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Research dossier · version 1 · updated Oct 30, 2026

AI for Mathematics & Formal Proof: State of the Field (October 2026)

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.

3,259 words35 sources29 evidence-mapped claims7 benchmarks16 timeline events✓ citation-verified Oct 30, 2026

AI-assisted synthesis of the cited literature, independently fact-checked against its sources; not peer reviewed.

Contents

  1. Executive summary
  2. Background and core concepts
  3. Timeline of key milestones
  4. State of the art
  5. Neural provers and expert iteration
  6. Autoformalization and statement fidelity
  7. Olympiad-level and competition systems
  8. Agentic and harness-based provers
  9. Quantitative benchmarks
  10. Open problems and active debates
  11. Major programs and players
  12. Outlook: what to watch (November 2026 to April 2028)
  13. Key papers
  14. Glossary

Sample findings

  • 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.
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