A team of researchers at Google’s DeepMind project, reports that its AlphaGeometry2 AI performed at a gold-medal level when tasked with solving problems that were given to high school students participating in the International Mathematical Olympiad (IMO) over the past 25 years. In their paper posted on the arXiv preprint server, the team gives an overview of AlphaGeometry2 and its scores when solving IMO problems.
Prior research has suggested that AI that can solve geometry problems could lead to more sophisticated apps because they require both a high level of reasoning ability and an ability to choose from possible steps in working toward a solution to a problem.
To that end, the team at DeepMind has been working on developing increasingly sophisticated geometry-solving apps. Its first iteration was released last January and was called AlphaGeometry; its second iteration is called AlphaGeometry2.
The team at DeepMind has been combining it with another system they developed called Alpha Proof, which conducts mathematical proofs. The team found it was able to solve 4 of 6 problems listed in the IMO this past summer. For this new study, the research team expanded testing of the system’s ability by giving it multiple problems used by the IMO over the past 25 years.
The research team built AlphaGeometry2 by combining multiple core elements, one of which is Google’s Gemini language model. Other elements use mathematic rules to come up with solutions to the original problem or parts of it.
The team notes that to solve many IMO problems, certain constructs must be added before proceeding, which means their system must be able to create them. Their system then tries to predict which of those that have been added to a diagram should be used to make the necessary deductions required to solve a problem. AlphaGeometry2 suggests steps that might be used to solve a given problem and then checks the steps for logic before using them.
To test their system, the researchers chose 45 problems from the IMO, some of which required translating into a more useable form, resulting in 50 total problems. They report that AlphaGeometry2 was able to solve 42 of them correctly, slightly higher than the average human gold medalist in the competition.
More information:
Yuri Chervonyi et al, Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2, arXiv (2025). DOI: 10.48550/arxiv.2502.03544
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DeepMind AI achieves gold-medal level performance on challenging Olympiad math questions (2025, February 10)
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