How is it that natural systems---such as tectonic plates, snow slopes, and financial markets---exhibit the power-law and fractal behaviors characteristic of a critical state? In 1987, physicists Bak, Tang, and Wiesenfeld developed a widely cited explanation known as Self-Organized Criticality (SOC). I will present Hoffman, Johnson, and my recent article arxiv.org/abs/2406.01731, in which we give one of the first rigorous mathematical demonstrations of SOC by proving the density conjecture in dimension one for the Activated Random Walk model.