As a member of the so-called Milesian school of Greek philosophers, Anaximander of Miletus (c.611—546 BC) followed Thales and was possibly his pupil. Like most of Ptolemy's predecessors, very little of his writing survives, and the few that is known of his work comes from reconstruction and reportage by the later Greek doxographers including Aristotle and Theophrastus. Almost all of them point to Anaximander as a pioneer explaining 'the order of things'.
According to Eratosthenes, Anaximander ‘was the first to publish a geographical map’, which would seem to have been the “a tablet of bronze, on which was engraved a map of the whole Earth, with all the sea and all the rivers” mentioned by Herodotus History, V, 49)
While they are often regarded as members of the same (Miletan) school, Anaximander criticised Thales's identification of water as the fundamental element of the universe and posited that the first principle was not a particular substance (water or air) but an eternal boundlessness he called the apeiron or the indefinite. The apeiron secreted a 'seed' which in turn produced an enveloping 'flame'. That, in turn, created 'rings' of planets, stars, the moon and the sun which encircled the earth.
Rather than floating on water, the Earth sat unsupported in any way at the centre of a symmetrical universe in perfect equilibrium with the other bodies that surrounded it. His purely geometrical and mathematical cosmology is the earliest known concept of a geocentric universe.
He was also the first philosopher to speculate on the origin of man, suggesting that living creatures first emerged from primaeval moisture and that humans must have developed from some other species that had matured more quickly.
Anaximander is also credited with determining the timings of the solstices and equinoxes and producing the first map of the known world as he knew it. He presented a basic outline of the oikumene, or inhabited world (Europe, Asia and Libya separated by the Mediterranean, Black Sea and the Nile) as one side of a circular drum, with an uninhabited world on the other side with both encircled by the ocean. Subsequent writers on geography refined and developed Anaximander's map, but few could match his cosmology, and his rational explanation of creation influenced all those who followed him.
Sources:
A Dictionary of Scientists
Jerry Brotton, A History of the World in Twelve Maps
Chambers Biographical Dictionary
W. A. Heidel, Hecataeus and Xenophanes;
Herototus, The History
Neil Rennie, Far-fetched facts: the literature of travel and the idea of the south seas