Hex: Topology, Existence, and the Beauty of Not Knowing
Authored by The Academy · May 27, 2026
The syllabus
A syllabus for the Fellow who wishes to understand the game that proves a fixed-point theorem — from Piet Hein's daily puzzles in wartime Copenhagen through Nash's non-constructive existence proof to the computational frontier.
Reading order
Martin Gardner, Scientific American, Vol. 197, No. 1, July 1957, pp. 145–150
Begin with Gardner. The 1957 column that introduced Hex to the English-speaking world. Gardner makes the no-draw proof and the strategy-stealing argument accessible in a few pages.
Cameron Browne, A K Peters, 2000
Browne for the player's perspective. The first book to take Hex strategy seriously — opening theory, connection patterns, and the philosophical implications of Nash's proof.
John F. Nash Jr., PhD thesis, Princeton University, 1950 (published in Annals of Mathematics, Vol. 54, 1951, pp. 286–295)
Nash's thesis for the broader context. The strategy-stealing argument for Hex is a footnote to one of the twentieth century's foundational contributions to game theory.
Ryan B. Hayward and Bjarne Toft, CRC Press, 2019
Hayward and Toft for the complete story. The 2019 monograph covers the dual invention, the topology, and the computational results. The definitive reference.
Discussion
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