# Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning

arXiv: https://arxiv.org/abs/2512.10534 · HTML: https://mlsanity.com/paper/2512.10534/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Educational agents and math problem solving, one of 16 directions in LLM agents and tool use.
- Builds on 35 of its 40 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Placed in

- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 30 of 35)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Leveraging Procedural Generation to Benchmark Reinforcement Learning](https://mlsanity.com/paper/1912.01588/) (2019)
- [MineDojo: Building Open-Ended Embodied Agents with Internet-Scale Knowledge](https://mlsanity.com/paper/2206.08853/) (2022)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [WebRL: Training LLM Web Agents via Self-Evolving Online Curriculum Reinforcement Learning](https://mlsanity.com/paper/2411.02337/) (2024)
- [Thinking Fast and Slow with Deep Learning and Tree Search](https://mlsanity.com/paper/1705.08439/) (2017)
- [Benchmarking the Spectrum of Agent Capabilities](https://mlsanity.com/paper/2109.06780/) (2021)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [ToRL: Scaling Tool-Integrated RL](https://mlsanity.com/paper/2503.23383/) (2025)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Agentic Reasoning and Tool Integration for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2505.01441/) (2025)
- [Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving](https://mlsanity.com/paper/2507.23726/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning](https://mlsanity.com/paper/2506.06632/) (2025)
- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [Agent RL Scaling Law: Agent RL with Spontaneous Code Execution for Mathematical Problem Solving](https://mlsanity.com/paper/2505.07773/) (2025)
- [rStar2-Agent: Agentic Reasoning Technical Report](https://mlsanity.com/paper/2508.20722/) (2025)
- [Satori: Reinforcement Learning with Chain-of-Action-Thought Enhances LLM Reasoning via Autoregressive Search](https://mlsanity.com/paper/2502.02508/) (2025)
- [Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning](https://mlsanity.com/paper/2502.06781/) (2025)
- [START: Self-taught Reasoner with Tools](https://mlsanity.com/paper/2503.04625/) (2025)
- [EnvGen: Generating and Adapting Environments via LLMs for Training Embodied Agents](https://mlsanity.com/paper/2403.12014/) (2024)
- [DUMP: Automated Distribution-Level Curriculum Learning for RL-based LLM Post-training](https://mlsanity.com/paper/2504.09710/) (2025)
- [Synthetic Data Generation & Multi-Step RL for Reasoning & Tool Use](https://mlsanity.com/paper/2504.04736/) (2025)

## Built on by (most cited first, 7 of 7)

- [Dynamic Skill Lifecycle Management for Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.10923/) (2026)
- [Youtu-LLM: Unlocking the Native Agentic Potential for Lightweight Large Language Models](https://mlsanity.com/paper/2512.24618/) (2025)
- [Progressive Agent Skill Generation via Reinforcement Learning](https://mlsanity.com/paper/2608.01678/) (2026)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)
- [AdvancedMathBench: A Benchmark Suite for Advanced Mathematical Proof Generation and Verification](https://mlsanity.com/paper/2607.11849/) (2026)
- [Splicing Hints into Reasoning Traces: Learning from Demonstrator Failures](https://mlsanity.com/paper/2610.13996/) (2026)

## Abstract (arXiv)

Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions.