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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

Whether or not we attribute the Pythagorean theorem to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the musical scale, since this plays a key role in many other areas of the Pythagorean tradition and since no evidence remains of earlier Greek or Egyptian musical theories. Another important discovery of this school -- which upset Greek mathematics, as well as the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties -- was the incommensurability of the diagonal of a square with its side. This result showed the existence of irrational numbers.

By the end of the 14th century, a poetic form called mantinada became popular; it was a rhyming couplet of fifteen syllables.

Hellenistic sculpture was also marked by an increase in scale, which culminated in the Colossus of Rhodes (late 3rd century), which was the same size as the Statue of Liberty. The combined effect of earthquakes and looting have destroyed this as well as other very large works of this period.

Greek music is a mixture of influences from its own indigenous culture with Western and Middle Eastern cultures. Turkish and Ottoman elements can be most clearly heard in the traditional songs, dhimotiká, as well as the modern bluesy rembétika music.

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.

The art of ancient Greece has exercised an enormous influence on the culture of many countries from ancient times until the present, particularly in the areas of sculpture and architecture. In the West, the art of the Roman Empire was largely derived from Greek models. In the East, Alexander the Great's conquests initiated several centuries of exchange between Greek, Central Asian and Indian cultures, resulting in Greco-Buddhist art, with ramifications as far as Japan. Following the Renaissance in Europe, the humanist aesthetic and the high technical standards of Greek art inspired generations of European artists. Well into the 19th century, the classical tradition derived from Greece dominated the art of the western world.

As noted above, the Archaic age is usually dated from about 1000 BC, although in reality little is known about art in Greece during the preceding 200 years (traditionally known as the Dark Ages). The onset of the Persian Wars (480 BC to 448 BC) is usually taken as the dividing line between the Archaic and the Classical periods, and the reign of Alexander the Great (336 BC to 323 BC) is taken as separating the Classical from the Hellenistic periods.

The Greek Constitution claims absolute freedom of religion. It also states that all persons living within the Greek territory shall enjoy full protection of their religious beliefs. Note however, that apart from Christian churches and Jewish synagogues, visibly operational temples of other religions do not exist in the capital, mainly due to opposition from the Greek Church. The Orthodox Church, as well as the secular state must approve any activities related to building official temples. The Constitution defines the "prevailing religion" of Greece as the Eastern Orthodox Church of Christ.

In the 19th century, opera composers like Nikolaos Mantzaros (1795 - 1872), Spyridion Xyndas (1812 - 1896) and Spyros Samaras (1861 - 1917) helped revitalize Greek classical music

The Greek economy is growing fast after the implementation of stabilization policies in recent years. Greece remains a net importer of industrial and capital goods, foodstuffs, and petroleum. Leading exports are manufactured goods, food and beverages, petroleum products, cement, chemicals, and pharmaceuticals.

The Greeks decided at a very early period that the human form was the most important subject for artistic endeavour. Since they saw their gods as having human form, there was no distinction between the sacred and the secular in art — the human body was both secular and sacred. A male nude could just as easily be Apollo or Herakles or that year's current Olympic boxing champion. In the Archaic Period the most important sculptural form was the kouros (plural kouroi), the standing male nude (See for example Biton and Kleobis). The kore (plural korai), or standing female figure, was also common, but since Greek society did not permit the public display of female nudity until the 4th century BC, the kore is considered to be of less importance in the development of sculpture.

The shores of the Aegean Sea saw the emergence of the first civilizations in Europe, namely the Minoan and Mycenaean civilisations. After these subsided a Dark Age followed until around 800 BC a new era of Greek civilization emerged. This Greece of city-states established colonies along the Mediterranean and partially resisted Persian invasions. Greek culture would later become the basis of the Hellenistic civilisation that followed the empire of Macedonian King Alexander of Macedon.

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.