Anaxagoras left his birthplace in Asia Minor (now Turkey) in about 480 bc and taught in Athens during its most brilliant period under Pericles, who was himself one of Anaxagoras's pupils. In about 450 bc he was exiled to Lampsacus after being prosecuted for impiety by the enemies of Pericles.

Although he wrote a book, On Nature, only fragments of his writings survive; his work is known through later writers, notably Aristotle and Simplicius, and is open to contradictory interpretations. The difficulty consists in reconciling his principle of homoemereity, which states that matter is infinitely divisible and retains its character on division, with his statement “there is a portion of everything in everything.” His work can be seen as a criticism of the Eleatic school of Parmenides and Zeno of Elea, who had argued against plurality and even motion.

Anaxagoras's astronomy was more rational than that of his predecessors; he stated that the Sun and stars were incandescent stones, that the Moon derived its light from the Sun, and he gave the modern explanation for eclipses of the Sun and Moon.