David J. Thouless, at the University of Washington, together with Mahito Kohmoto, M. P. Nightingale, and Marcel den Nijs, publish in 1982 "Quantized Hall Conductance in a Two-Dimensional Periodic Potential", a paper mathematically explaining why the Hall conductance measured by von Klitzing, Dorda, and Pepper in 1980 is quantized with extraordinary precision — ten significant figures — even in real samples full of impurities and disorder, something no calculation based on a perfect, ideal crystal could explain. The four authors show that the quantized value of the Hall conductance is determined by a topological integer — today known as the Chern number or TKNN invariant — associated with the structure of the electronic wave functions in the material's Brillouin zone. Being a topological invariant, this integer does not change under continuous perturbations of the system, such as small impurities or disorder, as long as the energy gap between bands does not close: this fundamentally explains the astonishing experimental robustness of the quantization von Klitzing observed. The paper does not mention the word "topology" in its title, and Thouless did not begin using that language in his publications until 1985, but retrospectively this work is recognized as the starting point of all modern topological materials physics — topological insulators, topological superconductors, the anomalous quantum Hall effect — and is one of the two papers explicitly cited by the Nobel committee in awarding Thouless the 2016 Nobel Prize in Physics, shared with F. Duncan M. Haldane and J. Michael Kosterlitz for their theoretical discoveries of topological phase transitions and topological phases of matter.