2023–2025 年（第十六至第十八届）获奖趋势与代表性论文

从 2023–2025 年的总决赛名单可以看出，数学学科课题在保持纯数学（数论、组合、代数几何、动力系统等方向）传统优势的同时，应用与交叉课题的比重明显上升：2024 年金奖《Optimizing Dart Throwing Strategies for the Elderly Based on Markov Decision Process》将马尔可夫决策过程应用于老年人投飞镖策略，2025 年金奖《Quasiconformal Normalization of Random Meromorphic Function》（Trinity School）继续延续纯数学方向的高水平；银、铜奖中既有 Temperley–Lieb 代数、Hurwitz zeta 函数等经典代数方向，也有 SDP 松弛、Markov 决策、神经网络等机器学习背景的应用问题。可以说，传统纯数学课题仍是冲击金奖的最稳路径，但用现代数学工具解决一个具体应用问题的论文，在银/铜奖区间显著增多。

代表性获奖论文深度解读

2023 金奖 ·《Desargues’ Involution at Action》

学生 / 学校： YU Hanzhang，Raffles Institution（新加坡莱佛士书院）
指导老师： YU Sixia

研究的是什么问题？ 这篇论文研究的是古典射影几何中的一个核心对象——"对合"（involution）。直观地说，"对合"是一种"做两次就回到原点"的变换：比如把数轴上每个点 $x$ 映成 $-x$，再做一次就回到 $x$。在射影几何里，最著名的对合定理是 19 世纪法国数学家 Desargues（笛沙格）发现的"对合定理"：当一条直线穿过一个完整四边形（quadrangle）的六条边时，它与这些边的交点会两两成对、形成一个对合关系。论文的题目"at Action"（"在动作中"）暗示作者并不是简单复述定理，而是把这一对合机制运用到一系列实际的几何配置中，去推出新的恒等式或简化经典构型的证明。

用了什么方法？ 从论文题目和射影几何研究的常见路径看，作者最可能采用的工具是：（1）射影几何中的交比（cross-ratio）和透视投影；（2）将 Desargues 对合定理作为"扳手"，去拆解圆锥曲线、束（pencil）与四边形的配置；（3）用动点方法（即让某个点沿直线滑动，研究对合关系如何同步变化）寻找几何不变量。这种从一个经典定理出发、把它打磨成"瑞士军刀"应用到多个场景的研究路线，正是纯数学竞赛论文最受欢迎的范式之一。

为什么评委青睐？ 评委看重的不只是新结果，而是研究方法的优雅与作者对古典几何的真正掌握。Desargues 对合是一个 19 世纪的老定理，但要把它用得活、用得新，需要作者对欧氏几何、射影几何、圆锥曲线理论都有体系化的理解——这对一名中学生来说极不容易。论文摘要里使用的术语严格遵循射影几何的标准写法，整体结构接近发表级的论文，这本身就是丘奖评委高度认可的"学术成熟度"。

对参赛者的启发： 对于想冲击数学金奖的同学，这篇论文给出了一条非常清晰的范式——选择一个经典几何或代数问题作为"母定理"，深入掌握它的所有变体，然后用它去重新审视一组现代问题或推广原有的构型。不必追求"证明哥德巴赫"那种宏大目标，把一个老定理用得"既深又广"同样可以拿金奖。

2024 铜奖 ·《Mathematical Modeling of Long-Wave for Interfacial Waves in Two-Layer Fluids Based on the Dirichlet-Neumann Operator》

学生 / 学校： 李润博（RunBo Li），北京师范大学附属实验中学
指导老师： 崔旺（Wang Cui）、郭振宇（ZhenYu Guo）

研究的是什么问题？ 想象一个透明的玻璃容器里，下面装着盐水（密度大），上面装着淡水（密度小），两层水的交界面是一个隐形的"界面"。当你晃动容器时，这个界面会上下起伏，形成"内波"（interfacial wave）。海洋里就充满了这种波——海水温度跃层之间的内波可以高达上百米，对潜艇航行、海洋通信都有重大影响。这篇论文研究的是当波长远大于水深时，两层流体之间的内波满足怎样的简化方程（即"长波近似"），并用一个叫做 Dirichlet–Neumann 算子的工具去构造方程。

用了什么方法？ 从题目看，作者的方法路径很清晰：（1）写下完整的两层流体 Euler 方程；（2）引入 Dirichlet–Neumann 算子——这是一个把"界面上知道势函数（Dirichlet 条件）"翻译成"界面上知道法向速度（Neumann 条件）"的算子，是分析水波问题的现代标准工具，由 Craig–Sulem 等人推广；（3）在长波尺度下展开 Dirichlet–Neumann 算子，得到诸如 Boussinesq 类、KdV 类或 Benjamin–Ono 类的简化方程。这一思路与著名数学家 Walter Craig 在 1990 年代以来推动的水波方程严格化研究方向完全一致。

为什么评委青睐？ 一名高二学生能掌握偏微分方程、谱分析和算子展开这些研究生水平的工具本身就极为罕见。评委同时也看到论文不是"凑应用"，而是站在 Craig–Sulem 方法的现代前沿，对真实的海洋内波问题给出了数学化的建模框架。即使只拿到铜奖，论文的技术含量已经接近一篇本科生荣誉毕业论文的水准。

对参赛者的启发： 应用数学并非"二等公民"。只要你愿意花时间真正把一个工程或物理问题（比如海洋内波、气候流体、生物医学）翻译成严格的数学语言，再用现代分析工具（算子、谱、变分原理）去攻克它，你的论文就完全有竞争力。关键在于不要停留在"我用 MATLAB 跑了一下"的层次，而要进入到"我推导了这个方程为什么是这样"的层次。

2025 银奖 ·《Standard modules of the Temperley-Lieb algebra at zero》

学生 / 学校： Eddy Li，The Nueva School（美国加州）
指导老师： Kenta Suzuki

研究的是什么问题？ Temperley–Lieb 代数（简称 TL 代数）是 20 世纪 70 年代起源于统计物理（Potts 模型）的一类重要代数，后来在低维拓扑、纽结理论（Jones 多项式）、量子群表示论中都扮演了核心角色。它的一组生成元 $e_1, e_2, \ldots, e_{n-1}$ 满足一个具体的关系$e_i e_{i\pm 1} e_i = e_i$ 和 $e_i^2 = \delta e_i$，其中参数 $\delta$ 决定了代数的性质。论文研究的就是当这个参数 $\delta = 0$ 时的"标准模"（standard modules）——这是一种特殊但极其重要的极限情形，对应统计物理中的临界点和拓扑场论中的特殊参数。

用了什么方法？ 从题目和这一研究领域的常见路径看，作者很可能采用：（1）显式构造 TL 代数在 $\delta=0$ 时的"cell modules" 或 "standard modules"；（2）分析这些模的结构——是否不可约、是否有合成列、Jordan–Hölder 因子是什么；（3）与已知 $\delta \neq 0$ 时的结果对比，揭示 $\delta=0$ 这个"退化点"的特殊代数现象。这条路径属于现代表示论的核心研究范式。

为什么评委青睐？ TL 代数在 $\delta=0$ 时已知会出现一系列"恶劣行为"（非半单、模可约但非完全约化），这恰恰是数学家最关心的"奇点"。一名高中生敢碰这种"代数奇点"，并能写出一份严格的、专门讨论标准模分类的论文，是非常少见的。论文得到来自 MIT 的研究生（Kenta Suzuki，组合表示论方向）指导，也保证了技术细节的严格性。

对参赛者的启发： 如果你对纯代数感兴趣，不必从"证明菲尔兹奖级别的猜想"开始。许多重要代数（TL 代数、Hecke 代数、Brauer 代数）在"特殊参数"下都还有未完全分类的模，这些恰恰是大学到研究生过渡阶段的好题目。找到这类"具体但深刻"的问题，往往能写出一篇结构完整、技术扎实的获奖论文。

（以上论文获奖信息均来自 yau-awards.com 官方公示页面，详见 ¹）

奖项数量统计：2023 年共评出 金 1、银 1、铜 3、优胜 5；2024 年共评出 金 1、银 1、铜 3、优胜 5；2025 年共评出 金 1、银 1、铜 4、优胜 5、入围 5。

数学课程基础

丘成桐数学竞赛包含了众多的分支，包括梳理逻辑、数论、代数、几何、代数几何、数学分析、拓扑学等等。学生需要一定的知识基础，包括:

统计学：数据的基本分析方法，频数、直方图、相关系数、最小二乘回归、抽样调查、正态分布、假设检验。

微积分：初等函数（幂函数、指数函数、对数函数、三角函数）、极限、导数。

通常情况下，参赛课题涉及的内容多为高等数学的知识。学生在展开研究之前，可能掌握的对课题研究内容所需要的基础基本为零。因此，对于课题研究的展开，在没有指导的情况下学生会无从下手。值得注意的是，上述课程内容通常与研究课题没有直接联系，但是无论是纯数学、应用数学还是统计学课题，掌握上述内容对于对于快速展开课题研究，理解课题相关的理论知识都有很大帮助。

编程语言

对于丘成桐数学学科的竞赛， 计算是其中的一个重要部分， 主要用于方法的实验验证， 尤 其对于应用数学类型的课题。因此， 建议学生具备一定的编程计算能力。学生需要掌握C/C++、Python、MATLAB、JAVA 中的任意一门编程语言，具体使用哪种编程语言可以根据学生的兴 趣和基础自主选择。在充分掌握编程语言的基本语法和变量类型、数据结构的基础上，学生需要能够掌握基本的库函数调用方法。最后，需要掌握算法（计算方法）编程实现的方法。值得注意的是，丘成桐竞赛的重点在于作品的创新性。这就意味着，学生需要通过至少一种算法的编程掌握算法实现的基本流程和方法，然后在完成课题的理论方法的推导后，通过编程对课题中使用的算法进行实现。编程需要一个经验积累的过程，对于中学生而言，至少需要掌握算法编程仿真的基本方法，然后在课题研究中慢慢探索和实践。

