Somewhere with face to face weiqi

Nonsense! There’s lots of math related to Go, and lots of Go related to math.

A field of research called “Combinatorial Game Theory” was developed basically to study endgame position of the game of Go. There was some sparse research in this field from long ago, involving simple games like Nim, but it wasn’t until the 60’s that this field really started developing, when famous mathematician John H. Conway started studying the endgame of Go and came up with the surreal numbers, which forms a very elegant generalisation of the real numbers. Afterwards, Conway, Elwyn Berlekamp and Richard Guy wrote several books about mathematical games that were inspired by this discovery, including a book specifically about the mathematics behind Go, called “Mathematical Go: Chilling Gets the Last Point” (by Berlekamp & David Wolfe).

Concepts first studied as part of combinatorial game theory are now being studied as part of actual applications within computing science and artifical intelligence.

I can however confirm, that being a good mathematician does not automatically make you a good Go player, and vice versa.


“My play was perfect, I shouldn’t have lost…”


A very fictional movie indeed.


I think this is what John Forbes Nash is supposed to have said (or something like it) after losing his first (and only) game of go, when introduced to it in the common room of the Math(s) department of Princeton University. His biography, A Beautiful Mind was made into a film of the same name. Possibly those exact words were put into his mouth in the film, though.

He is said to have returned the next day, having invented “a better game”, Hex, although this same game had already been invented a few years earlier by mathematician and poet Piet Hein.


Quite surely it was made up for the movie. Let’s not spread romantic history without fact checking.

Nash was a mathematician who had a very good understanding of game theory. In fact, you can argue that he may be one of the most important mathematicians in that field. No mathematician who knows game theory would ever use the words “My play was perfect” in seriousness, unless they actually have a perfect winning strategy (which is a technical term), in which case they’d win the game. In particular, I find it impossible to believe that a game theorist would be surprised that their perfect strategy is beaten. Perhaps they’d be surprised that their strategy is not perfect, but they wouldn’t claim that it is perfect after having just lost.

In his biography, the quote is nowhere to be found. In fact, your anecdote that he came back having invented a better game is not found either.

The reason Hex is interesting, is that you can prove that the first player has a winning strategy, even though it is not known what this strategy is. That is, it is certain that under perfect play the first player wins, but we have no idea what it is.

Here's some snippets of the relevant page(s)

(the source for this is Gale himself, by the way, that’s what the little 18 refers to)


There is math to be found in go and go in math, but I think it’s a bit esoteric.

You don’t need to be good at math to be good at go, and vice versa.
It’s not a given that good mathematicians are good go players, and vice versa.

That being said, a significant proportion of go players are also interested in math, but I think this is more the case in the West than in the East.


I think if we consider a mathematician who doesn’t know Go and a Go player who doesn’t know mathematics, that it’s more likely that the mathematician will start playing Go, than that the Go player will start doing mathematics.

Go can be interesting from mathematical perspective, but mathematics probably isn’t too interesting from a Go perspective.


I have read a bit about his efforts before, but to me it seems that he is just using go as a vehicle to teach math to children. Although he is a go player, my impression is that he is more focused on teaching math through go than in spreading go for its own merits.

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I think you can find a similar phenomenon in other arts (I consider go to be more an art than a science), most specifically in music.


Thanks. Are those extracts from the book, A Beautiful Mind?

Funnily enough, although I read the book maybe fifteen years ago, I’ve never seen the film. I must have picked up the myths from people talking or writing about the film, I suppose. Just goes to show that an oft-repeated lie can blot out the truth.

Anyway, at least I mentioned the (purported) source of the quote delivered with no reference by @BHydden.

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I think it is no accident that Xinming Simon Guo works with grade 1 to 5 kids — here, to me, being slightly dyscalculic, the interconnection between Go and Math seems to be quite strong, as kids are just beginning to grasp the differences between “one”, “two”, and “many” (etc.) … and this way they train their visual imagination as well as distinguishing larger from smaller groups of stones …?