The Garden of Learning

General Knowledge

Which mathematician founded graph theory with the Konigsberg bridges?

  • Leonhard Euler
  • Carl Gauss
  • Pierre Fermat

The answer is Leonhard Euler. Euler, in 1736.

Euler, in 1736, answering a local puzzle: whether you could walk through Königsberg crossing each of its seven bridges exactly once. He proved you could not - and the proof mattered far more than the answer.

What he did was throw away the map. The distances, the shapes of the islands and the positions of the bridges are all irrelevant; what matters is only which landmasses connect to which, and how many bridges meet at each. Reduced to points and lines, the answer falls out immediately - such a walk needs every point to have an even number of connections except at most two, and Königsberg had four odd ones.

That abstraction founded both graph theory and topology, and it now underlies routing, circuit design, epidemiology and every social network. Euler himself is the most prolific mathematician in history, wrote about half his output after going blind, and is responsible for so much notation - e, i, f(x), sigma for summation - that reading mathematics at all means reading Euler. Königsberg is now Kaliningrad, two bridges were destroyed in the war, and the walk is possible today.