这也就需要学生学会代码的调试。程序的调试是测试代码和查找错误的过程。课题研究中涉及的算法实现是一个复杂的工程，在编程过程中需要不断的调试，逐步完成最终整个项目。

论文写作及规范表达方法

写作在竞赛作品的呈现中有着至关重要的作用。对于丘成桐数学竞赛，我们不仅仅需要对课题研究内容给出正确的方法和结果，如何将自己的研究成果进行呈现也是至关重要的。纵观近年来丘成桐数学竞赛的作品，优秀的论文通常以标准的期刊论文标准进行撰写。对于课题研究工作的撰写，需要有良好的组织结构，而中学生通常没有接触过这类文章的撰写。因此，需要大量阅读相关的文献资料，学习如何撰写一篇合格的学术论文，尤其是数学学科的文章，需要严密的逻辑和正确的表达，对于文章的撰写有着更加严苛的要求。

数学表达是撰写参赛论文的关键。数学表达与文学性文字得撰写不同，一方面需要使得自己撰写得内容更加专业规范。另一方面，数学表达中涉及许多变量、符号和公式等。对于变量和公式等内容的定义，需要遵循一定得规范，从而使得文章看起来更加规范专业。一般来说，在数学表达中，我们可以定义任意一个符号，来表示某一变量，但是我们同时需要在研究背景下，遵循一定的习惯，比如，速度我们通常用符号v表示，σ表示标准差，Σ表示协方差矩阵。此外，我们还需要了解不同类型变量的表达方式，包括数值变量、向量、矩阵、集合等，比如x，x，X是同一英文字母，但是字体和格式不同，则分别表示了数值变量，向量和矩阵。最后，数学问题中涉及了大量的运算，求和、连乘、最小值、最小值、求根等等对应了不同的运算符号。

此外，还需要学习使用专业的工具来编辑数学公式。这里，我们推荐使用Latex 进行论文的编译。

2021数学奖金奖

1. 学生背景简述

Max Liu 为2021 年丘成桐中学科学奖数学金奖得主。该学生来自 Shanghai High School International Division（上海中学国际部），该学校为国内顶尖的公立中学，2003 年成为上海唯一一所联合国教科文组织联系学校。由于论文中没有选题的相关信息，对于项目来源我们不得而知。值得注意的是指导老师是清华大学的左怀青，副教授、博导，其主要研究方向中就包括了代数几何奇点理论。同时，左怀青与丘成桐是有合作的，该学生的研究就是在左怀青和丘成桐共同发表的一篇论文的基础上展开的。因此，可以猜测该题目可能来自于指导老师的研究工作。从背景来看，2021 年数学金奖的学生有着坚实的学术背景，完全能够在指导老师的指导下完成相关工作，并且选题内容为 Yau（丘成桐： Shing-Tung Yau）的几何猜想，可以说十分符合竞赛的要求。当然，能够使得该学生在竞赛中取得佳绩，主要还是靠出色的作品和个人演讲能力。下面，我们结合学生的论文，对学生能够在众多优秀作品中取得如此优异成绩的原因进行分析。

2. 论文概述

这里，我们对论文的研究内容进行分析。首先，我们来看论文的题目和摘要。下面，我们给出了论文的原文题目和摘要以及对应的翻译：

Title: On sharp upper estimate of lattice points: Yau geometric conjecture
Abstract: The simple problem of counting the number of lattice points in n-dimensional simplexes, in fact has a much greater significance in singularity theory and number theory. The number of lattice points is equal to the geometric genus of an isolated singularity of a weighted homogeneous polynomial. This paper estimates the number of lattice points in a seven-dimensional simplex, and proves the Yau Geometric Conjecture in seven dimensions, which gives an upper bound to the number. We do so by dividing the simplex to several layers of cross section sixth-dimensional simplexes and sums up the upper bound of lattice points in each layer. This proof provides potential insight to extend the upper bound estimate to the general n-dimensional case.

题目：格点的上界估计：Yau几何猜想
摘要：在n维单形中计算格点数的简单问题，实际上在奇点理论和数论中有更大的意义。格点的个数等于加权齐次多项式的孤立奇点的几何亏格。本文估计了七维单纯形中格点的个数，证明了七维Yau几何猜想，给出了格点个数的上界。我们通过将单纯形划分为几层横截面的第六维单纯形来实现这一点，并总结每层晶格点的上界。本文的证明内容为格点上界估计的n维一般形式的推广提供了潜在的见解。

从论文的题目和摘要来看，研究内容十分明了，也就是对七维情形下的 Yau 几何猜想进行证明，并指出了研究工作的意义。在纯数学课题的研究中，有很多类似的猜想证明的研究工作。这类猜想有很多，并且很多是未被证明或者未被完全证明的。对于数学课题的研究，我们的目的是完成具有一定学术价值的研究工作。作为一个中学生想要对一个猜想完全证明是十分困难的。因为这类猜想本身十分复杂，且未被证明的。因此，许多人的研究工作是对猜想的一部分内容进行证明。比如我国著名数学家陈景润当初被誉为“哥德巴赫猜想”第一人，其发表的《1+2》对于哥德巴赫猜想的证明具有里程碑意义。

3. 获奖点分析

1. 选题: Max Liu 的选题是丘成桐和左怀青等人研究工作的拓展工作。从题目和论文内容 可以看出，该论文选题为纯数学的理论推导证明。在数学相关的研究当中，方法的创新性更容易获得评委老师的认可。数学定理和猜想的证明需要严密的逻辑和推理能力，该论文在七维情形下对 Yau几何猜想进行了证明。该工作是对n-维一般情形下的 Yau 几 何猜想的重要补充，具有很高的理论价值。论文中将整体的证明过程分解成7种不同的情形分情况讨论，并给出了严密的证明推导过程，这在纯数学的研究中是十分重要的。在数学相关的研究中，实现方法和理论上的创新是十分困难的。因此，丘成桐数学奖的评审中，对于数学方法理论的推导和创新也更容易收到评委老师的青睐。从以往所有的晋级半决赛和决赛的作品当中，我们都可以看到大部分晋级的优秀作品中，都有较强的理论基础和方法上的创新。从整体来看，论文整体篇幅达到了54页，除去封面、目录等信息，仅论文本身的研究中推导过程部分就占据了43 页之多，并给出了相关的定理和证明。这对于高中学生来书是十分难得的，因为理论方法的研究需要学生花费大量的时间和精力去理解相关的基础知识和推导、证明方法。因此，我们希望参赛学 在研究数学相关课题时，能够充分学习课题相关的基础方法，并结合相关知识，针对课题研究内容中的难点，对方法进行创新。

2. 逻辑严密：该金奖论文主体部分的撰写完全遵循了 SCI 科研论文投稿的格式，结构完整，逻辑清晰，条理分明。

   数学课题相关的论文的重点在于文章逻辑的严密性和条理清晰。对于这一点，该论文作者无论是从数学的表达还是从内容的安排上，都表现出了极高的专业水平。当然，相信这与指导老师的专业指导是分不开的。

   首先，纯理论性的数学研究不同于应用研究或计算机、物理、生物等其他学科课题，需要通过图表等内容使得论文看起来更专业、更丰富。纯理论的数学课题更加简洁，其内容全部是对猜想或者定理的证明和推导过程。因此，整体论文仅仅包含了5个部 分:Introduction, Som Lemmas, Proof of Main Theorem, Conclusion, and Reference。 其中 Introduction对研究内容Yau几何猜想的内容和相关基础知识进行了介绍，包括正 积分点、非负积分点的数学定义和基本性质、GLY 猜想、修正的 GLY 猜想等。Some Lemmas部分内容则介绍了后文中关于Yau猜想证明需要的一些引理。第3 部分 Proof of Main Theorem是整篇论文的主要部分，该部分内容则针对本文中对七维情形下的 Yau 几何猜想的证明和推导过程进行了详细的介绍。第 4 部分 Conclusion 则对全文进行了总结。第5部分Reference则给出了文中引用的参考文献。

   针对论文中的研究工作，在论文的第3部分，采用了总分结构对研究工作的总体思路进行介绍。如下图2所示：

   

   第 3 部分的开端部分，作者首先对后续证明的思路进行了介绍，七维情形下的证明过程分为 7 种情形进行讨论，然后针对 7 种不同的情形，分别通过数学表达进行了界定。后续的 3.1-3.7 部分，则分别对应 7 种不同的情形进行了推导和证明。

3. 论文撰写: 这篇金奖论文在近年来所有的获奖论文中，是少见的长篇幅的论文，主要是 由于推导过程相对复杂，包含了7种不同的情形，推导过程严密仔细。该学生的指导老师本身就是该领域的专家，并且发表有相关的学术论文。在论文内容的撰写方面，作者也 表现出极高的专业水平。主要包括以下几个方面：

   (1) 符号的定义。上文中，我们介绍过，在数学课题的研究中，对于变量和符号的定义，存在一些规范。作者在对符号的定义上，完全遵循了相关内容的规范，包括对正积分点、非负积分点、自然数集合、素数等符号的定义。

   (2) 数学表达。上文中，我们指出，在数学相关的论文中，表达要规范、客观、简明并且富有逻辑。对此，我们从Yau几何猜想的介绍中就可以看出。在学术论文的撰写中，文字表达要客观、科学，也就是我们常说的学术表达，而一般学生在写这类论文时，不可避免地偏向于大白话。

