The seven bridges of Königsberg
The old city of Königsberg had seven bridges linking two islands and both riverbanks. Citizens tried for years to find a walk crossing every bridge exactly once. Can it be done?
Reveal the answer
No — and proving why founded an entire branch of mathematics. Euler showed such a walk requires zero or exactly two land areas with an odd number of bridges; Königsberg's four areas all had odd counts. His 1736 proof was the birth of graph theory, the maths behind every route planner and social network today.
— Leonhard Euler, Solutio problematis ad geometriam situs pertinentis — 1736 — public domain