Trees: The Most Versatile Structure | From Computer Science to Set Theory
Audience: undergraduate
Tags: set-theorytreescomputer-science
What do file systems, websites, binary search algorithms, and infinite mathematical sequences all have in common? Trees. In this video, we explore the many lives of trees across computer science and mathematics; starting with familiar examples like your file explorer and the DOM, and branching out into data structures like tries and binary search trees. Then, we leave the real world behind and dive into the world of set-theoretic trees: structures that help mathematicians explore infinity, build fractals, and make sense of the strange shapes hidden in logic and topology. Whether you’re new to data structures or deep into descriptive set theory, this video shows how simple rules can create complex objects. Created as part of the 2025 Summer of Math Exposition, hosted by 3Blue1Brown.
Analytics
Comments
It gave me that sense of making connections between different ideas that I really love in Math. Really well organized, high quality video with thoughtful narration and helpful animations that really added to the narration. Great job!
While I had heard about trees before, this video had some real-world examples (except maybe the last one :D). So I got a better trees and their applications, without going into too much math. The illustrations are also good and I liked the content of the homework folder in the video. There were quite many definitions in the beginning of the video but the color coding made it easy to understand each definition.
Most of the video was quite math-free, but then you started talking about complexity and O(N) and O(log(N)) and I believe some people with a non-math background or who have not dealt with complexity might have trouble following you there.
pleasant and interesting browsing of tree structures.
Nive way to tease the curiosity of students
I love the humor and the structure of this video. You also explained perfectly Binary Search Trees - how they are built, their advantages, and possible problems. I would suggest writing some of the things you explain on the screen, since I think it is easier to pay attention and remember than if you are just listening. For example, when you mention the complexity order of finding a number in an array, you could have added O(n).
I like your content because it’s engaging and informative and structured so that a novice or expert can know what to expect. I also enjoy your narrative voice, and the pace and explanations are straightforward. I hope you seek to improve upon video editing. What I mean by this is that although this video is well structured, there are moments where the viewer is left with a black screen then there is an abrupt transition into the next topic, or a reference image to what is being said. It’s possible this might be a deliberate design choice, which I don’t mind in terms of style, but I think user engagement and attention would increase if you placed transitions the way you did with those elegant section overlays where each section presented a similar style but a different color. This is all to say, I hope you make more content and hope to see you for the next SoME event. I’ve rated your Ranking score as an average of these individual scores, good luck! Motivation: 9 Clarity: 8.5 Novelty: 5 Memorability: 8.5
Excellent! With how broad of a range of topics this video covers, you really feel how versatile the concept of a tree is. The examples are well-motivated, and everything is conveyed in simple terms or adequately explained jargon. Given the ubiquity of trees, I assume I’ll end up thinking about this video soon enough in the future.