Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline
This addresses the problem of enhancing AI reasoning for complex mathematical tasks, representing an incremental advancement through a novel pipeline design.
The authors tackled the challenge of solving difficult International Mathematical Olympiad (IMO) problems with large language models by developing a model-agnostic verification-and-refinement pipeline, which improved accuracy from baseline rates of 21.4-38.1% to 85.7% on IMO 2025 problems.
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 ($\approx$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.