Core Viewpoint - The founder and CEO of Sohu, Zhang Chaoyang, emphasizes the importance of personal understanding and derivation of formulas in the age of AI, suggesting that while AI can assist in repetitive calculations, true comprehension requires individual effort and thought [1][3]. Group 1 - Zhang Chaoyang advocates for the necessity of personal research and understanding of physics, stating that relying solely on AI for answers diminishes critical thinking [3]. - The approach of hands-on calculation in physics education is highlighted as essential for grasping the core principles and logic of the subject, rather than indulging in superficial understanding [3]. - Zhang notes that physics serves as a rich source of mathematical inspiration, citing historical examples such as Newton's invention of calculus and Einstein's use of differential geometry in formulating the theory of relativity [3]. Group 2 - The discussion includes the assertion that mastering certain mathematical concepts is beneficial for understanding physical systems, which often involve differentiation and integration [3].

Core Insights - The discussion on "Is Calculus Really Difficult?" has gained significant attention on Zhihu, attracting top scholars and engaging a wide audience in a dialogue that combines academic depth with public interest [1][2] Group 1: Academic Contributions - Ma Xiao, an assistant professor at the University of Michigan, recently made a breakthrough in the study of Hilbert's sixth problem, which had been dormant for 125 years [1] - Wang Mengdi, a professor at Princeton University, suggests that calculus may serve as a "natural language of the universe," simplifying complex operations into intuitive actions [2] Group 2: Community Engagement - The event coincides with China's first official Science Popularization Month in September, marking the launch of Zhihu's 2025 Science Season [2] - Zhihu aims to create a platform for public scientific dialogue, enhancing the accessibility and engagement of scientific discussions within the community [2]

Core Viewpoint - The article highlights the extraordinary achievements of Hannah Cairo, a 17-year-old prodigy who solved the Mizohata-Takeuchi conjecture, a significant mathematical problem that had remained unsolved for 40 years, showcasing her exceptional talent and dedication to mathematics [4][6][69]. Group 1: Background and Early Life - Hannah Cairo learned calculus at the age of 11 and had university-level math skills by 14 [1][2]. - She grew up in Nassau, Bahamas, and was homeschooled alongside her siblings [9]. - Initially, she engaged with math through online courses from Khan Academy, completing all available courses quickly [11][12]. Group 2: Academic Journey - Due to her advanced skills, her parents arranged for remote tutoring with two math professors [13][14]. - Hannah felt constrained by homeschooling and sought broader academic experiences [16][17]. - The COVID-19 pandemic allowed her to connect with the Chicago Math Circle, which further fueled her passion for mathematics [23][25]. Group 3: Breakthrough in Mathematics - In 2023, after spending a summer at the Berkeley Math Circle, she began contemplating her next steps and applied to several universities [33][34]. - Despite being rejected by most due to her incomplete high school education, she was accepted by the University of California, Davis [34][72]. - Hannah's engagement with advanced coursework led her to a pivotal moment when she tackled the Mizohata-Takeuchi conjecture as part of her assignments [48][49]. Group 4: Solving the Conjecture - The Mizohata-Takeuchi conjecture connects harmonic analysis, partial differential equations, and geometric analysis, and its resolution required innovative thinking [6][52]. - Hannah constructed a complex function that defied the conjecture's restrictions, leading to her breakthrough [65][68]. - After confirming her findings with her professor, she decided to apply directly for a PhD program, bypassing undergraduate studies [69][72]. Group 5: Future Prospects - Hannah has been accepted into PhD programs at the University of Maryland and Johns Hopkins University, marking the beginning of her formal academic journey [72][73]. - Upon graduation, she will earn her first official degree, a PhD, at a remarkably young age [74].

Group 1 - Zhang Chaoyang, founder and CEO of Sohu, analyzed challenging physics questions from the 2025 Gaokao during a live stream, demonstrating complex problem-solving techniques [2] - He emphasized the need for rigorous treatment of real-world physics problems, despite the simplifications made in exam models [2] - Zhang highlighted the increasing difficulty of Gaokao physics questions, which often incorporate advanced topics like dark matter and general relativity, suggesting that such high difficulty may lead to student frustration [4] Group 2 - Zhang recommended that high school students should have a foundational understanding of calculus and other basic tools before entering university [4] - He advised students to consider personal interests and future job prospects when choosing their majors, emphasizing the importance of communication with parents [5]