At his native town of Clazomenae in Asia Minor, he had, it appears, some amount of property and prospects of political influence, both of which he surrendered, from a fear that they would hinder his search after knowledge. Nothing is known of his teachers; there is no reason for the theory that he studied under Hermotimus of Clazomenae, the ancient miracle-worker.
In early manhood (c. 464-462 BC) he went to Athens, which was rapidly becoming the headquarters 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. Some authorities assert that even Socrates was among his disciples. His influence was due partly to his astronomical and mathematical eminence, but still more to the ascetic dignity of his nature and his superiority to ordinary weaknesses—traits which legend has embalmed. It was he who brought philosophy and the spirit of scientific inquiry from Ionia to Athens. His observations of the celestial bodies led him to form new theories of the universal order, and brought him into collision with the popular faith. He attempted, not without success, to give a scientific account of eclipses, meteors, rainbows and the sun, which he described as a mass of blazing metal, larger than the Peloponnesus; the heavenly bodies were masses of stone torn from the earth and ignited by rapid rotation. The polytheism of the time could not tolerate such explanation, and the enemies of Pericles used the superstitions of their countrymen as a means of attacking him in the person of his friend.
Anaxagoras was arrested on a charge of contravening the established dogmas of religion (some say the charge was one of Medism), and it required all the eloquence of Pericles to secure his acquittal. Even so he was forced to retire from Athens to Lampsacus (434-433 BC), where he died about 428 BC, honoured and respected by the whole city.
It is difficult to present the cosmological theory of Anaxagoras in an intelligible scheme. All things have existed in a sort of 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 were the seeds (spermata) or miniatures of corn and flesh and gold in the primitive mixture; but these parts, of like nature with their wholes (the omoiomere of Aristotle), had to be eliminated from the complex mass before they could receive a definite name and character. The existing species of things having thus been transferred, with all their specialities, to the prehistoric stage, they were multiplied endlessly in number, by reducing their size through continued subdivision; at the same time each one thing is so indissolubly connected with every other that the keenest analysis can never completely sever them. The work of arrangement, the segregation of like from unlike and the summation of the omoiomere into totals of the same name, was the work of Mind or Reason; panta chremata en omou eita nous elthon auta diekosmese. This peculiar thing, called Mind (nous), was no less illimitable than the chaotic mass, but, unlike the Intelligence of Heraclitus, it stood pure and independent (mounos ef eoutou), 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 originated a rotatory movement in the mass (a movement far exceeding the most rapid in the world as we know it), which, arising in one corner or point, gradually extended till it gave distinctness and reality to the aggregates of like parts. But even after it has done its best, the original intermixture of things is not wholly overcome. No one thing in the world is ever abruptly separated, as by the blow of an axe, from the rest of things. The name given to it signifies merely that in that congeries of fragments the particular "seed" is preponderant. Every a of this present universe is only a by a majority, and is also in lesser number b, c, and d. It is noteworthy that Aristotle accuses Anaxagoras of failing to differentiate between nous and psyche, while Socrates (Plato, Phaedo, 98 B) objects that his nous is merely a deus ex machina to which he refuses to attribute design and knowledge.
Anaxagoras proceeded to give some account of the stages in the process from original chaos to present arrangements. The division into cold mist and warm ether first broke the spell of confusion. With increasing cold, the former gave rise to water, earth and stones. The seeds of life which continued floating in the air were carried down with the rains and produced vegetation. Animals, including man, sprang from the warm and moist clay. If these things be so, then the evidence of the senses must be held in slight esteem. We seem to see things coming into being and passing from it; but reflection tells us that decease and growth only mean a new aggregation (sugkrisis) and disruption (diakrisis). Thus Anaxagoras distrusted the senses, and gave the preference to the conclusions of reflection. Thus he maintained that there must be blackness as well as whiteness in snow; how otherwise could it be turned into dark water?
Anaxagoras marks a turning-point in the history of philosophy. With him speculation passed from the colonies of Greece to settle at Athens. By the theory of minute constituents of things, and his emphasis on mechanical processes in the formation of order, he paved the way for the atomic theory. By his enunciation of the order that comes from reason, on the other hand, he suggested, though he seems not to have stated explicitly, the theory that nature is the work of design. The conception of reason in the world passed from him to Aristotle, to whom it seemed the dawn of sober thought after a night of disordered dreams. From Aristotle it descended to his commentators, and under the influence of Averroes became the engrossing topic of speculation.