# google-deepmind/alphageometry

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4,865 stars · 577 forks · Python · Apache-2.0

## Links

- GitHub: https://github.com/google-deepmind/alphageometry
- awesome-repositories: https://awesome-repositories.com/repository/google-deepmind-alphageometry.md

## Description

AlphaGeometry is a neuro-symbolic AI system designed as an automated geometry solver and theorem prover. It integrates a large language model with a formal proof engine to derive geometric conclusions from given premises and generate step-by-step formal proofs.

The system distinguishes itself by combining a symbolic deduction engine with neural-driven auxiliary constructions. This architecture uses a language model to propose additional points or lines to bridge gaps in a proof, while a deductive database and algebraic reasoning system verify the mathematical correctness of each step against strict axioms.

The project covers formal mathematical verification and symbolic geometric reasoning through an iterative proof search and a symbolic-neural hybrid loop.

## Tags

### Scientific & Mathematical Computing

- [Formal Mathematical Proofs](https://awesome-repositories.com/f/scientific-mathematical-computing/formal-mathematical-proofs.md) — Converts geometric conjectures into rigorous, machine-verifiable formal mathematical proofs.
- [Automated Geometry Solvers](https://awesome-repositories.com/f/scientific-mathematical-computing/automated-geometry-solvers.md) — Provides an automated tool that derives geometric conclusions from premises using symbolic logic.
- [Neural Construction Proposals](https://awesome-repositories.com/f/scientific-mathematical-computing/automated-proof-construction/neural-construction-proposals.md) — Proposes additional geometric points or lines using a language model to enable proof completion.
- [Automated Theorem Provers](https://awesome-repositories.com/f/scientific-mathematical-computing/automated-theorem-provers.md) — Generates formal step-by-step proofs for geometric theorems by combining symbolic deduction and neural networks.
- [Computer Algebra Systems](https://awesome-repositories.com/f/scientific-mathematical-computing/computer-algebra-systems.md) — Implements a system for performing symbolic algebraic manipulations to validate geometric claims.
- [Automated Proof Construction](https://awesome-repositories.com/f/scientific-mathematical-computing/automated-proof-construction.md) — Employs an iterative search process to generate formal proof terms by combining deduction and probabilistic guesses.
- [LLM-Driven Construction](https://awesome-repositories.com/f/scientific-mathematical-computing/automated-proof-construction/llm-driven-construction.md) — Uses a large language model as an engine to propose additional constructions to complete mathematical proofs.

### Artificial Intelligence & ML

- [Geometric Problem Solving](https://awesome-repositories.com/f/artificial-intelligence-ml/complex-problem-solving/geometric-problem-solving.md) — Solves geometry problems by deriving conclusions from premises using a deductive database and algebraic engine.
- [Auxiliary Construction Prediction](https://awesome-repositories.com/f/artificial-intelligence-ml/language-model-architectures/auxiliary-construction-prediction.md) — Uses a language model to predict the placement of auxiliary points and lines to bridge proof gaps.
- [Rule-Based Neural Hybrids](https://awesome-repositories.com/f/artificial-intelligence-ml/neural-networks/rule-based-neural-hybrids.md) — Integrates a deterministic symbolic reasoner with a neural model in a hybrid loop to refine theorem proofs.
- [Neuro-Symbolic Architectures](https://awesome-repositories.com/f/artificial-intelligence-ml/neuro-symbolic-architectures.md) — Implements a hybrid architecture integrating a language model for constructions and a deductive database for reasoning.

### Data & Databases

- [Deductive Databases](https://awesome-repositories.com/f/data-databases/deductive-databases.md) — Utilizes a deductive database to store geometric properties and derive new conclusions via symbolic logic.

### Software Engineering & Architecture

- [Geometric Auxiliary Proposals](https://awesome-repositories.com/f/software-engineering-architecture/transaction-proposals/proposal-frameworks/geometric-auxiliary-proposals.md) — Proposes additional geometric points or lines to facilitate proofs when direct deduction is insufficient. ([source](https://cdn.jsdelivr.net/gh/google-deepmind/alphageometry@main/README.md))