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. Considering geometry problem solving is a relatively nascent field with limited suitable datasets and currently almost no work on solid geometry problem solving, we collect a geometry question-answer dataset by sourcing geometric data from Chinese high school education websites, referred to as GeoMath. It contains solid geometry questions and answers with accurate reasoning steps as compensation for existing plane geometry datasets. Additionally, we propose a Large Multi-modal Model (LMM) framework named Geo-LLaVA, which incorporates retrieval augmentation with supervised fine-tuning (SFT) in the training stage, called meta-training, and employs in-context learning (ICL) during inference to improve performance. Our fine-tuned model with ICL attains the state-of-the-art performance of 65.25% and 42.36% on selected questions of the GeoQA dataset and GeoMath dataset respectively with proper inference steps. Notably, our model initially endows the ability to solve solid geometry problems and supports the generation of reasonable solid geometry picture descriptions and problem-solving steps. Our research sets the stage for further exploration of LLMs in multi-modal math problem-solving, particularly in geometry math problems.

Addressing the challenge of automated geometry math problem-solving in artificial intelligence (AI) involves understanding multi-modal information and mathematics. Current methods struggle with accurately interpreting geometry diagrams, which hinders effective problem-solving. To tackle this issue, we present the Geometry problem sOlver with natural Language Description (GOLD) model. GOLD enhances the extraction of geometric relations by separately processing symbols and geometric primitives within the diagram. Subsequently, it converts the extracted relations into natural language descriptions, efficiently utilizing large language models to solve geometry math problems. Experiments show that the GOLD model outperforms the Geoformer model, the previous best method on the UniGeo dataset, by achieving accuracy improvements of 12.7% and 42.1% in calculation and proving subsets. Additionally, it surpasses the former best model on the PGPS9K and Geometry3K datasets, PGPSNet, by obtaining accuracy enhancements of 1.8% and 3.2%, respectively.

Recent advancements in Large Language Models (LLMs) and Multi-Modal Models (MMs) have demonstrated their remarkable capabilities in problem-solving. Yet, their proficiency in tackling geometry math problems, which necessitates an integrated understanding of both textual and visual information, has not been thoroughly evaluated. To address this gap, we introduce the GeoEval benchmark, a comprehensive collection that includes a main subset of 2000 problems, a 750 problem subset focusing on backward reasoning, an augmented subset of 2000 problems, and a hard subset of 300 problems. This benchmark facilitates a deeper investigation into the performance of LLMs and MMs on solving geometry math problems. Our evaluation of ten LLMs and MMs across these varied subsets reveals that the WizardMath model excels, achieving a 55.67\% accuracy rate on the main subset but only a 6.00\% accuracy on the challenging subset. This highlights the critical need for testing models against datasets on which they have not been pre-trained. Additionally, our findings indicate that GPT-series models perform more effectively on problems they have rephrased, suggesting a promising method for enhancing model capabilities.

Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems. Additionally, the current research predominantly focuses on geometry calculation problems, while overlooking other essential aspects like proving. In this study, we address these limitations by proposing the Geometry-Aware Problem Solver (GAPS) model. GAPS is specifically designed to generate solution programs for geometry math problems of various types with the help of its unique problem-type classifier. To achieve this, GAPS treats the solution program as a composition of operators and operands, segregating their generation processes. Furthermore, we introduce the geometry elements enhancement method, which enhances the ability of GAPS to recognize geometry elements accurately. By leveraging these improvements, GAPS showcases remarkable performance in resolving geometry math problems. Our experiments conducted on the UniGeo dataset demonstrate the superiority of GAPS over the state-of-the-art model, Geoformer. Specifically, GAPS achieves an accuracy improvement of more than 5.3% for calculation tasks and an impressive 41.1% for proving tasks. Notably, GAPS achieves an impressive accuracy of 97.5% on proving problems, representing a significant advancement in solving geometry proving tasks.