arXiv:2511.18760v2 Announce Type: replace Abstract: Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that are difficult to detect and correct. In contrast, formal theorem proving provides rigorous, verifiable mathematical reasoning, where each inference step is checked by a trusted compiler, but lacks the exploratory freedom of informal problem-solving. This mismatch leaves current LLM-based math agents without a princi
The paper addresses a critical limitation of current LLMs, which excel at informal reasoning but struggle with the rigorous verifiability needed for complex mathematical and logical tasks, appearing now as LLM capabilities mature.
Improving LLMs' ability for verifiable mathematical reasoning enhances their reliability and expands their application to fields requiring high precision and provable correctness beyond simple text generation.
LLMs will move from being primarily informal reasoning tools to potentially becoming trusted partners in formal theorem proving and complex problem-solving, closing a significant gap in their capabilities.
- · AI researchers
- · Software engineers
- · Mathematics education
- · Formal verification industry
- · Manual theorem provers
- · Informal reasoning-reliant systems
LLMs gain a new dimension of capability, making them useful for tasks requiring high logical rigor.
This could lead to widespread adoption of AI in scientific discovery, advanced engineering, and legal reasoning where proofs are paramount.
The development of highly reliable and verifiable AI reasoning could accelerate the pace of scientific and technological innovation across multiple domains, ultimately leading to more robust AI agents.
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Read at arXiv cs.AI