翻读黄钢教授所著的《近现代数学群星录》，有一种登顶俯瞰、荡气回肠的感觉，让人感叹原来数学书 也可以写得这么有趣、这么有温度。 牛顿首创微积分，"仿佛为世界带来了一把金钥匙"。《近现代数学群星录》从牛顿起笔，讲述近现代史 上60多位数学大家的生平事迹，展现其数学思想的成就和贡献。上册介绍的数学家，涉及分析学、代数 学、几何学等经典数学分支的发展；下册增加了维度，讲述第三次数学危机、各国数学学派，其中第四 篇以"华夏之光"为题，集中介绍了陈省身、华罗庚、苏步青、许宝騄、丘成桐等在"数学银河"里熠熠生 辉的华人数学家。 大道至简。《近现代数学群星录》揭示了数学之美在于简洁准确，在于它解开了大自然的奥秘。从天体 物理到流体力学，从声音传播到光线描述，从机器运转到星球运行，数学家们通过发展完善数学理论， 不断解释大自然规律。数学有思维之美、逻辑之美、形式之美、深刻之美。《近现代数学群星录》多处 引述数学大家关于数学之美的经典名句，黑格尔说"数学是上帝描述自然的符号"，雅可比说"数学如同 音乐或诗"。作者受此熏陶，写道："牛顿力学的三大定律，如同《道德经》，大音希声，大哲风范；麦 克斯韦的电磁理论，仿佛《楚辞》，姿态高雅 ...

Core Viewpoint - The founder and CEO of Sohu, Zhang Chaoyang, emphasizes the importance of personal understanding and derivation of formulas in the age of AI, suggesting that while AI can assist in repetitive calculations, true comprehension requires individual effort and thought [1][3]. Group 1 - Zhang Chaoyang advocates for the necessity of personal research and understanding of physics, stating that relying solely on AI for answers diminishes critical thinking [3]. - The approach of hands-on calculation in physics education is highlighted as essential for grasping the core principles and logic of the subject, rather than indulging in superficial understanding [3]. - Zhang notes that physics serves as a rich source of mathematical inspiration, citing historical examples such as Newton's invention of calculus and Einstein's use of differential geometry in formulating the theory of relativity [3]. Group 2 - The discussion includes the assertion that mastering certain mathematical concepts is beneficial for understanding physical systems, which often involve differentiation and integration [3].

Core Viewpoint - The integration of artificial intelligence (AI) and mathematics is essential for further advancements in AI, as mathematics provides foundational theoretical tools while AI presents new challenges that can drive mathematical progress [4][6]. Group 1: AI and Human Thought - AI has shown the ability to solve complex problems quickly, but it still struggles with higher-level challenges, indicating that human thought remains crucial for significant scientific breakthroughs [2][5]. - Over-reliance on AI may weaken human critical thinking skills, which are vital for innovation and problem-solving [5][6]. Group 2: Importance of Mathematics - Mathematics is fundamental to various scientific disciplines and is increasingly important in the context of AI development [4][6]. - There is a growing recognition among mathematicians of the importance of AI, leading to increased interest in AI-related research [4]. Group 3: Education and Talent Development - Education should focus on developing students' independent thinking skills alongside their ability to use AI tools, ensuring they can contribute to AI advancements rather than solely relying on AI [7]. - There is a challenge in implementing AI education due to a lack of qualified teachers, highlighting the need for a phased approach to AI education in schools [7].

Group 1 - The core logic of the ongoing technological revolution is mathematics, which serves as the underlying code for advancements in AI and technology [1] - Huawei's computing power has reached 1.67 times that of Nvidia, and the release of its new Kirin chip has garnered significant attention [1] - Oracle's market value surged by 1.73 trillion due to its AI business, highlighting the competitive landscape for AI and Asian mathematical talent [1] Group 2 - China's investment in basic research is only 6.91% of total R&D expenditure in 2024, significantly lower than the US (17%) and Germany (12%), with corporate investment below 5% [2] - This trend of "heavy application, light foundation" in research is likened to focusing on aesthetics in fitness while neglecting core strength training [2] Group 3 - The establishment of the He Tao Mathematics and Interdisciplinary Research Institute in Shenzhen, initiated by Fields Medal winner Shing-Tung Yau, aims to enhance basic and applied mathematics research [3] - The institute will expand to 50-60 researchers by the end of the year, covering various fields including high-performance computing and AI [3] Group 4 - Shenzhen's high-tech enterprise cluster and Hong Kong's foundational research create an ideal environment for the transformation of mathematical achievements into practical applications [5] - The integration of resources between Shenzhen and Hong Kong is already showing results, with collaborations established with institutions like the Quantum Science Center [5]

