借一双皮鞋去领百万大奖 一切都是秘密进行的。20多年前，一位乐善好施的香港富豪决定设立一项国际性的科学奖。他希望获奖人 不分国籍和种族，只看其对人类社会的贡献。每笔奖金初定为100万美元。 这项被视为"东方诺贝尔奖"的三个领域中，较为特殊的是数学奖。经过几近一年的反复讨论，一个人选胜 出。 最后，在2004年9月7日，设奖人邵逸夫在颁奖典礼上见到了这位获奖人——他93岁，来自天津的南开大 学。他原本身材高大，但此刻坐在轮椅里，脚上套着一双借来的有些挤脚的皮鞋，被护工推到了领奖台 上。西装和衬衣是新的。他赴香港前，发现壁橱里的那些旧西装被虫子蛀了小洞。他还宣布，把百万美元 奖金分成几份，捐给国内外几所大学和研究机构。 颁奖礼上，数学家吴文俊说，获奖人是"我们这个时代最重要的几何学家"，"他自己一个人，就影响了20世 纪下半世纪数学的发展。" 这是邵逸夫数学奖的第一次颁发，也是"现代微分几何之父"陈省身获得的又一项科学殊荣。 如今，在中国和美国各有一个著名数学研究所的大楼以陈省身的姓名命名。国际数学联盟设立了终身成就 奖陈省身奖章，四年颁发一次。在一个多世纪的历史上，国际数学联盟从来没有像这样，以一个东方人的 名 ...

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]