Mathematics
The Shortest Path Problem and Dijkstra's Algorithm
Quick fact
Dijkstra's algorithm, developed by Edsger Dijkstra in 1956, can find the shortest path between two points in a graph with non-negative edge weights, and it does so in near-linear time when implemented with a priority queue—the same approach used in modern GPS navigation.
Why this is interesting
When you ask your map app for the quickest route, it finds the path in milliseconds. How does it know?