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Heraclitus had a unique view of reality. For him change was the most important fact about the world, as the lines quoted illustrate. Brooks in his Introduction and brief Notes points out that it is very difficult to translate such ancient writing into contemporary English. The changes in the culture, the figures of speech, the chasm between the background of the contemporary reader and that of a Greek of twenty-five hundred years ago as relates to our understanding of the world, and so forth, makes literal translation pointless and freer translation subject to question. It is a point to keep in mind when considering any of these Pre-Socratics. Heraclitus also illustrates the point that these early philosophers do have important things to tell us about the world. Xenophanes

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.

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.

One minority possesses special rights (deriving mainly from the Treaty of Lausanne): the Muslim minority of Thrace.

Ancient Greece was also renowned for its pottery, which included everything from drinking vessels to urns. Black-figure pottery, in which the decorations appear as black silhouettes over a red background, are highly representative of early Greek craftsmanship. Later forms include red-figure pottery and white-figure pottery.

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.

Greek folk traditions are said to derive from the music played by ancient Greeks. There are said to be two musical movements in Greek folk music: akritic and klephtic. Akritic music comes from the 9th century akrites, or border guards of the Byzantine Empire. Following the end of the Byzantine period, klephtic music arose before the Greek Revolution, developed among the kleftes, warriors who fought against the Ottoman Empire. Klephtic music is monophonic and uses no harmonic accompaniment.

The range of colours which could be used on pots was restricted by the technology of firing: black, white, red, and yellow were the most common. In the three earlier periods, the pots were left their natural light colour, and were decorated with slip that turned black in the kiln.

It is certain that Greek philosophy, particularly Platonism, contributed to the early development of Christianity, which spread to Greece in the first century A.D. After the legalisation of Christianity by the Roman Emperor Constantine I in 313, the Christian faith became the dominant religion of the Roman Empire, of which Greece was a part. In the Great Schism of 1054, the Eastern and Western churches split, and Eastern Orthodox Christianity remains the predominant religion in Greece until this day. Since 1833, the Orthodox Church of Greece has remained an autocephalous church within the Eastern Orthodox Communion. The majority of modern Greeks (95 to 98 percent) remain at least nominally members of the Orthodox church.

Surviving examples of the ancient Greek sculpture are more common, particularly the works of the Greek master sculptors, such as Phidias and Praxiteles. These artists and their followers were frequently emulated by the Romans. However, the Christians of the 4th and 5th centuries viewed the destruction of pagan idols as an act of piety. Many ancient marble sculptures were burned to form lime in the Middle Ages, and most bronze statues were melted down for their metal. The marble statues that escaped destruction were spared as they were either buried and forgotten, or in the case of bronzes, lost at sea.