In a groundbreaking achievement, Google’s AI systems, AlphaProof and AlphaGeometry 2, have achieved silver medal-level performance at the prestigious International Mathematical Olympiad (IMO). This remarkable feat underscores the rapid progress in artificial intelligence, particularly its ability to tackle complex mathematical problems. AlphaProof, a system developed by Google, specializes in formal mathematical reasoning. It leverages a combination of language models and the AlphaZero reinforcement learning algorithm, a powerful tool previously known for mastering games like chess and Go. Through this combination, AlphaProof trains itself to solve intricate mathematical problems using Lean, a formal language designed for mathematical expressions. Demonstrating its capabilities during the IMO, AlphaProof successfully tackled two challenging algebra problems and one number theory problem, including the competition’s most difficult problem. This feat was only matched by five human contestants, highlighting the advanced capabilities of this AI system.
AlphaGeometry 2, the second AI system involved, represents a notable improvement over Google’s earlier geometry-solving AI. Utilizing a neuro-symbolic hybrid method, it integrates an advanced language model with a robust symbolic engine, enhancing its ability to efficiently solve intricate geometry problems. During the IMO, AlphaGeometry 2 impressively solved Problem 4 in just 19 seconds, a problem requiring complex geometric constructions and a deep understanding of angles, ratios, and distances. Trained on an extensive dataset encompassing 25 years of historical IMO geometry problems, AlphaGeometry 2 boasts an impressive 83 percent success rate in solving these challenges. The AI systems, combined, achieved a score of 28 out of 42 points at the IMO, falling just one point short of a gold medal. Renowned mathematicians, including Fields Medal recipient Prof Sir Timothy Gowers and Dr. Joseph Myers, Chair of the IMO 2024 Problem Selection Committee, reviewed the AI’s solutions. They were impressed by the AI’s ability to produce impressive and non-obvious solutions, recognizing this as a significant milestone in AI’s mathematical reasoning capabilities.
This remarkable achievement underscores Google’s significant strides in advancing AI technology. These AI systems have the potential to revolutionize various fields by assisting mathematicians in exploring new hypotheses, solving long-standing problems, and automating time-consuming elements of mathematical proofs. Looking ahead, Google plans to share further technical information about AlphaProof and continue exploring various AI methodologies to enhance mathematical reasoning. Their ultimate goal is to create AI systems that collaborate with human mathematicians, ultimately pushing the boundaries of science and technology.
