AlphaProof: learning local proof strategies through Lean-grounded test-time training

What changed

AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation.

Scientific scope

AlphaProof combined Lean-grounded reinforcement learning, AND–OR proof search and test-time training on related problem variants, proving three non-geometry problems from the 2024 IMO with expert formalization and multi-day computation. The target is the Nature paper published online in November 2025. AlphaProof uses Lean, search and test-time reinforcement learning; humans formalized the competition problems. It solved IMO 2024 problems 1, 2 and 6 after roughly two to three days. The combined 28/42 score also includes AlphaGeometry2 on problem 4 and was not obtained within normal competition time. Reported training and test-time resources are part of the method. Lean acceptance depends on the actual statement and allowed logical assumptions; it does not certify that every natural-language problem was translated faithfully. WRS has not replayed the training or certified every proof/translation.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• All39 source-listed authors (complete byline retained in record) · SCIENCE: Scientific design, formalization, training, engineering and paper; exact source contribution statement retained, no equal effort shares inferred.
• AlphaProof / Gemini answer and variant generation · EXECUTION: Source-reported automated execution on formal mathematics under stated compute and human-input conditions.
• Lean / Mathlib open-source communities · INFRASTRUCTURE: Inherited trusted prover, mathematical library, human proofs and maintained infrastructure; not novel work transferred to AlphaProof.
• Timothy Gowers / Joseph Myers · VERIFICATION: Source-reported independent IMO judging, not a new WRS audit or scientific certification of all benchmark results.

• Hubert et al., Olympiad-level formal mathematical reasoning with reinforcement learning — Nature 651,607–613 and Methods/Extended Data

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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