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Google DeepMind, a leading AI lab, has developed an advanced AI system called AlphaGeometry. This system can solve complex geometry problems at a level similar to a gold medalist in the International Mathematical Olympiad (IMO), a prestigious contest for high school students.
AlphaGeometry combines two different approaches: a neural language model for generating ideas and a symbolic deduction engine for verifying them using formal logic and rules. The language model uses the same technology as Google’s search engine and natural language systems, while the deduction engine is inspired by a method created by Chinese mathematician Wen-Tsün Wu in 1978.
The team tested AlphaGeometry with 30 challenging geometry problems from the IMO. The system successfully solved 25 out of 30 problems within the standard time limit of 4.5 hours, matching the average performance of human gold medalists. Previously, the best system based on Wu’s method could solve only 10 problems.
Published in Nature, these results demonstrate that AI can reason logically and contribute to discovering new mathematical knowledge.
Mathematics, especially geometry, has been a tough area for AI because it requires both creativity and strict logical reasoning. Unlike text-based models trained on vast web data, mathematics relies on symbolic and domain-specific data, which is scarce. Additionally, solving math problems demands logical reasoning, where most current AI models fall short.
To tackle these issues, the researchers developed a new neuro-symbolic approach. Neural networks excel at recognizing patterns and predicting next steps but can often make errors. Symbolic systems, grounded in formal logic and rules, can correct and explain these decisions. This dual approach aligns with the concept of “thinking, fast and slow,” where one system provides quick, intuitive ideas, while the other ensures deliberate, rational decisions.
AlphaGeometry can also handle unseen problems and discover new theorems not explicitly stated in the initial problem. For instance, it proved a theorem about the angle bisector of a triangle, which was neither a given premise nor a goal.
The researchers have open-sourced AlphaGeometry, aiming to inspire further research and applications in mathematics, science, and AI. They acknowledge existing limitations, such as the need for more human-readable proofs, scalability to more complex problems, and ethical considerations of AI in mathematics.
While AlphaGeometry is currently focused on geometry proofs, the team believes their approach could enable AI to thrive in other areas of math and science with limited human-generated training data. By automating the discovery and verification of new knowledge, machine learning could soon accelerate human understanding across various disciplines.
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