Group 1 - The global wave of artificial intelligence is significantly impacting the technology landscape, with Huawei claiming its technology surpasses Nvidia's by 1.67 times in computing power [1] - Oracle's AI business has seen a massive surge, with its market value increasing by 1.73 trillion [3] - The underlying theme connecting these developments is the critical role of mathematics in technology and innovation [4] Group 2 - Mathematics is integral to various applications, including AI models like ChatGPT and recommendation algorithms on platforms like Douyin and Bilibili, which rely on matrix operations [5] - The blockchain technology, particularly stablecoins, is an advanced application of number theory, highlighting the importance of mathematics in technological advancements [6] - Insufficient investment in basic research can hinder technological progress, as evidenced by China's basic research funding being only 6.91% of total R&D expenditure, compared to 17% in the U.S. and 12% in Germany [7] Group 3 - Shenzhen has recognized the importance of foundational research and has taken steps to enhance its capabilities by establishing the He Tao Mathematics and Interdisciplinary Research Institute, which aims to attract top mathematicians [9] - The institute will focus on basic mathematics, applied mathematics, and interdisciplinary research, collaborating with institutions like the Chinese University of Hong Kong [11] - Shenzhen's strategic location and resources, including over 200 high-end research projects and 447 tech companies, make it an attractive hub for scientific talent [13] Group 4 - The future of Shenzhen is poised for exponential growth in technology innovation, driven by foundational research in mathematics [14] - The collaboration between mathematics and technology in Shenzhen is expected to unlock significant advancements in AI, robotics, and new energy sectors [14]

Core Points - The article highlights the achievements of Tao Zhongkai, a 26-year-old Chinese scholar who has recently been appointed as a junior professor at the Institut des Hautes Études Scientifiques (IHES) in France, a prestigious institution in the field of mathematics [2][5][23] - Tao has an impressive academic background, having entered Xi'an Jiaotong University at the age of 15 and achieving outstanding grades, including 16 courses with a perfect score and maintaining a GPA of 96.94 during his undergraduate studies [4][7][10] - His research interests include spectral theory, microlocal analysis, general relativity, condensed matter physics, and dynamical systems, showcasing a strong interdisciplinary approach [4][7][15][18] Academic Achievements - Tao has received numerous awards in national and international mathematics competitions, including a fourth-place finish in the National College Student Mathematics Competition and a bronze award in the Qiu Chengdong Mathematics Competition [8][10] - During his time at UC Berkeley, he excelled in graduate courses, receiving A+ grades, including a rare A+ in algebraic geometry, which was the first of its kind from the professor [10][11] - He has published several papers on topics such as partial differential equations and spectral theory, contributing to significant advancements in the understanding of complex mathematical concepts [14][15][18] IHES Overview - The IHES is known for its high-caliber faculty, with 8 out of 13 permanent professors being recipients of the Fields Medal, the highest award in mathematics [3][23][26] - The institution focuses on cutting-edge research in mathematics and theoretical physics, similar to the Princeton Institute for Advanced Study [23] - Tao's appointment adds to the growing roster of talented mathematicians at IHES, which includes other notable scholars like Wang Hong and Wang Yilin [28][31][34]