   

   (3) 数学公式和符号的编辑。作者使用了专业的编辑软件对论文中的符号、变量和公式进行了编辑。上文中我们指出，在数学中，即使同一字符在不同字体下所代表的内容也是不同的，因此我们在撰写论文时需要尤为注意，具体的需要多研究文献资料，进行学习。对于公式符号的编辑和定义，属于表达上的规范，并没有专门的资料介绍。因此，一篇论文是否够专业，够水准，从内容的撰写上就可窥一斑。

   (4) 参考文献的引用。该论文中涉及了大量的定理、引理。对此，作者在每个需要引用的地方进行了标注，并提供了大量的参考文献，为文章的研究工作提供了坚实的基础。

   

2023–2025 年（第十六至第十八届）获奖趋势与代表性论文

2023–2025 年物理学科的获奖课题延续了"力学+流体+声学+实验装置"的主流——例如 2024 年金奖《Number Recognition by Listening》通过声学特征加机器学习识别黑箱中小球数量，2025 年金奖《"Phase Transition" in a Mechanical System》研究力学系统中的对称性自发破缺与滞后回线——可见评委对来自日常生活的力学/流体/声学课题的偏好十分稳定。同时，2024 年银奖《The Inseparable "Paper Vice"》、2025 年银奖《Development of a High-Efficiency Objective-Prism Stellar Spectrograph》等课题体现了"自制装置 + 现象分析 + 模型构建"的获奖范式。天体物理与凝聚态等需要重型实验设备的课题在 2023–2025 年仍属少数，但 2024 年铜奖《Investigating Physical Conditions and Critical Factors across the Center of the Galaxy M82》表明：若学生能够获取专业级望远镜数据并在指导老师协助下完成统计分析，天体方向同样有获奖可能。

代表性获奖论文深度解读

2023 银奖 ·《Dynamics and Abnormal Sway Precession of Euler’s Magnetic Pendulum》

学生 / 学校： 周厚希，中国人民大学附属中学
指导老师： 张永平、马宇翰

研究的是什么问题？ 想象一个用绳子吊起来的小磁铁，下方放上若干块固定的强磁铁，松开手让小磁铁摆动——它的运动会变得极其复杂，时而绕这个磁铁转、时而绕那个磁铁转，看似随机却又遵循确定的物理定律，这就是著名的"磁摆"（magnetic pendulum），是非线性动力学和混沌理论的经典实验装置。Euler 磁摆是其中一种特殊变体，研究者通常感兴趣的是它的"进动"（precession）——即摆动平面缓慢绕中心轴旋转的现象。本论文的关注点在于一种"反常"的进动模式：在某些初始条件下，进动方向、速度甚至旋转的稳定性都会出现违反常识的现象。

用了什么方法？ 从题目可以推测，作者使用了"理论 + 实验"两条路径并行：理论上写下含磁偶极相互作用的拉格朗日量，推导摆的运动方程，并对小振幅情形做线性化分析以预测进动频率；实验上通过高速摄像或位置传感器记录摆的轨迹，分析其相空间结构（庞加莱截面、李雅普诺夫指数等是这类研究的标准工具）。"反常进动"的成因很可能是磁力非线性 + 摆动平面外耦合带来的非保守效应。

为什么评委青睐？ 这是一个标准的"丘奖味"课题——选题来自一个能在桌面上做的简单装置，但现象背后隐藏着深刻的非线性动力学。评委不是被磁摆本身吸引，而是被作者敢于追问"为什么进动会反常"以及给出的定量分析所打动。这种从一个具体现象出发，引出力学、电磁学、混沌理论交叉的研究路径，恰恰是丘奖物理学科最青睐的范式。

对参赛者的启发： 物理学科金、银奖很少给凝聚态、量子计算这类需要大设备的课题，更多给那些"在自家书桌上能做"但具有数学深度的实验。一个磁摆、一根牙签、一杯水，都可以成为深挖的对象。关键是要：（1）选一个"反直觉"的现象；（2）拍下高质量数据；（3）用力学/流体方程定量解释；（4）通过参数变化得出普适规律。

2024 金奖 ·《Number Recognition by Listening——Traditional Acoustic Feature Analysis and Machine Learning Method for Estimating the Number of Balls in a Black Box》

学生 / 学校： 彭子轩（Zixuan Peng）、周小希（Xiaoxi Zhou）、张济帆（Jifan Zhang），南京外国语学校
指导老师： 章东（Dong Zhang）

研究的是什么问题？ 给你一个不透明的密闭盒子，里面装有若干个小球，摇晃时小球互相碰撞、撞击盒壁会发出声音。仅凭这段声音，你能数出里面到底有几个小球吗？这听起来像一个魔术题，但其实背后是一个极具实用价值的反问题（inverse problem）：从声学信号反推出系统的物理状态。工业领域中"听声辨故障"（如轴承诊断、管道泄漏）、医学领域中的"声学成像"，都属于同类问题。

用了什么方法？ 论文采用了"传统声学特征 + 机器学习"的双线方法。传统声学特征包括：（1）能量包络——多个球碰撞越多、声音的能量积分越大；（2）频谱质心和带宽——球数越多，碰撞频率分布越宽；（3）撞击事件密度——通过短时能量阈值检测峰值，统计单位时间内的撞击事件。机器学习部分则把上述特征作为输入，训练一个回归或分类模型（很可能是 SVM、随机森林或浅层神经网络）来预测小球数。论文标题专门强调"Traditional Acoustic Feature Analysis"，说明作者不是单纯把声音丢进黑箱网络，而是先做了认真的物理特征工程——这是论文得金奖的关键技术亮点。

为什么评委青睐？ 这个课题完美符合丘奖物理的"日常现象 + 严肃物理 + 现代工具"三要素：摇盒子是几乎所有人都做过的动作；但要把摇动的声音准确还原为球数，需要刚体碰撞动力学、Hertz 接触力学、声学传播、信号处理、机器学习等多学科知识。论文不是"机器学习硬解物理"，而是先建立物理直觉、再让机器学习来精化预测，这种克制而严谨的方法论极受评委推崇。三位作者的团队配置也展示了课题的开放性和工作量。

对参赛者的启发： 当你想用机器学习做物理课题时，要避免"端到端深度学习"的诱惑——把原始声音丢进神经网络确实能跑出结果，但缺少物理洞察，评委会觉得"这是计算机课题不是物理课题"。正确的姿势是：先做物理上有意义的特征工程（能量、频谱、相位），再用机器学习帮你做最后一公里的拟合。这样既体现物理深度，又展示了现代工具的运用。

2025 金奖 ·《"Phase Transition" in a Mechanical System: Rotation-Induced Spontaneous Symmetry Breaking and Hysteresis Loop》

学生 / 学校： 牟天昊（Tianhao Mu）、罗海艺（Haiyi Luo），重庆市育才中学校
指导老师： 张程鑫（Chengxin Zhang）

研究的是什么问题？ "相变"通常出现在统计物理课本里——水结冰、磁铁失磁，都是相变。但本论文研究的是一个纯粹的力学系统，它在某个旋转速度阈值之上会"自发对称性破缺"，即原本对称的平衡态会突然偏向某一侧，并且当你慢慢降低转速、再缓慢回升时，系统的位置不会按照原路返回——而是形成一个"滞后回线"（hysteresis loop），就像磁铁的磁化曲线一样。这意味着一个看似平凡的力学装置，其行为却展示出与统计物理中相变完全同构的特征。

用了什么方法？ 从题目可推测，作者使用了：（1）理论建模——写下旋转参考系下系统的总势能函数，分析其极小点随转速的演化（典型的"叉式分岔"或"鞍–结分岔"理论）；（2）实验验证——搭建一个可以精确控制转速的装置（很可能是带配重的旋转臂或离心结构），用位置传感器或高速摄像记录位置随转速的演化；（3）滞后回线测量——慢速增减转速，记录"上行"和"下行"两条曲线的差异，作为对比"二级相变"和"一级相变"的判据。

为什么评委青睐？ 这篇论文最优雅之处在于把统计物理中的高阶概念（对称性自发破缺、有序参量、滞后回线、二级相变）用一个高中生能亲手搭建的力学装置"翻译"了出来。它告诉评委：作者不仅理解了相变的数学本质，还能识别出在哪些非传统系统中相变会再现。这种"跨领域类比"是顶级物理学家的核心能力之一。评委也欣赏作者把朗道（Landau）唯象理论的精神引入到经典力学中——这是一次非常漂亮的物理学跨尺度教学示范。

对参赛者的启发： 一个金奖物理课题往往不在于设备多贵、数据多大，而在于你能否在两个看似不相干的领域之间架起一座桥。如果你既懂经典力学又对相变略有了解，你就有机会找到这种"小机械里的大物理"。建议同学们多读 Landau 等的《Statistical Physics》前几章，把"相变"作为一种思维框架，去重新审视日常的力学和流体现象。

（以上论文获奖信息均来自 yau-awards.com 官方公示页面，详见 ²）

奖项数量统计：2023 年共评出 金 0、银 2、铜 3、优胜 5；2024 年共评出 金 1、银 1、铜 3、优胜 5；2025 年共评出 金 1、银 1、铜 3、优胜 5、入围 5。

力学分析、流体力学、微积分等理论知识

在掌握高中基础物理力学知识的基础上，学生还需要加深其他内容的学习。丘成桐奖中力学的分析过程基本属于大学三年级左右的经典力学的范畴和难度。除去传统的牛顿矢量力学外，有大量的课题都使用了拉格朗日等分析力学的解决方法，这一部分力学内容需要极强的数学微积分方面的知识背景，所以对于高中生而言难度较大。但是，分析力学的解决方法通常较为优雅，专业性较强，更容易得到评委的青睐。

