The teaching of evolution in American high schools has long been a source of controversy. The past decade has seen an important shift in the rhetoric of anti-evolutionists, toward arguments of a strongly mathematical character. These mathematical arguments, while different in their specifics, follow the same general program and rely on the same underlying model of evolution. We shall discuss the nature and history of this program and model and describe general reasons for skepticism with regard to any anti-evolutionary arguments based upon them. We shall then survey the major arguments used by anti-evolutionists, to show how our general considerations make it possible to quickly identify their weakest points.