Plato had a brilliant mind, and looking deep into many of his philosophies and belief brings out basic math concepts that are taught in schools today. For example, in his definition of wisdom, which he equates with courage prudence, he follows a chain of logic. He says courage and prudence are not the same and defines each. The foundation of his argument is simple: A is equal to B and also A is not equal to C. Therefore B is not equal to C. This basic chain of logic can be attributed to Plato's work.
In Plato's "Timaeus," he creates a mathematical construction of the elements earth, wind, air, fire and water represented by various geometrical shapes. These shapes that he defined are the cube, octahedron, icosahedron and tetrahedron. He also defined the entire universe as a dodecahedron, or shape with 12 sides. Modern geometry draws from these principles.
In his studies with Socrates, Plato laid out a square and divided it into four smaller squares. After many trials with squares and triangles, Plato concluded that a line is an object having length but no depth. His work on lines and squares was extensive and led to the definitions of types of triangles and other shapes.
Plato's greatest discovery may have been that math is the most important subject for the human mind. He wrote "that the reality which scientific thought is seeking must be expressible in mathematical terms, mathematics being the most precise and definite kind of
thinking of which we are capable."