Philolaus (circa 480 BC – circa 405 BC) was a Greek Pythagorean and Presocratic.

As is the case with most other Presocratic thinkers, "any chronology constructed for his life is a fabric of the loosest possible weave." Huffman, Carl. Philolaus of Croton Pythagorean and Presocratic: A Commentary on the Fragments and Testimonia With Interpretive Essays. New York: Cambridge University Press, 1993. p. 1–16. But that should not diminish the importance of establishing such a chronology, which helps scholars see his relationship to other Pre-Socratics. A passage out of Plato's Phaedo reveals his influence on two of the characters within the dialogue:

''What, Cebes? Have you and Simmias not heard about such things in your association with Philolaus? Nothing definite, at least, Socrates... Why ever then do they deny that it is unlawful to kill oneself Socrates? For, to answer the question that you were just now asking, I already heard from Philolaus, when he was spending time with us, and before that from some others as well, that it was not right to do this.

This passage makes clear thatPhilolaus had spent time in Thebes and was heard by Simmias and Cebes around the time the Phaedo was written, in 399 BC. The dates of his birth and death are culled from his known association with other Pre-Socratics, as well as the date of the burning of the Pythagorean meeting-place (which he fled from), around 454 BC. Besides this chronological outinle the details of Philolaus life are unknown to us.

Philolaus was a contemporary of Socrates and Democritus, but senior to them, and was probably somewhat junior to Empedocles, and a contemporary of Zeno of Elea, Melissus and Thucydides, so that his birth may be placed at about 480 BC.

Philolaus was born in either Croton, Tarentum, or Heraclea, according to the doxography of Diogenes Laertius.

He was said to have been intimate with Democritus, and was probably one of his teachers. Philolaus was the first Pyhtagorean to write and disemminate any philosophical treatise at all; he published a book, of whick remain only extant fragments of other philosophers and doxographers. 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), all three of whom were subsequently 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 either Pythagoras or the 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 revolve around the central fire. In this model the Earth and the Sun lie 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 position in relation to the Earth was parallel to the relative positions of the Earth and the Sun; that of two spheres, connected at fixed points along a circle. He further advanced ideas about the Earth's rotation around its axis: this influenced Aristarchus of Samos dramatically. Such a theory about the solar system quite well explained the movement of the Sun and the differing lengths of days through the year. It is not known how accurate it was.

Nicolaus Copernicus mentions in De revolutionibus that Philolaus already knew about the Earth's revolution around a central fire.

He supposed the Sun to be a disk of glass which reflects the light of the universe. He made the lunar month consist of 29 1/2 days, the lunar year of 354, and the solar year of 365 1/2 days.

He was the first to publish 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 was deeply involved in the distinctively Pythagorean number theory, dwelling particularly 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 motivating boost to the study of science. Following Parmenides' philosophy, 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.

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