Inspect the formal statement, imported axioms, admitted lemmas, checker version and correspondence with the informal theorem. A successful compiler exit alone does not prove that the intended question was formalized.
There are no positive whole numbers a, b and c with aⁿ + bⁿ = cⁿ for n bigger than two. Humans proved this in the 1990s. Claude's new achievement is turning the proof into instructions a computer can check.
Formal verification · preprint
While progress in informal mathematics has come largely from scaling the chain-of-thought and agentic reasoning of frontier language models, formal theorem proving has increasingly relied
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Even a carefully proofread paper can leave small gaps in its proofs or its stated assumptions. We introduce PaperFormalizer, a Lean-based agentic pipeline that helps
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Lean is increasingly used to verify mathematical proofs and software produced by LLM agents, but writing formal proofs remains hard. Existing prover systems take a
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Language models have recently solved open Erdős problems and achieved gold-medal level performance on International Mathematical Olympiad problems. But their solutions, written in natural language,
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We introduce NanoProof, to our knowledge the first factorized execution-guided theorem prover in Lean 4 whose training data, extraction tooling, training pipeline, and weights are
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Program verification establishes software correctness through machine-checkable proofs constructed in theorem provers. It's a guarantee especially valuable for code generated by large language models (LLMs),
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In proof assistants such as Lean, a generated proof must pass machine compilation checks, so evaluation needs no human scoring. Direct generation fails on multi-step
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OpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.
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Diffusion language model (dLLM) compression faces a known challenge because calibration is typically performed on clean, fully visible activations, whereas inference traverses partially masked intermediate
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Does structured mathematical knowledge help LLMs prove theorems in Lean 4? If so, for which models, and does the answer vary by problem? Formal libraries
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Neural theorem provers must both propose tactics and decide which valid successor states to explore. We study whether one-step Lean transitions provide a self-supervised signal
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Fine-tuned Large Language Models (LLMs) significantly advance Automated Theorem Proving (ATP), but are often deployed as guiding policies within tree search rather than for single-attempt
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