转自：光明日报 刘建亚山东大学供图 如果你不知道什么是数论，那你一定听说过哥德巴赫猜想。 有人说，它是数学"皇冠上的明珠"——200多年来，众多数学家为之倾注心血。在中国，潘承洞证明命 题"1+5"，后与王元各自证明了"1+4"，陈景润则证明了"1+2"…… 而在另一位数学家眼中，哥德巴赫猜想只是数论海洋中的一朵浪花，其所涉及的素数都是线性的。而数论 中，还有更广泛的非线性问题。 这位数学家叫刘建亚，中国科学院院士、山东大学讲席教授。 刘建亚在从事博士后研究期间攻关的一个难题，是美国数学家盖拉格1975年提出的猜想，即每个大偶数都可 表示成4个素数的平方与固定个数的2的方幂之和。多年来，很多人研究过这个猜测，但未有突破性进展。 那段时间，他一头钻进了这个问题。可大半年时间过去了，研究进展并不大。但由于长时间高压力地思考计 算，他常常吃不好、睡不着，身体几乎要垮掉。 有一天，在图书馆翻阅书刊时，一篇法语论文吸引了刘建亚的目光，那篇论文的题目如电流般，激活了他头 脑中长久淤积的疑惑——解决方法终于找到了！ 一个偶然的机会，17岁的刘建亚读到了那篇著名的报告文学《哥德巴赫猜想》。从此，数学世界的大门在他 面前打开了 ...

编辑｜杨文 你的童年我的童年好像不一样。 我的 17 岁，是坐在教室里苦哈哈地刷数学卷子；而这个名叫 Enrique Barschkis 的高中生，利用课间休息时间，成功解决了困扰数学家多年的埃尔德什第 347 号问 题。 这一成就不仅在社交平台 X 上引发热议，更得到了谷歌首席科学家 Jeff Dean 的盛赞。 什么是埃尔德什第 347 号问题？ 埃尔德什第 347 号问题，最初由埃尔德什和格雷厄姆在 1980 年提出，核心问题是：是否存在一个整数序列，其中相邻项的比值趋近于 2，并且对于该序列的任何 余有限子序列，其有限子集和构成的集合在自然数中的密度都是 1？ 这个问题触及了数论中完全序列理论的核心，其难度在于需要在严格的增长率限制下，保证几乎所有足够大的正整数都能表示为序列中某些项的和。 去年 10 月，著名数学家、菲尔兹奖得主陶哲轩在 Erdős 问题网站的讨论区里，用 ChatGPT 搜索相关文献，找到了一篇 Burr 和 Erdős 的旧论文。 然而数学家沃特很快发现，那篇论文中的结果使用的是相邻两项的比值条件，与本问题要求的相邻项比值条件略有不同。 陶哲轩提出了一个巧妙的构造思路：将序列分成 ...

Core Viewpoint - The article discusses the phenomenon of "interest disease" among university students, where they lose interest in learning after entering higher education, and emphasizes the importance of nurturing curiosity and imagination in students to combat this issue [3][4][5]. Group 1: The Issue of "Interest Disease" - The phenomenon of "interest disease" is prevalent among students who excelled in high school but lose their enthusiasm for learning in university [3]. - The excessive amount of information and repetitive content taught in primary and secondary education contributes to cognitive overload, leading to a lack of curiosity and imagination [4]. - Encouraging curiosity and imagination through storytelling and interdisciplinary connections can help reduce the likelihood of students developing "interest disease" [3][5]. Group 2: Educational Approach and Solutions - Teachers and parents should nurture children's curiosity and enhance their imagination, as curiosity is innate but tends to diminish with age [5]. - A balanced approach to education that combines academic rigor with the promotion of scientific culture and public understanding of science is essential [14]. Group 3: Mathematical Insights and Innovations - The integration of additive and multiplicative number theory in the work "Additive-Multiplicative Number Theory" represents a significant innovation in the field, addressing longstanding problems in number theory [10]. - The research includes conjectures related to the representation of integers as sums of powers and the generalization of Fermat's Last Theorem, which have garnered attention from notable mathematicians [10][11]. - The work emphasizes the connection between seemingly unrelated concepts, showcasing the importance of creativity and observation in mathematical research [9][10].

