Plato was born in Athens ca. 427 BCE. The son of wealthy parents, he was afforded a solid education. During his youth it’s almost certain that Plato was a follower of Socrates, as Plato makes mention of him in his Dialogues. In fact, the arrest, trial and execution of Socrates had a significant impact on Plato, and after the execution in 399 BCE he left Greece for Egypt, Sicily and Italy.
When in Italy, Plato learned of the works of the Pythagoreans, and from these developed his ideas on reality.
The Pythagoreans are considered the first group to study mathematics as an intellectual pursuit, helping to seperate the world of mathematics from the ‘real world’ an this affected Plato greatly.
Plato considered mathematical objects to be perfect forms, which cannot be created in the real world. In Phaedo, Plato talks of objects in the real world trying to be like their perfect forms. As an example, a line in mathematics has length but no width, therefore it’s impossible to draw a true line in reality, because a line on a page requires some width in order to be seen. A perfect line also continues forever, which is just as impossible to draw. Of course, we can draw lines with arrows on them to represent the infinite direction, but this is just a crude representation.
Plato and the Academy
Plato returned to Athens in 387 BCE and founded the academy where he worked until his death in 347 BCE. The academy was devoted to research into philosophy, science and mathematics.
Though very found of mathematics, Plato did not advanced mathematical thought, though the ideas of Pythagoras continued through him, and his reverence of mathematics extended to his students. This makes Plato a very important link in the chain of Greek mathematics. In fact, in The Republic Plato states that one must study the five mathematical disciplines: arithmetic, plane geometry, solid geometry, astronomy and music, before moving on to study philosophy.
Actually, there is some mathematics attached to Plato: the Platonic solids. Though they are named after him these five shapes with neat properties – the tetrahedron, cube, octahedron, dodecahedron and icosahedron – were known to many before Plato’s name was attached to them.