一水 发自 凹非寺 量子位 | 公众号 QbitAI 原来数学家张益唐加盟中大并非"一蹴而就"，这里头竟然还有被截胡的事儿！ 消息还是由张益唐本人亲口透露的。 事情是这样的。 今年6月，在阔别祖国学术圈四十余年之后，知名数学家张益唐最终"花落"中山大学，出任中大去年刚揭牌成立的 香港高等研究院首席科学家 ，举家定居粤港澳大湾区。 在这之前，他是美国加州大学圣塔芭芭拉分校数学系终身教授， 曾因实质性推进解决数论难题"孪生素数猜想"而享誉世界 。 据其本人在凤凰卫视《问答神州》的最新采访中透露，最近几年他一直有想着回国，尤其是近一两年，因为一些众所周知的国际原因，身边很 多在美华人学者教授都已经回来了 （没有回来的也正在考虑） 。 而在接触的所有选择中，中山大学实则是"半路杀出"，本人原话是这样的： 有其他一些学校，基本上都已经定了，中大好像是从中间又插进来的。 不过说完这话，他也提到了自己和中大的缘分—— 十年前，他和原北大副校长（现中大校长）高松共同参加了北大毕业典礼，当时对方的一些话 （在主持时引用张的话勉励学生） 给他留下了 深刻印象 （张益唐本硕皆学于北大） 。 △ 图源：中大官微（左高松，右张益唐） ...

Group 1 - The dialogue between Zhang Chaoyang and David Gross focused on fundamental aspects of the physical world and advancements in physical theories, including discussions on the four fundamental forces of nature and the concept of "asymptotic freedom" [2][3] - David Gross recounted the historical context of discovering quarks and the challenges faced in understanding their nature, leading to the development of Quantum Chromodynamics (QCD) [3][4] - The conversation explored the nature of spacetime, suggesting it may not be a fundamental property of the universe but rather an emergent phenomenon, challenging traditional views [5][6] Group 2 - The discussion on the origin of mass highlighted that the mass of protons is primarily derived from the kinetic energy and strong interactions of quarks, rather than the mass of the quarks themselves [7] - The role of artificial intelligence (AI) was clarified, with Gross emphasizing that AI is merely a tool and not a scientific field, distinguishing it from the work of physicists like John Hopfield [8][9] - The evolution of computational power was noted as a significant factor in advancing theoretical physics, with improvements in algorithms and computing capabilities enabling more efficient research [9][10]

Core Viewpoint - The current AI models are significantly overestimated, serving primarily as tools rather than independent scientific entities [1][2][5] Group 1: AI and Scientific Discovery - David Gross argues that solving major physical or mathematical problems relies on human intelligence and creativity, with AI acting as a powerful auxiliary tool [2][5] - There is skepticism regarding AI's ability to prove complex conjectures within a five-year timeframe, as highlighted by a bet between Zhang Yaqin and mathematician Shing-Tung Yau [1][2] - Gross expresses dissatisfaction with the current capabilities of AI, noting that early versions of ChatGPT struggled with basic tasks like counting [2] Group 2: Nobel Prize and AI - The 2024 Nobel Prize in Physics awarded to John Hopfield is not attributed to AI achievements, as his work extends physical methods into neuroscience [4][5] - Gross emphasizes that Hopfield's research is a continuation of physics rather than a contribution to AI, reinforcing the distinction between the two fields [5] Group 3: Computational Power and Theoretical Physics - The exponential growth in computational power has significantly advanced theoretical physics, allowing for complex calculations that were previously labor-intensive [5] - Gross reflects on the historical limitations of computational methods in quantum chromodynamics (QCD) and how modern advancements have transformed research capabilities [5] Group 4: Encouragement for Young Researchers - Gross encourages young researchers to enjoy the process of exploration and maintain curiosity, emphasizing that the joy of research lies in the journey of discovery [6]

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 Viewpoint - The article discusses the current state and future potential of AI in assisting mathematical research, highlighting both advancements and limitations in AI's capabilities to solve complex mathematical problems. Group 1: AI Advancements in Mathematics - The U.S. Defense Advanced Research Projects Agency (DARPA) launched the "Exponential Mathematics" program to develop AI systems that can significantly enhance mathematical research efficiency [1] - New generation large language models (LLMs) like OpenAI's o3 and Anthropic's Claude 4 Thinking have shown improvements, performing at levels close to excellent high school students in competitions [2] - Google's AlphaProof system combines LLMs with chess AI, achieving results comparable to silver medalists in the International Mathematical Olympiad [2] - The AlphaEvolve model from Google has found solutions to long-standing mathematical and computational problems that outperform existing human methods [2] Group 2: Limitations of AI in Mathematics - Despite impressive performances, experts believe that current AI models lack the capability to assist in genuine mathematical research, as competition problems are more like intellectual games with certain patterns [2] - A test by Epoch AI revealed that LLMs struggled with high-difficulty problems designed to avoid previously seen training data, indicating significant limitations in their problem-solving abilities [3] - AI faces challenges with "super long reasoning chains," where complex problems may require millions of steps to solve, making it difficult for AI to find the correct solutions [5] Group 3: Innovative Approaches and Future Directions - Researchers are developing methods to package multiple steps into "super steps" to tackle complex problems, which has led to breakthroughs in classic unsolved problems [5][6] - The exploration of new mathematical ideas is crucial, and AI tools like AlphaEvolve can generate and refine solutions, allowing for human intervention to provide inspiration [7] - AI is seen as a potential tool for discovering new mathematical objects, but it currently lacks true creativity, with significant innovations still attributed to human mathematicians [8]

Group 1 - AI is increasingly capable of writing code, with reports indicating that up to 90% of code can be generated by AI tools [1][2] - Zhang Yaqin predicts that AI will prove a mathematical conjecture or formula within five years, while his counterpart Qiu Chengtong disagrees [1] - AI excels in structured and rule-based tasks, such as coding and language processing, but struggles with more abstract concepts like quantum mechanics [2][3] Group 2 - The efficiency of the human brain, with its 86 billion neurons and low energy consumption, remains significantly superior to current AI models, which require vast computational resources [3] - The concept of "singularity" in AI development is debated, with Zhang suggesting it may take 15 to 20 years for AI to achieve general intelligence that surpasses human performance in most tasks [3] - Different types of intelligence are expected to develop at varying rates, with information intelligence potentially reaching human levels in four to five years, while physical and biological intelligence may take ten to twenty years [4]