Group 1 - The forum on "Mathematical Boundaries and Fundamental Reconstruction of Artificial Intelligence" is a key event at the World Artificial Intelligence Conference (WAIC) 2025, focusing on the intersection of AI and mathematics [1] - The dual demand for AI and mathematics has become increasingly urgent, with AI models requiring mathematical support for optimization and safety, while AI is also enhancing mathematical research capabilities [3][5] - The participation of two Fields Medal winners, Charles Fefferman and Shing-Tung Yau, highlights the forum's significance, showcasing a collaborative model where human mathematicians pose problems and AI systems provide solutions [3][5] Group 2 - The forum featured a "man-machine confrontation" where AI models from various institutions solved mathematical problems, demonstrating their reasoning capabilities and efficiency [5][6] - A roundtable discussion showcased the collaboration between mathematicians and AI teams, revealing the strengths and weaknesses of AI in solving complex mathematical problems [6][8] - An international student pairing ceremony was held, symbolizing the collaboration between global institutions and local universities in exploring AI-assisted mathematical research [8][10] Group 3 - Keynote speeches from prominent scholars addressed the challenges and advancements in AI architecture and reasoning evolution, emphasizing the need for mathematical foundations in AI development [10][12] - The establishment of two international mathematics laboratories in Shanghai marks a significant step in integrating top-tier mathematical research with AI applications [10][12] - The forum concluded with a vision for Shanghai to become a global hub for mathematical intelligence, leveraging its unique advantages in AI and mathematics [13][26] Group 4 - The evolution of AI's role in mathematics has transitioned from a verification tool to a collaborative partner, significantly altering research paradigms [14][20] - Historical milestones in mathematical verification and formalization have paved the way for AI's current capabilities in logic reasoning and theorem proving [14][15] - Recent advancements in deep learning and large models have enabled AI to actively participate in discovering mathematical patterns and generating conjectures [20][22] Group 5 - Shanghai's unique position as a center for AI and mathematics provides a fertile ground for interdisciplinary research, supported by advanced computational infrastructure and academic excellence [26][28] - The city is focusing on three core areas of intersection between mathematics and AI, aiming to drive innovation and application in these fields [28][29] - Initiatives to build a comprehensive ecosystem for AI and mathematics integration include talent development, research support, and industry collaboration [29][30]

AI and Education - The tech industry emphasizes the continued importance of learning mathematics, reasoning, logic, and computer programming, even with advancements in AI [1] - The industry suggests developing a deep-thinking mindset to interact with AI, define problems, and critically assess AI's solutions [1] Critical Thinking - The tech sector highlights the significance of critical thinking and reasoning from first principles, despite AI's problem-solving capabilities [1] - The industry stresses the need for discernment in evaluating the accuracy of AI's responses [1]

Core Insights - The forum titled "Mathematical Frontiers and Foundational Reconstruction of AI" will take place on July 26, 2025, at the Shanghai World Expo Exhibition and Convention Center, focusing on the intersection of AI and mathematics [3][13] - The forum aims to address three critical questions in AI: the mathematical foundations, scientific principles, and model applications, emphasizing their interdependence and collaborative innovation [3][5] Group 1 - The forum is organized by the Shanghai Putuo District People's Government and Fisoo China, with support from the Shanghai Artificial Intelligence Industry Association and the WAIC organizing committee [5] - It will feature prominent speakers from global research institutions, discussing topics such as large language model optimization and machine learning safety, thereby bridging the gap between mathematics and AI [6] - An international pairing ceremony for young mathematicians will take place, fostering collaboration between students from international summer schools and local universities [7] Group 2 - Two international mathematics laboratories will be inaugurated in China, focusing on the integration of mathematics and AI, aiming to create a new platform for global research collaboration [8] - High-profile roundtable discussions will address core challenges in AI and mathematics, exploring whether AI poses a threat to mathematicians or if breakthroughs in mathematics are essential for achieving AGI [9] - The forum will also launch a global call for solutions to "unsolved mathematical problems" in the AI domain, showcasing collaborative models between mathematicians and AI [10][11]

Core Points - The 2025 Kangaroo Math Asia Camp opened in Boao, Hainan, attracting over 1,000 young math talents, teachers, and international math experts from 15 countries and regions, including China, Canada, and India [2][3] - The event aims to inspire youth's love and creativity for mathematics, emphasizing that problem-solving is just the starting point for exploring the world [2] - The camp features a five-day program with different difficulty levels tailored to various grades, combining academic and social activities through new team competition formats [2] - Activities include individual challenges, team challenges, and a math carnival, designed to enhance students' confidence, independent thinking, teamwork, and problem-solving skills [2][3] Event Highlights - The competition questions are carefully selected by global mathematicians to allow participants to truly "experience the joy of mathematics" [3] - The "Math Carnival" includes fun games and practical experiences, showcasing the diverse applications of mathematics in everyday life [3] - Participants expressed excitement about collaborating with peers from Asia, highlighting the balance of competition and camaraderie in team events [3]