What were the Seven Bridges of Königsberg?

The Seven Bridges of Königsberg is a historical puzzle that asked whether a walking tour could cross every bridge of the city exactly once. In 1736, mathematician Leonhard Euler proved this task was impossible, creating a proof that laid the foundations of graph theory. The city containing these bridges, formerly known as Königsberg, is today called Kaliningrad.

What we know

• The Seven Bridges of Königsberg is a historical puzzle about finding a walking tour that crosses each of the city's bridges exactly once. [2]
• Leonhard Euler formalized and proved the impossibility of the walking tour puzzle in 1736. [2]
• Euler's proof regarding the bridges laid the foundations of graph theory and foreshadowed topology. [2]
• The city of Königsberg was renamed Kaliningrad after becoming part of the Soviet Union following World War II. [3, 5]

Where to go next

• how it workedHow did Leonhard Euler prove the puzzle was impossible?
• the bigger pictureWhat is graph theory?
• whenHow did Königsberg become Kaliningrad?
• what followedWhat is Kaliningrad like today?
• how we knowWhat role did the Teutonic Knights play in founding the city?
• an unexpected connectionHow does a mathematical puzzle about old bridges connect to modern Russian football?The historic area containing the river islands of the bridge puzzle was later redeveloped with the Kaliningrad Stadium for the 2018 FIFA World Cup.

Sources

• [1]Seven Bridges of Königsberg (Wikidata Q33100) · CC0 1.0
• [2]Seven Bridges of Königsberg · CC BY-SA 4.0
• [3]Königsberg · CC BY-SA 4.0
• [4]Oktyabrsky Island · CC BY-SA 4.0
• [5]Kaliningrad · CC BY-SA 4.0