Like Greek mathematicians long before Euclid, and some mathematicians today, Plato relied on diagrams as essential components of mathematical proof and sometimes as constituting proofs. This fact has not been adequately appreciated among modern interpreters of Plato because the geometric mode of representation of mathematical concepts used by the ancient Greeks has almost completely been superseded by the use of the abstract symbols of algebra in modern mathematical practice. I demonstrate that understanding the geometrical principles and practices with which Plato was operating can help us understand the many mathematical examples in Plato’s texts better—and not only that. I show that a clearer understanding of how and why Plato uses diagrammatic examples can give us insights into his ontological commitments and epistemological theory that are otherwise obscure.
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