Rigorous proof verification within the informal approach

Ascertain whether rigorous verification of mathematical proofs can be achieved using informal, natural-language-based methods without grounding in formal systems, for example via language-model self-verification or self-correction.

Background

The authors review efforts to use LLMs for self-verification and self-correction of proofs in the informal setting, noting mixed results and inherent brittleness when verifiers are themselves neural models.

They emphasize the difficulty of evaluating complex proofs without formal semantics and seek clarity on whether fully rigorous verification is attainable within the informal paradigm.