![]() This allowed him to reformulate the problem in abstract terms (laying the foundations of graph theory), eliminating all features except the list of land masses and the bridges connecting them. ![]() The only important feature of a route is the sequence of bridges crossed. The difficulty he faced was the development of a suitable technique of analysis, and of subsequent tests that established this assertion with mathematical rigor.Įuler, who never lived in Königsberg, first pointed out that the choice of route inside each land mass is irrelevant. accessing any bridge without crossing to its other endĮuler proved that the problem has no solution.reaching an island or mainland bank other than via one of the bridges, or.The problem was to devise a walk through the city that would cross each of those bridges once and only once.īy way of specifying the logical task unambiguously, solutions involving either The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands- Kneiphof and Lomse-which were connected to each other, and to the two mainland portions of the city, by seven bridges. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges
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