力学部分另外一个分支为流体力学，这一部分有着专属的体系和知识结构，同时其解决问题的方法需要进行计算机模拟涉及到大量的数值计算，比如说常见的有限元分析法，所以说对于流体力学有关的问题而言，存在了大量的新内容需要学习。学生在选取该方向题目的时候，需要做好充足的学习准备。这一部分的实验对于设备也存在一定的要求，需要考虑多方面的因素才能确保实验顺利的进行。

除去物理的有关知识外，丘成桐物理奖还需要大量的数学有关知识，最常用到的是微积分有关的知识，比如偏微分方程的解决等等。这些知识一方面可以巩固学生校内的学习（比如AP微积分），另一方面可以充分锻炼的思维和计算能力，所以这些理论内容虽然大多不属于传统的高中考试内容，但这一部分内容的学习会对学生的升学起到全面的帮助。

实验设计

对于高中生而言，一般情况下实验都是学生基于已有的实验手册，去完成所要求的一系列内容。然而在丘成桐比赛中，学生需要根据研究的课题来自行创作实验，这也就对学生，包括其指导老师提出了较高的要求。如何设计出科学严谨的实验步骤，如何消除过程中各种误差和客观因素的影响，如何确保实验结果可以充分体现想要获得结论，这些问题都直接决定了该作品是否具有参赛竞争力。

实验设计基本上可以理解为丘成桐物理奖的核心考察点，这一部分学生是否有兴趣，是否有天分做好，其实也能反映出学生未来能否很好地从事如物理、工程等相关的科研工作，所以对于参加物理学科竞赛的学生来说，也可以从这一个角度来帮助自己的人生进行规划。

Matlab、Mathematica、Python等模拟分析计算软件

对于当前的物理研究而言，计算机模拟和计算属于相当重要的一部分。对于很多的物理问题而言，我们可以通过将理论模拟来绕过实验去寻得该问题的答案。同时，我们也可以将模拟结果和实验结果进行交叉验证，来对该问题进行全面的探讨。在当前的物理科研过程中，有很多问题可以通过 Matlab 和 Mathematica 软件的仿真计算，Python 数据分析予以解决。所以在丘成桐奖的比赛中，有很多课题都通过计算机模拟进行问题的研究和验证，这一部分内容的重要性也在近些年的比赛中逐渐提高。

Matlab 和 Mathematica均属于功能非常强大的模拟计算软件，高中生如果能够借助丘成桐比赛对这些软件开始进行入门学习，这对于之后不管课程上的学习还是科研上的便利都有着很大的帮助。比如说，有很多数学问题可以用Mathematica进行验证和可视化分析。除此之外，Python 也在物理科研中发挥着很大的作用，学生也可以在解决物理问题的同时，学习大量的 编程知识，这对于学生之后的发展意义重大。

2020年全球物理金奖

1. 学生背景简述

该年获奖小组来自南京外国语学校的三位同学，这三位同学均在全国中学生物理竞赛，英国物理奥赛，物理碗等比赛中取得了较好的成绩，在物理学科上有着扎实的基础和较好的天赋。指导老师除本校老师外，还包括南京大学的王思慧教授，所以整篇论文有着很高的起点， 整体论文的结构以及实验的完成都有着非常好的逻辑性和完整性。

2. 论文概述

关于论文，我们首先来看一下题目和摘要，对整个论文的内容有个大概的了解。

题目：线绳自发打结的物理机制

摘要：本论文研究线绳自发打结的物理机制与过程，以及相关参数的影响。论文包括理论分析、转动实验以及振动实验。大多数理论推导都是在实验观察中得到启发而建立的。

首先通过理论分析打结过程，研究驱动（振动或转动）以及绳子这两类因素对打结的影响。在绳子驱动因素方面，推导了打结时转速、摩擦系数范围、振幅、最优驱动频率、时间等公式；在绳子的影响方面，导出了打结概率与绳长的公式，并对绳子盘绕方式、绳子材料的影响进行了定性分析。

通过反复尝试，自制了两种实验装置，分别进行振动和转动实验。在实验中，验证了振幅、频率（转速）、时间、盘绕方式、绳长、材质的影响，还对绳结的打结与解结进行了实验探究。还对打结的可逆性、容器尺寸等影响进行了讨论。大多数实验结果都和理论分析相符。最后，我们对问题进行了总结和展望。    

本文具体研究线绳自发打结的物理机制，这一现象在生活中极其常见， 比如说耳机线，数据线，水管等等，但是没有多少人会去想为什么这些线一不留心就会打结。论文主要研究了振动和转动这两种方式对于打结的影响，并考虑包括振幅，频率，绳长，材质等多个因素，从多个角度对于线绳自发打结这一现象进行解释。整篇文章讨论的主题是一个没有学习过物理的人都可以完全理解，但是这个问题究竟为什么会产生却没有一个较好的解释。

3. 获奖点分析

• 选题： 毫无疑问，选题应该是这个作品获得金奖最重要的因素。首先，线绳自发打结这个现象在生活中极为普遍，这一现象或多或少给大家的生活带来各种各样的困扰。但是，这个现象产生的原因究竟是什么，可能就算是研究物理方向的教授都很难讲清楚。于是，这种能够产生充分共鸣，但其机制却鲜为人知的课题，能够更好地得到各位评委老师的青睐。其次，该课题并没有涉及到较多比较高深的物理学知识。从整个论文来看，只有高中阶段的物理理论有所涉及，除此之外仅有基础的微积分和统计学内容。用基础的知识去解决复杂的实际问题是丘成桐物理方向极为推崇的。第三，该课题研究问题可以用较少的实验器材进行测试，这里不会用到很多复杂的器材和设备，这也就让该课题变得更加有亲和力。最后，该课题可以与其他物理内容做结合，比如热力学第二定律自发性，材料物理等等，这些扩展都使得该课题有着深刻的研究意义。

  类似于线绳自发打结的问题实际生活中非常多，这也就需要学生与指导老师多多留意这些问题，并去深刻思考如何用最简单直接的研究方法去解决。人类社会中存在类似的问题数不胜数，但大部分时候人们都选择无视或者被动地接受，丘成桐物理奖对于这一现象提出了自己的看法和解决方案。

• 论文：

  摘要
  目录
  一、引言
  二、预实验
  2.1 振动时间与绳子长度对打结个数的影响
  2.2 振动方式与绳子材质对打结个数的影响
  三、理论分析
   3.1 驱动的影响
   3.1.1 转动与转速
   3.1.2 驱动参数
  3.1.3 时间的影响
  3.2 绳子的影响
   3.2.1 盘绕方式的影响
   3.2.2 绳长的影响
   3.2.3 绳子材料的影响
  四、振动实验
  4.1 振动参数的影响
   4.1.1 绳结个数与振动方向的关系
   4.1.2 绳结个数与振幅的关系
   4.1.3 绳结个数与振动频率的关系
   4.1.4 绳结个数与振动时间的关系
  4.2 绳子的影响
  4.2.1 绳结个数与盘绕方式的关系
  4.2.2 打结概率与绳子长度的关系
  4.2.3 绳结个数与绳子材质的关系
  4.2.4 绳结的打结与解结
  五、转动实验
  5.1 转动参数的影响
  5.1.1 转动时间对绳结个数的影响
  5.1.2 转动频率对绳结个数的影响
  5.2 绳子参数的影响
   5.2.1 绳子盘绕方式对绳结个数的影响
  5.2.2 摩擦系数的测量
   5.2.3 绳子材质对绳结个数的影响
   5.2.4 绳长对绳结个数的影响
   5.2.5 配重对绳结个数的影响
  5.3 讨论
   5.3.1 打结的可逆性
   5.3.2 转动容器尺寸与形状的影响
  六、总结与展望
  参考文献
  致谢

  从目录中， 我们可以看出作者对于该课题的研究思路。这里可以看出，作者从很多个角度都对于这个问题进行了研究和实验。从多个维度对于同一问题进行探寻对于培养学生思维的逻辑性和辩证性意义重大，也符合了国外教育中辩证思维（Critical Thinking）这一重要组成部分，研究对象的全面性也是该作品获得极高赞赏的重要原因。

  

  除了目录外，我们从文章的以下几个方面来看一下这篇文章的优秀之处。首先，该文章中理论部分书写清晰，整体上由高中的物理知识出发，进行实际问题的应用和解答，如图8所示。这里我们可以看出，该论文并不需要高深的物理背景知识，但是整体理论推导极其工整逻辑，非常易于读者理解。

  

  

  此外，对于实验部分，学生选择了生活中非常常见的材料进行测试。这些实验器材均极为容易获取。但就是通过这些非常简易的器材，学生可以对线绳打结问题进行多角度的探索，这是非常难得的一点。

  

  最后，该组学生对于整个实验的内容进行了充分的总结。这里系统地将理论和实验相结合，对于整个问题进行了详细的解释，这一部分体现了物理研究的科学性和完整性，也完美契合了康德《纯理性批判中》后验（A posteriori）知识的获取方式和过程。

2023–2025 年（第十六至第十八届）获奖趋势与代表性论文

化学学科在 2023–2025 年继续呈现"实验为主、合成与电化学并重、紧扣双碳与生物医药热点"的特点。2023 年金奖《CRISPR-enabled signal amplification for visual antigen detection》（上海宋庆龄学校）将 CRISPR 信号放大用于抗原可视化检测；2024 年金奖《Improving Intracellular Synthesis Efficiency of GFP Catenane through Directed Evolution》通过定向进化提升 GFP 连环蛋白的细胞内合成效率；2025 年金奖《Fabrication of an NTO/Ag/g-C₃N₄ Self-Supporting Membrane》关注海水光催化制氢。这些课题共同的特点是：选题紧扣环境/能源/生物医药热点，研究方法以实验合成为主，并辅以系统的物理化学表征。

