What is the largest possible family of \(k\)-subsets of an \(n\)-element set such that every pair of sets intersects? This simple-sounding question, due to Paul Erd\H{o}s, Chao Ko, and Richard Rado, launched what is now known as Erd\H{o}s--Ko--Rado theory. The answer is equally simple: the largest intersecting families are just all sets sharing a common element.
But like many good combinatorial questions, this one refused to stay in its lane and transformed itself into problems about permutations, graphs, vector spaces, group actions, and much more. In this talk we start with the original question and let it wander through different parts of mathematics, seeing the interplay it encounters along the way. The goal of the talk is to enjoy the many disguises of a simple combinatorial idea and to see how a problem about overlapping sets ended up overlapping with many other areas.
