A few months ago, the International Mathematical Olympiad announced the AIMO Prize, a $10 million award for an AI model that can achieve a gold medal in an International Math Olympiad (IMO). IMOs are elite high school competitions where the top six students from each participating country must answer six different questions over two days, with a four-hour time limit each day. Some of the most renowned mathematicians of the past few decades have been medalists in IMO competitions. Geometry, an important and one of the hardest aspects of IMO tests, combines visual and mathematical challenges. We might intuitively think that this would be the hardest type of problem for AI models to solve. The most interesting aspect of AlphaGeometry is its architecture, which combines a Large Language Model (LLM) with a symbolic model. Neuro-symbolic architectures have long attempted to bridge the gap between the two most established machine learning schools: neural networks and rule-based models....
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