# Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline

arXiv: https://arxiv.org/abs/2507.15855 · HTML: https://mlsanity.com/paper/2507.15855/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 28 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 17 of 17)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [REFINER: Reasoning Feedback on Intermediate Representations](https://mlsanity.com/paper/2304.01904/) (2023)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [A Survey on Data Contamination for Large Language Models](https://mlsanity.com/paper/2502.14425/) (2025)
- [Brains vs. Bytes: Evaluating LLM Proficiency in Olympiad Mathematics](https://mlsanity.com/paper/2504.01995/) (2025)

## Built on by (most cited first, 30 of 82)

- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [AutoHarness: improving LLM agents by automatically synthesizing a code harness](https://mlsanity.com/paper/2603.03329/) (2026)
- [Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics](https://mlsanity.com/paper/2601.14027/) (2026)
- [Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience](https://mlsanity.com/paper/2512.17260/) (2025)
- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning](https://mlsanity.com/paper/2509.25300/) (2025)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [MoReBench: Evaluating Procedural and Pluralistic Moral Reasoning in Language Models, More than Outcomes](https://mlsanity.com/paper/2510.16380/) (2025)
- [InT: Self-Proposed Interventions Enable Credit Assignment in LLM Reasoning](https://mlsanity.com/paper/2601.14209/) (2026)
- [Self-Jailbreaking: Language Models Can Reason Themselves Out of Safety Alignment After Benign Reasoning Training](https://mlsanity.com/paper/2510.20956/) (2025)
- [LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks](https://mlsanity.com/paper/2606.03303/) (2026)
- [HERMES: Towards Efficient and Verifiable Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2511.18760/) (2025)
- [LSPO: Length-aware Dynamic Sampling for Policy Optimization in LLM Reasoning](https://mlsanity.com/paper/2510.01459/) (2025)
- [Semantic Soft Bootstrapping: Long Context Reasoning in LLMs without Reinforcement Learning](https://mlsanity.com/paper/2512.05105/) (2025)
- [HalluHard: A Hard Multi-Turn Hallucination Benchmark](https://mlsanity.com/paper/2602.01031/) (2026)
- [Escaping the Cognitive Well: Efficient Competition Math with Off-the-Shelf Models](https://mlsanity.com/paper/2602.16793/) (2026)
- [SorryDB: Can AI Provers Complete Real-World Lean Theorems?](https://mlsanity.com/paper/2603.02668/) (2026)
- [PhysicsMinions: Winning Gold Medals in the Latest Physics Olympiads with a Coevolutionary Multimodal Multi-Agent System](https://mlsanity.com/paper/2509.24855/) (2025)
- [SciAgent: A Unified Multi-Agent System for Generalistic Scientific Reasoning](https://mlsanity.com/paper/2511.08151/) (2025)
- [Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning](https://mlsanity.com/paper/2512.10534/) (2025)
- [Multimodal Reasoning for Science: Technical Report and 1st Place Solution to the ICML 2025 SeePhys Challenge](https://mlsanity.com/paper/2509.06079/) (2025)
- [Population-Evolve: a Parallel Sampling and Evolutionary Method for LLM Math Reasoning](https://mlsanity.com/paper/2512.19081/) (2025)
- [Profile-Aware Maneuvering: A Dynamic Multi-Agent System for Robust GAIA Problem Solving by AWorld](https://mlsanity.com/paper/2508.09889/) (2025)
- [Off-Trajectory Reasoning: Can LLMs Collaborate on Reasoning Trajectory?](https://mlsanity.com/paper/2510.06410/) (2025)
- [CapGeo-Bench: Decoupling Visual Perception from Reasoning and Evaluating Geometric Understanding](https://mlsanity.com/paper/2510.09302/) (2025)
- [Honesty over Accuracy: Trustworthy Language Models through Reinforced Hesitation](https://mlsanity.com/paper/2511.11500/) (2025)
- [MechMath Agent Team: LLM Driven Agents for Mathematical Research](https://mlsanity.com/paper/2607.04394/) (2026)
- [MarsRL: Advancing Multi-Agent Reasoning System via Reinforcement Learning with Agentic Pipeline Parallelism](https://mlsanity.com/paper/2511.11373/) (2025)
- [Intern-S1-MO: Long-horizon Reasoning Agent for Olympiad?Level Mathematical Problem Solving](https://mlsanity.com/paper/2512.10739/) (2025)
- [The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learning](https://mlsanity.com/paper/2603.15914/) (2026)

## Abstract (arXiv)

The International Mathematical Olympiad (IMO) is widely regarded as the world championship of high-school mathematics. IMO problems are renowned for their difficulty and novelty, demanding deep insight, creativity, and rigor. Although large language models perform well on many mathematical benchmarks, they often struggle with Olympiad-level problems. Using carefully designed prompts, we construct a model-agnostic, verification-and-refinement pipeline. We demonstrate its effectiveness on the recent IMO 2025, avoiding data contamination for models released before the competition. Equipped with any of the three leading models -- Gemini 2.5 Pro, Grok-4, or GPT-5 -- our pipeline correctly solved 5 out of the 6 problems (≈85.7% accuracy). This is in sharp contrast to their baseline accuracies: 31.6% (Gemini 2.5 Pro), 21.4% (Grok-4), and 38.1% (GPT-5), obtained by selecting the best of 32 candidate solutions. The substantial improvement underscores that the path to advanced AI reasoning requires not only developing more powerful base models but also designing effective methodologies to harness their full potential for complex tasks.