Mathematics
The Seven Bridges of Königsberg and Graph Traversal
Quick fact
Euler's 1736 solution showed that a walk crossing every bridge exactly once is possible only if the graph has either zero or exactly two vertices of odd degree; since Königsberg had four such vertices, the tour was impossible.
Why this is interesting
You are standing in 18th-century Königsberg, trying to cross all seven bridges exactly once and return to your starting point. Is it possible? Euler said no—and in solving it, he gave birth to a whole new branch of mathematics.