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]