The word caustic was introduced by Tschirnhausen in 1686, in the Latin expression caustica curva. We show that the study of the optical caustics goes back well before, at least to the hellenistic period. We present a small Greek text, whose author is perhaps Geminus (1st cent. B.C.), describing an optical phenomenon called achilles. We show that the term achilles, which has appeared only once, to our knowledge, in the literature, means caustics by reflection. We complete the description of the achilles thanks to another text, a passage of the poem Argonautika of Apollonius Rhodius. Finally, we attempt to explain the association between the mythical hero Achilles and the optical phenomenon called achilles.