mlsanityData to 14 Oct 2026

Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2

arXiv 2502.03544 ↗First posted 5 Feb 2025cs.AI cs.LGcited by 97

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Cited by 43 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We present AlphaGeometry2 (AG2), a significantly improved version of AlphaGeometry introduced in (Trinh et al., 2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with support for non-constructive problems, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AG2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that enables effective communication between search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AG to 84% on all geometry problems over the last 25 years, compared to 54% previously. AG2 was also part of the system that achieved the silver-medal standard at IMO 2024 https://deepmind.google/blog/ai-solves-imo-problems-at-silver-medal-level/. Finally, we report progress towards using AG2 as a part of a fully automated system that reliably solves geometry problems from natural language input. Code: https://github.com/google-deepmind/alphageometry2.

Key facts. Cited by 97 papers in the map (data through 14 Oct 2026). Builds on 22 of its 42 references that are in the map. First posted on arXiv 5 Feb 2025.

Builds on

22 of 42 references.

References · 22

  1. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,276
  2. 2023Let's Verify Step by Stepcited by 3,789
  3. 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,442
  4. 2024Gemini 1.5: Unlocking multimodal understanding across millions of tokens of contextcited by 3,224
  5. 2023Large Language Models Cannot Self-Correct Reasoning Yetcited by 1,017
  6. 2023Teaching Large Language Models to Self-Debugcited by 988
  7. 2024Generative Verifiers: Reward Modeling as Next-Token Predictioncited by 480
  8. 2020Generative Language Modeling for Automated Theorem Provingcited by 388
  9. 2024Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Modelscited by 268
  10. 2022Autoformalization with Large Language Modelscited by 263
  11. 2024On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Taskscited by 142
  12. 2024Tokenization counts: the impact of tokenization on arithmetic in frontier LLMscited by 115
10 more
  1. 2023Multilingual Mathematical Autoformalizationcited by 39
  2. 2024Reliable Evaluation and Benchmarks for Statement Autoformalizationcited by 32
  3. 2024Autoformalizing Euclidean Geometrycited by 27
  4. 2024Proving Olympiad Algebraic Inequalities without Human Demonstrationscited by 20
  5. 2024Proposing and solving olympiad geometry with guided tree searchcited by 19
  6. 2024Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Modelscited by 11
  7. 2024Wu's Method can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometrycited by 11
  8. 2024T-FREE: Subword Tokenizer-Free Generative LLMs via Sparse Representations for Memory-Efficient Embeddingscited by 10
  9. 2020Automatically Building Diagrams for Olympiad Geometry Problemscited by 8
  10. 2025Do Large Language Models Truly Understand Geometric Structures?cited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 52; 2026: 45.

97 papers.

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  1. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 320
  2. 2025Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correctioncited by 154
  3. 2025Seed-Prover: Deep and Broad Reasoning for Automated Theorem Provingcited by 101
  4. 2025DeepSeekMath-V2: Towards Self-Verifiable Mathematical Reasoningcited by 94
  5. 2025Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipelinecited by 82
  6. 2026AutoHarness: improving LLM agents by automatically synthesizing a code harnesscited by 76
  7. 2025Towards Robust Mathematical Reasoningcited by 73
  8. 2025Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modelingcited by 45
  9. 2025Feedback Descent: Open-Ended Text Optimization via Pairwise Comparisoncited by 44
  10. 2025ReflAct: World-Grounded Decision Making in LLM Agents via Goal-State Reflectioncited by 31
  11. 2025Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physicscited by 31
  12. 2025ICL-Router: In-Context Learned Model Representations for LLM Routingcited by 28
38 more
  1. 2025Cognitive Foundations for Reasoning and Their Manifestation in LLMscited by 26
  2. 2025Critique of World Modelcited by 25
  3. 2025Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Modelscited by 20
  4. 2025Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integrationcited by 18
  5. 2025From Problem-Solving to Teaching Problem-Solving: Aligning LLMs with Pedagogy using Reinforcement Learningcited by 17
  6. 2025TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solvingcited by 13
  7. 2025Bottom-up Domain-specific Superintelligence: A Reliable Knowledge Graph is What We Needcited by 13
  8. 2025The Art of Scaling Test-Time Compute for Large Language Modelscited by 12
  9. 2025Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Informationcited by 10
  10. 2026Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematicscited by 10
  11. 2025GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimizationcited by 9
  12. 2026Autonomous Research Agents: A Survey of AI Scientists and the Verification Gapcited by 9
  13. 2025Towards Geometry Problem Solving in the Large Model Era: A Surveycited by 8
  14. 2025PuzzleWorld: A Benchmark for Multimodal, Open-Ended Reasoning in Puzzlehuntscited by 8
  15. 2026Riemann-Bench: A Benchmark for Moonshot Mathematicscited by 8
  16. 2025Reliable Proof Generation with LLMs via Analogical Retrieval and Symbolic Verification: A Case Study in Euclidean Geometrycited by 7
  17. 2025The Need for Verification in AI-Driven Scientific Discoverycited by 7
  18. 2025Semantic Voting: A Self-Evaluation-Free Approach for Efficient LLM Self-Improvement on Unverifiable Open-ended Taskscited by 7
  19. 2025Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learningcited by 7
  20. 2026SAGE: Benchmarking and Improving Retrieval for Deep Research Agentscited by 7
  21. 2025Diverse Inference and Verification for Advanced Reasoningcited by 6
  22. 2025Population-Evolve: a Parallel Sampling and Evolutionary Method for LLM Math Reasoningcited by 6
  23. 2025Step-Wise Formal Verification for LLM-Based Mathematical Problem Solvingcited by 5
  24. 2025LogicPuzzleRL: Cultivating Robust Mathematical Reasoning in LLMs via Reinforcement Learningcited by 5
  25. 2025LLM Unlearning Without an Expert Curated Datasetcited by 5
  26. 2025Efficient and Transferable Agentic Knowledge Graph RAG via Reinforcement Learningcited by 5
  27. 2025A Survey of Deep Learning for Geometry Problem Solvingcited by 4
  28. 2025A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimizationcited by 4
  29. 2026Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoningcited by 4
  30. 2026Milestones over Outcome: Unlocking Geometric Reasoning with Sub-Goal Verifiable Rewardcited by 4
  31. 2026MathlibLemma: Folklore Lemma Generation and Benchmark for Formal Mathematicscited by 4
  32. 2026The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learningcited by 4
  33. 2026Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisationcited by 4
  34. 2025Rethinking Large Language Model Distillation: A Constrained Markov Decision Process Perspectivecited by 3
  35. 2025GeoFM: Enhancing Geometric Reasoning of MLLMs via Synthetic Data Generation through Formal Languagecited by 3
  36. 2025Model-Based and Sample-Efficient AI-Assisted Math Discovery in Sphere Packingcited by 3
  37. 2026TangramSR: Can Vision-Language Models Reason in Continuous Geometric Space?cited by 3
  38. 2026From AI Assistant to AI Scientist: Autonomous Discovery of LLM-RL Algorithms with LLM Agentscited by 3

50 most cited of 97 All 97 (JSON)