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Definition
Automated theorem proving (ATP) uses formal logic and computational methods to construct or verify mathematical proofs without full human derivation. Modern LLM-based approaches combine multi-agent search with formal verification tools (Lean, Coq, Isabelle).
Key Points
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2026-08-01: OpenAI ten-proofs Lean 4 certificates for Astra-generated arguments (2026-08-01-openai-ten-proofs-github)
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2026-07: levent-alpoge + claude-fable-5 jacobian-conjecture counterexample (jacobian-conjecture-claude-fable-counterexample, ai-mathematical-discovery)
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Distinct from informal mathematical reasoning — ATP requires machine-checkable proof certificates
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openai’s July 2026 cycle-double-cover-conjecture claim used 64 parallel subagents but published only informal PDF, not Lean/Coq verification
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Related to formal-verification and test-time-scaling in AI-for-science applications