Looking forward to a few family board games at Christmas? Good, good. Steer clear of Monopoly V, a dreadful, grinding game. Settlers of Catan is the game Monopoly wishes it was — although, for committed players, Puerto Rico is even better. (Agricola is the best game. But you knew that already.) Games are a serious business in the Harford household but they, along with puzzles and other fripperies, have long been important elsewhere. Consider the puzzle of the bridges of Königsberg — 18th-century Königsberg had seven bridges connecting two sides of a river and two large islands. The puzzle was: is there a walking route through the city that crosses each bridge only once? When the great mathematician Leonhard Euler heard about the problem, he found it "banal" but was intrigued by the fact that, despite its apparent simplicity, "neither geometry nor algebra nor even the art of counting" could solve it. And so Euler invented an entirely new branch of mathematics, graph theory. "That was...

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