A classic philologist August Boeckh (1785-1867) places his life between the 70th and 95th Olympiadss (496 BC-396 BC). Philolaus was a contemporary of Socrates and Democritus, but senior to them, and was probably somewhat junior to Empedocles, and a comtemporary of Zeno of Elea, Melissus and Thucydides, so that his birth may be placed at about 480 BC.
He was said to have been intimate with Democritus, and was probably one of his teachers. He was an immediate pupil and transcriber of Pythagoras and after the death of his teacher great dissentions prevailed in the cities of lower Italy. According to some accounts, Philolaus, obliged to flee, took refuge first in Lucania and then at Thebes, where he had as pupils Simmias and Cebes (Crito), who subsequently, being still young men, were present at the death of Socrates in 399 BC. Before this Philolaus had returned to Italy, where he was the teacher of Archytas (428 BC - 347 BC). Philolaus was perhaps also connected with the Pythagorean exiles at Phlius mentioned in Plato's Phaedo.
Philolaus spoke and wrote in a Greek Doric dialect and was the first to propound the doctrine of the motion of the Earth; some attribute this doctrine to Pythagoras, but there is no evidence in support of their view and also to younger Hicetas (circa 400 BC - circa 335 BC) of Syracuse. Philolaus supposed that the sphere of the fixed stars, the five planets, the Sun, Moon and Earth, all moved round the central fire, but as these made up only nine revolving bodies he conceived, in accordance with his number theory, a tenth, which he called counter-earth. The central holy fire was not the Sun for him, but some mysterious thing between the Earth and counter-earth. He named it "estia", the hearth of the universe, the house of Zeus, and the mother of the gods, after the goddess of fire and hearth Hestia. He kept an idea of the Earth's rotation around its axis. Probably he misunderstood his teacher, because he entangled the idea and he introduced a certain "primordial Earth", the "antichthon", for these numerological reasons, which together with the Earth and the Sun revolves around the central fire. The Earth and the Sun lie in this occasion always opposite to each other. His idea was restored and resumed around 345 BC by Heraclides of Heraclea (circa 388 BC-310 BC). This mysterious counter-earth was never seen, because its positions in view to the Earth was the same as mutual position of the Earth and the Sun as at two spheres, which are connected with a rope. In his deliberations Philolaus used a lot of his imagination and he did't explain what he might be able to do in another way. His further advanced idea about the Earth's rotation around its axis was important and it influenced on Aristarchus. The Earth has several kind of movements and it belongs to the planets. Such a solar system theory quite well explained the movement of the Sun and different lengths of days through the year. It is not known how accurate it was.
He was the first who published a book on the Pythagorean doctrines, a treatise of which Plato made use in the composition of his Timaeus. Philolaus represented the philosophical system of his school in a work Peri fyseos (About the nature). Speusipus, the Plato's successor at the Academy summarized Philolaus's work.
Philolaus entered deeply into the distinctively Pythagorean number theory, particularly dwelling on the properties inherent in the decad - the sum of the first four numbers, consequently the fourth triangular number, the tetractys - which he called great, all-powerful, and all-producing. The great Pythagorean oath was taken by the sacred tetractys. The discovery of the regular solids is attributed to Pythagoras by Eudemus, and Empedocles is stated to have been the first who maintained that there are four classical elements. Philolaus, connecting these ideas, held that the elementary nature of bodies depends on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to water, and the cube to earth; the dodecahedron he assigned to a fifth element, aether, or, as some think, to the universe. This theory, however superficial from the standpoint of observation, indicates considerable knowledge of geometry and gave a great impulse to the study of the science. Following Parmenides, Philolaus regarded the soul as a "mixture and harmony" of the bodily parts; he also assumed a substantial soul, whose existence in the body is an exile on account of sin.
Partly adapted from the 1911 Encyclopedia Britannica.