代表性获奖论文深度解读

2023 金奖 ·《CRISPR-enabled signal amplification for visual antigen detection》

学生 / 学校： 樊泓萱、郑好，上海宋庆龄学校
指导老师： 陈易新、李江

研究的是什么问题？ 新冠疫情让全民熟悉了"抗原检测试纸"——把鼻拭子液体滴到试纸上，10 分钟后看条线。这种试纸用的是抗体识别病毒抗原的原理，灵敏度有限，往往要等到病毒载量较高时才显色。这篇论文要解决的问题是：能不能在保留试纸的简易性的同时，把灵敏度大幅提升？作者的创新点是引入近些年生命科学领域最炙手可热的工具——CRISPR-Cas 系统（基因编辑剪刀），把它当作"信号放大器"接到抗原检测的反应链下游，使得即便微量抗原也能被放大成肉眼可见的颜色变化。

用了什么方法？ 整个反应链可以理解为三段接力：（1）抗体捕获抗原——常规免疫层析的第一步；（2）抗原触发一段 DNA"激活信号"——通常通过抗体偶联 DNA 探针实现；（3）CRISPR-Cas12a（或 Cas13a）酶被激活后开始"无差别剪切"——切割大量带荧光基团或显色基团的报告分子，从而把一份抗原信号放大为成百上千份信号。这正是 SHERLOCK 和 DETECTR 等近年明星检测方法的核心机制，被作者首次拿来做"可视化"抗原检测。

为什么评委青睐？ 评委看重三点：（1）选题极具时代意义——抗原检测是疫情期间和后疫情时代每个人都关心的话题；（2）方法极具前沿性——CRISPR 诊断（CRISPR-Dx）是 2017 年以来才兴起的方向，把它跨界用到抗原检测属于真创新；（3）作者展现了高强度的实验能力——CRISPR 体系涉及克隆、蛋白纯化、核酸化学、免疫化学多个技术栈，对高中生而言挑战极大。这是一个典型的"交叉学科 + 前沿工具 + 实用场景"获奖案例。

对参赛者的启发： 如果你对化学/生物方向感兴趣，"CRISPR + 检测 / 治疗 / 成像"是 2023–2026 年最容易出成果的方向之一。不必从零开发新酶，更可行的路径是把已经被生物学家成功用过的工具，跨界到化学传感器、光声成像、可穿戴检测等"接口"应用中。这种课题既能蹭到前沿热度，又有清晰的化学实验主干。

2024 金奖 ·《Improving Intracellular Synthesis Efficiency of GFP Catenane through Directed Evolution》

学生 / 学校： 孔繁淏（FanHao Kong），北京师范大学附属实验中学
指导老师： 张文彬（WenBin Zhang）、孔婀静（EJing Kong）

研究的是什么问题？ "Catenane"（连环烷）是化学中一种神奇的分子——两个或多个环像奥运五环一样机械咬合在一起，没有共价键却无法分开，必须把环切断才能解开。GFP（绿色荧光蛋白）是生物学家最熟悉的"显色标签"。本论文研究的是如何把 GFP 改造成连环结构（GFP catenane），并且让细胞自己"高效组装"这些机械互锁的蛋白质——这相当于让细胞工厂生产乐高积木，并自动咔嗒一声拼合到一起。研究的难点是细胞内组装效率很低，绝大多数 GFP 都没有完成自缠绕。

用了什么方法？ 作者用的是合成生物学的经典工具——"定向进化"（directed evolution）。定向进化的核心思路是：（1）对编码 GFP catenane 前体的 DNA 序列做大量随机突变，建立一个"基因库"；（2）让大肠杆菌或其他宿主细胞表达这些突变体；（3）通过荧光检测或活性筛选，从数百万个突变体中挑出组装效率最高的那几个；（4）把它们再做几轮突变和筛选，"进化"出超级版本。这一方法的"教父"是 2018 年诺贝尔化学奖得主 Frances Arnold——本论文相当于把诺奖级方法落地到了一个具体、漂亮的目标分子上。

为什么评委青睐？ 这个课题展现了三种顶尖能力：（1）深刻的分子设计——把蛋白质做成连环烷本身就是国际化学/生物界最前沿的拓扑化学课题；（2）扎实的合成生物学技术——定向进化需要分子克隆、深度测序、文库构建、自动化筛选等完整技术栈；（3）清晰的工程化目标——不是为了"展示能做"，而是为了把效率从 10% 提高到接近 100%。指导老师张文彬教授本身就是这方面国际知名学者，论文的学术起点极高。

对参赛者的启发： "定向进化"是一种通用的化学/生物优化工具，原理简单（突变+筛选+迭代），但能应用到酶设计、抗体设计、生物材料、合成生物学的几乎所有方向。如果你能找到一个具体的、可定量评价的优化目标（比如某个酶的活性、某个蛋白的表达量、某个材料的性能），就可以用定向进化的框架打造一个完整的研究课题。

2025 银奖 ·《Fluoride-Ion Triggers Stable and Active Seawater Oxidation at 1A/cm²》

学生 / 学校： 陈思睿（Sirui Chen），北京师范大学附属实验中学国际部
指导老师： 孙晓明（Xiaoming Sun）、孔婀静（Ejing Kong）

研究的是什么问题？ 全世界 97% 的水是海水。如果能直接电解海水产氢，就能绕过淡水制氢面临的水资源瓶颈，把可再生电力（风电、太阳能）大规模转化为绿氢。但海水中含有大量 Cl^-（氯离子），电解时阳极会和氧化反应（OER, 析氧反应）竞争产生有毒的氯气（CER, 析氯反应），同时阳极催化剂也会被氯离子快速腐蚀。这篇论文的关键发现是：在体系中引入氟离子（F^-）作为"调控剂"，能在工业级电流密度 1 A/cm² 下同时实现"稳定"和"高活性"——这是工业可用海水电解的硬指标。

用了什么方法？ 从题目可以推测的研究路径是：（1）合成一种过渡金属基催化剂（极可能是 NiFe 或 NiCo 基的层状双氢氧化物 LDH，因为指导老师孙晓明教授正是该领域国际权威）；（2）在电解液中加入不同浓度的氟盐，对比加 F^- 与不加 F^- 的稳定性和活性曲线；（3）用 XPS、TEM、原位 Raman 等手段揭示 F^- 究竟是"改造了催化剂表面"还是"屏蔽了 Cl^- 攻击"还是"参与了反应中间体的稳定"。最终找出 F^- 起作用的微观机制。

为什么评委青睐？ 海水电解制氢是双碳战略中最具落地价值的方向之一。论文不是停留在实验室小电流（毫安级），而是直接攻击 1 A/cm² 这个工业级阈值，这意味着结果具备直接转化的潜力。同时，用 F^- 这一非贵金属、非毒性的"小添加剂"实现性能跃升，方法上极为优雅。指导老师孙晓明教授是国际著名的电催化专家，论文的科学含量直追硕士论文水平。

对参赛者的启发： 化学课题想要拿大奖，"性能突破到工业级"是一个非常硬的卖点。不要停留在"我合成了一个新材料，光催化效率比对照高 30%"——这种数据很常见。如果你能让一个性能指标突破到学术界公认的"工业可用"门槛（电流密度 1 A/cm²、电解电压 1.6 V 以下、稳定运行 1000 小时等），评委一眼就能看出研究的真实价值。

（以上论文获奖信息均来自 yau-awards.com 官方公示页面，详见 ³）

奖项数量统计：2023 年共评出 金 1、银 1、铜 3、优胜 5；2024 年共评出 金 1、银 1、铜 3、优胜 5；2025 年共评出 金 1、银 1、铜 3、优胜 5、入围 3。

学科知识

对于理论方面，一定要非常熟练高中阶段已学习的基础知识，这是万丈高楼的根基。当然，仅仅是高中的知识还远远不够，学生在后续的学习中，可引入一些比较深入的理论基础知识（大学化学方面），便于进一步开拓视野，并构建思路体系。

1. 掌握基本电化学基础知识： 分析可知，很多获奖的论文都与电化学有关，例如催化、电池、超级电容器等，这就要求学生能熟练掌握高中所讲的电化学相关知识，并将其很好应用。比如氧化还原反应及其原理，得电子与失电子反应、电解池的基本原理、化学电源及化学电路的知识。只有打好了这些基础，才能在后面的实验和比赛中游刃有余。当然，还需对这些知识有进一步的延伸，比如催化剂的结构筛选、电解反应的阴阳极材料的特征、电催化的基本性能分析等，推荐参考书目：

2. 掌握有机合成的几种基本方法： 有机化学与生活息息相关，部分学生团队选择有机化学类的课题作为其研究方向。有机化学体系复杂，反应多变，尤其受到温度、压力、湿度、反应时间等因素的控制，这需要学生在高中阶段严格打好有机化学的基础，比如什么样的反应条件可以合成具有什么特征的产物，这一点对于即将选择有机化学作为参赛题目的同学而言非常重要。这也需要进一延展，最直观有效的方法就是，了解更多的有机化学反应，从别人的合成条件中寻找灵感，找到复合自己想法合成的物质的方法。

实验操作

对于实验方面，丘赛化学（实验性学科）实验操作在所难免，实验是基于理论知识的纵深，因此，扎实基础适当拓展相当有必要。学生在初高中已对基础实验操作有一定训练（主要是瓶瓶罐罐的实验），但是对于化学分析、测试仪器的操作有些陌生，因此学生适当掌握一些常见实验仪器的操作即可。

