Google scientists have developed a cutting-edge AI (artificial intelligence) system capable of solving complex geometry problems at a level beyond top human competitors.
The system, called AlphaGeometry2 (AG2), outperformed gold medalists in the International Mathematical Olympiad (IMO), correctly solving 84% of geometry problems. By comparison, top human participants typically score around 81.8%, according to researchers at Google DeepMind.
AG2, an upgraded version of the original AlphaGeometry, introduced in January 2024, represents a major leap in AI-driven mathematical reasoning.
Unlike traditional AI, which relies on recognizing patterns, AG2 combines logical reasoning with advanced problem-solving techniques, allowing it to tackle geometry questions that require both logic and visual interpretation.
AI Math Race Intensifies Between Google and Microsoft
Google’s announcement comes a month after Microsoft introduced its own advanced AI math system, rStar-Math, which uses small language models (SMLs) to solve complex equations. Both tech giants are vying for dominance in AI-powered mathematics.
Scientists believe that mastering math could be a stepping stone for AI to develop broader human-like reasoning skills. However, AG2 and rStar-Math approach problem-solving differently.
.@GoogleDeepMind's AlphaGeometry2 (AG2) has outperformed an average gold medalist in the International Math Olympiad (IMO).
AG2 now solves 84% of IMO geometry problems from 2000-2024, and it's a big jump from the original AlphaGeometry’s 54%.
Here are the key improvements, that… pic.twitter.com/v2faG4sgij
— TuringPost (@TheTuringPost) February 8, 2025
AG2 specializes in high-level geometry, using a hybrid model that blends logical reasoning and symbolic computation. Microsoft’s rStar-Math, in contrast, employs smaller language models to tackle a wider variety of problems across different mathematical disciplines.
How AG2 solves difficult math problems
DeepMind’s innovation lies in its ability to bridge human language and mathematical logic. AG2 consists of two key components: a language-based model that suggests possible solutions and a symbolic engine that verifies them.
The system translates written geometry problems into step-by-step constructions that a computer can process. If an initial attempt fails, AG2 quickly revises its approach, sharing information between both components until it finds the correct answer.
Google presents Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2 pic.twitter.com/5qvOloSSI8
— AK (@_akhaliq) February 7, 2025
The latest version of AG2 improves upon its predecessor by using a larger and more diverse dataset for training, employing a faster symbolic engine capable of testing more complex solutions and incorporating a specialized algorithm to search for and verify geometric proofs.
Challenges and Limitations
Despite its advancements, AG2 has notable limitations. It struggles with 3D geometry, non-linear equations, and problems involving infinite points or moving variables.
Another major drawback is its inability to explain its reasoning in human language. Unlike a human tutor, AG2 cannot provide a step-by-step explanation of how it arrived at an answer.
Experts caution that AG2’s progress does not equate to artificial general intelligence (AGI) – a level where AI surpasses humans across multiple disciplines.
“AlphaGeometry2 represents a form of intelligence, but human intelligence goes far beyond this — we invent, rather than simply apply knowledge or create the illusion of thought,” said John Bates, CEO of AI company SER Group and a computer science expert from the University of Cambridge.
Future Potential and Next Steps
DeepMind researchers believe that AG2’s advancements in mathematical reasoning could have far-reaching implications beyond education and competition. The system’s capabilities could enhance fields such as engineering design, robotics, pharmaceutical research, and genomics.
The long-term goal is to fully automate geometry problem-solving while ensuring accuracy. Future updates will focus on expanding AG2’s understanding of more complex geometric concepts, improving its ability to break problems into smaller steps, and speeding up its processing time.
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