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[2602.12463] Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof
Summary
This paper examines the relationship between correctness in mathematical proofs and their epistemic value, arguing that formal correctness is not a necessary condition for a proof's value. It also discusses implications for AI applications in mathematics.
Why It Matters
Understanding the epistemic value of mathematical proofs is crucial as AI increasingly engages in theorem proving. This paper challenges traditional views on correctness, potentially reshaping how we evaluate AI's contributions to mathematics and logic.
Key Takeaways
- Formal correctness is not essential for a proof's epistemic value.
- The relationship between mathematics and logic is clarified through this lens.
- Implications for automated theorem provers and AI applications in mathematics are significant.
Mathematics > History and Overview arXiv:2602.12463 (math) [Submitted on 12 Feb 2026] Title:Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof Authors:James Owen Weatherall, Jesse Wolfson View a PDF of the paper titled Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof, by James Owen Weatherall and Jesse Wolfson View PDF HTML (experimental) 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. Comments: Subjects: History and Overview (math.HO); Artificial Intelligence (cs.AI) Cite as: arXiv:2602.12463 [math.HO] (or arXiv:2602.12463v1 [math.HO] for this version) https://doi.org/10.48550/arXiv.2602.12463 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: James Weatherall [view email] [v1] Thu, 12 Feb 2026 22:44:03 UTC (43 KB) Full-text links: Access Paper: View a PDF of the paper titled Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof, by James Owen Weatherall and Jesse WolfsonView PDFHTML (experimental)TeX Source ...