1. 掌握基础无机化学实验： 丘赛化学获奖课题大部分为无机化学相关实验，首先学生需要掌握基本的实验仪器操作，比如高中实验课所讲到的滴定分析、加热合成等，这是化学实验的基础，也是第一部。随后就是要利用这些基本操作来掌握物质的分离和提纯方法，常见的分离提纯方法有过滤、沉淀、离心、离子交换等，几乎所有的合成方法最后都会将所合成的物质分离提纯，因此掌握这些方法尤其重要。

2021年全球化学金奖

这里，我们以2021 年全球化学金奖论文“Planted Bean Sprouts-Derived Transition Metal-Doped Carbon Nanosheets for Electrocatalysis of CO2 Reduction and Hydrogen Evolution Reaction”（种植豆芽菜衍生的碳负载过渡金属纳米颗粒在电催化中能源转化的应用）为例进行解析。

1. 研究课题选择及获奖情况分析

朱清瑗为2021年丘成桐中学生科学奖化学金奖得主，来自上海外国语大学附属外国语学校，是周恩来总理亲自批示成立的七所外国语学校之一，是全国著名高中，直属国家教育部，为全国外国语学校工作研究会会长学校和理事长学校、全国中小学外语教研示范学校，被誉为“培养外语外交人才的摇篮”。该课题导师郑耿锋教授为复旦大学先进材料实验室和化学系教授、博导，国家杰出青年科学基金获得者、教育部青年长江学者、中国化学会青委会委员，重点研究碳基小分子的电化学催化与能源存储、纳米-生物复合界面，已在国际著名学术期刊上发表论文120余篇，邀请专著与章节 4部，论文的总他引次数 8000多次，h-index因子达到37（全球高水平），兼任目前兼任国际期刊J. Colloid and Interface Science（影响因子8.128）的编辑，J. Materials Chemistry A（影响因子12.732）杂志的编委，是一位非常优秀的青年教师，研究成果曾被美国国家广播电台、福布斯杂志、MSNBC，Science等多个新闻媒体和杂志报道。从履历上看，学生履历非常完美，教师履历极其杰出，学生本人身处上海市，具有广阔的国际视野和教育资源，同时，其被选拔为校化学英才班学员，得天独厚的资源和自身扎实的学科背景使得朱清瑗同学在高手如云的丘赛化学赛中脱颖而出。

该论文是获得金奖的关键所在。首先，我们从选题学科上解析，该选题《种植豆芽菜衍生的碳负载过渡金属纳米颗粒在电催化中能源转化的应用》理论知识在高中化学的基础上还涉及了“生物化学”（大学课程）、“电化学原理”（大学本科及硕士课程）、“物理化学”（大学课程）等诸多课程，证明了该同学有极强的理论功底。其次，该课题不是单一的化学学科课题，也结合了大量生物学方面的知识，是标准的创新型交叉学科课题，这种交叉学科课题是国家非常支持的，在2021年教育部也积极出台《交叉学科设置与管理办法》来鼓励大学开展交叉学科教学、激励硕博士进行交叉学科选题，因此可以看出交叉学科是未来发展的大势所趋，而一个高中生竟具有如此前瞻性的思考能力，并将其付诸实践，可能这就是该同学能以此获得丘赛金奖的点睛之笔。再次，选题背景围绕二氧化碳还原开展，是“双碳”背景下的重点研究方向，选题结合了国家战略发展的大背景，也与“十四五”规划所提出的发展目标不谋而合，因此若后续深入研究并形成完善的研究体系，那么其成果将具有很强的商业化应用价值。最后，此篇论文想法创新性极强，此前从未有人尝试，为二氧化碳的还原提供了一种新方法，并启发了后续研究者一系列的思考，这也是该论文能获得成功的关键所在。

2. 论文概述

Title：Planted Bean Sprouts-Derived Transition Metal-Doped Carbon Nanosheets for Electrocatalysis of CO2 Reduction and Hydrogen Evolution Reaction
Abstract：Electrocatalysis CO2 reduction can convert CO2 into important fuels and chemicals to reach artificial carbon sequestration. This subject puts forward a new concept "planted catalyst", which means that during the growth of soybeans into bean sprouts, metal ions are absorbed into the plants and fixed. Compared with the traditional soaking-method catalysts, this “planted catalyst” with the special structure and good performance can be obtained. It can be seen that plant-derived carbon catalyst has the feasibility of higher performance and has a good prospect.
Keywords：CO2 electrocatalysis, water electrolysis, catalyst, bean sprouts, biomass carbon materials

论文标题中文：种植豆芽菜衍生的碳负载过渡金属纳米颗粒在电催化中能源转化的应用
论文摘要中文：电催化CO2还原可将CO2转换成重要的燃料和化学品，实现人工固碳。本课题提出一个新概念“种出来的催化剂”，其为黄豆在生长成为豆芽菜的过程中，将金属离子吸收进体内并将其固定。通过与传统浸泡所得的催化剂做对照试验，可得到特殊结构与性能良好的催化剂。可见植物衍生碳材料催化剂具有更高性能的可行性，具有良好前景。
论文关键字中文：二氧化碳还原，电解水，催化剂，豆芽菜，生物质碳材料

3. 获奖点解析

1. 从选题背景上看：论文的出发点在于选取合适的催化剂固定二氧化碳（化学式CO2）。众所周知，二氧化碳浓度过高不仅会对人体健康造成影响，也会影响自然环境。但是随着人类活动范围扩大，工业革命后工业迅猛发展，地球上的工厂、矿山林立，各种交通工具骤增，二氧化碳的排放与日俱增，再加上森林的砍伐减少了二氧化碳的吸收固化，大气中的二氧化碳越积越多，继而引发的各种环境问题使得人类不得不去关注 CO2 的问 题。如前文所说，课题研究方向的选择适应了时代发展潮流，响应了党中央“双碳”的政策，符合国家“十四五”战略规划，因此这样的课题，更容易得到支持，也会有更多的参考资料予以佐证，最重要的是，这样的研究成果更容易应用到现实生产中，对国家发展和生态建设具有相当积极的作用。

2. 从选题创新性看：该论文创新性地提出了一种固定二氧化碳的方法，使用了生长过程中吸收金属离子的豆芽菜制备催化剂，而在传统的制备过程中，是拿生长好的植物直接浸泡在金属溶液中的，这种方法的性能是比传统的方法要好的，因此被称为“种出来的催化剂”。该选题创新实在“大胆”，对于新一代的高中生，尤其是在培养创造性思维的时代，这样“大胆”创新实属不易，更为可贵的是，这样的创新并不是空穴来风， 实验结果证明了“大胆”的可行性。

   

   该研究发现，铜离子浓度越高，CO2 还原产物对CH4 的选择性也更高，在0.2mol%下能高达95%，数据非常漂亮。

3. 从研究逻辑看：该论文逻辑紧密，研究的顺序环环相扣，前后相互佐证。从前期的植物种植到后面的催化剂测试及二氧化碳固定测试，种植的植物可以提取催化剂用于后续实验，后续实验证明了前期种植植物固碳的可行性，形成了良好的逻辑闭环。 从实验结果看：该实验效果显著，在0.2mol%下种植出来的豆芽菜衍生催化剂在二氧化碳（CO2）还原中产甲烷（CH4）的效率高达30%，而传统方法的效率仅有2%，可见其性能上显著的优越性；不同铜溶液浓度下种植的豆芽菜相比，浓度越高，产CH4效率越高，且产CH4的选择性更高，在铜离子0.2mol%下达到了95%；性能非常优异，也证明了选题的正确性。长远来看，具有商业化应用的潜在优势。

   

   该研究发现，种植下产甲烷的法拉第效率在-1.37V 电位下高达30%，而浸泡下的法拉第效率仅在-1.97V 下达到2%，可见种植相对于浸泡法在性能上有显著的提升，远远高于了传统的催化剂提取法。这也进一步说明了，创新课题搭配完美的结果支撑是很容易取得高级别奖的。

2023–2025 年（第十六至第十八届）获奖趋势与代表性论文

生物学科 2023–2025 年的获奖论文反映出三个显著趋势：（1）医工交叉与生物医学工程上升——2024 年金奖（同时获 2024 跨学科科学金奖）《Design, Optimization, and Mechanism Study of Antithrombotic Microstructure Surfaces on Mechanical Heart Valves Inspired by Shark-Skin Riblet》（北师大实验中学）将鲨鱼皮仿生学应用于机械心脏瓣膜抗血栓表面设计；（2）AI for biology 显著加强——多个获奖课题（如 2023 优胜奖《Optimizing human SIRT6 protein with deep learning of 3D structures based on maximum lifespan》、2024 优胜奖《AI-Guided Design and Preliminary Validation of Anti-Tuberculosis Subunit Vaccine》、2025 金奖《Design a "Molecular Universe" within Cells》）将深度学习引入蛋白质设计、疫苗设计或细胞内液液相分离建模；（3）植物学/基因组学等传统强项仍稳——2023 跨学科金奖《Mechanisms underlying climbing-morphogenesis of Boston ivy and discovery of shoot apex gravitropism》（上海中学）即典型代表。

代表性获奖论文深度解读

2023 金奖（兼跨学科科学金奖）·《Mechanisms underlying climbing-morphogenesis of Boston ivy and discovery of shoot apex gravitropism》

学生 / 学校： 晁楚言，上海中学
指导老师： 廖辉、徐麟

研究的是什么问题？ 爬山虎（Boston ivy，学名 Parthenocissus tricuspidata）是城市里常见的攀爬植物，能沿着光滑的墙壁、玻璃面一直向上生长，仿佛"自带吸盘"。它到底是怎么做到的？传统答案是它的卷须末端有粘附性的吸盘状结构，但作者注意到一个更深层的问题：爬山虎的"嫩芽顶端"（shoot apex）似乎本身就具有"反重力"的生长倾向——即使没有支撑物，它也会先朝上探出一段，再寻找可以附着的表面。本论文系统研究了爬山虎攀爬形态发生（climbing-morphogenesis）的整套机制，并发现了一种过去未被报告的"嫩芽顶端向重性"（shoot apex gravitropism）现象。

