Biography: What was Plato Known for
Plato, often remembered as a philosopher, was a significant supporter of mathematics in ancient Greece. He established the Academy in Athens in 387 BCE, drawing inspiration from Pythagoras, and emphasized the role of mathematics in gaining a deeper understanding of reality. Plato firmly believed that geometry held the key to unraveling the universe’s mysteries, and a sign above the Academy’s entrance declared, “Let no-one ignorant of geometry enter here.”
Plato played a crucial role in motivating and influencing Greek intellectuals to explore both mathematics and philosophy. His Academy integrated mathematics into the realm of philosophy, much like Pythagoras had done. The first decade of the Academy’s 15-year curriculum focused on the study of science and mathematics, encompassing plane and solid geometry, astronomy, and harmonics. Plato earned the title “maker of mathematicians,” and his Academy boasted some of the most prominent mathematicians of the ancient world, including Eudoxus, Theaetetus, and Archytas.
He held his students to high standards, demanding precise definitions, clearly articulated assumptions, and rigorous deductive reasoning. Plato insisted that geometric proofs be executed with no tools other than a straight edge and compass. Among the numerous mathematical challenges Plato presented to his students were the Three Classical Problems – “squaring the circle,” “doubling the cube,” and “trisecting the angle.” While these problems have become somewhat synonymous with Plato, it’s important to note that he was not their originator.
Platonic Solids
Plato, the mathematician, is renowned for his recognition of five regular symmetrical three-dimensional shapes, which he believed formed the foundation of the entire universe. These shapes are commonly referred to as the Platonic Solids. They include the tetrahedron (constructed from four regular triangles, symbolizing fire), the octahedron (comprising eight triangles, representing air), the icosahedron (constructed from 20 triangles, signifying water), the cube (made up of six squares, symbolizing earth), and the dodecahedron (composed of 12 pentagons, which Plato cryptically described as the entity used to arrange the constellations in the entire heavens).
It’s likely that Pythagoras was already familiar with the tetrahedron, cube, and dodecahedron, while the octahedron and icosahedron were probably discovered by Theaetetus, a contemporary of Plato. It was Euclid, around half a century later, who demonstrated that these were the only possible convex regular polyhedra. Nevertheless, these shapes became widely known as the Platonic Solids and served as a source of inspiration for mathematicians and geometers for many centuries.
For instance, in the early 17th century, the German astronomer Johannes Kepler devised a clever system of nested Platonic solids and spheres to reasonably approximate the distances of the known planets from the Sun. Kepler, however, maintained his commitment to scientific accuracy and eventually abandoned his elegant model when it fell short of the required precision.
