Core Insights - The "2025 National Academic Annual Conference on Partial Differential Equations Theory and Application and Operations Research and Artificial Intelligence Academic Forum" was held in Qingyuan, Guangdong, featuring 24 invited reports from experts across numerous universities and research institutions [1][2][3] - The conference focused on the intersection of partial differential equations, operations research, and artificial intelligence, covering topics such as fluid mechanics, plasma physics, biomathematics, geometric analysis, and nonlinear analysis [1][2] Group 1: Key Presentations - Professor Li Fucai from Nanjing University presented on the latest advancements in the dynamical-MHD model, emphasizing its applications in plasma physics [1] - Professor Zhang Ting from Zhejiang University demonstrated the overall existence of strong solutions for the anisotropic Navier-Stokes equations under certain conditions [2] - Researcher Ren Xiao from Fudan University expanded on the geometric characterization of potential singularities in the Navier-Stokes equations [2] Group 2: Advances in Operations Research and AI - Professor Lv Zhaosong from the University of Minnesota introduced first-order methods for bilevel optimization, providing efficient solutions for complex decision-making problems in economics, logistics, and machine learning [2] - Professor Han Derun from Beihang University discussed improved error bounds for linear and tensor complementarity problems, surpassing classical results [2] - Professor Chen Xiaojun from the Hong Kong Polytechnic University showcased optimization methods in proving the existence of spherical t-designs, highlighting the role of optimization theory in driving advancements in artificial intelligence and data science [2] Group 3: Event Organization - The event was organized by the Applied Mathematics Research Center of the Hong Kong Institute for Advanced Study at Sun Yat-sen University, the Mathematics School of Sun Yat-sen University, and the Guangdong-Hong Kong-Macao Applied Mathematics Center, with support from various academic and research associations [3]

为更好开展偏微分方程理论与应用领域研究进展的学术盘点，有效增强国内外偏微分方程及相关领域的 学术交流与合作，12月6日至7日，为期2天的"2025年全国偏微分方程理论与应用研究学术年会暨运筹学 与人工智能学术论坛"在广东清远举办。 本次活动由中山大学香港高等研究院应用数学研究中心、中山大学数学学院、粤港澳应用数学中心主 办，由粤港澳大湾区跨学科科学学会、广东省运筹学会、大湾区数智中低空经济研究会协办。来自全国 多所高校与科研院所的专家学者在专题报告与前沿研讨会上深入交流最新研究成果。 会议现场。 设多场高质量报告与分论坛 开幕式上，中山大学香港高等研究院应用数学研究中心主任姚正安教授表示，偏微分方程正迎来一个充 满机遇的新时代。 他认为，在人工智能时代，AI给出的解，最终需要偏微分方程的严格理论来检验与诠释。而偏微分方 程理论中那些关于稳定性、收敛性的深刻结果，也必将为AI模型的构建提供更可靠的数学基础。"这正 是一场深刻的、双向的奔赴。"他强调，本学术年会旨在通过高水平交流催生理论突破、培养青年人 才，并为国家重大科技需求提供数学支撑。 据介绍，本次学术年会上有多场高质量专题学习报告，并设多个分论坛让专家学 ...

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].

Core Viewpoint - The article highlights the extraordinary achievements of Hannah Cairo, a 17-year-old who solved the Mizohata-Takeuchi conjecture, a significant mathematical problem that had remained unsolved for 40 years, showcasing her exceptional talent and potential in 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 Khan Academy's online courses, completing all available content quickly [11][12]. Group 2: Academic Journey - Due to her advanced learning needs, her parents arranged for remote tutoring with two math professors [13][14]. - Despite having guidance, most of her learning was self-directed, leading her to read graduate-level textbooks [14][15]. - The COVID-19 pandemic allowed her to connect with the Chicago math community, further igniting 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]. - She was encouraged to participate in a concurrent enrollment program at Berkeley, allowing her to take graduate-level courses [35][37]. - During her studies, she encountered the simplified version of the Mizohata-Takeuchi conjecture as part of her homework, which led her to explore the problem deeply [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 demonstrated the conjecture's conditions, ultimately leading to her proof [63][65]. - 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 was accepted into the PhD programs at the University of Maryland and Johns Hopkins University, marking a significant milestone in her academic career [72][73]. - She is set to begin her doctoral studies this fall, which will be her first formal degree [74].

Core Viewpoint - Peter Lax, the first applied mathematician to receive the Abel Prize, passed away at the age of 99, marking the end of an era in mathematics and science [1][49]. Group 1: Contributions to Mathematics - Lax was a pioneer in applying computer technology to mathematical analysis and made significant contributions that are still widely used in scientific research and engineering practices [4][5]. - His notable works include the classic textbook "Functional Analysis" and other widely appreciated texts such as "Calculus and Its Applications" and "Linear Algebra and Its Applications" [2][6][7]. - Lax's research spanned various fields, including partial differential equations, fluid mechanics, numerical computation, scattering theory, and integrable systems, leading to profound theoretical results and practical algorithms [33]. Group 2: Awards and Recognition - Lax received numerous prestigious awards, including the National Medal of Science in 1986 and the Wolf Prize in 1987, culminating in being the first applied mathematician to win the Abel Prize in 2005 for his foundational work in partial differential equations [35][36]. - The Abel Prize committee described him as "the most versatile mathematician of his generation," highlighting his broad impact on the field [37]. Group 3: Personal Background and Legacy - Born on May 1, 1926, in Budapest, Lax showed exceptional mathematical talent from a young age, influenced by his family and mentors [15][16][17]. - His experiences during World War II, including his work on the Manhattan Project, shaped his understanding of the importance of computation in science [23][24][25]. - Lax's legacy includes not only his research and publications but also his commitment to education and mentorship, having trained over 55 doctoral students [46].