History Moves in Mysterious Ways

As one whose scope of history extends beyond the current decade, I found myself drawn to R. J. W. Evans article in the current issue of The New York Review, “In the Lost World of East Prussia.” Perhaps the best known city in East Prussia is Königsberg, which was renamed to Kaliningrad when the Soviets took over the territory after the Second World War. Königsberg’s most famous citizen is probably Immanuel Kant, who lived to the ripe old age of 79 and never ventured more than ten miles from his home town. Those who prefer mathematics to philosophy, on the other hand, know Königsberg for its configuration of seven bridges and their role in the birth of what we now call graph theory.

Evans saved recognition of this problem for the final paragraph of his article:

In 1735 the mathematician Leonhard Euler tackled the famous problem of the “Seven Bridges of Königsberg,” which crossed onto its two islands in the river Pregel (an aspect not mentioned by Egremont [the author of the book Evans was reviewing], although it mirrors his own deft interweaving of the evidence). In a theorem that initiated the study of topology and graph theory, Euler elegantly demonstrated that no route could be found whereby a walker crossed each of the bridges only once. In 1944–1945 all the bridges were destroyed. Only five have been rebuilt. Ironically, Stunde Null [“zero hour” for the Nazis] made that Eulerian path possible.

History has a reputation for the dispassionate destruction of icons. Carl Sandburg captured that objectivity best in his World War One poem “Grass” with the line:

I am the grass; I cover all.

Königsberg no longer has seven bridges, but graph theory has progressed far beyond the puzzle that inspired Euler. There is, indeed, irony behind the bombing of those two problematic bridges; but neither history nor mathematics (nor Sandburg) cares very much about that irony.