The Hodge theory of matroids illustrates how geometric ideas can lead to combinatorial results. In this talk, I will introduce a tangent class for a loopless matroid and explain how it provides a geometric interpretation of the Riemann–Roch formula for matroids. I will then discuss a numerical Kawamata–Viehweg vanishing theorem for rank 3 matroids, explain how it can be reduced to a stone game, and (if time permits) discuss a proof and the geometric ideas behind it.