Summary: We discuss the following fascinating problem. Suppose a is a positive number and consider the sequence \(a,a^a,a^{(a^a)}, a^{(a^{(a^a)})},\dots\). For which values of a does this sequence converge? This problem is remarkable both for its unexpected answer and the different threads that interweave in the development of its solution. We present a solution and provide some historical context.