Mathematics
The Traveling Salesman Problem and Its Computational Complexity
Quick fact
The number of possible routes for n cities grows factorially: for just 20 cities, there are ~2.4 × 10^18 possible tours—so many that checking them all would take billions of years even on a supercomputer.
Why this is interesting
You have to visit five friends spread across your city and return home. What's the shortest route? Now imagine fifty friends—your brain might give up, and a computer quickly runs out of patience too.