J. Michael Kosterlitz and David J. Thouless, at the University of Birmingham, introduce the concept of "topological order" to describe a new type of phase transition in two-dimensional systems that, according to the conventional wisdom of the time, could not have any long-range order or phase transition at all, due to random thermal fluctuations (the Mermin-Wagner theorem). Kosterlitz and Thouless show that these systems instead exhibit a vortex-mediated transition: at low temperature, vortices pair up into bound pairs; as temperature rises above a critical threshold, these pairs dissociate and vortices become free to move independently. This mechanism, completely different from conventional symmetry breaking, turned out to be the theoretical key to understanding phenomena such as superfluidity and superconductivity in two-dimensional thin films. The idea arose from conversations between Thouless and a young Kosterlitz, newly arrived to a field he was almost entirely unfamiliar with after leaving high-energy physics.