Mathematics
The Traveling Salesman Problem and Approximation Algorithms
Quick fact
The number of possible routes for just 20 cities is about 1.2 quintillion – that's more than the number of grains of sand on Earth.
Why this is interesting
Imagine you're a salesperson who must visit multiple cities and return home. What's the shortest route? For a handful of cities it's easy, but add just a few more and solving it perfectly might take longer than the age of the universe.