Mathematics
Dijkstra's Algorithm for Shortest Paths in Graphs
Quick fact
Dijkstra's algorithm, published in 1959 by Edsger Dijkstra, was conceived in a cafe in Amsterdam in twenty minutes as a way to demonstrate the power of a new computer, and it still forms the backbone of modern GPS navigation.
Why this is interesting
You're on a road trip and your GPS must instantly compute the fastest route. How does it manage to consider millions of possible paths in the blink of an eye?