Towards Robust Mathematical Reasoning

TL;DR

This paper introduces IMO-Bench, a comprehensive set of challenging mathematical reasoning benchmarks modeled after the IMO, to evaluate and improve foundation models' proof-writing and problem-solving skills, achieving state-of-the-art results.

Contribution

The paper presents IMO-Bench, a new suite of advanced mathematical reasoning benchmarks for foundation models, including both problem-solving and proof-writing evaluations, with automatic grading tools.

Findings

Achieved 80.0% on IMO-AnswerBench

Achieved 65.7% on IMO-Proof Bench

Surpassed previous models by large margins

Abstract

Finding the right north-star metrics is highly critical for advancing the mathematical reasoning capabilities of foundation models, especially given that existing evaluations are either too easy or only focus on getting correct short answers. To address these issues, we present IMO-Bench, a suite of advanced reasoning benchmarks, vetted by a panel of top specialists and that specifically targets the level of the International Mathematical Olympiad (IMO), the most prestigious venue for young mathematicians. IMO-AnswerBench first tests models on 400 diverse Olympiad problems with verifiable short answers. IMO-Proof Bench is the next-level evaluation for proof-writing capabilities, which includes both basic and advanced IMO level problems as well as detailed grading guidelines to facilitate automatic grading. These benchmarks played a crucial role in our historic achievement of the gold-level performance at IMO 2025 with Gemini Deep Think (Luong and Lockhart, 2025). Our model achieved 80.0% on IMO-AnswerBench and 65.7% on the advanced IMO-Proof Bench, surpassing the best non-Gemini models by large margins of 6.9% and 42.4% respectively. We also showed that autograders built with Gemini reasoning correlate well with human evaluations and construct IMO-GradingBench, with 1000 human gradings on proofs, to enable further progress in automatic evaluation of long-form answers. We hope that IMO-Bench will help the community towards advancing robust mathematical reasoning and release it at https://imobench.github.io/.