Plato (427-347 B.C.E.) is the ancient writer "to whom all of Western philosophy is merely a footnote" (Whitehead). Plato is notable for his recording of Socrates, the "despotic logician" (Nietszche) who forced Athens to look uncomfortably at itself during a period of considerable political instability, governmental incompetence and declining fortune. Plato was concerned above all else with answering the searching Socratic questions, "What can I know?", "How should I act?" and "How should the City be governed?"

In mathematics, Plato is responsible for an attitude of thinking known as mathematical realism. For the mathematical realist, the numbers, sets, functions and other objects the mathematician manipulates in his (her) imagination are real entities. They are actual supersensible things that resist the mathematician's efforts to understand them, and that when they give up their secrets often disclose a supernal beauty that no human mind could have invented. For the Platonic realist, supersensible things manifestly exist and they are the intimate companions of the trained mathematician whose daily exercise leads him into dimensions unknown to the ordinary sensibility.