Group 1 - The book "The Poincaré Conjecture" explores the century-long quest to solve a significant mathematical problem, highlighting the life of Grigori Perelman, who solved it but chose to withdraw from public recognition [2] - "Illustrated Algebra" presents the evolution of numerical systems from ancient civilizations and illustrates how mathematicians performed calculations before the invention of algebraic symbols [4] - "Reshaping Mathematics: The Journey of Infinity" discusses the concept of infinity through the works of five renowned mathematicians, emphasizing their contributions to the understanding of infinite quantities [6] Group 2 - "The Story of Chemistry" traces the historical development of chemistry from ancient philosophical inquiries to modern scientific achievements, focusing on key figures like Mendeleev and the periodic table [8] - "China's Ancient Technological Heritage" details 38 representative technological achievements from ancient China, covering their historical significance and value across various fields [10] - "How the Earth Became Round" examines humanity's evolving understanding of the Earth's shape through historical texts and scientific discoveries, marking the transition from myth to empirical knowledge [13] Group 3 - "The History of Hurricanes in North America" provides a comprehensive account of the impact of hurricanes on the land and society over the past 500 years, utilizing extensive data from meteorological sources [15] - "Nature and Humanity: The Shaping of Science and Modernity" analyzes the interplay between science and various cultural factors, illustrating how scientific advancements have influenced modern civilization [17] - "The Mystery of Meat: A Deep History of Animals, Humans, and Food" challenges traditional views on the role of meat in human evolution, exploring the complex relationship between humans and animals throughout history [19]

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].