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Seven Bridges of Königsberg
Leonhard Euler
Project Description:
Founded in 1255, the city of Königsberg sat on the banks of the Pregel River. Within the river were two large islands, which were connected to each other and the adjacent riverbanks by seven bridges. A popular pastime of Königsberg's citizens in the eighteenth century was to find a route where one could cross all seven bridges without crossing the same one twice.

Prolific Swiss mathematician Leonhard Euler (1707 - 1783) was amused by this dilemma and was determined to solve it. Euler's answer to the problem was shown in a paper published in 1736 entitled Solutio problematis ad geometriam situs pertinentis (Solution of a problem relating to the geometry of position) and in which he rigorously proves by means of a pioneering analytical method that such a path does not exist.

Euler essentially reformulated the problem in abstract terms, isolating the seven bridges as a series of edges (links) connecting the different landmasses represented by vertices (nodes). Even though Euler did not use any of these modern terms, he did however deconstruct the problem in such a way that suggests a type of simplified scheme, commonly called a graph in mathematics. Euler's ability to look at the problem from a topological perspective--by conceiving the bridges challenge as a graph--laid the foundation for graph theory (the study of graphs in mathematics and computer science) and, consequently, network science.

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