The Seven Bridges of Königsberg

In 1736, Leonhard Euler solved the puzzle of whether one could walk through Königsberg crossing each of its seven bridges exactly once. He proved it impossible, creating graph theory in the process. The city’s four land masses became vertices; the bridges edges. Euler showed a connected graph has an Eulerian path (using every edge once) iff zero or two vertices have odd degree. Königsberg had four odd‑degree vertices – no such walk. This birth of network mathematics now underlies everything from GPS routing to genome assembly.