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There is a scene in the movie "A Beautiful Mind" in which John Nash is talking to his friend Charles in Princeton Library. Nash shows Charles three pieces of mathematics - drawn on the windows - that describe a touch football game, a flock of pigeons and a woman getting her purse stolen. Below are two recreations of the drawings from the movie. The first is of the pigeons and the second the stolen wallet.

Maths describing the flock of pigeons

Stolen Wallet

Initially, is this even real mathematics? If it is what part of mathematics is it? I have a feeling its to do with game theory but everything I thought of searching has brought nothing vaguely similar to this. Can you suggest some key words I could search to find similar mathematics?

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  • $\begingroup$ It may be some form of commutative diagram (en.wikipedia.org/wiki/Commutative_diagram) $\endgroup$ – yoyostein Dec 17 '16 at 10:48
  • $\begingroup$ The stolen wallet looks a lot like a extensive form game tree, especially with the payoffs at the various nodes, but it looks non-standard from what I'm used to seeing. Nodes are action (decision) points, arrows take you to the next decision point, two arrows from a node denote two possible actions, and often the dotted lines denote information sets--meaning the player can't dell the difference between nodes surrounded by dotted lines. $\endgroup$ – Trurl Dec 19 '16 at 14:20
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David Bayer, the mathematical consultant of "A Beautiful Mind" talks about those drawings in an interview with Burkard Polster and Marty Ross, on page 26-27 of their book "Math Goes to the Movies", Johns Hopkins University Press (2012), 304 pages.

In summary, he says that the drawings are quite literal schematic representations of the stories that the John Nash character was telling in that scene. In his own words "I struggled with it [making up the math that would accompany that scene] [...] an it would ruin a day's filming if I didn't do something [...] And ultimately I ended up actually writing out a storyline for myself of what was taking place. I started translating it into graphs and then I started putting values like I was writing a game theory puzzle on the graph. And even thought I don't know of game theorists doing exactly this to such a storyline that was the basis for my drawing."

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