Core Points - The event "Science and China" and Guangdong Science Popularization in Southern Xinjiang series was held in Kashgar and the Third Division of the Xinjiang Production and Construction Corps, featuring prominent scientists to inspire local students [2][6][70] - Over 10,000 students participated in 13 science lectures, which aimed to promote scientific knowledge and support regional development [3][4][6] - The activities align with national policies on science popularization and support for Xinjiang, emphasizing high-quality educational initiatives [5][6][71] Group 1 - The series of lectures included topics such as astrophysics, mathematics, and biodiversity, delivered by renowned academicians and researchers [9][20][37] - The lectures sparked curiosity among students, encouraging them to explore scientific fields and understand the relevance of mathematics in technology and daily life [22][58][60] - The event was supported by various institutions, including the Chinese Academy of Sciences and local educational authorities, highlighting a collaborative effort in science education [72][80][81] Group 2 - The initiative aims to enhance the scientific literacy of youth in Southern Xinjiang, providing them with access to quality educational resources [86][88] - The program is part of a broader strategy to implement technology assistance and talent development in the region, focusing on agriculture, health, and digital technology [83][85][91] - Future plans include expanding cooperation with various sectors to enrich science education and foster innovation among local students [92][94]

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 a significant breakthrough in mathematics, where four mathematicians extended the modularity theorem from one-dimensional elliptic curves to the more complex two-dimensional abelian surfaces, marking a revolutionary step towards a unified theory in mathematics [5][14][46]. Group 1: Historical Context - The proof of Fermat's Last Theorem by Andrew Wiles in 1994 was a monumental event in mathematics, resolving a problem that had persisted for over 350 years [9][10]. - Wiles' proof revealed a deep connection between elliptic curves and modular forms, providing a powerful method for mathematicians to explore properties of elliptic curves through their corresponding modular forms [11][12][13]. Group 2: Recent Breakthrough - In February 2023, a team of four mathematicians proved that a large class of abelian surfaces has corresponding modular forms, extending the modularity theorem significantly [16][45]. - The team members include Frank Calegari, George Boxer, Toby Gee, and Vincent Pilloni, who collaborated to tackle a problem previously considered nearly impossible [14][16][30]. Group 3: Implications and Future Directions - This breakthrough is expected to provide new tools for solving unresolved problems in number theory, similar to how the proof of the modularity of elliptic curves opened new research avenues [20][46]. - The mathematicians aim to prove that all types of abelian surfaces satisfy the modularity condition, which could lead to further discoveries in the field [20][46].