Google DeepMind has developed an AI system, AlphaGeometry2, that outperforms top human competitors in solving geometry problems. The AI solved 84% of problems from the International Mathematical Olympiad (IMO) over the past 25 years, surpassing the average gold medalist score.
Why Does DeepMind Focus on Geometry?
DeepMind believes advanced AI needs strong problem-solving skills. Geometry problems require logical thinking and step-by-step reasoning. By mastering these, AI could improve its ability to solve complex scientific and engineering challenges.
How AlphaGeometry2 Works
AlphaGeometry2 combines two key elements:
- A language model from Google’s Gemini AI family
- A symbolic engine that follows mathematical rules
The Gemini model predicts useful steps to solve a problem, while the symbolic engine ensures logical consistency. The AI also uses a search algorithm to explore multiple solutions at once and stores useful findings.
Training the AI with Synthetic Data
A major challenge was the lack of training data. DeepMind solved this by generating over 300 million synthetic theorems and proofs. This helped train the AI to handle different types of geometry problems.
Test Results: Beating the Best
DeepMind tested AlphaGeometry2 on 50 modified IMO problems from 2000 to 2024. The AI solved 42, beating the human gold medalist average of 40.9.
However, the AI struggled with:
- Problems with a variable number of points
- Nonlinear equations
- Inequalities
When tested on 29 harder problems that hadn’t appeared in IMO yet, it solved 20.
Symbolic AI vs. Neural Networks: A Debate
AlphaGeometry2’s success reignites the debate between two AI approaches:
- Neural networks: Learn from large data sets, like OpenAI’s o1 model
- Symbolic AI: Uses rules to manipulate knowledge and reason logically
AlphaGeometry2 blends both, showing that hybrid AI models could be the future. Interestingly, OpenAI’s o1 model failed to solve any IMO problems that AlphaGeometry2 tackled successfully.
Future of AI in Math and Beyond
DeepMind found early signs that AlphaGeometry2’s language model could solve problems without the symbolic engine. However, for now, these external tools remain essential to reduce errors and improve accuracy.
AI like AlphaGeometry2 could transform problem-solving in engineering, science, and beyond. While challenges remain, this is a major step toward AI with human-like reasoning skills.
What do you think about AI competing with top human minds? Share your thoughts in the comments!
