In 1962, David Gale and Lloyd Shapley published "College Admissions and the Stability of Marriage," in which they proved that a stable matching — one in which no pair of agents would prefer to abandon their assigned partners for each other — always exists in a two-sided market and can be found by the deferred acceptance algorithm. The result transformed market design: Alvin Roth applied it to the National Resident Matching Program, school choice in New York and Boston, and kidney exchange, and shared the 2012 Nobel Memorial Prize with Shapley. But extend the problem to three sides — doctors, hospitals, and cities; students, courses, and time slots; workers, firms, and locations — and everything breaks. In three-dimensional stable matching, no stable solution is guaranteed to exist. The problem was shown to be NP-hard by Subramanian (1994) and others, meaning that even determining whether a stable three-sided matching exists is computationally intractable. Real-world multi-sided markets cope through a patchwork of heuristics, two-stage processes, and institutional workarounds, but no general theory of stable multi-dimensional matching exists. The Academy hosts this Wonder in the World School because it marks the exact boundary where the elegant theory of matching — one of game theory's greatest successes — meets a wall that no one has found a way around.