用了什么方法？ 从题目和植物形态学研究的常见路径推测，作者综合采用了：（1）形态学观察——记录爬山虎从种子萌发到攀爬生长的连续形态变化，结合显微和电镜观察吸盘的微结构；（2）重力响应实验——把植物倒置或侧放，观察嫩芽顶端在不同时间、不同重力方向下的生长轨迹，定量"向重性"的强弱；（3）激素生理研究——爬山虎攀爬涉及生长素（auxin）的不对称分布，作者很可能用免疫染色或激素含量测定描绘了生长素分布图；（4）分子层面的辅助实验，例如比较吸盘形成前后的基因表达。

为什么评委青睐？ 这是丘奖近年罕见的"既得学科金奖又得跨学科科学金奖"的双金奖作品，含金量极高。评委青睐的有三点：（1）选题源于人人都见过的植物现象，但发现的是过去文献从未报道的新机制（"shoot apex gravitropism"）——这是真正的"原创发现"；（2）研究跨越形态学、生理学、分子生物学多个层次，体现了对植物科学完整的研究范式的掌握；（3）发现具有重要应用潜力——理解爬山虎吸附机制对开发仿生胶带、可攀爬机器人都有启示。

对参赛者的启发： 生物金奖的最高境界往往不是"做出多炫的技术"，而是"在大家都见过的现象里发现新规律"。爬山虎几乎每个城市公园都有，但晁楚言能从中提炼出原创的"嫩芽向重性"概念，这种"在司空见惯中看见新东西"的能力，比任何昂贵的设备都珍贵。建议同学们多观察生活中的植物、动物、生态现象，往往最朴素的题目反而最具突破空间。

2024 金奖 ·《Design, Optimization, and Mechanism Study of Antithrombotic Microstructure Surfaces on Mechanical Heart Valves Inspired by Shark-Skin Riblet》

学生 / 学校： 刘广羽（GuangYu Liu），北京师范大学附属实验中学
指导老师： 樊瑜波（YuBo Fan）、方伟（Wei Fang）

研究的是什么问题？ 现代医学中，"机械心脏瓣膜"是替换损坏心脏瓣膜的常见选择，可以使用 20–30 年。但机械瓣膜有一个长期未解的问题——血液流过金属表面时容易形成血栓，患者必须终身服用抗凝药（如华法林），副作用大、出血风险高。本论文的灵感来自鲨鱼皮：鲨鱼皮表面布满细密的"沟纹"（riblet），不仅可以减少水流阻力（这就是著名的鲨鱼皮泳衣灵感来源），还能抑制细菌附着。作者把这一仿生策略应用到了机械心脏瓣膜表面，试图在不增加抗凝药剂量的前提下减少血栓形成。

用了什么方法？ 从题目可推测的研究链条：（1）"设计"——通过流体力学仿真（CFD）模拟瓣膜表面的血流，找出血液最易停滞、形成血栓的位置；（2）"优化"——设计不同尺度（数十到数百微米）、不同间距的微沟纹阵列，并在金属瓣膜表面通过激光刻蚀或微加工实现；（3）"机理研究"——在体外用模拟血液或动物全血做流动实验，用荧光显微镜观察血小板附着和纤维蛋白沉积；进一步用流体力学解释为什么仿生沟纹能"打散"血液中的局部停滞涡。整个流程横跨生物医学工程、流体力学、表面化学和血液学。

为什么评委青睐？ 这个课题斩获了 2024 年生物学科金奖和跨学科科学金奖双奖。评委的几个核心评价点：（1）选题极具临床价值——抗血栓机械瓣膜是世界范围内尚未解决的医工问题；（2）研究方法系统完整——从设计到优化到机理，每一步都有明确的工程交付物；（3）跨学科深度——既需要懂血液生理学，又要懂仿生学，还要会做流体仿真和微加工，这种全栈式研究能力在高中生中极为罕见；（4）指导老师樊瑜波教授是国内生物力学领域的领军学者，研究的学术起点很高。

对参赛者的启发： 医工交叉是 2025–2030 年最有奖项含金量的方向之一。如果你能在身边找到一个"被忽视的临床问题"——心脏瓣膜血栓、骨折愈合、伤口感染、糖尿病足、人工耳蜗等——并且找到一个"生物学/物理学/材料学的解决思路"，就有机会做出有重大意义的研究。仿生学（biomimetics）是这类研究最容易切入的工具，自然界中存在大量被进化优化过的"工程方案"，等待被人类借鉴。

2025 银奖 ·《Searching for "Smart-and-Sex" Genes —— Evolutionary Driver for Neuron and Germ Cell Development in Primates》

学生 / 学校： Andrea Qian Lei，上海中学国际部
指导老师： 廖辉（Hui Liao）、张燕捷（Yanjie Zhang）

研究的是什么问题？ 灵长类（包括人类）的两个最显著的演化特征是：（1）大脑相对体型异常发达，神经元数量远超其他哺乳动物；（2）生殖系统在某些方面也发生了显著演化（如卵巢/睾丸的细胞分化模式）。本论文提出了一个非常大胆的猜想——可能存在一组基因，同时驱动了神经元发育和生殖细胞（germ cell）发育，作者称之为"Smart-and-Sex"基因。这是一种"基因多效性"（pleiotropy）假说：同一组基因在不同组织中发挥不同但相关的功能，从而把两个看似不相关的演化特征绑定到了一起。

用了什么方法？ 从题目可推测，作者主要使用了比较基因组学（comparative genomics）的工具：（1）下载灵长类与非灵长类哺乳动物（小鼠、狗、马等）的基因组数据；（2）筛选在灵长类支系上呈现加速演化（accelerated evolution，即 dN/dS 比值升高）的基因；（3）用单细胞 RNA 测序数据（来自公开数据库）找出在脑（特别是皮层神经元）和性腺（生殖细胞）中同时高表达的基因；（4）取这两个集合的交集，提出"Smart-and-Sex"候选基因清单，再用生物信息学（GO 富集、PPI 网络）佐证其功能合理性。

为什么评委青睐？ 这是一篇"小成本大思想"的研究——作者很可能没有自己的实验室，所有工作基于公共基因组数据库和生物信息学工具完成，但提出的科学问题极有想象力。"为什么人类既聪明又有独特的生殖策略"是演化生物学的核心问题之一。把这两个问题用一组基因联系起来，是有原创意义的假说。论文学术性强、数据可重复、写作规范——这恰恰是丘奖银奖的典型画像。

对参赛者的启发： 如果你身处没有湿实验室条件的高中，也完全可以做一流的生物研究——基因组学、生物信息学、AI for biology 都是可以纯靠计算机完成的方向。NCBI、UCSC Genome Browser、Ensembl 等公共数据库免费开放海量数据，配合 Python/R 的生物信息学包（Biopython、Bioconductor 等），高中生足以做出一篇有原创性的论文。关键在于你能提出"一个值得问的科学问题"——而这一点恰恰只靠思考就能完成，不需要昂贵设备。

（以上论文获奖信息均来自 yau-awards.com 官方公示页面，详见 ⁴）

奖项数量统计：2023 年共评出 金 1、银 1、铜 3、优胜 5；2024 年共评出 金 1、银 1、铜 3、优胜 5；2025 年共评出 金 1、银 1、铜 3、优胜 5、入围 3。

细菌的分离培养技术

菌种分离主要在培养皿上进行，常用的方法是稀释法和划线法。菌种分离的目的是是微生物的一个个体通过繁殖,在固体培养基上长出肉眼能见的群体，然后根据培养特征，用接种针调取所需菌种并在显微镜下检查,证明为单一形状的菌体。改变培养基条件也有助于菌种分离。没有一种培养基或一种培养条件能够满足一切微生物生长的需要，在一定程度上所有的培养基都是选择性的。如果某种微生物的生长需要是已知的,也可以设计特定环境使之适合这种微生物的生长,因而能够从混杂的微生物群体中把这种微生物选择培养出来，尽管在混杂的微生物群体中这种微生物可能只占少数。

DNA和RNA提取技术

核酸是遗传信息的载体，是最重要的生物信息分子，是分子生物学研究的主要对象,因此核酸的提取是分子生物学实验技术中最重要、 最基本的操作。

PCR循环扩增技术

聚合酶链式反应（PCR）是一种用于放大扩增特定的DNA片段的分子生物学技术，它可看作是生物体外的特殊DNA复制，PCR的最大特点是能将微量的DNA大幅增加。由1983年美国Mullis首先提出设想，1985年由其发明了聚合酶链反应，即简易DNA扩增法，意味着PCR技术的真正诞生。到如今2022年，PCR已发展到第三代技术。1976年，中国科学家钱嘉韵，发现了稳定的Taq DNA聚合酶，为PCR技术发展也做出了基础性贡献。 PCR是利用DNA在体外摄氏95°高温时变性会变成单链，低温（经常是60°C左右）时引物与单链按碱基互补配对的原则结合，再调温度至DNA聚合酶最适反应温度（72°C左右），DNA聚合酶沿着磷酸到五碳糖(5’-3’)的方向合成互补链。基于聚合酶制造的PCR仪实际就是一个温控设备，能在变性温度，复性温度，延伸温度之间很好地进行控制。现已有实时荧光定量PCR （Quantitative Real-time PCR），数字PCR（Digital PCR）等多种PCR检测技术

