Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof

2026-02-12

Technology Category

Philosophy and Ethics of AI: AI & EpistemologyKnowledge Representation and Reasoning: Automated Reasoning and Theorem ProvingReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactionsWeb Mining and Content Analysis: Web data provenance, reliability, and authenticitySecurity and Privacy: Data transparency and provenance

Abstract

We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be"correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between mathematics and logic that clarifies the role of formal correctness in mathematics. Finally, we discuss the significance of these arguments for recent discussions about automated theorem provers and applications of AI to mathematics.

Problem

• correctness
• artificial intelligence
• epistemic value
• mathematical proof
• automated theorem proving

Innovation

• epistemic value
• formal correctness
• automated theorem proving
• mathematical proof
• AI in mathematics