Combinatorics

Leonhard Euler (1701-1783) was a Swiss mathematician who spent most of his life in Russia. He was responsible for making a number of the initial contributions to combinatorics both in graph theory and enumeration. One of these contributions was a paper he published in 1736. The people of an old town in Prussia called Königsberg (now Kaliningrad in Russia) brought to Euler's attention a stirring question about moving along bridges. Euler wrote a paper answering the question called "The Seven Bridges of Königsberg." The town was on an island in the Pregel river and had seven bridges. A frequently asked question there at the time was "Is it possible to take a walk through town, starting and ending at the same place, and cross each bridge exactly once?" Euler generalized the problem to points and lines where the island was represented by one point and the bridges were represented by lines. By abstracting the problem, Euler was able to answer the question. It was impossible to return to the same place by only crossing each bridge exactly once. The abstract picture he drew of lines and points was a graph, and the beginnings of graph theory. The study of molecules of hydrocarbons, a compound of hydrogen and carbon atoms, also spurred the development of graph theory.