presentation of one of my favorite theorems!