相关论文: Gold-Medal-Level Olympiad Geometry Solving with Ef…

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level…

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,…

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…

We present AlphaGeometry2 (AG2), a significantly improved version of AlphaGeometry introduced in (Trinh et al., 2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend…

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…

Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane…

We present a method for automatically building diagrams for olympiad-level geometry problems and implement our approach in a new open-source software tool, the Geometry Model Builder (GMB). Central to our method is a new domain-specific…

The International Mathematical Olympiad (IMO) is widely regarded as the world championship of high-school mathematics. IMO problems are renowned for their difficulty and novelty, demanding deep insight, creativity, and rigor. Although large…

This is the first part of a series of papers aiming to show how trigonometry and analytic tools can help into tackling demanding Olympiad geometry problems. We present several novel techniques for tackling hard problems from various…

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier.…

The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated,…

We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…

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,…

Finding the right north-star metrics is highly critical for advancing the mathematical reasoning capabilities of foundation models, especially given that existing evaluations are either too easy or only focus on getting correct short…

Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…

A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate…

This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a…

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…

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to…