Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions
Boyan Duan, Xiao Liang, Shuai Lu JD.com, Yaoxiang Wang, Yelong Shen, Kai-Wei Chang University of California, Los Angeles and Amazon, Ying Nian Wu, Mao Yang 等 10 位作者
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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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表