Core Viewpoint - The article discusses the life and achievements of Zhang Yitang, a mathematician known for solving the twin prime conjecture, emphasizing his unique approach to mathematics and the importance of pursuing significant problems over conventional academic success [6][12][40]. Group 1: Zhang Yitang's Journey - Zhang Yitang faced numerous challenges in his early career, including job rejections and living in a trailer, before achieving fame at the age of 58 by solving a century-old mathematical problem [3][6]. - His return to China in June 2023 to join Sun Yat-sen University reflects a growing emphasis on basic scientific research in the country [3][36]. Group 2: Approach to Mathematics - Zhang's methodology involves focusing on a few significant problems for many years without seeking interim results, which is atypical in modern academia [6][14][22]. - He believes that the most important problems are those that have remained unsolved for decades, and he emphasizes the need for unique perspectives to achieve breakthroughs [7][23]. Group 3: Twin Prime Conjecture and Future Work - The twin prime conjecture posits that there are infinitely many pairs of prime numbers that differ by two, and Zhang proved that there are infinitely many pairs with a difference of less than 70 million [8][12]. - Following his proof, mathematicians collaborated to reduce the gap from 70 million to 246, showcasing the collaborative nature of modern mathematical research [8][12]. Group 4: Current Research Focus - Zhang is currently working on the Langlands-Siegel zero conjecture, which is considered a foundational problem in number theory, with potential implications for the Riemann hypothesis [8][30]. - He has expressed confidence in having made significant progress on this conjecture, although he finds the process of simplifying his findings challenging [9][30]. Group 5: Views on AI and Mathematics - Zhang is skeptical about AI's ability to solve complex mathematical problems like the Riemann hypothesis, emphasizing that human intuition and creativity are irreplaceable [12][33]. - He acknowledges that while AI can assist in mathematical research, it cannot fully replace human thought processes [33][35]. Group 6: Personal Philosophy and Motivation - Zhang's motivation stems from a deep curiosity and a desire to push the boundaries of knowledge rather than material success [12][40]. - He believes that the ability to focus intensely on mathematical problems is a crucial trait for success in the field [38].

Core Viewpoint - The article discusses the return of renowned mathematician Zhang Yitang to China, specifically to Sun Yat-sen University, after over 40 years abroad, highlighting the competitive nature of academic recruitment in China and Zhang's significant contributions to mathematics [2][3][4]. Group 1: Zhang Yitang's Academic Journey - Zhang Yitang, a prominent mathematician known for his work on the twin prime conjecture, has recently joined Sun Yat-sen University as the chief scientist of the newly established Hong Kong Advanced Institute [2][3]. - Prior to this, he was a tenured professor at the University of California, Santa Barbara, and had been contemplating a return to China for several years due to various international factors [3][4]. - His decision to join Sun Yat-sen University was somewhat unexpected, as he had other institutions lined up, but the university managed to secure his commitment at the last moment [4]. Group 2: Contributions to Mathematics - Zhang gained international recognition at the age of 58 for his groundbreaking paper "Bounded Gaps Between Primes," which provided significant progress on the twin prime conjecture [12][16]. - His research demonstrated the existence of infinitely many pairs of prime numbers with gaps smaller than 70 million, marking a historic advancement in number theory [11][12]. - This achievement was particularly notable as many experts had previously deemed the problem unsolvable, showcasing Zhang's unique approach and capabilities in mathematics [13][14]. Group 3: Personal Background and Philosophy - Born in 1955 in Shanghai, Zhang displayed exceptional mathematical talent from a young age, independently proving the Pythagorean theorem at the age of 10 [18][20]. - He faced significant challenges in his early career, including difficulties finding academic positions in the U.S. after completing his Ph.D., which led him to work in a restaurant temporarily [28][33]. - Zhang emphasizes the importance of passion for mathematics over material success, stating that he values the ability to continue his work in mathematics regardless of his circumstances [34].

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].