The paper introduces a framework that combines a Geometric Vision Parser and a Symbolic Solver to enable a Large Language Model to solve complex plane geometry problems. By translating diagrams into symbolic representations and performing formal deductions, the approach reduces hallucinations and produces interpretable, human-like solutions. Experiments on a new benchmark from 2025 Chinese Zhongkao exams show performance comparable to Gemini 2.5 Pro.
By Weichen Dai, Rafael Medeiros Cabral, Ziyi Shou, Yan Cao, Xin Shen, Dongcai Lu, Yi Zhou
The paper introduces InternGeometry, a large language model agent that achieves medalist-level performance on International Mathematical Olympiad geometry problems. It overcomes traditional heuristic limitations by iteratively proposing and verifying auxiliary constructions with a symbolic engine, supported by a dynamic memory mechanism that allows over 200 interactions per problem. Using Complexity-Boosting Reinforcement Learning, InternGeometry trains on only 13,000 examples—0.004% of the data used by AlphaGeometry 2—and solves 44 of 50 IMO geometry problems, surpassing the average gold medalist score.
By Haiteng Zhao, Junhao Shen, Yiming Zhang, Songyang Gao, Kuikun Liu, Tianyou Ma, Fan Zheng, Dahua Lin, Wenwei Zhang, Kai Chen
arXiv:2607. 19374v1 Announce Type: new Abstract: Recent formal reasoning systems have reached IMO-level performance, yet they leave a fragmented landscape: algebra and number theory are handled in Lean, while geometry still relies on domain-specific languages with limited formal guarantees.
By Linbin Tang, Jingyan You, Zilin Kang, Hanzhang Liu, Sophia Zhang, Zenan Li, Chenrui Cao, Liangcheng Song, Jiaao Wu, Xian Zhang, Fan Yang
arXiv:2606. 27926v1 Announce Type: new Abstract: Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor.
By Can Li, Ting Zhang, Junbo Zhao, Hua Huang
arXiv:2608.30156v1 Announce Type: new
Abstract: Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precis...
By Xiaoqiang Kang, Shengen Wu, Maizhen Ning, Xiaobo Jin, Kaizhu Huang, Yutao Yue, Xiaowei Huang, Qiufeng Wang
arXiv:2606. 08728v1 Announce Type: new Abstract: Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers.
By Syed Rifat Raiyan, Mohsinul Kabir, Hasan Mahmud, Md Kamrul Hasan
NL2AGBench is a benchmark that evaluates how well large language models can translate English geometry problems into the formal language required by AlphaGeometry’s theorem‑proving engine. The study tests ten state‑of‑the‑art LLMs, comparing executable translation accuracy, syntactic correctness, and error types, and finds a large gap between closed‑source and open‑source models. The authors also propose an error taxonomy and test mitigation strategies such as few‑shot prompting, fine‑tuning, and human‑guided hinting, which improve performance across model families.
By Samuel Xiao, Judy Song, Rory Hu, Ziliang Zong
PhysElite is a new bilingual multimodal benchmark designed to evaluate large language models on Olympiad-level physics problems. It contains 11,586 problems, each paired with visual diagrams, step-by-step bilingual Chinese‑English solution derivations, and the final answer. Benchmarking 18 models revealed that even the best reaches only 33.7% accuracy, and a step‑level analysis highlights where models falter in reasoning.
By Ruoran Xu, Wending Gao, Liyunfeng Chen, Aixin Shi, Haoyu Cheng, Zixiang Fang, Yiqiang Zou, Qiufeng Wang
arXiv:2607. 12982v1 Announce Type: new Abstract: Math reasoning has achieved significant progress with the rapid advancement of Multimodal Large Language Models (MLLMs), however analytic geometry remains largely underexplored, primarily due to the scarcity of annotated samples.
By Ruoran Xu, Wending Gao, Qiufeng Wang
arXiv:2608.28600v1 Announce Type: new
Abstract: Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet the mathematically meaningful skills underlying their...
By Jonghyun Song, Sangjun Song, Minjae Oh, Haesung Pyun, Sungsik Lee, Yohan Jo
ProofEvolve is a neuro‑symbolic framework that evolves formally verified symbolic proof structures alongside neural models to expand the knowledge boundary in automated theorem proving. The neural component proposes variation operators such as decompositions, repairs, and schema recombinations, while the Lean kernel verifies every proof transition, ensuring formal soundness. Across three competition‑level Lean benchmarks, ProofEvolve achieves the highest average solve rate among evaluated proof systems.
By Wenqian Ye, Ziwei Guan, Eric Xie, Bohan Liu, Shivani Modi, Buyun Zhang, Ellie Dingqiao Wen, Henry Kautz, Aidong Zhang
arXiv:2606. 14176v1 Announce Type: new Abstract: Geometry problem generation is useful for AI-assisted education and multimodal mathematical reasoning, but reliable synthesis remains difficult because the problem statement, diagram, constraints, and solution should be mutually consistent.
By Xiaoxian Duan, Zequn Liu, Yingce Xia