Some say that Plato's real name was Aristocles, and that Plato was a nickname, meaning "the broad". The nickname might refer from the width of his shoulders or forehead or from the breadth of his style. As a young man, Plato studied under Cratylus, himself a student of Heracleitus. It almost certain that Plato became friends with Socrates when he was young.

Plato was in military service from 409 BC to 404 BC, at the end of the Peloponnesian War, but at this time he wanted a political career rather than a military one. However, the excesses of Athenian political life during peacetime seems to have persuaded him to give up political ambitions. In particular, the execution of Socrates in 399 BC had a profound effect on him and he decided that he would have nothing further to do with politics.

Plato travelled in Egypt, Sicily and Italy. In Egypt he learned of a water clock. In Italy he learned of the work of Pythagoras, and came to appreciate the value of mathematics. Again there was a period of war and again Plato entered military service.

On his return to Athens, Plato founded, around 387 BC a school of learning called the Academy. Plato presided over the Academy, an institution devoted to research and instruction in philosophy and the sciences until his death. His reasons for setting up the Academy were to train young men who would become better statesmen.

Plato's main contributions are in philosophy, mathematics and science. However, it is not as easy as one might expect to discover Plato's philosophical views. The reason for this is that Plato wrote no systematic treatise giving his views, rather he wrote about 30 dialogues written in the form of conversations. Not only are these dialogues important works of philospophy, but they are superb pieces of literature.

Through these dialogues, Plato contributed to the theory of art, in particular dance, music, poetry, architecture, and drama. He discussed a whole range of philosophical topics including ethics, metaphysics where topics such as immortality, man, mind, and Realism are discussed. He discussed the philosophy of mathematics, political philosophy, and religious philosophy. In his theory of Forms, Plato rejected the changeable, deceptive world that we are aware of through our senses proposing instead his world of ideas which were constant and true. In his Republic, Plato talks of geometrical diagrams as imperfect imitations of the perfect mathematical objects which they represent. He also contributed to logic and legal philosophy, including rhetoric.

Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely important in the development of the subject. Plato's contributions to the theories of education are shown by the way that he ran the Academy and his idea of what constitutes an educated person. Over the door of the Academy was written: "Let no one unversed in geometry enter here".

Plato concentrated on the idea of "proof" and insisted on accurate definitions and clear hypotheses. This laid the foundations for Euclid's systematic approach to mathematics. All of the most important mathematical work of the fourth century was done by friends or pupils of Plato, including Eudoxus, Aristotle, and Archytas.

In mathematics Plato's name is attached to the Platonic solids. In the Timaeus, there is a mathematical construction of the elements earth, fire, air, and water being represented by the cube, tetrahedron, octahedron, and icosahedron repectively. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

Plato's Academy flourished until 529 when it was closed down by the Christian Emperor Justinian, who claimed it was a pagan establishment. Having survived for 900 years it is the longest surviving university known.