Recently, Deepmind from Google had breakthrough AI Geometry improvements. The problem with large language models was there was insufficient data to understand and reason solutions to geometry. A simple example was to calculate the area of a triangle. LLMs did not have the understanding to maybe create 2 right hand triangles, and thereby solve the problem.

The International Mathematical Olympiad is a modern-day arena for the world’s brightest high-school mathematicians. The competition showcases young talent and has emerged as a testing ground for advanced AI systems in math and reasoning.

A Deepmind paper in Nature introduced AlphaGeometry. AphaGeometry is an AI system that solves complex geometry problems at a level approaching a human Olympiad gold-medalist, which is a breakthrough in AI performance. In a benchmarking test of 30 Olympiad geometry problems, AlphaGeometry solved 25 within the standard Olympiad time limit. The previous state-of-the-art system solved 10 of these geometry problems, and the average human gold medalist solved 25.9 problems.

Google Deepmind makes breakthrough in difficult artificial intelligence test | BBC News

Here are some key areas of improvement:

Problem-solving

• Hybrid systems: Combining neural networks (inspired by the human brain) with symbolic AI engines (using logical rules) has proven successful. DeepMind’s AlphaGeometry, for example, solved complex geometry problems from the International Mathematical Olympiad using this approach.
• Automated reasoning tools (ART). These tools, like FormalGeo7k, allow AI to tackle problems with formal and verifiable solutions, making them more transparent and trustworthy.
• Learning from synthetic data. Training AI on vast amounts of algorithmically generated data, like AlphaGeometry’s 100 million geometric proofs, enables learning without relying on limited human-labeled datasets.

Understanding and manipulation

• Shape modeling and generation. AI can now create and manipulate 3D shapes more accurately and efficiently, with applications in animation, robotics, and design.
• 3D point cloud processing. Advanced algorithms can analyze and understand the structure of 3D point clouds from sensors, enabling object recognition, navigation, and autonomous driving.
• Geometry-aware deep learning. Embedding geometric information into deep learning models has led to improvements in tasks like image and video processing, where spatial relationships are crucial.

Other Breakthrough AI Geometry

• AI-powered learning tools. Interactive geometry software incorporating AI assistance can enhance student learning by providing automated reasoning support and personalized feedback.
• Benchmarking and datasets: Standardized datasets and competitions like FormalGeo7k are crucial for comparing and advancing AI performance in geometric tasks.

The AI geometry research is still in its early stages but advancements showcase its potential to revolutionize various fields. Geometry provide machines with a deeper understanding and manipulation of geometric concepts.