Group 1 - The core achievement of Google's DeepMind is the advanced version of the Gemini AI model, which scored 35 points in the International Mathematical Olympiad (IMO), reaching gold medal level [1] - The Gemini model successfully solved 5 out of 6 problems from the 2025 IMO, with the official score confirming its performance [1] - The IMO has been a platform for testing AI models' capabilities in solving advanced mathematical problems since its inception in 1959 [1] Group 2 - DeepMind's AI models, AlphaProof and AlphaGeometry 2, solved 4 out of 6 problems in the 2024 IMO, achieving a score of 28 points, which corresponds to silver medal level [2] - The advanced Gemini model shows significant progress compared to the previous year, as it can directly provide mathematical proofs based on natural language descriptions [2] - The success of the Gemini model is attributed to its "deep reasoning" mode, which employs enhanced reasoning techniques to explore multiple potential solutions simultaneously [2]