The ability to resist small shear stresses is what distinguishes a solid from a liquid. This shear-rigidity is associated with broken translational symmetry. Most solids flow when they are sheared beyond a certain limit: the yield stress. It is not usual to associate shearing with increasing the rigidity of a fluid or solid. In athermal materials that are made up of macroscopic particles such as granular materials or dense suspensions, shear can actually induce solidification or a discontinuous increase in the viscosity. In this talk, I will explore the origin of these rigidity transitions: I will show that friction plays a large role in stabilizing these rigid states, and argue that we need to a paradigm shift to understand systems in which forces become independent dynamical variables. I will show that shear-induced rigidity is associated with a broken symmetry but in a space that is not characterized by positions and momenta but by forces.