Born in Meletus, Anaximander was a student of Thales and is regarded as the second of the Ionian naturalists. Like Thales, Anaximander was renowned for his mathematical prowess. He is known for inventing the sundial and gnomon, which is the triangular blade on the sundial that casts a shadow. In addition, Anaximander provided the first map of the Greek world, the first map of the stars and constellations placing the earth at the center as a disk, and determinations of the path of the sun.

Though he was Thales' student, Anaximander disagreed with his teacher. Anaximander contended that the original substance of the universe was not matter like water, but must be immaterial. He thought the fundamental, ultimate stuff of the universe must be the infinite. The Greek word is apeiron, meaning something that is “without limit” or “boundless.” His thinking was that prior to all perceptible material bodies there must have been an indefinite, immaterial something.

Let's try to understand Anaximander's thinking. He looks out on nature and sees the sky, water, soil, stone, and more. Such variety could not have come from one finite (and therefore limited) substance. From Axaximander's boundless all things came or were “separated out.” Here Anaximander hit upon an ingenious idea: if the purpose of cosmological investigation is to find a single substance from which all other entities can emerge, what could be better than something infinite, which contains within itself the capacity to produce any other thing? The boundless accounts for the multifarious creations and changes we observe. He also called this infinite stuff a “principle.” As Aristotle said in his Physics, “Everything is either a principle or derived from a principle. But the limitless has no principle — for then it would be a limit. It is ungenerated and indestructible and so is a principle.”

Anaximander also believed that the earth, a flat cylinder, hangs freely in space because of its equal distance from all parts of the spherical universe. The sun is the same size as the earth. This concept was the first of all attempts at a rational cosmogony and as such represents freedom from mythical modes of thought.