The river Pregel looped through the Prussian city of Konigsberg dividing it into four areas. Connecting the four areas were seven bridges. The townspeople all knew that the seven bridges could not all be crossed in a continuous walk. Or to rephrase it, the problem was to find a walk through the city that would allow you to cross each bridge once and only once (watch the animation).

The solution? Leonhard Euler proved that the problem had no solution, but realized an important principle in play. Euler reasoned (negative resolution) that in such a network some re-tracing was inevitable whenever there are three or more points at which an odd number of pathways converge. In doing so, he laid the foundations of graph theory, and presaged the development of topology. Euler’s work on re-tracing and observations about the network of lines connecting a number of points in 3-D laid the foundations for the modern network theory. The applications of which include you being able to access WWK and link through the site seamlessly.

The history of math is filled with interesting observations in the physical world leading to the development of applications of great value.