The game of the century and proof by contradiction

The Game of the Century is a chess game between 13 year old Bobby Fischer and Donald Byrne, played in 1956. Byrne was an established player, and had won the US Open championship in 1953. Although Fischer’s star was rising, Byrne was considered the favorite. Byrne, immaculately dressed, in a suit and tie, sits with a cigarette between his fingertips.

The opening moves in chess, pretty much fall into set patterns until about move 10 or 11. Then in a few more moves, something called “novelty” happens. This is when the chess game evolves into a unique position; one that has never ever before been played in this history of humanity. This is a combinatorial fact. This is where the game of chess leaves “the book”, and the players must innovate.

Byrne opens the game with Nf3; a pretty nondescript opening that evolves quickly into something called the Gruenfeld Defence. This is a fairly well known chess opening. Fischer defends based on “hypermodern principles”, inviting Byrne to establish a pawn stronghold in the center that he will attack in the mid-game.

10 moves pass, and they’re pretty evenly matched. On move 11, Fischer offers a knight sacrifice. There is usually a person recording chess games in chess notation. Fischer’s knight sacrifice is usually written as

    11 ... Na4!! 

“On the 11th move, black moves knight to position a4 on the chessboard”. The two exclamation marks at the end indicate that it’s a very interesting, delightful move that has strong consequences in favor of the mover. Byrne, the consummate chess master, wisely says “No thanks!” to Fischers clever ploy.

On moves 16 and 17 Byrne threatens Fischers queen. Fischer is in trouble now. He has problems with his queen, and stands to lose a knight if he protects his queen. Instead, Fischer moves Bishop to e6. Fischer does not protect his queen; instead, he moves his bishop and offers his queen up as sacrifice. This is considered the greatest move in all of chess history.

One can imagine Byrne dragging hard on his cigarette, inhaling deeply. “What’s this kid doing?” After some thought, Byrne takes the queen. After that Fischer begins a windmill – a series of discovered checks – that wins him a a rook, two bishops and a pawn for his lost queen. Experts say that after this move, there is nothing that white could have done to recover.

Proof by contradiction, in GH Hardy’s words (see A mathematicians apology (1941)), is much like a chess gambit. He says,

    Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. 

I find this a very appealing metaphor. I was listening to radiolab’s podcast (Games) which talks about The Game of the Century and was reminded about Hardy’s quote about chess and proof writing. Of course, the process of doing mathematics has nothing to with playing chess.