Anaximander, who was born and died in Miletus (now in Turkey), belonged to the first school of natural philosophy and was the pupil of Thales. He wrote one of the earliest treatises but none of his writings survive and his work is known only through later writers, notably Aristotle and Theophrastus.

Anaximander criticized Thales's idea that water was the basic element of the universe by pointing out that no one element gains the upper hand and that “they pay the penalty and retribution to one another…according to the ordering of time.” From this he deduced that the primal matter was what he called the apeiron or the indefinite. This idea was later developed by the atomists. He was the first to realize that the Earth did not have to float on water or be supported in any way; he stated that it was in equilibrium with the other bodies in the universe.

Anaximander was the first philosopher to speculate on the origin of man. He is also credited with the first determinations of the solstices and equinoxes and the production of the first map of the world as he knew it. He was the first to recognize that the Earth's surface is curved but believed it was curved only in the north–south direction and consequently represented the Earth as a cylinder.