AlphaGeometry is a geometry theorem prover that solves Olympiad-level geometry problems without requiring human demonstrations.
The tool addresses the challenge of automated geometric reasoning by combining two components: DDAR, a symbolic deduction engine, and a language model that guides proof search. DDAR operates using formal definitions and deduction rules provided in text files, building proofs step-by-step through logical inference. The language model learns to propose relevant premises and proof directions, effectively steering the search toward solutions. This hybrid approach avoids the need for human-annotated training data while tackling problems of competition-level difficulty.
Developers considering this tool should understand that it targets a specialized domain: formal geometry theorem proving rather than general-purpose mathematics. The system is designed to reproduce results from the Nature 2024 paper, with reproduction requiring specific computational resources—the paper's results used 4 V100 GPUs and 250 CPU workers with particular hyperparameter settings. A lighter configuration is provided for testing, though this yields fewer solutions. The DDAR solver can run independently without the language model components, making it accessible even without the full machine learning infrastructure. An updated version, AlphaGeometry2, has been released separately with its own codebase.
The project maintains clear separation between its symbolic and learning components, allowing users to run either independently. Installation requires manual setup of the meliad dependency outside of standard package management, and configuration relies on the gin library for managing model parameters. The codebase is structured around problem files in text format and produces detailed proof traces showing how each step derives from previous ones, with output optionally written to files for inspection.
