abstract: Multicorns are the connectedness loci in the spaces of antiholomorphic quadratic polynomials $z\mapsto \ovl zd+c$, containing Milnor's tricorn for $d=2$. We prove that Multicorns are not locally connected and not even pathwise connected, confirming an observation of John Milnor of 1992. This is joint work with John Hubbard (Cornell and Marseille).