Long-horizon Reasoning Agent for Olympiad-Level Mathematical Problem Solving

TL;DR

This paper introduces Intern-S1-MO, a hierarchical multi-round reasoning agent with a lemma-based memory system and an RL training framework, enabling it to solve ultra-hard IMO-level math problems beyond previous LRM capabilities.

Contribution

The paper presents a novel multi-agent, multi-round reasoning framework with a lemma memory system and an RL training method, significantly improving LRM performance on complex mathematical problems.

Findings

Achieved near-medal scores on IMO2025 non-geometry problems.

Surpassed existing LRMs on HMMT2025, AIME2025, and CNMO2025.

Reaching gold medal level in CMO2025 with human expert validation.

Abstract

Large Reasoning Models (LRMs) have expanded the mathematical reasoning frontier through Chain-of-Thought (CoT) techniques and Reinforcement Learning with Verifiable Rewards (RLVR), capable of solving AIME-level problems. However, the performance of LRMs is heavily dependent on the extended reasoning context length. For solving ultra-hard problems like those in the International Mathematical Olympiad (IMO), the required reasoning complexity surpasses the space that an LRM can explore in a single round. Previous works attempt to extend the reasoning context of LRMs but remain prompt-based and built upon proprietary models, lacking systematic structures and training pipelines. Therefore, this paper introduces Intern-S1-MO, a long-horizon math agent that conducts multi-round hierarchical reasoning, composed of an LRM-based multi-agent system including reasoning, summary, and verification. By maintaining a compact memory in the form of lemmas, Intern-S1-MO can more freely explore the lemma-rich reasoning spaces in multiple reasoning stages, thereby breaking through the context constraints for IMO-level math problems. Furthermore, we propose OREAL-H, an RL framework for training the LRM using the online explored trajectories to simultaneously bootstrap the reasoning ability of LRM and elevate the overall performance of Intern-S1-MO. Experiments show that Intern-S1-MO can obtain 26 out of 35 points on the non-geometry problems of IMO2025, matching the performance of silver medalists. It also surpasses the current advanced LRMs on inference benchmarks such as HMMT2025, AIME2025, and CNMO2025. In addition, our agent officially participates in CMO2025 and achieves a score of 102/126 under the judgment of human experts, reaching the gold medal level.