Plato, known as perhaps the greatest of all the ancient Greek philosophers and educators, was more interested in moral rather than natural (or scientific) philosophy. Nevertheless, he made many important contributions to the philosophy of mathematics and physics, primarily through his belief and teachings that mathematics provided the best training for the mind. Born in Athens, Greece, to wealthy and aristocratic parents, Plato was originally named Aristocles. He later was called "Platon," meaning broad, by schoolmates as a nickname because of his broad shoulders. Plato's first inclination was to enter politics, but he grew disillusioned with political life, especially after his teacher, the Greek philosopher Socrates, received a death sentence by the government of Athens. After the death of his mentor, who committed suicide in 399 B.C., Plato left Athens and traveled to Egypt and Italy, where he learned to appreciate mathematics from the disciples of Pythagoras.
When Plato returned to Athens he devoted his life to philosophy and founded the Academy, considered by some to be the first real university. Most of what is known about Plato and his philosophy can be found in Plato's dialogues, a series of writings in which his mentor Socrates discusses issues with students and others. Although Plato never introduces himself into these writings, many of the beliefs and statements are Plato's own. Plato emphasized that ideas represented what is constant and true in life, and was drawn to mathematics because it represented idealized abstractions, and seemed superior to the mundane material world. Plato was enamored with the possibility of developing a type of pure, rather than applied, mathematics to study the universe. For example, in his dialogue Timaeus, Plato expounds his believe that the heavenly bodies reveal a perfect geometric form. He also describes the existence of what has become known as the five Platonic solids, which he may have learned about from the Pythagoreans. These forms--the tetrahedron, cube, octahedron, icosahedron, and dodecahedron--represented mathematical models of the elements earth, fire, air, water, and, in the case of dodecahedron, the entire universe. German astronomer Johannes Kepler, nearly 2,000 years later, developed his own cosmology, or theory of the structure of the universe, based on these same shapes.
Plato's emphasis on proofs stemming from a clear hypothesis and accurate definitions, precluded Euclid's later systematic approach to mathematics. In addition, friends or pupils of Plato, including Archytas, conducted much of the most important mathematical work of the fourth century B.C. Through his academy, Plato also advocated that students should progress and learn four fields of mathematical study, beginning with arithmetic and then progressing to plane geometry, solid geometry, then astronomy and harmonics, both of which he believed were based on precise mathematical principles. Plato's adherence to the philosophy that mathematics represents precise and definite thinking is illustrated by the inscription over his Academy's main entrance, which read, "Let no one unversed in geometry enter here."
Plato lived to be approximately 80 years of age and is reported to have died peacefully, either in his sleep after attending a student's wedding or while working quietly on his studies. Plato's influence on philosophy and the development of mathematics continued long after his death. His academy remained in existence for about 900 years, until 529 A.D., when the Eastern Roman Emperor, Justinian, ordered it closed because he considered it a pagan establishment in what had become a Christian world.
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