What is recorded here?
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. An unsolved formal theorem can be surrounded by related, easier statements that teach a prover useful local strategies. AlphaProof uses a three-billion-parameter policy/value network and search in Lean, first learning from a large auto-formalized curriculum and then adapting to difficult targets through test-time reinforcement learning. It builds on Lean, Mathlib, AlphaZero, earlier neural theorem proving and established mathematical problem-solving heuristics. At the 2024 IMO, experts formalized the non-geometry questions; Gemini 1.5 Pro generated candidate answers, and AlphaProof proved P1, P2 and P6 after 2–3 days of adaptation for each. AlphaGeometry2 separately solved P4. Together they achieved 28/42 points, a silver-equivalent score under the judging protocol, without the human competition time constraint. The paper reports improved corrected formal benchmarks, with its strongest results using hundreds of TPU days per target on average. The reported training required roughly 100000 TPU days for auto-formalization and 80000 for main reinforcement learning, beyond general pretraining. Final proof terms were checked with standard Lean and an allowed-axiom check. That establishes the formal statements under the declared trust assumptions; it does not automatically prove correspondence to every informal question, broad research-mathematics novelty or independent WRS replication. The paper appeared online in November2025 and in a March2026 Nature issue.
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Scientific scope
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.
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People and systems
Thomas Hubert; Rishi Mehta; Laurent Sartran; Miklós Z. Horváth; Goran Žužić; Eric Wieser; Aja Huang; Julian Schrittwieser; Yannick Schroecker; Hussain Masoom; Ottavia Bertolli; Tom Zahavy; Amol Mandhane; Jessica Yung; Iuliya Beloshapka; Borja Ibarz; Vivek Veeriah; Lei Yu; Oliver Nash; Paul Lezeau; Salvatore Mercuri; Calle Sönne; Bhavik Mehta; Alex Davies; Daniel Zheng; Fabian Pedregosa; Yin Li; Ingrid von Glehn; Mark Rowland; Samuel Albanie; Ameya Velingker; Simon Schmitt; Edward Lockhart; Edward Hughes; Henryk Michalewski; Nicolas Sonnerat; Demis Hassabis; Pushmeet Kohli; David Silver
Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.
AlphaProof · Google DeepMind · AlphaProof 3B encoder–decoder policy/value network
Lean tactic proof/disproof search with general and test-time reinforcement learning under reported budgets.. Source-reported attribution; provider attestation is unavailable.
Gemini · Google DeepMind · Gemini 1.5 Pro and source-described Gemini variant-generation models
Auto-formalization, candidate answer generation and problem variants; distinct from AlphaProof formal proof execution.. Source-reported attribution; provider attestation is unavailable.
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English catalogue narrative
AlphaProof: learning local proof strategies through Lean-grounded test-time training
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.
An unsolved formal theorem can be surrounded by related, easier statements that teach a prover useful local strategies. AlphaProof uses a three-billion-parameter policy/value network and search in Lean, first learning from a large auto-formalized curriculum and then adapting to difficult targets through test-time reinforcement learning. It builds on Lean, Mathlib, AlphaZero, earlier neural theorem proving and established mathematical problem-solving heuristics. At the 2024 IMO, experts formalized the non-geometry questions; Gemini 1.5 Pro generated candidate answers, and AlphaProof proved P1, P2 and P6 after 2–3 days of adaptation for each. AlphaGeometry2 separately solved P4. Together they achieved 28/42 points, a silver-equivalent score under the judging protocol, without the human competition time constraint. The paper reports improved corrected formal benchmarks, with its strongest results using hundreds of TPU days per target on average. The reported training required roughly 100000 TPU days for auto-formalization and 80000 for main reinforcement learning, beyond general pretraining. Final proof terms were checked with standard Lean and an allowed-axiom check. That establishes the formal statements under the declared trust assumptions; it does not automatically prove correspondence to every informal question, broad research-mathematics novelty or independent WRS replication. The paper appeared online in November2025 and in a March2026 Nature issue.
Scientific scope
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.
People and systems
Thomas Hubert; Rishi Mehta; Laurent Sartran; Miklós Z. Horváth; Goran Žužić; Eric Wieser; Aja Huang; Julian Schrittwieser; Yannick Schroecker; Hussain Masoom; Ottavia Bertolli; Tom Zahavy; Amol Mandhane; Jessica Yung; Iuliya Beloshapka; Borja Ibarz; Vivek Veeriah; Lei Yu; Oliver Nash; Paul Lezeau; Salvatore Mercuri; Calle Sönne; Bhavik Mehta; Alex Davies; Daniel Zheng; Fabian Pedregosa; Yin Li; Ingrid von Glehn; Mark Rowland; Samuel Albanie; Ameya Velingker; Simon Schmitt; Edward Lockhart; Edward Hughes; Henryk Michalewski; Nicolas Sonnerat; Demis Hassabis; Pushmeet Kohli; David Silver
AlphaProof / Google DeepMind / AlphaProof 3B encoder–decoder policy/value network: Lean tactic proof/disproof search with general and test-time reinforcement learning under reported budgets. (source reported).
Gemini / Google DeepMind / Gemini 1.5 Pro and source-described Gemini variant-generation models: Auto-formalization, candidate answer generation and problem variants; distinct from AlphaProof formal proof execution. (source reported).