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AI Achieves Silver-Medal Standard at International Math Olympiad

AI Achieves Silver-Medal Standard at International Math Olympiad

Alicia Shapiro
July 26, 2024 • Estimated Reading Time: 5 minutes

An AI interface showcasing the results of AlphaProof and AlphaGeometry 2 from Google DeepMind solving problems from the 2024 International Mathematical Olympiad (IMO). The screen displays detailed mathematical solutions with diagrams and formal proofs, highlighting the complex algebra and geometry problems solved. The background is sleek and modern, emphasizing advanced AI technology and mathematical reasoning capabilities

AI Achieves Silver-Medal Standard at International Math Olympiad

Google DeepMind's AI systems, AlphaProof and AlphaGeometry 2, have achieved a significant milestone in AI’s mathematical reasoning capabilities by attaining a silver medal-equivalent score at this year's International Mathematical Olympiad (IMO).

Remarkable Achievement

The AI system solved 4 out of 6 problems from the 2024 IMO, scoring 28 out of 42 points. This achievement marks a significant leap from previous AI attempts, which could barely solve 1 in 100 past IMO problems. Attaining a silver medal-equivalent score places AlphaProof and AlphaGeometry 2 on par with some of the best young mathematicians in the world.

The International Mathematical Olympiad is known for its exceptionally challenging problems, often requiring thousands of hours of training from elite pre-college students to solve. In the official competition, students submit answers in two sessions of 4.5 hours each. For the AI systems, the problems were manually translated into formal mathematical language to facilitate understanding. The AI systems solved one problem within minutes and took up to three days to solve the others.

AlphaProof solved two algebra problems and one number theory problem by determining the answer and proving its correctness. This included the hardest problem in the competition, which was solved by only five contestants at this year’s IMO. AlphaGeometry 2 successfully solved the geometry problem, while the two combinatorics problems remained unsolved.

See the IMO 2024 Scores

Graph displaying the performance of the AI system relative to human competitors at the 2024 International Mathematical Olympiad (IMO). The graph shows the AI system earning 28 out of 42 total points, achieving the same level as a silver medalist in the competition. The x-axis represents human participant rank, and the y-axis represents total points, with categories for gold, silver, bronze, and other participants

Image Source: Google DeepMind

AlphaProof and AlphaGeometry 2

AlphaProof: Utilizes a fine-tuned Gemini model to translate and solve complex math problems, solving two algebra problems and one number theory problem.

AlphaGeometry 2: Demonstrated remarkable speed by solving a complex geometry problem in just 19 seconds and improving its success rate on historical IMO geometry problems to 83%.

Implications for AI and Mathematics

By solving these problems, the AI systems demonstrate a level of advanced reasoning and problem-solving skills that were previously thought to be exclusive to top human intellects. This success showcases AI's potential to tackle complex mathematical problems, which could have profound implications for various fields including scientific research, engineering, finance, and legal analysis. The ability of AI to perform at such a high level in a prestigious competition like the IMO highlights its growing capabilities and the potential for future advancements in artificial general intelligence (AGI).

Advanced Mathematical Reasoning and AI Progress

Artificial general intelligence (AGI) with advanced mathematical reasoning could unlock new frontiers in science and technology. While current AI systems still struggle with general math problems, the progress made by AlphaProof and AlphaGeometry 2 is noteworthy.

AlphaProof’s Capabilities

AlphaProof is a reinforcement-learning-based system designed for formal math reasoning. It trains itself to prove mathematical statements in the formal language Lean, using a pre-trained language model coupled with the AlphaZero reinforcement learning algorithm. This approach ensures formally verified correctness in proofs, overcoming the limitations of natural language-based approaches that can hallucinate incorrect reasoning steps.

Process infographic of AlphaProof’s reinforcement learning training loop. It shows the translation of around one million informal math problems into formal math language by a formalizer network, followed by a solver network that searches for proofs or disproofs of the problems. The system uses the AlphaZero algorithm to progressively train itself to solve more challenging problems, resulting in formal proofs

Image Source: Google DeepMind

AlphaGeometry 2’s Enhancements

AlphaGeometry 2, a significantly improved version of its predecessor, uses a neuro-symbolic hybrid system based on Gemini. It tackles challenging geometry problems with a symbolic engine two orders of magnitude faster than before, solving complex problems involving object movements, angles, ratios, and distances.

Collaborative Potential with Mathematicians

DeepMind envisions a future where mathematicians work alongside AI tools to explore hypotheses, try bold new approaches, and complete time-consuming elements of proofs more efficiently. The continued development of systems like AlphaProof and AlphaGeometry 2 highlights the potential for AI to enhance mathematical research and problem-solving.