@inproceedings{duan-etal-2026-gold,
title = "Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions",
author = "Duan, Boyan and
Liang, Xiao and
Lu, Shuai and
Wang, Yaoxiang and
Shen, Yelong and
Chang, Kai-Wei and
Wu, Ying Nian and
Yang, Mao and
Chen, Weizhu and
Gong, Yeyun",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.acl-long.991/",
pages = "21725--21747",
ISBN = "979-8-89176-390-6",
abstract = "Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a highly efficient method for geometry theorem proving that runs entirely on CPUs without relying on neural network{--}based inference. Our initial study shows that a simple random strategy for adding auxiliary points can achieve ``silver-medal'' level human performance on IMO. Building on this, we propose HAGeo, a Heuristic-based method for adding Auxiliary points in Geometric deduction that solves 28 of 30 problems on the IMO-30 benchmark, achieving ``gold-medal'' level performance and surpassing AlphaGeometry, a competitive neural network{--}based approach, by a notable margin. To evaluate our method and existing approaches more comprehensively, we further construct HAGeo, a benchmark consisting of 409 geometry problems with human-assessed difficulty levels. Compared with the widely used IMO-30, our benchmark poses greater challenges and provides a more precise evaluation, setting a higher bar for geometry theorem proving."
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%0 Conference Proceedings
%T Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions
%A Duan, Boyan
%A Liang, Xiao
%A Lu, Shuai
%A Wang, Yaoxiang
%A Shen, Yelong
%A Chang, Kai-Wei
%A Wu, Ying Nian
%A Yang, Mao
%A Chen, Weizhu
%A Gong, Yeyun
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F duan-etal-2026-gold
%X Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a highly efficient method for geometry theorem proving that runs entirely on CPUs without relying on neural network–based inference. Our initial study shows that a simple random strategy for adding auxiliary points can achieve “silver-medal” level human performance on IMO. Building on this, we propose HAGeo, a Heuristic-based method for adding Auxiliary points in Geometric deduction that solves 28 of 30 problems on the IMO-30 benchmark, achieving “gold-medal” level performance and surpassing AlphaGeometry, a competitive neural network–based approach, by a notable margin. To evaluate our method and existing approaches more comprehensively, we further construct HAGeo, a benchmark consisting of 409 geometry problems with human-assessed difficulty levels. Compared with the widely used IMO-30, our benchmark poses greater challenges and provides a more precise evaluation, setting a higher bar for geometry theorem proving.
%U https://aclanthology.org/2026.acl-long.991/
%P 21725-21747
Markdown (Informal)
[Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions](https://aclanthology.org/2026.acl-long.991/) (Duan et al., ACL 2026)
ACL
- Boyan Duan, Xiao Liang, Shuai Lu, Yaoxiang Wang, Yelong Shen, Kai-Wei Chang, Ying Nian Wu, Mao Yang, Weizhu Chen, and Yeyun Gong. 2026. Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 21725–21747, San Diego, California, United States. Association for Computational Linguistics.