Graph theory emerged in the 18th century, connecting geometry with fields like topology and set theory. Leonhard Euler formulated graph theory during his time in Königsberg, now Kalingrad. His seminal work began with the 1736 paper, “The Seven Bridges of Königsberg.”
Residents of Königsberg enjoyed crossing the city’s seven bridges in one outing – considered impossible, but not proven. Euler approached this challenge not by traditional geometry or algebra, but through an abstraction where cities and bridges became vertices and edges in a graph. This approach showed that a path crossing each bridge once was impossible if more than two vertices had an odd number of edges.
Euler’s insights created the foundation for graph theory, now used in various applications from computer algorithms for facial recognition to network and process design. Or perhaps a bit of frustration by myself in graduate school studying math in the physics department at Penn State. Crossing all the bridges became possible later on in Kalingrad due to war, as they were partly destroyed.
See
- Euler, Leonhard, “Solutio problematis ad geometriam situs pertinentis,” 1741.
- https://maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem