The trajectory of speciation involves geographic isolation of ancestral populations followed by divergence by natural selection, genetic drift or sexual selection. Once started, the process may experience fits and starts, as sometimes diverging populations intermittently reconnect. In theory populations might cycle between stages of differentiation and never attain species status, a process we refer to as Sisyphean evolution. We argue that the six putative ground finch species (genus Geospiza) of the Galápagos Islands represent a dramatic example of Sisyphean evolution that has been confused with the standard model of speciation. The dynamic environment of the Galápagos, closely spaced islands, and frequent dispersal and introgression have prevented the completion of the speciation process. We suggest that morphological clusters represent locally adapted ecomorphs, which might mimic, and have been confused with, species, but these ecomorphs do not form separate gene pools and are ephemeral in space and time. Thus the pattern of morphological, behavioural and genetic variation supports recognition of a single species of Geospiza, which we suggest should be recognized as Darwin's ground finch (Geospiza magnirostris). We argue that instead of providing an icon of insular speciation and adaptive radiation, which is featured in nearly every textbook on evolutionary biology, Darwin's ground finch represents a potentially more interesting phenomenon, one of transient morphs trapped in an unpredictable cycle of Sisyphean evolution. Instead of revealing details of the origin of species, the mechanisms underlying the transient occurrence of ecomorphs provide one of the best illustrations of the antagonistic effects of natural selection and introgression.