The first pre-Socratic philosophers existed in the city of Miletus, along the western coast of Anatolia (modern Turkey). From Miletus came three important pre-Socratic philosophers: Thales, Anaximander, and Anaximenes.
Philosopher and mathematician Pythagoras (570-497 B.c.), perhaps most famous for the Pythagorean theorem named after him, believed that the basis of all reality was mathematical relations and that mathematics governed everything. To Pythagoras, numbers were sacred, and with the use of mathematics, everything could be measured and predicted. The impact and image of Pythagoras was astounding. His school was cult-like, with followers listening to his every word … and even his strange rules, which covered anything from what and what not to eat, how to dress, and even how to urinate. Pythagoras philosophized on many areas, and his students believed that his teachings were the prophecies of the gods.
The Ephesian school was based on the work of one man, Heraclitus of Ephesus (535-475 B.c.). Heraclitus believed that everything in nature is constantly changing, or in a state of flux. He is perhaps most famous for his notion that one cannot step in the same river twice. Heraclitus believed that the single element was fire and that everything was a manifestation of fire.
The Eleatic school was based in Colophon, an ancient city not far from Miletus. From this region came four important pre-Socratic philosophers: Xenophanes, Parmenides. Zeno, and Melissus.
The Atomist school, started by Leucippus in the fifth century e.c. and passed down by his student, Democritus (460-370 B.c), believed that every physical object is made up of atoms and void (empty space that atoms move in) that are arranged in different ways. This idea is not too far from the concepts of atoms that we know today This school believed that atoms were incredibly small particles (so small that they could not be cut in half) that differed in size, shape. motion, arrangement, and position, and that when put together, these atoms created what is seen in the visible world.