AI Achieves Silver-Medal Level at 2024 International Mathematical Olympiad

In an impressive demonstration of artificial intelligence capabilities, Google DeepMind’s AI programs reached a silver-medal level at the 2024 International Mathematical Olympiad (IMO). This achievement marks a significant milestone in the application of AI to complex mathematical problem-solving.

In July, over 600 students from nearly 110 countries gathered in Bath, England, for the IMO. The participants had to solve six problems from various mathematical disciplines in two sessions of four and a half hours each. Chinese student Haojia Shi achieved a perfect score, claiming first place in the individual rankings. The U.S. team topped the country rankings.

However, the standout performance came from Google DeepMind’s AI programs, AlphaProof and AlphaGeometry 2, which solved four out of six problems, scoring 28 out of a possible 42 points. This placed the AI at a level equivalent to a silver medalist, outperforming many human competitors.

Mathematician and Fields Medalist Timothy Gowers, a former gold medalist at the IMO, highlighted the AI’s achievement on X (formerly Twitter), noting that only around 60 students scored better than the AI.

AlphaProof and AlphaGeometry 2 achieved these results through reinforcement learning, a technique where the AI competes against itself and improves iteratively. Unlike board games, solving mathematical problems requires the AI to verify its reasoning steps. AlphaProof employs proof assistants—algorithms that validate logical arguments step-by-step.

DeepMind’s team trained a large language model, Gemini, to translate over a million problems solved by humans into the Lean programming language. This allowed the proof assistant to use them for training. When presented with a problem, AlphaProof generates solution candidates and proves or disproves them by searching possible proof steps in Lean.