arXiv:2509.14274v3 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called Conjecturing-Proving Loop (CPL), which iteratively generates mathematical conjectures and attempts to prove them in Lean 4. A key feature of CPL is that each iteration conditions the LLM on previously generated theorems and their formal proofs, enabling parameter-free improvement of proof strategies via in-context lea
The rapid advancements in LLM capabilities and increased research focus on formal methods and automated theorem proving are converging.
This development indicates a significant step towards autonomous scientific discovery and knowledge generation, impacting fields reliant on complex mathematical proofs.
LLMs can now not only assist in proving known theorems but also discover novel mathematical conjectures and iteratively refine proof strategies.
- · AI research labs
- · Mathematics
- · Formal verification
- · Software engineering
- · Tasks requiring manual theorem proving
- · Traditional academic publication models (long-term)
Increased efficiency and speed in formal theorem proving and mathematical discovery are achieved.
AI systems gain the capacity for truly novel scientific contributions, fundamentally altering research paradigms.
The development of 'AI mathematicians' could lead to new branches of mathematics unrecognizable to human-led research.
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Read at arXiv cs.LG