Matthew Hastings’ work combines physical insight and mathematical power to make profound contributions to a range of topics in physics and related fields. His Ph.D. thesis produced breakthrough insights into the multifractal nature of diffusion-limited aggregation, a problem that had stymied statistical physicists for more than a decade. Hastings’ recent work has focused on proving rigorous results on fundamental questions of quantum theory, including the stability of topological quantum order under local perturbations. His results on area laws and quantum entanglement and his proof of a remarkable extension of the Lieb-Schulz-Mattis theorem to dimensions greater than one have provided foundational mathematical insights into topological quantum computing and quantum mechanics more generally. Hastings resigned his Investigatorship in 2013 to move to Microsoft Research.