Seven Bridges of Königsberg

Here's a drawing of the city of Königsberg, Prussia in the early 18th century.

A lovely place for a stroll...

The city was set on both sides of the Pregel River (shown in blue), and included two large islands which were connected to each other and the mainland by seven bridges (shown in red). Someone had posed the question of whether it was possible to walk through the city and cross every bridge exactly once.

In 1735, a mathematician named Leonhard Euler proved that such a route could not exist. In doing so, he basically invented a field of mathematics, which we now call graph theory.

("Euler" is pronounced more or less like "oiler", by the way.)