An artificial intelligence system developed by the Google DeepMind lab has outperformed the average gold medalist in solving geometry problems at an international mathematics competition. The new version of the system, called AlphaGeometry2, is capable of solving 84% of all geometry problems that have appeared at the International Mathematical Olympiad (IMO) over the past twenty-five years.
AlphaGeometry2 uses a language model from the Gemini family by Google and a “symbolic engine.” The Gemini model assists the engine, which applies mathematical rules to derive solutions, in finding possible proofs for a given geometric theorem. System tests showed that it successfully solved 42 out of 50 problems, surpassing the average score of gold medalists, which is 40.9 points.
However, AlphaGeometry2 has its limitations. It cannot solve problems with a variable number of points, nonlinear equations, or inequalities. In addition, the system performed worse on more challenging problems proposed for the IMO but not yet featured in the competition. Out of 29 such problems, AlphaGeometry2 managed to solve only 20.
Nevertheless, the research results spark interest in a combined approach that merges symbolic manipulation and neural networks. According to DeepMind researchers, the AlphaGeometry2 model demonstrates the promise of this approach in the quest for universal AI systems. This is supported by the fact that other neural networks, such as o1, were unable to solve any of the problems that AlphaGeometry2 conquered.
