The bridges of Königsberg

A town has four districts, $A$, $B$, $C$ and $D$, joined by seven bridges. Five bridges meet at $A$, and three bridges meet at each of $B$, $C$ and $D$.

Is there a walk that crosses every bridge exactly once? It may begin and end wherever it likes. Prove your answer.

This is where graph theory began, and its first proof still fits in a few lines.