We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems.
This repository contains code necessary to reproduce solving some olympiad geometry problems (for example, IMO 2005 P1, IMO 2008 P6, IMO 2013 P3 and others). This is done by running the symbolic part of AlphaGeometry2 system called DDAR. DDAR runs on problems formalized into the AlphaGeometry2 language and supplemented by the point coordinates. Some problems can be solved by DDAR alone and others require auxiliary points provided by a language model.
Installation is done in a virtual environment:
$ sudo apt install python3
$ sudo apt install python3-pip
$ sudo apt install python3-venv
$ python3 -m venv ag2
$ source ag2/bin/activate
$ pip install numpy
Command below runs the prover on some IMO problems solved by AlphaGeometry2:
$ python -m test
You will see the following output:
We run the logical core DDAR on some easier IMO problems that can be solved by DDAR alone.
Problem: 2000_p1
..... Proven :-)
Problem: 2002_p2a
.... Proven :-)
Problem: 2002_p2b
.... Proven :-)
Problem: 2003_p4
... Proven :-)
Problem: 2004_p5
... Proven :-)
Problem: 2005_p5
...... Proven :-)
Problem: 2007_p4
.... Proven :-)
Problem: 2010_p4
.... Proven :-)
Problem: 2012_p1
...... Proven :-)
Problem: 2013_p4
..... Proven :-)
Problem: 2014_p4
.... Proven :-)
Problem: 2015_p4
... Proven :-)
Problem: 2016_p1
..... Proven :-)
Problem: 2017_p4
..... Proven :-)
Problem: 2022_p4
..... Proven :-)
We run the logical core DDAR on some challenging IMO problems, with manually provided
auxiliary points. This is not a full AlphaGeometry system, only a test of the logical core.
Problem: 2001_p5a
......... Proven :-)
Problem: 2003_p4b
..... Proven :-)
Problem: 2005_p1
...... Proven :-)
Problem: 2008_p1b
........ Proven :-)
Problem: 2008_p6
...... Proven :-)
Problem: 2009_p4a
..... Proven :-)
Problem: 2009_p4b
...... Proven :-)
Problem: 2011_p6
...... Proven :-)
Problem: 2013_p3
....... Proven :-)
Problem: 2019_p2
.... Proven :-)
Problem: 2021_p3
......... Proven :-)
Please cite this work as:
@misc{chervonyi2025goldmedalistperformancesolvingolympiad,
title={Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2},
author={Yuri Chervonyi and Trieu H. Trinh and Miroslav Olšák and Xiaomeng Yang and Hoang Nguyen and Marcelo Menegali and Junehyuk Jung and Vikas Verma and Quoc V. Le and Thang Luong},
year={2025},
eprint={2502.03544},
archivePrefix={arXiv},
primaryClass={cs.AI},
url={https://arxiv.org/abs/2502.03544},
}
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