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No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. And ancient Pythagoreans usually quoted their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the essentially oral nature of his teaching

The European renaissance was primarily the rediscovery and reintroduction of the culture and learning of ancient Greek religion and society by western Europe.

Thales of Miletus is regarded by many as the father of science; he was the first Greek philosopher to seek to explain the physical world in terms of natural rather than supernatural causes. Pythagoras was a Greek mathematician who is known as the "father of numbers"; it is believed that he had the pioneering insight into the numerical ratios that determine the musical scale, and the Pythagorean theorem is commonly attributed to him. Diophantus of Alexandria is sometimes called the "father of algebra", and much of modern geometry is based on the work of Euclid. Eratosthenes was one of the first scientific geographers, calculating the circumference of the earth and making the first maps based on scientific principles. Hipparchus is considered to be the greatest astronomical observer of the ancient world, and was probably the first to develop an accurate method of predicting solar eclipses. Aristarchus was the first known astronomer to propose a heliocentric model of the solar system, though the geocentric model of Ptolemy was more commonly accepted until the sixteenth century. Ptolemy also contributed much to cartography and to the science of optics. Archimedes was the first to calculate the value of p and the first to calculate a geometric series; he also was the first mathematical physicist, discovered the law of buoyancy, and invented the irrigation device known as Archimedes' screw.

Syncretism was an essential feature of Greek paganism. Hellenistic culture in the age that followed Alexander the Great was itself syncretic, essentially a blend of Persian, Anatolian, Egyptian (and eventually Etruscan-Roman) elements within a Hellenic overall formula.

Most of the best known surviving Greek buildings, such as the Parthenon and the Temple of Hephaestus in Athens, are Doric. The Erechtheum, next to the Parthenon, however, is Ionic. The Ionic order became dominant in the Hellenistic period, since its more decorative style suited the aesthetic of the period better than the more restrained Doric. Some of the best surviving Hellenistic buildings, such as the Library of Celsus, can be seen in Turkey, at cities such as Ephesus and Pergamum. But in the greatest of Hellenistic cities, Alexandria in Egypt, almost nothing survives.

Thales is said to have died in his seat, while watching an athletic contest.

The history of the Greeks, however, extends far beyond the current borders of Greece. As early as the 7th century BC the Greeks were colonising parts of what are now Turkey, Cyprus, Italy and Libya. The conquests of Alexander the Great in the 4th century BC established Greek rule over Anatolia, Egypt, Syria and Mesopotamia. As parts of the Byzantine Empire, these areas and others were part of the Greek world for many centuries. By the 15th century, however, nearly all the Greeks were living under the rule of the Ottoman Empire.

Out of the vague and limitless body there sprung a central mass — this earth of ours, cylindrical in shape, poised equidistant from surrounding orbs of fire, which had originally clung to it like the bark round a tree, until their continuity was severed, and they parted into several wheel-shaped and fire-filled bubbles of air.