The River Pregolya is not one of those rivers that make decisively for the sea. On the contrary, the Pregolya, especially in its lower reaches downstream from Gvardeysk, is braided into a lattice of a thousand islands. The water meadows and marshlands that lie around the many arms of the river are inhospitable places. Every now and again a little elevation, barely perceptible to the eye, affords slightly drier conditions - good habitats for thickets of alder interspersed with birch.

The Russian city of Kaliningrad lies at the seaward end of the Pregolya, just as the lazy river eventually reaches the shallow Vistula Lagoon on the Baltic. And like everywhere along the Pregolya, Kaliningrad is watery. Long abandoned secondary channels of the river have left ribbons of ponds and lakes, often fringed by parkland, that run through the very heart of the city.

But it is mathematics rather than fluvial geomorphology that lies at the heart of this essay. For the bridges over the Pregolya in Kaliningrad turn out to have a very august position in the history of mathematics. The average Russian walking to work along Leninsky prospekt probably does not stop to ponder the bridge problem which so excited mathematicians three hundred years ago. In those days, the city that is now Kaliningrad was known as Königsberg, part of the Kingdom of Prussia.