Core Viewpoint - The article highlights the achievements and contributions of mathematician Richard S. Sun, who recently received the "Intelligent Science or Mathematics Award" from the World Top Scientists Association, marking him as the first mathematician to receive this honor [1]. Group 1: Achievements and Recognition - Richard S. Sun has made groundbreaking contributions in geometric analysis and differential geometry, reshaping the understanding of mathematics and its connection to the physical world [2]. - He has received numerous prestigious awards, including the MacArthur Fellowship, the Rolf Schock Prize, and the Wolf Prize in Mathematics [1]. - Sun's work on the "Mountain Pass Theorem" took him six years to solve, significantly advancing the study of partial differential equations and nonlinear geometric analysis [3]. Group 2: Teaching Philosophy and Mentorship - Sun emphasizes the importance of patience in mathematical research and values clear communication with students to refine ideas [4]. - He has guided over 50 doctoral students, with many achieving significant research advancements, and he prioritizes one-on-one interactions over group meetings [5][6]. - Sun believes that a substantial part of a mathematician's work should focus on nurturing the next generation, as evidenced by his receipt of the Dean's Teaching Award at Stanford University [4]. Group 3: Personal Insights and Work Ethic - Sun maintains a rigorous work ethic, often arriving at the office early and working on weekends, demonstrating his dedication to both research and teaching [4]. - He encourages students to explore various fields and believes that breakthroughs often arise from interdisciplinary communication [8]. - Sun's personal background, including being one of thirteen siblings, contributed to his early interest in mathematics, supported by his family [8][9].

Core Viewpoint - The article highlights the life and contributions of mathematician Chen Shengshen, emphasizing his significant impact on modern differential geometry and his role in promoting mathematics in China. It also discusses the establishment of the Chen Shengshen Mathematics Institute and his legacy in the field of mathematics. Group 1: Awards and Recognition - Chen Shengshen was awarded the first Shaw Prize in Mathematics in 2004, which was established by Hong Kong philanthropist Sir Run Run Shaw, with an initial prize of 1 million USD [1] - The Chen Shengshen Medal, awarded by the International Mathematical Union, is named after him, marking a significant recognition for an Eastern mathematician [2] Group 2: Academic Contributions - Chen's pivotal paper on the Gauss-Bonnet theorem, published in 1943, is considered a cornerstone of modern differential geometry [28][30] - His work revitalized the field of differential geometry, which had been deemed "dead" prior to his contributions [30] Group 3: Educational Impact - Chen established the Chen Shengshen Mathematics Institute at Nankai University, focusing on nurturing young mathematicians and fostering mathematical research in China [32][40] - He emphasized the importance of supporting young mathematicians financially and encouraged them to pursue their research without the pressure of competition [48][41] Group 4: Personal Philosophy and Legacy - Chen believed in the beauty of mathematics and often stated that mathematics should not be driven by competition but by a genuine passion for the subject [48][49] - His final years were dedicated to continuing his research and preparing for the future of mathematics in China, even as he faced health challenges [52][53]

Core Insights - The live broadcast "Zhang Chaoyang's Physics Class" celebrated its fourth anniversary, focusing on the theme of expressing differential geometry through vector calculus [1][3] - Zhang Chaoyang, the founder and CEO of Sohu, initiated the physics class out of personal interest and curiosity, leading to significant improvements in his theoretical physics knowledge [1][5] Group 1: Educational Approach - The course utilizes vector calculus as a starting point to make the abstract concepts of differential geometry more accessible to beginners [3][5] - Zhang emphasizes the importance of hands-on calculation in understanding physics, arguing that true comprehension comes from personal engagement with the material [5][6] Group 2: Course Impact and Reach - Since its inception, "Zhang Chaoyang's Physics Class" has aired 265 episodes, accumulating over 26,322.82 minutes of online content, covering topics from Einstein's famous equation E=mc² to cutting-edge theories in quantum field theory and string theory [5][6] - The program has expanded its influence beyond live broadcasts by publishing a series of popular science books and engaging with students at prestigious universities like Tsinghua [6][7] Group 3: Personal Development and Lifelong Learning - Zhang Chaoyang shares his personal journey of learning and teaching, suggesting that individuals can learn at any stage of life and should actively engage in the learning process [7]

