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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

In astronomy, the Pythagoreans were well aware of the periodic numerical relations of the planets, moon, and sun. The celestial spheres of the planets were thought to produce a harmony called the music of the spheres. These ideas, as well as the ideas of the perfect solids, would later be used by Johannes Kepler in his attempt to formulate a model of the solar system in his work The Harmony of the Worlds. Pythagoreans also believed that the earth itself was in motion.

An overview of the 2004 Olympic infrastructureDespite the country's numerically small and ill-equipped armed forces, Greece made a decisive contribution to the Allied efforts in World War II. At the start of the war Greece sided with the Allies and refused to give in to Italian demands. Italy invaded Greece on 28 October 1940, but Greek troops repelled the invaders after a bitter struggle. This marked the first Allied victory in the war. Hitler then reluctantly stepped in, primarily to secure his strategic southern flank: troops from Germany, Hungary, Bulgaria and Italy successfully invaded Greece, overcoming Greek, British, Australian and New Zealand units.

The fully mature black-figure technique, with added red and white details and incising for outlines and details, originated in Corinth during the early 7th century BC and was introduced into Attica about a generation later; it flourished until the end of the 6th century BC. The red-figure technique, invented in about 530 BC, reversed this tradition, with the pots being painted black and the figures painted in red. Red-figure vases slowly replaced the black-figure style. Sometimes larger vessels were engraved as well as painted.

There were two main styles (or "orders") of Greek architecture, the Doric and the Ionic. These names were used by the Greeks themselves, and reflected their belief that the styles descended from the Dorian and Ionian Greeks of the Dark Ages, but this is unlikely to be true. The Doric style was used in mainland Greece and spread from there to the Greek colonies in Italy. The Ionic style was used in the cities of Ionia (now the west coast of Turkey) and some of the Aegean islands. The Doric style was more formal and austere, the Ionic more relaxed and decorative. The more ornate Corinthian style was a later development of the Ionic. These styles are best known through the three orders of column capitals, but there are differences in most points of design and decoration between the orders. See the separate article on Classical orders.

Greece must realign its economy as part of an extended transition to full EU membership that began in 1981. Greek businesses are adjusting to competition from EU firms and the government has had to liberalize its economic and commercial regulations and practices. However, Greece has been granted waivers from certain aspects of the EU's 1992 single market program.

Greek painters worked mainly on wooden panels, and these perished rapidly after the 4th century AD, when they were no longer actively protected. Today nothing survives of Greek painting, except some examples of painted terra cotta and a few paintings on the walls of tombs, mostly in Macedonia and Italy. Of the masterpieces of Greek painting we have only a few copies from Roman times, and most are of inferior quality. Painting on pottery, of which a great deal survives, gives some sense of the aesthetics of Greek painting. The techniques involved, however, were very different from those used in large-format painting.

Sculpture is by far the most important surviving form of Ancient Greek art, although only a small fragment of Greek sculptural output has survived. Greek sculpture, often in the form of Roman copies, was immensely influential during the Italian Renaissance, and remained the “classic” model for European sculpture until the advent of modernism in the late 19th century.

Thales' most famous belief was his cosmological doctrine, which held that the world originated from water. Aristotle considered this belief roughly equivalent to the later ideas of Anaximenes, who held that everything in the world was composed of air. Thus it is sometimes assumed that Thales considered everything to be made from water. According to Lloyd, however, it's likely that while Thales saw water as an origin, he never pondered whether water continued to be the substance of the world.

The basic cube or rectangle was usually flanked by colonnades (rows of columns) on either two or on all four sides. This is the format of the Parthenon. Alternatively, a cube-shaped building would have a columned portico (or pronaos in Greek) forming its entrance, as seen at the Pantheon. The Greeks understood the principles of the masonry arch but made little use of it, and did not put domes on their buildings— these refinements were left to the Romans. The Greeks roofed their buildings with timber beams covered with overlapping terra cotta (or occasionally marble) tiles.