Group 1 - The "Intelligent Science or Mathematics Award" was awarded to Richard S. Palais from Stanford University for his groundbreaking work in geometric analysis and differential geometry, which has practical applications in fields like computer graphics and cryptography [1] - The "Life Sciences or Medicine Award" was awarded to Scott Emmer from Cornell University and Wes Sundquist from the University of Utah for their significant discoveries related to receptor membrane protein transport and degradation mechanisms, which are crucial for understanding viral budding and infection processes [1] - The 2025 World Top Scientists Forum will open on October 24 in the Lingang New Area, featuring the award ceremony for the Top Science Association Awards [3] Group 2 - Wes Sundquist expressed excitement about his upcoming first visit to China, highlighting China's leadership in the scientific field and the potential for collaboration with local scientists [2]

Core Viewpoint - The article highlights the recent appointment of Chinese mathematician Wang Hong, known for solving the Kakeya conjecture, as a permanent professor at the Institut des Hautes Études Scientifiques (IHES) in France, marking a significant achievement in her career and the mathematics community [1][2][10]. Group 1: Appointment Details - Wang Hong will officially join IHES on September 1, 2025, and will also hold a position as a mathematics professor at New York University's Courant Institute of Mathematical Sciences [6]. - IHES currently has only seven permanent professors, with five being prominent mathematicians, including two Fields Medal winners [3][4]. Group 2: Academic Background - Wang Hong was born in 1991 in Guilin, Guangxi, and demonstrated exceptional academic ability from a young age, entering Peking University at 16 [15]. - She obtained her bachelor's degree in mathematics in 2011, followed by an engineering degree from École Polytechnique and a master's degree from Paris XI University in 2014, and completed her PhD at MIT in 2019 [16]. Group 3: Research Contributions - Wang Hong, along with UBC mathematics associate professor Joshua Zahl, solved the Kakeya conjecture, a long-standing problem in mathematics that has implications across various fields such as harmonic analysis and number theory [10][12]. - The Kakeya conjecture in three dimensions asserts that a set containing unit-length line segments in every direction must have Minkowski and Hausdorff dimensions equal to three [11]. Group 4: Community Reception - The announcement of Wang Hong's appointment was met with enthusiasm in the mathematics community, with notable figures expressing their support and anticipation for her contributions [7][9]. - Many believe her recent achievement could position her as a strong candidate for the Fields Medal [14].

Core Viewpoint - The article discusses the recent proof of the Kakeya conjecture in three-dimensional space by Chinese mathematician Wang Hong and Columbia University professor Joshua Zahl, which has generated significant interest and could position Wang as a strong candidate for the Fields Medal in 2026 [1][5][6]. Group 1: Kakeya Conjecture Overview - The Kakeya conjecture, proposed by Japanese mathematician Sōichi Kakeya in 1917, involves determining the minimum area that a needle can sweep when rotated in a confined space [8][9]. - The conjecture states that a Kakeya set in three-dimensional space must have both Minkowski and Hausdorff dimensions equal to three, indicating that these sets geometrically fill the space despite appearing sparse [10][11][12]. Group 2: Proof Details - Wang Hong and Joshua Zahl published a 127-page paper proving the three-dimensional Kakeya conjecture, employing complex strategies including non-concentration conditions and multi-scale analysis [3][20]. - Their proof involves defining a situation K(d) and demonstrating a relationship that allows for the induction of dimension parameters towards three [21][23]. - The authors utilized multi-scale analysis to study the organization of pipe-like structures, leading to insights about the density and overlap of these structures [24][25][28]. Group 3: Background on Wang Hong - Wang Hong, born in 1991, is a notable mathematician who could become the first Chinese woman to win the Fields Medal if awarded [7][34]. - She has an impressive academic background, having studied at prestigious institutions and focusing on Fourier transform-related problems [36][38].