About 5 years ago, the Heron-Rota-Welsh conjecture (log-concavity of the coefficients of the characteristic polynomial of a matroid) was proven by Adiprasito, Huh, and Katz via the exciting development of a new combinatorial Hodge theory for matroids. In very recent work with Petter Brändén, we have given a new short "polynomial proof" of the Heron-Rota-Welsh conjecture. Our proof uses an extension of the theory of Lorentzian polynomials to convex cones. In this talk, I will briefly discuss the basics of Lorentzian (aka completely log-concave) polynomials, and then I will give an overview of our new proof of the Heron-Rota-Welsh conjecture.