{"slug":"ai-mathematics","topic":"ai-mathematics","title":"AI for Mathematics & Formal Proof: State of the Field (October 2026)","summary":"This dossier surveys AI systems that prove theorems, translate informal mathematics into machine-checkable form and evaluate mathematical reasoning, as of October 2026. It covers neural provers for Lean and other proof assistants, olympiad-level results, benchmarks and open problems. The main takeaway is that a machine-checked proof is only as trustworthy as the formal statement it proves, which makes statement fidelity the central bottleneck.","version":1,"published_at":"2026-10-30","updated_at":"2026-10-30","stats":{"words":3259,"citations":35,"claims":29,"timeline":16,"benchmarks":7,"open_problems":7,"key_papers":14,"glossary":13},"verification":{"status":"verified","method":"automated figure and citation-relevance triage against cited abstracts, targeted AI review with web checks of flagged statements, and a close-out pass hedging or removing unconfirmed statements; automated citation resolution","claims_checked":15,"issues_fixed":3,"verified_at":"2026-10-30"},"ai_assisted":true,"price":{"usd":"0.20","protocol":"x402","network":"eip155:84532","asset":"USDC"},"url":"https://space-kitty.com/dossiers/ai-mathematics","preview_url":"https://space-kitty.com/api/v1/dossiers/ai-mathematics/preview","purchase_url":"https://space-kitty.com/api/v1/dossiers/ai-mathematics","toc":[{"level":2,"text":"Executive summary","anchor":"executive-summary"},{"level":2,"text":"Background and core concepts","anchor":"background-and-core-concepts"},{"level":2,"text":"Timeline of key milestones","anchor":"timeline-of-key-milestones"},{"level":2,"text":"State of the art","anchor":"state-of-the-art"},{"level":3,"text":"Neural provers and expert iteration","anchor":"neural-provers-and-expert-iteration"},{"level":3,"text":"Autoformalization and statement fidelity","anchor":"autoformalization-and-statement-fidelity"},{"level":3,"text":"Olympiad-level and competition systems","anchor":"olympiad-level-and-competition-systems"},{"level":3,"text":"Agentic and harness-based provers","anchor":"agentic-and-harness-based-provers"},{"level":3,"text":"Quantitative benchmarks","anchor":"quantitative-benchmarks"},{"level":2,"text":"Open problems and active debates","anchor":"open-problems-and-active-debates"},{"level":2,"text":"Major programs and players","anchor":"major-programs-and-players"},{"level":2,"text":"Outlook: what to watch (November 2026 to April 2028)","anchor":"outlook-what-to-watch-november-2026-to-april-2028"},{"level":2,"text":"Key papers","anchor":"key-papers"},{"level":2,"text":"Glossary","anchor":"glossary"}],"sample_claims":["DeepSeek-Prover-V2 reports an 88.9% pass rate on miniF2F-test; its abstract does not state the sampling budget.","DeepSeek-Prover-V2 reports 49 of 658 PutnamBench problems solved."],"includes":["markdown","claims","timeline","benchmarks","open_problems","key_papers","glossary","bibliography"],"citation_count":35,"how_to_buy":"GET https://space-kitty.com/api/v1/dossiers/ai-mathematics with an x402 client ($0.20, USDC on Base Sepolia (testnet))."}