Scientists finally solve 40-year-old physics puzzle about how things grow

Understanding how surfaces grow has long been one of physics' most important challenges. In 1986, researchers introduced the Kardar-Parisi-Zhang (KPZ) equation, a theory designed to describe growth across a wide range of systems. Over time, this framework has been applied to everything from crystal formation and population dynamics to flame fronts and even machine learning. The idea is simple but powerful: very different systems may follow the same underlying rules when they grow.<...