On Thursday, Google DeepMind revealed that their AI systems, AlphaProof and AlphaGeometry 2, have made significant progress in solving complex mathematical problems. These systems were able to solve four out of six problems from the International Mathematical Olympiad (IMO), achieving a score equivalent to a silver medal. This breakthrough marks the first time an AI has performed at this level in the prestigious math competition.
AlphaProof uses reinforcement learning to prove mathematical statements in the formal language called Lean. The system trains itself by generating and verifying millions of proofs, gradually tackling more challenging problems. On the other hand, AlphaGeometry 2 is an upgraded version of Google’s previous geometry-solving AI model, now powered by a Gemini-based language model trained on a vast amount of data.
The AI systems were evaluated by distinguished mathematicians Sir Timothy Gowers and Dr. Joseph Myers using official IMO rules. Google reported that their combined system achieved 28 out of 42 possible points, coming close to the gold medal threshold of 29 points. The AI models excelled in solving algebra and number theory problems, with AlphaGeometry 2 successfully tackling the geometry question. However, they struggled with combinatorics problems and required varying amounts of time to find solutions.
Before the competition, Google translated the IMO problems into a formal mathematical language for the AI models to process, a step that human contestants do not have to take during the official competition. While Google’s claims are impressive, Sir Timothy Gowers offered a more nuanced perspective. He acknowledged the achievement as a significant advancement but highlighted that the AI models required much longer processing times than human competitors and that humans had to perform the initial translation of problems into formal language.
Gowers raised important questions about the future role of mathematicians in light of AI advancements. While he believes that AI systems like AlphaProof and AlphaGeometry 2 could serve as valuable research tools, he emphasized that they are not yet capable of fully replacing human mathematicians. The systems may be able to provide quick answers to a wide range of questions, but solving complex and open mathematical problems still requires human creativity and insight.
Overall, Google’s AI models represent a remarkable step forward in the field of mathematical research. While they demonstrate impressive problem-solving capabilities, they also highlight the complementary nature of AI and human intelligence in tackling complex challenges. As technology continues to advance, the collaboration between AI systems and mathematicians may lead to exciting developments in the field of mathematics.