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

2026/02/12 by James Owen Weatherall, Jesse Wolfson · 1 voice · 1 citation
Computer Science · Mathematics · #cs.AI #math.HO

paper · pdf · doi:10.48550/arxiv.2602.12463

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.

Citations

• On the non-existence of elements of Kervaire invariant one
• On the nonexistence of elements of Kervaire invariant one
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds
• The entropy formula for the Ricci flow and its geometric applications
• Why Do We Prove Theorems?
• On proof and progress in mathematics
• A manifold which does not admit any differentiable structure

Cited by

• That Damned Equation. Rigour, Credit Attribution, and the Wheeler-DeWitt Equation 1962-1967

Discussions

• James Owen Weatherall, Jesse Wolfson: Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof https://arxiv.org/abs/2602.12463 https://arxiv.org/pdf/2602.12463 https://arxi [bsky, 0 points, 0 comments]

Related

• Artifical intelligence and inherent mathematical difficulty
• Mathematical Proof Between Generations
• Artificial Intelligence and Inherent Mathematical Difficulty
• Formal Mathematical Reasoning: A New Frontier in AI
• How Mathematicians Determine if an Argument Is a Valid Proof