Responding to the claims of Parmenides on the impossibility of change, Anaxagoras described the world as a mixture of primary imperishable ingredients, where material variation was never caused by an absolute presence of a particular ingredient, but rather by its relative preponderance over the other ingredients; in his words, "each one is... most manifestly those things of which there are the most in it". He introduced the concept of Nous (Mind) as an ordering force, which moved and separated out the original mixture, which was homogeneous, or nearly so.
He also gave a number of novel scientific accounts of natural phenomena. He produced a correct explanation for eclipses and described the sun as a fiery mass larger than the Peloponnese, as well as attempting to explain rainbows and meteors.
Anaxagoras is believed to have enjoyed some wealth and political influence in his native town of Clazomenae, in Asia Minor. However, he supposedly surrendered this out of a fear that they would hinder his search for knowledge. The Roman author Valerius Maximus preserves a different tradition: Anaxagoras, coming home from a long voyage, found his property in ruin, and said: "If this had not perished, I would have"—a sentence described by Valerius as being "possessed of sought-after wisdom!" Although a Greek, he may have been a soldier of the Persian army when Clazomenae was suppressed during the Ionian Revolt.
In early manhood (c. 464 – 461 BC) he went to Athens, which was rapidly becoming the centre of Greek culture. There he is said to have remained for thirty years. Pericles learned to love and admire him, and the poet Euripides derived from him an enthusiasm for science and humanity.
Anaxagoras brought philosophy and the spirit of scientific inquiry from Ionia to Athens. His observations of the celestial bodies and the fall of meteorites led him to form new theories of the universal order, and to a putative prediction of the impact of a meteorite in 467 BC. He attempted to give a scientific account of eclipses, meteors, rainbows, and the sun, which he described as a mass of blazing metal, larger than the Peloponnese. The heavenly bodies, he asserted, were masses of stone torn from the earth and ignited by rapid rotation. He explained that, though both sun and the stars were fiery stones, we do not feel the heat of the stars because of their enormous distance from earth. He was the first to explain that the moon shines by reflecting the sun's light. He thought that the earth is flat and floats supported by 'strong' air under it and disturbances in this air sometimes causes earthquakes. These speculations made him vulnerable in Athens to a charge of impiety. Diogenes Laertius reports the story that he was prosecuted by Cleon for impiety, but Plutarch says that Pericles sent his former tutor, Anaxagoras, to Lampsacus for his own safety after the Athenians began to blame him for the Peloponnesian war.
According to Laertius, Pericles spoke in defense of Anaxagoras at his trial, c. 450 BC. Even so, Anaxagoras was forced to retire from Athens to Lampsacus in Troad (c. 434 – 433 BC). He died there in around the year 428 BC. Citizens of Lampsacus erected an altar to Mind and Truth in his memory, and observed the anniversary of his death for many years.
Anaxagoras wrote a book of philosophy, but only fragments of the first part of this have survived, through preservation in work of Simplicius of Cilicia in the 6th century AD.
According to Anaxagoras all things have existed in some way from the beginning, but originally they existed in infinitesimally small fragments of themselves, endless in number and inextricably combined throughout the universe. All things existed in this mass, but in a confused and indistinguishable form. There was an infinite number of homogeneous parts (ὁμοιομερῆ) as well as heterogeneous ones.
The work of arrangement, the segregation of like from unlike and the summation of the whole into totals of the same name, was the work of Mind or Reason (νοῦς). Mind is no less unlimited than the chaotic mass, but it stood pure and independent, a thing of finer texture, alike in all its manifestations and everywhere the same. This subtle agent, possessed of all knowledge and power, is especially seen ruling in all the forms of life. Its first appearance, and the only manifestation of it which Anaxagoras describes, is Motion. It gave distinctness and reality to the aggregates of like parts.
Decease and growth represent a new aggregation (σὐγκρισις) and disruption (διάκρισις). However, the original intermixture of things is never wholly overcome. Each thing contains in itself parts of other things or heterogeneous elements, and is what it is, only on account of the preponderance of certain homogeneous parts which constitute its character. Out of this process arises the things we see in this world.