Plato remained at the Academy for the rest of his life, except for two brief periods in the 360s. At that time he visited Syracuse, the chief city of Greek Sicily, to serve as tutor for the new king, Dionysius II. Here was his chance to make a king a philosopher. It turned out very badly. The king insisted on behaving like a king and of course made the Athenian democrats look good by comparison. Plato managed only with difficulty to return safely to Athens. His end was peaceful and happy, for he is suppos ed to have died in his sleep at the age of eighty after having attended the wedding feast of one of his students.
Plato's works, perhaps the most consistently popular and influential philosophic writings ever published, consist of a series of dialogues in which the discussions between Socrates and others are presented with infinite charm. Most of our knowledge of Socrates is from these dialogues, and which views are Socrates' and which are Plato's is anybody's guess. (Plato cautiously never introduced himself into any of the dialogues.)
Like Socrates, Plato was chiefly interested in moral philosophy and despised natural philosophy (that is, science) as an inferior and unworthy sort of knowledge. There is a famous story (probably apocryphal and told also of Euclid of a student asking Plato the application of the knowledge he was being taught. Plato at once ordered a slave to give the student a small coin that he might not think he had gained knowledge for nothing, then had him dismissed from school. To Plato, knowledge had no practical use, it existed for the abstract good of the soul.
Plato was fond of mathematics because of its idealized abstractions and its separation from the merely material. Nowadays, of course, the purest mathematics manages to be applied, sooner or later, to practical matters of science. In Plato's day this was not so, and the mathematician could well consider himself as dealing only with the loftiest form of pure thought and as having nothing to do with the gross and imperfect everyday world. And so above the doorway to the Academy was written, "Let no one ignorant of mathematics enter here."
Plato did, however, believe that mathematics in its ideal form could still be applied to the heavens. The heavenly bodies, he believed, exhibited perfect geometric form. This he expresses most clearly in a dialogue called Timaeus in which he presents his scheme of the universe. He describes the five (and only five) possible regular solids -- that is, those with equivalent faces and with all lines and angles, formed by those faces, equal. These are the four-sided tetrahedron, the six-sided hexahed ron (or cube), the eight-sided octahedron, the twelve-sided dodecahedron, and the twenty-sided icosahedron. Four of the five regular solids, according to Plato, represented the four elements, while the dodecahedron represented the universe as a whole. These solids were first discovered by the , but the fame of this dialogue has led to their being called the Platonic solids ever since.
Plato decided also that since the heavens were perfect, the various heavenly bodies would have to move in exact circles (the perfect curve) along with the crystalline spheres (the perfect solid) that held them in place. The spheres were another Pythagorean notion, and the Pythagorean preoccupation with sound also shows itself in Philolaus belief that the spheres of the various planets made celestial music as they turned -- a belief that persisted even in the time of two thou sand years later. We still use the phrase "the music of the spheres" to epitomize heavenly sounds or the stark beauty of outer space.
This insistence that the heavens must reflect the perfection of abstract mathematics in its simplest form held absolute sway over astronomical thought until Kepler's time, even though compromises with reality had to be made constantly, beginning shortly after Plato's death with Eudoxus and Callippus.
In the dialogue Timaeus, by the way, Plato invented a moralistic tale about a thoroughly fictitious land he called Atlantis. If there is a Valhalla for philosophers, Plato must be sitting there in endless chagrin, thinking of how many foolish thousands, in all the centuries since his time, down to the very present day -- thousands who have never read his dialogue or absorbed a sentence of his serious teachings -- nevertheless believed with all their hearts in the reality of Atlantis. (To be s ure, recent evidence of an Aegean island that exploded volcanically in 1400 B.C. may have given rise to legends that inspired Plato's fiction.)
Plato's influence extended long past his own life and, indeed, never died. The Academy remained a going institution until A.D. 529, when the Eastern Roman Emperor, Justinian, ordered it closed. It was the last stronghold of paganism in a Christian world.
Plato's philosophy, even after that date, maintained a strong influence on the thinking of the Christian Church throughout the early Middle Ages. It was not until the thirteenth century that the views of gained dominance.