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

2026-02-12

Technology Category

• Philosophy and Ethics of AI: AI & Epistemology
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning 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 interactions
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Security 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