Anaximander~ Born in the Ionian polis of Miletus, Anaximander was an astronomer and mathemetician. He believed that all things developed from some unknown, eternal thing that had no limits.

Empedocles~ A student of Parmenides, Empedocles believed that everything (be it animal, vegetable, or mineral) originated in the four elements. The elements themselves were unchanging but love (Eros) or strife (Eris) could change how the elements manifested. Empedocles, like his teacher, is also Pre-Socratic.

Heraclitus~ An Archaic age philosopher, his ideas seem to be the most "modern to come from the time period. Heraclitus found that truth lies in constant change, as illustrated by his idea that one "can't cross the same river twice". This led him to believe that struggle is necessary for progress to occur.

Parmenides~ He believed that the world was unchanging and unmoving, and could best be understood through human reasoning. Parmenides led the school in Elea and is considered a Pre-Socratic philosopher. Like all Pre-Socratics, he was concerned with figuring out the nature of the physical.

Pythagoras~ The mathematician most remembered for the Pythagorean theorem and pi was also a philosopher. He led the Sicilian school, which rejected the materialist philosophies of the Milesian school. Instead, Pythagoras claimed, "Everything is made of numbers." This, meaning that math explained nature, made him an idealist.

Thales~ An Ionian mathematician and astronomer from Melitus. Thales was a materialist philosopher, "materialist" because he believed that everything is made of matter (or, more specifically, that everything is made of water). He also founded the Milesian school.