Core Insights - The article highlights the collaboration between renowned mathematician Terence Tao and AI, specifically ChatGPT-5 Pro, in exploring the potential of AI in mathematical research [2][3] - Tao's experience emphasizes the importance of evaluating AI tools from multiple perspectives to understand their value [3][14] Research Process - The problem addressed involves determining whether a smooth immersed sphere in R^3 with principal curvatures bounded by 1 encloses a volume at least equal to that of a unit sphere [7] - AI proved useful in small-scale tasks such as specific calculations, while its assistance was limited in medium-scale tasks like strategy selection [7][12] - At a macro level, AI demonstrated value in understanding the overall structure and key difficulties of the problem [7][14] AI's Contributions - AI accurately computed necessary quantities and provided a complete proof for the star-shaped case, utilizing both familiar and novel mathematical tools [9][10] - Tao was surprised by AI's ability to derive a proof in just one line, which led him to further validate AI's steps [10] - AI also suggested a numerical approach to tackle the problem, although it was recognized as a brute-force method lacking theoretical insight [11][12] Challenges and Limitations - Despite AI's strong performance in specific calculations, Tao recognized the need for a differential geometry expert to make substantial progress [12][14] - AI's tendency to reinforce Tao's incorrect assumptions at the medium scale highlighted its limitations in strategic decision-making [13][14] - The core difficulty of the problem was identified as understanding extreme non-round geometries, which AI did not adequately address [13][14] Conclusion - Tao concluded that while AI can be beneficial in exploring mathematical problems, caution and contextual awareness are essential to avoid being misled by seemingly plausible intuitions [17]

Core Insights - The collaboration between Terence Tao and GPT-5 Pro successfully addressed a three-year-old unsolved problem in differential geometry, showcasing the potential of AI in academic research [1][4][22]. Group 1: Problem Solving Process - The original problem involved determining if a smooth topological sphere in three-dimensional space, with a principal curvature absolute value not exceeding 1, encloses a volume at least equal to that of a unit sphere [8]. - Tao's initial approach was to restrict the problem to star-shaped regions and utilize integral inequalities, but he sought AI assistance for complex calculations [9]. - GPT-5 Pro completed the calculations in 11 minutes and 18 seconds, providing a complete proof for the star-shaped case using various inequalities and identities, some of which Tao was familiar with [10]. Group 2: AI's Role and Limitations - Although AI made minor errors in estimating a perturbation nonlinear term, it also identified a special case that reverted to the star-shaped result [17]. - The AI's performance was effective for small-scale problems, contributing useful ideas from literature that Tao was previously unaware of [23]. - However, for medium-scale strategies, AI reinforced Tao's incorrect intuition without questioning it, indicating a limitation in critical analysis [26][27]. Group 3: Insights on AI in Research - Tao reflected on the multi-scale value of AI tools, emphasizing the need for human oversight to maintain awareness of task structures across different scales [36]. - He proposed that the optimal level of automation lies between 0% and 100%, allowing for sufficient human involvement to address local issues while reducing repetitive tasks [36]. - The experience reinforced Tao's earlier assertion that the effectiveness of a tool must be evaluated across multiple scales [33]. Group 4: Historical Context of AI Collaboration - Tao's exploration of AI's potential in mathematics began three years ago with the release of ChatGPT, where initial interactions yielded disappointing results [41]. - A turning point occurred with GPT-4, which demonstrated significant efficiency in handling statistical data and familiar mathematical problems, leading to increased expectations for AI integration in research tools [43]. - By July, following OpenAI's achievements, Tao began tackling more complex mathematical problems with AI, finding it particularly useful for numerical searches, which saved considerable time [52]. Group 5: Future Implications - Tao concluded that AI is reshaping the scientific paradigm, serving as a "co-pilot" for mathematicians rather than replacing human creativity and intuition [54]. - The collaboration with AI is expected to lead to more experimental approaches in mathematics, moving beyond purely theoretical work [55].

Group 1 - The "Intelligent Science or Mathematics Award" was awarded to Richard S. Palais from Stanford University for his groundbreaking work in geometric analysis and differential geometry, which has practical applications in fields like computer graphics and cryptography [1] - The "Life Sciences or Medicine Award" was awarded to Scott Emmer from Cornell University and Wes Sundquist from the University of Utah for their significant discoveries related to receptor membrane protein transport and degradation mechanisms, which are crucial for understanding viral budding and infection processes [1] - The 2025 World Top Scientists Forum will open on October 24 in the Lingang New Area, featuring the award ceremony for the Top Science Association Awards [3] Group 2 - Wes Sundquist expressed excitement about his upcoming first visit to China, highlighting China's leadership in the scientific field and the potential for collaboration with local scientists [2]