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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

Anaximander offered up the theory of the apeiron in direct response to the earlier theory of Thales, who had claimed that the primary substance was water. Anaximander reasoned that water cannot embrace all of the opposites found in nature — for example, water can only be wet, never dry — and therefore, it can not be the one primary substance. Nor could any of the other candidates, so Anaximander postulated the apeiron as a substance that, although it could not be perceived directly, could explain the opposites he could clearly see around him.

Every Greek town of any size also had a palaestra or a gymnasium. These were essentially enclosed spaces, open to the sky and lined with shaded colonnades, used for athletic contests and exercise: they were the social centres for male citizens. Greek towns also needed at least one bouleuterion or council chamber, a large square building which served as both a meeting place for the town council (boule) and as a court house. Because the Greeks did not use arches or domes, they could not build large rooms with unsupported rooves: the bouleuterion thus had rows of internal columns to hold the roof up. No examples of these buildings survive.

Since Greek law does not permit the operation of private universities in Greece, a large and growing number of students are pursuing higher education abroad. The Greek Government decides through an evaluation procedure whether to recognize degrees from specific foreign universities as qualification for public sector hiring. Other students attend private, post-secondary educational institutions in Greece that are not recognized by the Greek Government.

During this period sculpture became more and more naturalistic. Common people, women, children, animals and domestic scenes became acceptable subjects for sculpture, which was commissioned by wealthy families for the adornment of their homes and gardens. Realistic portraits of men and women of all ages were produced, and sculptors no longer felt obliged to depict people as ideals of beauty or physical perfection. At the same time, the new Hellenistic cities springing up all over Egypt, Syria, and Anatolia required statues depicting the gods and heroes of Greece for their temples and public places. This made sculpture, like pottery, an industry, with the consequent standardisation and some lowering of quality. For these reasons many more Hellenistic statues have survived than is the case with the Classical period.

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.

Pythagoras has the reputation of having taught a doctrine of reincarnation. His other teachings appear framed in pithy sayings, or sumbola, often in question-and-answer format. Some of these teachings took a simple form: "What is wisest?" "Number"; "What is truest?" "Most men are bad." Others were more cryptic: "What is the Delphic oracle?" "The tetraktys, in which the Sirens sing." Other sumbola related to sexual, dietary and other taboos, including the proper way to stir a fire or place one's shoes before going to sleep.