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

Researchers published a paper on arXiv on February 12, 2026, arguing that formal correctness in mathematical proofs is neither necessary nor sufficient for them to have epistemic value, challenging traditional views on the relationship between mathematics and logic while addressing implications for automated theorem provers and AI applications. The paper presents a significant philosophical stance on mathematical proofs, suggesting that the traditional view requiring formalizability in a formal proof system may be too restrictive. The authors explore how mathematical proofs derive their value not merely from their formal correctness but from other epistemic properties such as explanatory power, insight, and conceptual understanding, challenging the formalist tradition that has dominated much of the 20th century. The researchers then develop a framework that distinguishes between mathematical practice and formal logic, arguing that while formal systems serve important functions in mathematics, they don't capture the full richness of mathematical knowledge, explaining why some proofs that resist formalization can still be considered valuable while some formally correct proofs may be mathematically uninteresting. Finally, the paper addresses contemporary debates in artificial intelligence and automated theorem proving, suggesting that current approaches may be overly focused on formal verification at the expense of the deeper epistemic values that make mathematics meaningful, proposing that future AI systems should consider these broader values rather than merely aiming for formal correctness.