If an invertible integer matrix has an eigenvalue that is not a root of unity, then its spectral radius is strictly greater than 1 by a 19th century result due to Kronecker. But how close to 1 can the spectral radius be? This question, asked by Schinzel and Zassenhaus in 1965, remains unanswered to this day. We discuss the precise formulation of this problem and the known partial results. Finally, we reformulate the question in terms of a comparison of orientation-preserving and orientation-reversing self-maps of topological surfaces.