According to Plutarch in his work On exile, Anaxagoras is the first Greek to attempt the problem of squaring the circle, a problem he worked on while in prison. He is considered to be both the geographical and theoretical successor to the earliest Ionian philosophers, particularly Anaximenes. Eventually, Anaxagoras made his way to Athens and he is often credited with making her the home of Western philosophical and physical speculation. 

Anaxagoras (/ˌænækˈsæɡərəs/; Greek: Ἀναξαγόρας, Anaxagóras, “lord of the assembly”; c. 500 – c. 428 BC) was a Pre-Socratic Greek philosopher. Born in Clazomenae at a time when parts of IONIA(= “Asia Minor”) came under the control of the Persian Empire, untill when later Alexander the Great liberated and became Greek again Anaxagoras came to Athens. Although Anaxagoras lived in Athens when Socrates was a youth and young adult, there are no reports that Anaxagoras and Socrates ever met.

About 480 Anaxagoras moved to Athens, then becoming the centre of Greek culture, and brought from Ionia the new practice of philosophy and the spirit of scientific inquiry. He was a philosopher of nature remembered for his cosmology and for his discovery of the true cause of eclipses. He was associated with the Athenian statesman Pericles. Although Anaxagoras proposed theories on a variety of subjects, he is most noted for two theories. First, he speculated that in the physical world everything contains a portion of everything else. His observation of how nutrition works in animals led him to conclude that in order for the food an animal eats to turn into bone, hair, flesh, and so forth, it must already contain all of those constituents within it. The second theory of significance is Anaxagoras’ postulation of Mind (Nous) as the initiating and governing principle of the cosmos.

After 30 years’ residence in Athens, he was prosecuted on a charge of impiety for asserting that the Sun is an incandescent stone somewhat larger than the region of the Peloponnese. The attack on him was intended as an indirect blow at Pericles, and, although Pericles managed to save him, Anaxagoras was compelled to leave Athens. He spent his last years in retirement at Lampsacus.