This paper is a personal reflection rather than a demonstration. It discusses the relationship between two properties of species: resilience , which allows species to resist perturbations, and serendipity , which allows them to change even under weak perturbations. Among the great problems raised by the transformation of species, the most astonishing fact is that species are extraordinarily stable. This stability, to which we hardly pay attention, is part of our everyday life, up to the point that it forms the basis of our deepest thought, the eternal Ideas of Plato and the substance of Aristotle. This suspected stability has also been used to support doctrines of the loathed creationists. All the definitions of species, even the arbitrary boundaries and nominalist conventions, bear the embarrassing sign of resilience, which contradicts the idea of evolution.