The Seven Bridges of Königsberg  is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. Our city of Porto has also seven bridges. The city 0f Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River,  which were connected to each other by seven bridges. The problem was to devise a walk through the city that would cross each of those bridges once and only once. By way of specifying the logical task unambiguously, solutions involving either reaching an island or mainland bank other than via one of the bridges, or accessing any bridge without crossing to its other end are explicitly unacceptable.

Euler proved that the problem has no solution. The difficulty he faced was the development of a suitable technique of analysis, and of subsequent tests that established this assertion with mathematical rigor.

Philosophers have noted that Euler’s proof is not about an abstraction or a model of reality, but directly about the real arrangement of bridges. Hence the certainty of mathematical proof can apply directly to reality.