Group 1 - The core viewpoint of the article is that AI is reshaping human scientific paradigms, and while it will become an important partner in exploring ultimate questions in mathematics and physics, it cannot replace human intuition and creativity [2][3]. - Terence Tao discusses the importance of collaboration in creating superior intelligent systems, suggesting that a collective human community is more likely to achieve breakthroughs in mathematics than individual mathematicians [3]. - The article highlights Tao's insights on various world-class mathematical problems, including the Kakeya conjecture and the Navier-Stokes regularity problem, emphasizing the interconnectedness of these problems with other mathematical fields [4][16]. Group 2 - Tao emphasizes that in undergraduate education, students encounter difficult problems like the Riemann hypothesis and twin prime conjecture, but the real challenge lies in solving the remaining 10% of the problem after existing techniques have addressed 90% [5]. - The Kakeya problem, which Tao has focused on, involves determining the minimum area required for a needle to change direction in a plane, illustrating the complexity and depth of mathematical inquiry [6][7]. - The article discusses the implications of the Kakeya conjecture and its connections to partial differential equations, number theory, geometry, topology, and combinatorics, showcasing the rich interrelations within mathematics [10][14]. Group 3 - The Navier-Stokes regularity problem is presented as a significant unsolved issue in fluid dynamics, questioning whether a smooth initial velocity field can lead to singularities in fluid flow [16][18]. - Tao explains the challenges in proving general conclusions for the Navier-Stokes equations, using the example of Maxwell's demon to illustrate statistical impossibilities in fluid dynamics [19][20]. - The article notes that understanding the Kakeya conjecture can aid in comprehending wave concentration issues, which may indirectly enhance the understanding of the Navier-Stokes problem [18][26]. Group 4 - Tao discusses the concept of self-similar explosions in fluid dynamics, where energy can be concentrated in smaller scales, leading to potential singularities in the Navier-Stokes equations [22][24]. - The article highlights the mathematical exploration of how energy can be manipulated within fluid systems, suggesting that controlling energy transfer could lead to significant breakthroughs in understanding fluid behavior [26][30]. - Tao's work aims to bridge the gap between theoretical mathematics and practical applications, indicating a future where AI could play a role in experimental mathematics [55][56].

Core Insights - The article emphasizes that mathematics is a practical tool for survival rather than an eternal truth, evolving to meet the demands of different eras [4][11][14] - It highlights the historical context of mathematical advancements, showing how they were developed to solve pressing real-world problems, such as navigation and engineering [5][7][15] - The current landscape of AI and technology necessitates a rethinking of mathematical foundations to adapt to new challenges and opportunities [22][30][31] Historical Context - Mathematics has historically contributed approximately 25-35% to economic growth, serving as a critical tool for various industries [7] - Key mathematicians like Newton and Euler created mathematical tools to address immediate needs in navigation and engineering, rather than for abstract purposes [10][15] - The evolution of mathematics reflects humanity's need to adapt and innovate in response to crises and technological advancements [14][20] Modern Applications - The article argues for the importance of modern mathematical concepts such as category theory and functional programming in shaping AI and technology [22][30] - It suggests that understanding advanced mathematical tools is essential for professionals in technology to remain relevant and innovative [27][30] - The shift towards AI hardware design requires a blend of traditional and modern mathematical insights to create efficient and scalable systems [28][30] Future Directions - The article posits that the future of AI and technology lies in the ability to construct models rather than merely running them, emphasizing the need for a strong mathematical foundation [28][31] - It encourages professionals to deepen their understanding of mathematical abstractions to maintain a competitive edge in an increasingly automated landscape [31] - The integration of advanced mathematical tools into hardware design is seen as crucial for overcoming traditional limitations in AI development [30]

以下文章来源于量子学派 ，作者十七进制 量子学派 . 专注于科普（数理哲）的教育平台，"典赞·2019科普中国"十大科普自媒体 本文来自微信公众号： 量子学派 ，作者：十七进制，题图来自：视觉中国 "大家好，我叫韦东奕，这是我的账号。" 衣服朴素，形象呆萌，非常认真，略显笨拙。在这个物欲横流时代，他精准契合了公众对数学家的想 象。 一、数学明星≠数学家 社会大众眼中的数学明星与数学家存在明显鸿沟。 这一点一定要说清楚，否则是对公众的又一次误导。 1、竞赛能力≠学术能力 竞赛的本质：国际数学奥林匹克竞赛 （IMO） 等赛事强调在有限时间内解决高度结构化的难题，考 验的是逻辑推理、心理素质和解题技巧。 学术研究的特质：学术研究的核心是探索未知领域，提出原创性理论，并通过同行评审验证其价值。 韦东奕的两次IMO满分金牌令人惊叹，但这类成就更多体现的是"解题机器"的能力，而非学术创新的 潜力。 数学史上的里程碑式人物 （如欧拉、高斯、黎曼） 的贡献不仅在于解决具体问题，更在于开辟新的 数学分支或提出颠覆性理论。 2、公众误解的根源 在童年的记忆里，这就是陈景润2.0。一条4秒的自我介绍视频。三天之内，抖音涨粉2225 ...

Core Viewpoint - The article discusses the emergence of a social media account belonging to Wei Dongyi, a renowned mathematician from Peking University, aimed at sharing mathematical content and engaging with the public [1]. Group 1: Wei Dongyi's Social Media Presence - Wei Dongyi, known as "Wei Shen," confirmed the authenticity of his social media account, which was registered with the help of his family [1]. - The account plans to publish content related to mathematics to enhance communication between Wei Dongyi and the public [1]. Group 2: Public Reactions and Expectations - Many students and parents expressed their hopes in the comments section, wishing for high scores in mathematics, such as "130+" in the college entrance examination [3][4]. - The comments reflect a cultural phenomenon where individuals seek blessings from Wei Dongyi for academic success, showcasing his influence and the admiration he commands [4]. Group 3: Background of Wei Dongyi - Wei Dongyi has a distinguished academic background, having won gold medals at the International Mathematical Olympiad in 2008 and 2009, and later graduated from Peking University [5]. - He has held various academic positions, including assistant professor at Peking University, and received the Alibaba Damo Academy Qicheng Award in 2021 [5].

鱼羊 一水 发自 凹非寺 量子位 | 公众号 QbitAI 如果有这么一个人，写下这样的复杂公式，并声称是受女神梦中启发所得，大家伙儿通常会送他两个字： 民科 。 但当这个人一生中数千次写下类似的数学公式和命题，并在此后的100年间，不断地被证实正确，那么就只有一个可能—— 他是拉马努金。 之所以再度火爆，是因为直到今天，数学界还不断有最新发现，在验证他当年留下的"谜题"。 拉马努金， 一位全数学界公认的神人 ，被认为是数学史上最伟大的天才之一： 没有接受过正统数学教育 ，在印度挂科到本科学位都没拿到，却凭借自己惊人的数学直觉征服数学大师G.H.哈代，使得剑桥大学三一学院的 大门破例向他打开。 32岁就英年早逝，职业搞数学的时间只有短短6年，但他的数学笔记至今仍是传奇—— 留下了近4000个公式，很多都在后来被证明正确 。 他的恩师哈代甚至开玩笑说，自己对数学最大的贡献就是发现了拉马努金： 和拉马努金的交往是我一生中唯一的浪漫事件。 △ 中间为拉马努金，最右为G.H.哈代 直到今天，后辈数学家们仍在追赶着拉马努金的步伐。 "梦中女神的启示" 拉马努金传奇故事的构成要素之一，是他独特的做数学的方式。 简单来说就 ...