AI Proof Checking Creates Verification Abundance, Adjudication Scarcity

The rapid advancement of AI models, exemplified by a recent OpenAI model producing a counterexample to a major mathematical conjecture and generating numerous machine-checkable results, is fundamentally altering the landscape of mathematical verification. While AI can now provide effectively free checks for derivational validity—ensuring a proof's logical steps are correct—it does not eliminate the need for human oversight. Instead, the burden shifts to two higher layers of verification: representational fidelity, which assesses whether a formal statement accurately captures the intended mathematical question, and epistemic significance, which evaluates the importance and implications of the result. These layers remain dependent on the scarce attention of human experts. Analysis of a corpus of AI-generated mathematical claims showed that while kernel-checked proofs were voluminous, the statements requiring human audit were much smaller but contained a high number of bespoke definitions. This highlights that the audit surface is compact but demands irreducible expert judgment, leading to a scenario where machine checking creates an abundance of verification but a scarcity of human adjudication. The paper proposes a taxonomy for representational mismatch and a disclosure schema for AI-generated claims.