---
license: mit
task_categories:
- question-answering
language:
- en
tags:
- code
size_categories:
- n<1K
---

# Dataset Card for the HAGeo-409 Benchmark

<p align="center">
  <!-- <a href="https://mastervito.github.io/SvS.github.io/"><b>[🌐 Website]</b></a> • -->
  <a href="https://huggingface.co/datasets/HAGeo-IMO/HAGeo-409"><b>[🤗 Benchmark]</b></a> •
  <a href="https://arxiv.org/abs/2512.00097"><b>[📜 Paper]</b></a> •
  <a href="https://github.com/boduan1/HAGeo"><b>[🐱 GitHub]</b></a> •
  <a href="X"><b>[🐦 Twitter]</b></a> •
  <a href="R"><b>[📕 Rednote]</b></a>
</p>

The HAGeo-409 benchmark includes 409 IMO-level geometry theorem-proving problems and typically presents greater difficulty than the widely used IMO-30 benchmark.


<p align="center">
    <img src="IMO-HAGeo-Difficulty.png" width="1000">
    <em>Figure 1: Problem difficulity distribution of the IMO-30 benchmark and our new HAGeo-409 benchmark. 
    </em>
</p>


<br>

# Data Loading
```
from datasets import load_dataset
dataset = load_dataset("HAGeo-IMO/HAGeo-409")
```

<br>

# Data Instance
Each instance contains the following fields: 'Problem\_ID', 'Natural\_Language', 'AlphaGeometry', and 'HAGeo'.

* **Problem\_ID**: The unique identifier of each problem, indicating the source competition and the corresponding problem index.
* **Natural\_Language**: The problem statement written in natural language.
* **AlphaGeometry**: The problem expressed in AlphaGeometry’s geometry-specific representation language.
* **HAGeo**: The problem expressed in HAGeo’s geometry-specific representation language (Cases in Appendix C, D).

<br>



# Cite Us

If you find this dataset helpful, please consider citing our paper:

```
@misc{duan2025goldmedallevelolympiadgeometrysolving,
      title={Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions}, 
      author={Boyan Duan and Xiao Liang and Shuai Lu and Yaoxiang Wang and Yelong Shen and Kai-Wei Chang and Ying Nian Wu and Mao Yang and Weizhu Chen and Yeyun Gong},
      year={2025},
      eprint={2512.00097},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2512.00097}, 
}
```