Gemini 2.5 Pro Capable of Winning Gold at IMO 2025
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This paper demonstrates that Google’s Gemini 2.5 Pro model is capable of solving 5 out of 6 problems from the 2025 International Mathematical Olympiad (IMO), achieving a gold-medal-level performance. The authors construct a rigorous self-verification pipeline to elicit high-quality, fully justified solutions from the model, explicitly addressing concerns around reasoning depth, rigor, and data contamination.
A key contribution is a multi-step refinement pipeline involving initial solution generation, self-improvement, and repeated verification using a mathematically rigorous “verifier” agent. This setup isolates critical errors and justification gaps and ensures only fully validated solutions are accepted.
Gemini 2.5 Pro solves 5 out of 6 IMO 2025 problems, covering combinatorics, geometry, functional equations, number theory, and game theory. In the only unsolved problem (Problem 6), the model reports a trivial bound without deeper insight, exposing current limits.
The paper underscores how thinking budget constraints (32768 tokens) hamper LLM performance on deep problems. The authors mitigate this by breaking down the task into modular steps, effectively doubling the reasoning budget via staged self-improvement.
Prompting strategy is critical: the authors prompt the model to emphasize rigor over answer accuracy, including detailed step-by-step proof formatting, and inject minimal yet effective domain hints (e.g., “use induction”) without leaking solution strategies.
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