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Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains…

Computer Vision and Pattern Recognition · Computer Science 2025-06-04 Yurui Zhao , Xiang Wang , Jiahong Liu , Irwin King , Zhitao Huang

Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions -- failing to capture the nature of mathematics…

Artificial Intelligence · Computer Science 2025-10-21 Jie Zhang , Cezara Petrui , Kristina Nikolić , Florian Tramèr

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…

Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic…

Computer Vision and Pattern Recognition · Computer Science 2025-02-20 Junxiao Wang , Ting Zhang , Heng Yu , Jingdong Wang , Hua Huang

Large language models (LLMs) have shown strong performance on mathematical reasoning under well-defined conditions. However, real-world engineering problems involve uncertainty, context, and open-ended settings that extend beyond symbolic…

Artificial Intelligence · Computer Science 2026-05-05 Xiyuan Zhou , Xinlei Wang , Yirui He , Yang Wu , Ruixi Zou , Yuheng Cheng , Yulu Xie , Wenxuan Liu , Huan Zhao , Yan Xu , Jinjin Gu , Junhua Zhao

We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…

Logic in Computer Science · Computer Science 2021-08-03 Anthony Bordg , Nicolò Cavalleri

Traditional approaches for validating molecular simulations rely on making software open source and transparent, incorporating unit testing, and generally employing human oversight. We propose an approach that eliminates software errors…

Statistical Mechanics · Physics 2025-08-19 Ejike D. Ugwuanyi , Colin T. Jones , John Velkey , Tyler R. Josephson

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This…

Computer Vision and Pattern Recognition · Computer Science 2025-01-13 Renqiu Xia , Mingsheng Li , Hancheng Ye , Wenjie Wu , Hongbin Zhou , Jiakang Yuan , Tianshuo Peng , Xinyu Cai , Xiangchao Yan , Bin Wang , Conghui He , Botian Shi , Tao Chen , Junchi Yan , Bo Zhang

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the…

Machine Learning · Computer Science 2025-03-04 Roozbeh Yousefzadeh , Xuenan Cao , Azim Ospanov

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have…

Computer Vision and Pattern Recognition · Computer Science 2026-04-17 Peijie Wang , Ming-Liang Zhang , Jun Cao , Chao Deng , Dekang Ran , Hongda Sun , Pi Bu , Xuan Zhang , Yingyao Wang , Jun Song , Bo Zheng , Fei Yin , Cheng-Lin Liu

Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of…

Computation and Language · Computer Science 2023-10-20 Xueliang Zhao , Xinting Huang , Wei Bi , Lingpeng Kong

Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a…

Machine Learning · Computer Science 2025-03-07 Adarsh Kumarappan , Mo Tiwari , Peiyang Song , Robert Joseph George , Chaowei Xiao , Anima Anandkumar

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…

Artificial Intelligence · Computer Science 2025-02-28 Zenan Li , Zhaoyu Li , Wen Tang , Xian Zhang , Yuan Yao , Xujie Si , Fan Yang , Kaiyu Yang , Xiaoxing Ma

Large Language Models (LLMs) have demonstrated strong performance across various natural language processing tasks, yet their proficiency in mathematical reasoning remains a key challenge. Addressing the gap between natural and mathematical…

Artificial Intelligence · Computer Science 2025-02-18 Xuhan Huang , Qingning Shen , Yan Hu , Anningzhe Gao , Benyou Wang

Geometric problem solving has always been a long-standing challenge in the fields of mathematical reasoning and artificial intelligence. We built a neural-symbolic system, called FGeo-HyperGNet, to automatically perform human-like geometric…

Artificial Intelligence · Computer Science 2025-08-01 Xiaokai Zhang , Yang Li , Na Zhu , Cheng Qin , Zhenbing Zeng , Tuo Leng

Geometry mathematics problems pose significant challenges for large language models (LLMs) because they involve visual elements and spatial reasoning. Current methods primarily rely on symbolic character awareness to address these problems.…

Computer Vision and Pattern Recognition · Computer Science 2024-12-17 Shihao Xu , Yiyang Luo , Wei Shi

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either…

Computation and Language · Computer Science 2021-07-22 Pan Lu , Ran Gong , Shibiao Jiang , Liang Qiu , Siyuan Huang , Xiaodan Liang , Song-Chun Zhu

The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This…

Artificial Intelligence · Computer Science 2024-02-15 Yiming He , Jia Zou , Xiaokai Zhang , Na Zhu , Tuo Leng

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the…

Machine Learning · Computer Science 2025-09-26 Bing Liu , Wenqiang Yv , Xuzheng Yang , Shichang Wang , Junzhuo Liu , Peng Wang , Guoqing Wang , Yang Yang , Heng Tao Shen