Core Insights - The "2025 National Academic Annual Conference on Partial Differential Equations Theory and Application and Operations Research and Artificial Intelligence Academic Forum" was held in Qingyuan, Guangdong, featuring 24 invited reports from experts across numerous universities and research institutions [1][2][3] - The conference focused on the intersection of partial differential equations, operations research, and artificial intelligence, covering topics such as fluid mechanics, plasma physics, biomathematics, geometric analysis, and nonlinear analysis [1][2] Group 1: Key Presentations - Professor Li Fucai from Nanjing University presented on the latest advancements in the dynamical-MHD model, emphasizing its applications in plasma physics [1] - Professor Zhang Ting from Zhejiang University demonstrated the overall existence of strong solutions for the anisotropic Navier-Stokes equations under certain conditions [2] - Researcher Ren Xiao from Fudan University expanded on the geometric characterization of potential singularities in the Navier-Stokes equations [2] Group 2: Advances in Operations Research and AI - Professor Lv Zhaosong from the University of Minnesota introduced first-order methods for bilevel optimization, providing efficient solutions for complex decision-making problems in economics, logistics, and machine learning [2] - Professor Han Derun from Beihang University discussed improved error bounds for linear and tensor complementarity problems, surpassing classical results [2] - Professor Chen Xiaojun from the Hong Kong Polytechnic University showcased optimization methods in proving the existence of spherical t-designs, highlighting the role of optimization theory in driving advancements in artificial intelligence and data science [2] Group 3: Event Organization - The event was organized by the Applied Mathematics Research Center of the Hong Kong Institute for Advanced Study at Sun Yat-sen University, the Mathematics School of Sun Yat-sen University, and the Guangdong-Hong Kong-Macao Applied Mathematics Center, with support from various academic and research associations [3]

Core Viewpoint - The collaboration between two Tsinghua University alumni has successfully enhanced the Gemini 2.5 Pro model to achieve a gold medal level in the International Mathematical Olympiad (IMO) through a self-iterative verification process and prompt optimization [1][4][10]. Group 1: Model Performance and Methodology - Gemini 2.5 Pro achieved a 31.55% accuracy rate in solving IMO problems, significantly outperforming other models like O3 and Grok 4 [9]. - The research team utilized a structured six-step self-verification process to improve the model's performance, which includes generating initial solutions, self-improvement, and validating solutions [16][18]. - The model was able to generate complete and mathematically rigorous solutions for 5 out of 6 IMO problems, demonstrating the effectiveness of the structured iterative process [24][23]. Group 2: Importance of Prompt Design - The use of specific prompt designs significantly improved the model's ability to solve complex mathematical problems, highlighting the importance of prompt engineering in AI model performance [12][14]. - The research indicated that detailed prompts could reduce the computational search space and enhance efficiency without granting the model new capabilities [23]. Group 3: Research Team Background - The authors, Huang Yichen and Yang Lin, are both Tsinghua University alumni with extensive academic backgrounds in physics and computer science, contributing to the credibility of the research [26][28][33]. - Yang Lin is currently an associate professor at UCLA, focusing on reinforcement learning and generative AI, while Huang Yichen has a strong background in quantum physics and machine learning [30][35]. Group 4: Future Directions and Insights - The research team plans to enhance the model's capabilities through additional training data and fine-tuning, indicating a commitment to ongoing improvement [42]. - Yang Lin expressed the potential for AI to play a more significant role in mathematical research, especially in addressing long-standing unresolved problems [44].