The School of Athens in the context of "Lyceum (classical)"

Academic skepticism was the philosophy of the skeptical period of the Academy dating from around 266 BCE, when Arcesilaus became scholarch, until around 90 BCE, when Antiochus of Ascalon rejected skepticism, although individual philosophers, such as Favorinus and his teacher Plutarch, continued to defend skepticism after this date. Unlike the existing school of skepticism, the Pyrrhonists, they maintained that knowledge of things is impossible. Ideas or notions are never true; nevertheless, there are degrees of plausibility, and hence degrees of belief, which allow one to act. The school was characterized by its attacks on the Stoics, particularly their dogma that convincing impressions led to true knowledge. The most important Academics were Arcesilaus, Carneades, and Philo of Larissa. The most extensive ancient source of information about Academic skepticism is Academica, written by the Academic skeptic philosopher Cicero.

Western civilization traces its roots back to Europe and the Mediterranean. It began in ancient Greece, transformed in ancient Rome, and evolved into medieval Western Christendom before experiencing such seminal developmental episodes as the development of Scholasticism, the Renaissance, the Reformation, the Scientific Revolution, the Enlightenment, the Industrial Revolution, and the development of liberal democracy. The civilizations of classical Greece and Rome are considered seminal periods in Western history. Major cultural contributions also came from the Christianized Germanic peoples, such as the Longobards, the Franks, the Goths, and the Burgundians. Charlemagne founded the Carolingian Empire and he is referred to as the "Father of Europe". Contributions also emerged from pagan peoples of pre-Christian Europe, such as the Celts and Germanic pagans as well as some significant religious contributions derived from Judaism and Hellenistic Judaism stemming back to Second Temple Judea, Galilee, and the early Jewish diaspora; and some other Middle Eastern influences. Western Christianity has played a prominent role in the shaping of Western civilization, which throughout most of its history, has been nearly equivalent to Christian culture. (There were Christians outside of the West, such as China, India, Russia, Byzantium and the Middle East). Western civilization has spread to produce the dominant cultures of modern Americas and Oceania, and has had immense global influence in recent centuries in many ways.

Following the 5th century Fall of Rome, Europe entered the Middle Ages, during which period the Catholic Church filled the power vacuum left in the West by the fall of the Western Roman Empire, while the Eastern Roman Empire (or Byzantine Empire) endured in the East for centuries, becoming a Hellenic Eastern contrast to the Latin West. By the 12th century, Western Europe was experiencing a flowering of art and learning, propelled by the construction of cathedrals, the establishment of medieval universities, and greater contact with the medieval Islamic world via Al-Andalus and Sicily, from where Arabic texts on science and philosophy were translated into Latin. Christian unity was shattered by the Reformation from the 16th century. A merchant class grew out of city states, initially in the Italian peninsula (see Italian city-states), and Europe experienced the Renaissance from the 14th to the 17th century, heralding an age of technological and artistic advance and ushering in the Age of Discovery which saw the rise of such global European empires as those of Portugal and Spain.

Leonardo da Vinci (April 15, 1452 – May 2, 1519) was an Italian Renaissance painter and polymath who achieved legendary fame and iconic status within his own lifetime. His renown primarily rests upon his brilliant achievements as a painter, as his Mona Lisa and The Last Supper are two of the most famous artworks ever created. But Leonardo is also known for his diverse skills as a scientist, inventor, engineer, theorist, sculptor, architect, descriptions and study of the human body, and more. He became so highly valued during his lifetime that the King of France bore him home like a trophy of war, supported him in his old age and, according to legend, cradled his head as he died.

Leonardo's portrait was used, within his own lifetime, as the iconic image of Plato in Raphael's School of Athens. His biography was written in superlative terms by Vasari. He has been repeatedly acclaimed the greatest genius to have lived. His painting of the Mona Lisa has been the most imitated artwork of all time and his drawing the Vitruvian Man iconically represents the fusion of Art and Science.

The Parnassus (Italian: Il Parnaso, referring to Mount Parnassus) is a fresco painting by the Italian High Renaissance artist Raphael in the Raphael Rooms ("Stanze di Raffaello"), in the Palace of the Vatican in Rome, painted at the commission of Pope Julius II.

It was probably the second wall of the Stanza della Segnatura to be painted between 1509 and 1511, after La Disputa and before The School of Athens, which occupy other walls of the room.

Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.

The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.

Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.

Already during Pythagoras's life it is likely that the distinction between the akousmatikoi ("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the mathematikoi ("those who learn") existed. The ancient biographers of Pythagoras, Iamblichus (c. 245 – c. AD 325) and his master Porphyry (c. 234 – c. AD 305) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the mystery schools of antiquity, the adherents, akousmatikoi, following initiation became mathematikoi. It is wrong to say that the Pythagoreans were superseded by the Cynics in the 4th century BC, but it seems to be a distinction mark of the Cynics to disregard the hierarchy and protocol, ways of initiatory proceedings significant for the Pythagorean community; subsequently did the Greek philosophical traditions become more diverse. The Platonic Academy was arguably a Pythagorean cenobitic institution, outside the city walls of Athens in the 4th century BC. As a sacred grove dedicated to Athena, and Hecademos (Academos). The academy, the sacred grove of Academos, may have existed, as the contemporaries seem to have believed, since the Bronze Age, even pre-existing the Trojan War. Yet according to Plutarch it was the Athenian strategos (general) Kimon Milkiadou (c. 510 – c. 450 BC) who converted this, "waterless and arid spot into a well watered grove, which he provided with clear running-tracks and shady walks". Plato lived almost a hundred years later, circa 427 to 348 BC. On the other hand, it seems likely that this was a part of the re-building of Athens led by Kimon Milkiadou and Themistocles, following the Achaemenid destruction of Athens in 480–479 BC during the war with Persia. Kimon is at least associated with the building of the southern Wall of Themistocles, the city walls of ancient Athens. It seems likely that the Athenians saw this as a rejuvenation of the sacred grove of Academos.