DeepMind, a Google subsidiary specializing in artificial intelligence (AI) research, has announced new achievements for its AlphaGeometry2 AI model in solving geometry problems. In a recently published study, DeepMind reported that AlphaGeometry2 successfully solved 84% of the problems (42 out of 50) in the International Mathematical Olympiad (IMO) from 2000 to 2024, achieving an average gold medalist score of 40.9.
AlphaGeometry2 is an improved version of the AlphaGeometry AI system released in January last year. In July, DeepMind demonstrated a system combining the AlphaProof and AlphaGeometry2 models, which solved 4 out of 6 IMO problems. This advancement highlights AI’s increasing capability in mathematical reasoning.
How AlphaGeometry2 Works
AlphaGeometry2 utilizes a linguistic model based on the Gemini architecture and an enhanced symbolic deduction engine, enabling it to infer problem-solving strategies with superior accuracy compared to most human experts.
The model operates through two main components:
- A linguistic model that generates solution proposals based on a detailed geometric description.
- A symbolic DDAR (Deductive Database Arithmetic Reasoning) engine that verifies the logical consistency of these solutions by creating a deductive closure based on available information.
Simply put, the Gemini AlphaGeometry2 model suggests steps and constructions in a formal mathematical language, and the symbolic engine verifies their logical consistency.
One of the key improvements over its predecessor is the SKEST (Shared Knowledge Ensemble of Search Trees) algorithm, which enables iterative search with knowledge sharing between multiple parallel search trees. This approach allows the system to explore several solution paths simultaneously, significantly improving processing speed and the quality of generated proofs. Additionally, the new C++ implementation of DDAR is 300 times faster than its Python version, further boosting performance.
Challenges and Future Development
Despite these advancements, AlphaGeometry2 has limitations in solving problems involving a variable number of points, nonlinear equations, or inequalities, adds NIXsolutions. To overcome these challenges, DeepMind is exploring strategies such as breaking down complex problems into subproblems and using reinforcement learning to improve AI’s problem-solving capabilities.
While AlphaGeometry2 is not the first AI system to achieve gold medal-level performance in geometry, it is the first to do so across such a large problem set. It employs a hybrid approach, where the Gemini model has a neural network architecture, while its symbolic engine follows rule-based logic.
DeepMind continues to explore the balance between neural networks, which rely on large datasets and statistical approximation, and symbolic AI, which encodes structured rules for problem-solving. Finding new ways to tackle complex geometric problems, particularly in Euclidean geometry, could be a key step in advancing AI’s logical reasoning capabilities. We’ll keep you updated as more breakthroughs emerge in this field.