Let ${\mathrm{Poly}}_n\mathbb{C}$ be the space of monic, squarefree, degree $n$ polynomials in one variable over $\mathbb{C}$. Ferrari’s solution to the quartic equation gives rise to a holomorphic map $R:{\mathrm{Poly}}_4\mathbb{C}\to {\mathrm{Poly}}_3\mathbb{C}$. We show that every holomorphic map ${\mathrm{Poly}}_n\mathbb{C}\to {\mathrm{Poly}}_m\mathbb{C}$ for $m\le n$ is equivalent in a certain sense to a constant map, the identity map, or Ferrari’s map $R$. This is joint work with Jeroen Schillewaert.