A Human Audit of OpenAIs AI-Generated Mathematical Proofs

Verification abundance, adjudication scarcity: what happens to mathematical knowledge when proof checking becomes free

It is argued that machine checking produces verification abundance while leaving adjudication scarce, and proposes a six-category taxonomy of representational mismatch, a disclosure schema for machine-generated mathematical claims, and implications for software, cryptography, and regulated decision systems.

G¨odel’s Incompleteness Theorems: The Plaintext Distillation

Computer-assisted Proof Under Audit: Typos, Certificate Errors, and Reproducible Exact Checks for a Symbolic Invertibility Proof

We audit the exact-arithmetic certificate in arXiv:2310.19781v2, its 2025 \emph{Communications in Mathematical Physics} version, and their shared MATLAB archive. CMP corrects none of the audited items; we therefore treat both versions together and use the openly accessible arXiv source for exact provenance. We found 11...

ProofJudge: Tool-Grounded LLM Evaluation of Formal Proof Quality in Mathlib

ProofJudge is introduced, an agentic LLM-as-judge system that scores formal proof quality along five dimensions beyond correctness: library leverage, automation fit, structural clarity, statement quality, and Mathlib conventions.

Long-horizon autoformalization of a core theorem underlying MIP* = RE

This work completed a machine-checked Lean 4 proof of the quantum soundness of the classical low individual-degree test, a core theorem underlying MIP* = RE, and provides a verified foundation for quantum complexity.

MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

This work introduces MathAdv, a diagnostic benchmark spanning 13 domains across undergraduate- and graduate-level mathematics, and shows how component-wise evaluation can reveal model capabilities and failure modes that aggregate theorem-proving accuracy obscures.