Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

How a 4000 Year Old Game Broke Mathematics

Audience:

Tags: infinitesimalsinfinityrecreational-mathematicsgame-theorycombinatorial-game-theorygoboard-gamenumber-systemsmathematical-games

Go is one of the oldest surviving board games in the world (believed to have been created by Yao, an ancient king of China, almost 4000 years ago), possessing more legal positions than there are atoms in the observable universe. Yet, its highly complex endgame led mathematician John Conway to a profound realization: games and numbers are fundamentally the same. This video explores Combinatorial Game Theory by starting from the simple rules of Go and building up to Conway’s Surreal Numbers. We journey from basic territory counting to fractions, infinities, and infinitesimals, exploring concepts like game “temperature” and the “chilling” operator.



Analytics

6.16 Overall score*
53 Rank
22 Votes
16 Comments

Comments

7

At around 01:30 you should have used a real game. Overall, a very nice introduction to GAMES and surreal numbers!

8.8

Great video! I haven’t seen any other video bridge go and modern math! Very novel topic, I also enjoyed the animations and the mix with the real footage of the board.

9

the video articulated this new idea very well for me surreal numbers do seem very interesting related to the game of go

a literal new category, of these, wow

i will go chill my games now

9

A remarkably clear and engaging exposition. I especially liked how the video moves naturally from the simple rules of Go to Conway’s much deeper idea that numbers themselves can be understood as games, and then brings the abstraction back to concrete positions on the board. The visuals and examples make a difficult topic surprisingly intuitive and memorable. Excellent work!

6

The game could have been explained a bit better which would have helped the explanation of the math later on. The introduction kept me hooked to keep on watching. The concept of temperature might have been better explained with the hot potato analogy before explaining the mathematics of it.

1.3

Sureal numbers are certainly fascinating. However, I found the pace of your video to be too fast for me. I read about sureal numbers many years ago and have forgotten most of the details. I would have appreciated you spending more time on the basic definitions and examples so I could rebuild my intuition. The videos of you placing stones on the go board might have been more effective if you had used animation and indicated the places on the board as you mentioned them.

4

Coincidentally, I was looking for a video to learn more about Go, so this video was the perfect opportunity! The explanation for simple Go games were good. The ideas are interesting enough to make me check out the references.

Sadly, the goal of the video was unclear, as a result, the video turned out to be a collection of great but not well-presented ideas, terms like “simplicity theorem” are used before they are explained, the “chilling” operator’s significance is unclear, the famous Lee Sedol game is shown multiple times but never discussed and concepts learnt in the video aren’t applied to it. The title of the video is about breaking math, which I assume was due to “infinitesimals”, but again not enough care was devoted to it.

8

Thank you for making this video! You’ve introduced me to this incredible game!

3.1

I think there’s a really good concept in here and I’m glad you made the video, but I really couldn’t follow it. I think you might need to slow down in several places and really flesh out some details (and I’m guilty of the same thing when I make videos). I couldn’t follow how positions correspond to numbers and where those numbers were coming from. But it’s a well motivated topic and the video is really well made.

9

I’ve seen many people try to explain how Conway came up with surreal numbers by looking at Go, and this is the best one by far. The content and the structure of the explanation are superb

The main weak point is the quality of the narration. It’s clearly someone reading a script line by line (sometimes moving too quickly from one paragraph to the next), and sure the script is really good, but in my opinion narration is better when it sounds more natural, like a conversation

Also, while I understand the goal was to explain surreal numbers, I would have also enjoyed if the whole thing focused more on Go

6.3

Great content!

However, the pacing is a bit of an issue. It speeds up incredibly in the last few minutes and introduces a lot of jargon, which takes a bit to digest.

I think there are a few existing good videos on surreal numbers already on the internet, so its not very clear how much it adds on top of those.

3.8

I’ll be honest, I could not really understand this video. I’ll begin with the positives: The animation is good, albeit a bit out of sync at times, and the voiceover is clear and understandable as well. However, I found it difficult to understand the concepts presented. First of all, I was unsure the rules of Go were explained properly, and I didn’t see how games progressed. The unusual definition of games and left and right could’ve used more explanation. Most of all, you never explained the simplicity theorem, or what it means for a number to be simple, or how {L|R} was calculated in this way. Overall, I couldn’t fully appreciate what you were explaining. A good try, but could be better.

4.4

you are overloading your microphone.

5.2

a number system using * is not a surreal number. But what is the system that uses *? I kept waiting for the video to explain that one system is surreal numbers and the other system is _____ but it never said the new system other than pointing out that go endgames use that system. Whats is the name of that other system?

3

I felt a little lost as to the point. I’m not sure what was meant by every game being a number, nor what surreal numbers actually were. The connection between theory and practice was difficult to follow. Thanks for giving references. Thanks for uploading.

5.5

The overall structure and execution are very good but I feel like you lost me within the details and motivation. Specifically, the motivation for the connection to surreal numbers, and everything past that, was lost on me. Similarly the details of chilling etc. Perhaps more time could have been put there.

How does this break mathematics? How is this different from other numbers?