arXiv:2606.05632v1 Announce Type: new Abstract: Within the past few years, the ability of Large Language Models (LLMs) to generate formal mathematical proofs has improved drastically. We provide a comparison of various LLMs' effectiveness in producing formal proofs in Lean 4 with the goal of assisting those seeking to use LLMs to support their own projects. We utilize both pass@$k$ and refine@$k$ metrics as the benchmark for our comparison and evaluate on subsets of both miniF2F and miniCTX datasets. Our testing shows that overall, Gemini 3.1 Pro and Claude Opus 4.7 perform best. Gemini 3.1 Pr
The rapid advancement of LLMs is pushing their capabilities into complex logical reasoning, making mathematical formalization a natural next frontier for evaluation and application.
The ability of LLMs to generate formal mathematical proofs could profoundly impact fields reliant on logical validation, software engineering, and scientific discovery, accelerating human efficiency.
LLMs are evolving from text generators to powerful tools in formal verification, changing how complex proofs and code are developed and validated at scale.
- · AI companies (Google, Anthropic)
- · Academia (researchers, mathematicians)
- · Software developers
- · Formal verification specialists
- · Tasks requiring manual formal proof
- · Traditional theorem proving software (if not integrated with LLMs)
Increased automation in theorem proving and formal verification pipelines.
Accelerated development of mathematically sound software and hardware designs.
The potential redefinition of mathematical research and discovery processes through AI assistance.
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Read at arXiv cs.AI