The Australian Research Council (ARC) Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) brings together for the first time a critical mass of Australia’s best researchers in applied mathematics, statistics, mathematical physics and machine learning. With partner researchers, ACEMS engages in research programs that combine innovative methods for the analysis of data with theoretical, methodological and computational foundations, provided by advanced mathematical and statistical modelling. ACEMS will focus on the impact of new insights for end users working in the Collaborative Domains of Healthy People, Sustainable Environments and Prosperous Societies.