[FOUNTAIN]The bridges of Koenigsberg

Recently, a meeting of the Council of Baltic Sea States was held in St. Petersburg, Russia. Vladimir Putin, the president of Russia, attended the meeting personally, an unusual event, to assert the freedom of movement for the people of Kaliningrad, an exclave of Russia.

Kaliningrad was originally called Koenigsberg when it was the capital of East Prussia. The city was annexed by the Soviet Union in 1945. When the states around the Baltic Sea became independent after the collapse of the Soviet Union, Kaliningrad was isolated from the main body of Russia.

Russians have to travel to and from Kaliningrad via Poland or Lithuania. Since those two countries are set to join the European Union and, accordingly, to become the members of the Schengen visa regime -- the system that enables free movement within the European Union while reinforcing its external borders -- problems have arisen. Since the Schengen visa regime will require visas for travelers to and from Kaliningrad, it will interrupt the exchange of people and goods and leave the city very isolated.

Kaliningrad is divided into four areas by the river Pregel. The two areas and two islands on the river are connected by seven bridges. The beautiful port city is closely linked to the history of philosophy and mathematics.

The Koenigsberg Bridge problem, an early geometric puzzle, originated in the city. The question was: "Is it possible to walk across the seven bridges without crossing any of them twice?"

Leonhard Euler (1707 - 1783) solved the problem. After turning the locations connected by bridges into vertices and turning the bridges into edges, Euler proved that if more than 2 vertices have an odd number of edges meeting there, then it is impossible to trace each edge of the diagram exactly once without lifting the pencil, and so it is impossible to walk over each bridge exactly once.

We can understand how the mathematician from Switzerland came to take an interest in the bridges of Koenigsberg, a city far from the center of Europe, if we recall the strategy of Russian emperors in the 18th century. They took great interest in inviting noted scholars from developed European countries in order to nurture Russian arts and science.

Another important figure who is closely related with the bridges of Koenigsberg is Immanuel Kant (1724-1804). He was born in the city, lived his whole life there and is buried there. We should hope that the city will not become isolated from the world.

The writer is an editorial writer of the JoongAng Ilbo.

by Kim Seok-hwan