starting in 1979, the physicist giorgio parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking, which allowed him to predict a solution for the sherrington-kirkpatrick (sk) model by breaking the symmetry of replicas infinitely many times. this is known as full-step replica symmetry breaking (frsb). in this talk, we will provide a mathematical proof of parisi's frsb prediction at zero temperature for the more general mixed p-spin model. more precisely, we will show that the functional order parameter of this model is not a step function. this talk is based on joint work with antonio auffinger and wei-kuo chen.