When trying to reconstruct the cosmology of Anaximander of Miletus, one of the challenges is the issue of whether he assumed that universe to have some concrete boundaries. In particular, it is unclear whether heaven, in addition to being identical with the area of the sky, also formed the boundary of the universe. To wit, given that Anaximander allegedly said the ‘origin’ of existing things was the ‘boundless’, one might assume he viewed the universe as boundless, open. In contrast, for other archaic Ionian thinkers one can suppose they viewed the universe as closed, be- cause the Earth formed the lower boundary of the universe and heaven its upper boundary. Although Anaximander’s conception in many respects differed from theirs, one could argue that his universe was similarly closed. This hypothesis finds support especially in the concept of ‘surrounding’, which appears in Anaximander’s thoughts in many areas and expresses the constitution of various phenomena. It seems therefore likely that it might also apply to defining the boundaries of the universe. Nonetheless, given the uniqueness of Anaximander’s universe, which consisted of Earth in the middle of circles of heavenly bodies that passed even under it, later reports on his theories focused mainly on describing this centre of the universe. Although the shape of a column is a tempting candidate, surviving sources do not provide enough evidence to help us identify the shape of Anaximander’s universe with any certainty. The notion of a celestial sphere, assumed by many scholars, is nonetheless clearly an anachronism.