In a stunning display of mathematical prowess, Google’s AI systems, AlphaProof and AlphaGeometry 2, have achieved silver medal-level performance at the prestigious International Mathematical Olympiad (via India Today).
AlphaProof, a groundbreaking AI system introduced by Google, excels in formal mathematical reasoning, reported the publication. Utilizing a blend of language models and the AlphaZero reinforcement learning algorithm—renowned for mastering chess and Go—AlphaProof trains itself to tackle complex math problems using Lean, a formal language for mathematics. Demonstrating its capabilities, AlphaProof successfully solved two challenging algebra problems and one number theory problem during the IMO, including the competition’s most difficult problem, a feat achieved by only five human contestants.
Reportedly, the second AI system, AlphaGeometry 2, is a notable advancement over Google’s earlier geometry-solving AI. Using a neuro-symbolic hybrid method, it integrates an advanced language model with a robust symbolic engine.
This enhancement enabled AlphaGeometry 2 to solve intricate geometry problems more efficiently. During the IMO, AlphaGeometry 2 impressively solved Problem 4 in just 19 seconds, which involved complex geometric constructions and a deep understanding of angles, ratios, and distances. Trained on a vast dataset encompassing 25 years of historical IMO geometry problems, AlphaGeometry 2 boasts an impressive 83 per cent success rate in solving these challenges.
Google’s AI systems achieved a score of 28 out of 42 points at the IMO, falling just one point short of a gold medal. Renowned mathematicians, such as 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 concluded that the AI could produce impressive and non-obvious solutions, highlighting a significant milestone in AI’s ability to perform complex mathematical reasoning.
This achievement underscores Google’s progress in advancing AI technology, with the potential to revolutionize various fields by assisting mathematicians in exploring new hypotheses, solving longstanding problems, and automating time-consuming elements of mathematical proofs.
In the future, Google intends to share additional technical information about AlphaProof and to further investigate various AI methodologies to improve mathematical reasoning, adds the publication. Their goal is to create AI systems that collaborate with human mathematicians, thereby advancing the frontiers of science and technology.