Natural-language LLM mathematical reasoners are fundamentally limited by lacking machine-checkable semantics, which blocks autonomous verification needed for open-ended research.

However, these LLM reasoners that generate informal reasoning in natural language are fundamentally limited by the lack of precise, machine-checkable semantics, making their outputs prone to hallucinations [Huang et al., 2025b] and precluding autonomous verification, a prerequisite for tackling open-ended mathematical research.