Can a Picture Prove a Theorem? Using Empirical Methods to Investigate Diagrammatic Proofs in Mathematics

摘要

The necessity of results obtained through formal proof is a defining feature of modern mathematics, and so it is not surprising that the question of what constitutes a valid proof is of central concern in the philosophy of mathematics.Currently, the dominant view is that a proof must consist of a series of propositions in which each statement follows logically from those preceding. Diagrams, while widely recognized as useful heuristic devices, are generally not considered an acceptable means of mathematical proof. Recently, however, various scholars have argued for an expanded role for visual representations in mathematical justification [1], with some going so far as to claim that "pictures can prove theorems" [2].