Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions
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 constructions 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-409, 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.
692f338d26742347f61daa57
Boyan Duan
692f338d26742347f61daa58
Xiao Liang
claimed_verified
2025-12-04T08:49:19.034Z
6560763e152b659e623865ae
https://cdn-avatars.huggingface.co/v1/production/uploads/6560763e152b659e623865ae/cTT2jGnPU_8XMrUTvqZ2h.jpeg
Xiao Liang
MasterVito
user
MasterVito
692f338d26742347f61daa59
Shuai Lu
692f338d26742347f61daa5a
Yaoxiang Wang
692f338d26742347f61daa5b
Yelong Shen
692f338d26742347f61daa5c
Kai-Wei Chang
692f338d26742347f61daa5d
Ying Nian Wu
692f338d26742347f61daa5e
Mao Yang
692f338d26742347f61daa5f
Weizhu Chen
692f338d26742347f61daa60
Yeyun Gong
Gold-Medal-Level Olympiad Geometry Solving with Efficient Heuristic Auxiliary Constructions
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 constructions 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-409, 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.
HAGeo, a heuristic-based method for adding auxiliary constructions in geometric deduction, achieves gold-medal level performance on IMO geometry problems, surpassing neural network-based approaches.
automated theorem proving Euclidean geometry International Mathematical Olympiad random strategy auxiliary points heuristic-based method geometric deduction HAGeo AlphaGeometry HAGeo-409 geometry problems human-assessed difficulty levels