Related papers: FormalGeo: An Extensible Formalized Framework for …
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…
We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO…
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…
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…
Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth,…
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…
Geometry problem solving presents distinctive challenges in artificial intelligence, requiring exceptional multimodal comprehension and rigorous mathematical reasoning capabilities. Existing approaches typically fall into two categories:…
The human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdiscipline of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
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…
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…
Geometric problem solving (GPS) requires precise multimodal understanding and rigorous, step-by-step logical reasoning. However, developing capable Multimodal Large Language Models (MLLMs) for GPS is heavily bottlenecked by the scarcity of…
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…
Multi-modal Large Language Models (MLLMs) have gained significant attention in both academia and industry for their capabilities in handling multi-modal tasks. However, these models face challenges in mathematical geometric reasoning due to…
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…
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…
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…
Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by using symbolic…
Plane Geometry Problem Solving (PGPS) is a multimodal reasoning task that aims to solve a plane geometric problem based on a geometric diagram and problem textual descriptions. Although Large Language Models (LLMs) possess strong reasoning…
Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and…