Euler - The Father of Graph Theory

In the days of Euler, there was a famous unsolved problem known as the Konisberg Bridge Problem. A park in Konisberg had islands linked to each other and to the banks of the Pregel River by seven bridges. The task is to begin at any one of the four land areas, walk across each bridge exactly once and return to the point of departure. Empirical attempts to solve this puzzle will inevitably be unsuccessful and the case with Euler was no different. Once convinced of its insolvability, Euler now attempted to prove the fact mathematically. He replaced each land area with a point and each bridge with a line joining the corresponding points, thereby producing a ‘graph’. Thus, showing the problem is insolvable amounts to showing that the graph is untraversable. This was done by Euler in a neat and decisive fashion and in doing so he proved the very first theorem of Graph Theory, the fact that for a graph to be traversable it must be connected and every point must be incident with an even number of lines. The graph under question, though it is connected, does not satisfy the second criterion. This completes the elegant proof.