Related papers: LeanGeo: Formalizing Competitional Geometry proble…

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane…

Geometric problem solving constitutes a critical branch of mathematical reasoning, requiring precise analysis of shapes and spatial relationships. Current evaluations of geometric reasoning in vision-language models (VLMs) face limitations,…

Geometric spatial reasoning forms the foundation of many applications in artificial intelligence, yet the ability of large language models (LLMs) to operate over geometric spatial information expressed in procedural code remains…

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two…

Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry…

Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving…

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved…

We present NoReGeo, a novel benchmark designed to evaluate the intrinsic geometric understanding of large language models (LLMs) without relying on reasoning or algebraic computation. Unlike existing benchmarks that primarily assess models'…

Recent neuro-symbolic geometry theorem provers have made significant progress on Euclidean problems by coupling neural guidance with symbolic verification. However, most existing systems operate almost exclusively in a symbolic space,…

Evaluating the symbolic reasoning of large language models (LLMs) calls for geometry benchmarks that require multi-step proofs grounded in both text and diagrams. However, existing benchmarks are often limited in scale and rarely provide…

Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial…

Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to…

Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the…

LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…

Recent advances in large language models have demonstrated impressive capabilities in mathematical formalization. However, existing benchmarks focus on logical verification of declarative propositions, often neglecting the task of…

Solid geometry problem solving demands spatial mathematical reasoning that integrates spatial intelligence and symbolic reasoning. However, most existing multimodal mathematical reasoning benchmarks focus primarily on 2D plane geometry,…

As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…

Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must…