arXiv:2605.28365v1 Announce Type: new Abstract: Lean is increasingly used to judge natural-language mathematical answers, but its signal is partial: many answers never formalize, and a failed proof may reflect an ill-typed statement or a missing library fact, not a wrong answer. On MATH-500 we show this signal is (i) sharply coverage-dependent, that is the proof-winning answer is correct 96% of the time at high proved coverage but 20% at low, and (ii) sparse and often unfaithful: a 7B autoformalizer proves a class for only 28% of problems, and a manual audit finds only approximately 43% of tho
The accelerating development of advanced AI models necessitates reliable and robust methods for verifying their reasoning, especially in complex domains like mathematics.
This research highlights critical limitations in current AI evaluation methods for mathematical reasoning, underscoring the need for more sophisticated and trustworthy systems before broad deployment.
The understanding of AI's capability in mathematical reasoning shifts from a perception of near-perfect formalization to one of significant fragility and conditional reliability.
- · Formal verification researchers
- · AI safety and alignment researchers
- · Lean (proof assistant) developers
- · Companies investing in robust AI verification methods
- · Developers relying solely on autoformalizers for critical applications
- · AI companies overstating mathematical reasoning capabilities
- · Academic communities without rigorous AI evaluation protocols
AI systems will require more sophisticated, hybrid evaluation frameworks combining automated and human oversight for complex tasks.
Increased investment and research in bridging the gap between natural language understanding and formal mathematical verification will follow.
The development and adoption of AI will be partially constrained by the ability to reliably audit and trust its reasoning processes, especially in sensitive domains.
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Read at arXiv cs.AI