酶联免疫吸附试验（ELISA）

酶联免疫吸附测定（enzyme linked immunosorbent assay，简写ELISA或ELASA）指将可溶性的抗原或抗体结合到聚苯乙烯等固相载体上，利用抗原抗体特异性结合进行免疫反应的定性和定量检测方法。酶联免疫吸附测定（ELISA）为免疫学中的经典实验。

Westernblot法

Westernblot法应用分子生物学、生物化学和免疫遗传学中时常会用到的一种实验方法，并且是一种能对蛋白进行定性和半定量的分析方法。是通过特异性抗体对凝胶电泳处理过的细胞或生物组织样品进行着色，并且通过分析着色的位置和着色深度获得特定蛋白质在所分析的细胞或组织中的表达情况的信息。

综上所述，基于不同课题的研究方向，选择不同的试验进行结果论证，每一次实验都要预先设计好阴性和阳性对照样本，每组实验要多次重复，减少误差。实验结果出来以后进行数据分析与整理、运用绘图软件进行图片的制作。最后完成论文的撰写工作，整理好ppt，进行最终丘成桐生物学奖的答辩、汇报。

2021年生物金奖

1. 学生背景简述

Bob Guan 管泊宁是2021年丘成桐生物金奖得主，来自于温彻斯特公学（Winchester College），是英国第一所培养神职和公职人员的学校，开创了英国公学教育的历史。而今天的温切斯特公学虽然已经演变成为一所贵族寄宿制学校，但依然保持了自己悠久的传统与文化。

导师是Edmund Donovan，同样来自英国温彻斯特公学。致谢中还感谢了两位导师Mr. Jiusi Yang, and Dr. Zhuqing He，文中也感谢了自己她的父亲陪自己伴去广西。

2. 论文概述

Title: A molecular phylogeny of cavernicolous Oniscidea (Isopoda) in Southern China reveals multiple origins of troglodytic behavior and a new species of blind Armadillidae (Oniscidea, Isopoda)

Abstract: Despite the high diversity of Oniscidea in the Guangxi province, with many rock-face dwelling and fully troglobitic species, we still lack a comprehensive phylogeny for them. We infer these relationships in this paper by utilizing the genetic markers COI and 16S and build a topology using the Maximum Likelihood and Bayesian Inference methods. By comparing the phylogeny of Guangxi Oniscidea with that of other related taxa, we found troglobitic behavior to have arisen multiple times through convergent evolution, and the genera Spherillo and Burmoniscus to be in need of revision. Additionally, we discovered a new eyeless and pigmentlacking species by using morphology and molecular biology in conjunction.

题目：中国南方海绵体虫科（等足纲）的分子系统发育揭示了穴居行为的多个起源和潮虫的一个新种

摘要
尽管广西省的潮虫具有高度的多样性，多为岩石面居、全穴居物种，但我们仍然缺乏对它们的全面系统发育。 本文利用遗传标记COI和16S推断出这些关系，并利用极大似然和贝叶斯推理方法构建拓扑。 通过与其他相关类群的系统发育进行比较，我们发现，同源类群经过多次趋同进化而出现，球形属和Burmoniscus属有待修订。 此外，我们利用形态学和分子生物学相结合的方法，发现了一个新的无眼和无色素的物种。  
本文具体研究方向为动物学的研究，采用形态学和COI和16S基因的分子学鉴定，通过MEGA和贝叶斯构建系统发育进化树，从而发现了一个新的潮虫。

3.获奖亮点分析

1. 选题：动物的新种类物种的发现是最大的亮点。潮虫是一种节肢动物。鼠妇是一种节肢动物又名鼠负、负蟠、鼠姑、鼠黏、地虱等，全世界有150种以上，多为广布的世界性种。它们身体大多呈长卵形，从海边一直到海拔5000米左右的高地都有它们的分布。中国常见种有鼠妇、光滑鼠妇等。关于鼠妇的记载最早可见于《本草纲目》虫部2014年，共发现潮虫科37科527属3710种，有文献指出总数估计在5000到7000之间。题材的选择为常见的动物，2016年以来的丘奖比赛中涉及的动物研究有：蚂蚁、蚊子、蝴蝶等。未来会有更多的动物，以及媒介生物研究的方向，比如：蜱，蝇，蟑螂，臭虫，另外还有蠓，虻，白蛉等物种。

   本论文从样本的采集，形态学的鉴定，通过手工绘画出样本的解剖图并进行标注，提高了学生的能动性，培养了对动物的研究兴趣。如图22 是Bob Guan 管泊宁绘制的潮虫背面标记图。图22 是Bob Guan 管泊宁绘制的潮虫的头部图和腹部标记图。

   

   

2. 论文：整篇论文逻辑清晰，英文书写流畅，以及应用到很多专业级拉丁文词汇。作者对物种背景知识的了解丰富。实验理论和实践能力突出，对于高中生而言是具有挑战性和成就性的。实验中涉及到基因组DNA的提取，所涉及到的操作可以在相关学习网站或者对应试剂盒厂家的官网上查找到操作步骤的视频，进行学习。

   对于识别物种的基因序列，以及PCR循环的原理和条件，均可以在文献或者网络中找到。同时也依赖于指导老师的背景以及对于物种的研究，实验设备等。还与学生对于未知领域的探索欲望，学习知识的踏实态度，以及永不放弃的精神密不可分。对于物种鉴定上，高中生需要掌握物种鉴定的基因，一般选取在三个以上的平行基因进行结果的论证，使证据更加充分、可信。

   该同学还掌握物种的分子进化知识和一些计算机对于分子研究的程序应用。比如提取总基因DNA，使用AxyPrep Genomic DNA Miniprep Kit (AXYGEN)试剂盒。分别用以下引物对扩增COI、16S、18S、28S rDNA: COBU (5’-GGT CAA CAA ATC ATA AAG ATA TTG G-3’) and COBL (3’-TAA ACT TCAGGG TG ACC AAA AAA TCA-5’), 16S-AR (5’-GCC GCA GTA THC TRA CTG TGC T-3’)and 16S-BR (3’-CCG GTC TGA ACT CAG ATC ACG T-5’)。列举出PCR循环条件。对于物种鉴定上，高中生需要掌握物种鉴定的基因，一般选取在三个以上的平行基因进行结果的论证，使证据更加充分、可信。

   在COI上，16S, 18S,28S和NAK等基因层面的分，运用MEGA软件析上，序列显示了它和它最多样化的属，分子间差异性很大。碱基对上ATGC中的波函数首次被用于人工校正和调整核苷酸缩短链。每个序列的这些修正链然后与默认对齐参数的MEGA7手动切割成通过移除所有缺失数据的部分来达到相同的长度。序列是分别以整理FASTA序列格式保存，并存入PhyloSuite软件的应用和PS等绘图软件的使用。实验原理和操作的讲解可以在b站或者公众号上自行学习，或者浏览百度学术、谷歌学术、SCI-HUB等学术网站都有相应的背景知识可以学习。

   在PhyloSuite，流程图功能使用的参数如下:序列比对与MAFFT和MACSE，用IQ-TREE重建树和MrBayes。IQ-TREE进行极大似然分析。在MrBayes中进行贝叶斯推理分析。本文采用两种模型进行双边分析，允许最终结果相互比较，以检查不准确性。分析手法上也要严谨、多方位分析，多软件联合分析使用，比如MEGA、PhyloSuite等。如图24和图25。

   

   

   对于动物新种的鉴定，不仅要在基因层面上比如COI、16S、18S、28S rDNA分类水平的鉴定，更需要电子显微镜电镜照片从形态学区分新的物种，。电子显微镜的分辨率较高，主要是通过扫描电镜观察分析比如体表表面结构（如眼睛、翅膀及体表微结构）及细菌病毒等微生物形态结构、大小等研究。比如图26和27。

   

   

此次在广西发现新物种潮虫，也可能存在球形虫属和 Burmoniscus 属多品种，需要再验证。一个新物种，球形球虫，发现它的主要特点也是缺乏眼睛和色素沉着，和背腹扁平特点。新物种的发现不仅需要形态学的鉴定，直观上了解和认识物种。更要从基因的层面去了解物种。

希望参赛生物课题的学生能尽可能多的了解所研究课题的背景知识，多在网站上搜索新物种是如何鉴定的？媒介生物是如何传播疾病的？疾病的传播链条有哪些？为什么有的病毒在动物身上不发病，传染到人身上会感染发病？希望同学们能通过丘成桐中学科学奖在心里埋下一颗对于大自然探索的种子。在未来可以从事到生物研究，疾病溯源，疫苗的研制等有利于人类的科研当中来!

2023–2025 年（第十六至第十八届）获奖趋势与代表性论文

2023–2025 年计算机学科获奖论文几乎被"基础模型 / 多模态学习 / 智能系统应用"三条主线主导：2023 年金奖《Word in Word: A Novel Word Embedding Method》在词嵌入层面引入上下文与形态结构；2024 年金奖《LLM Mathematical Reasoning Grounded with Formal Verification》（华润小径湾贝赛思）将形式化验证与大语言模型数学推理结合，是当下"LLM + formal methods"研究最前沿方向之一；2025 年金奖《Beyond Reactive Assistance: PV-Care Using Low-Density EEG and AI to Provide Proactive, Context-Aware Help for MCI》将低密度脑电与 AI 用于轻度认知障碍患者的主动情境感知辅助。三年的论文整体呈现出一个清晰的"由判别式深度学习 → 生成式与具身智能"的演进趋势，与产业界的发展方向高度一致。

代表性获奖论文深度解读

2023 银奖 ·《AI-based Glaucoma Diagnoses Based on Phone-taken Colored Fundus Retinal Images》

学生 / 学校： 谢昕然，中国人民大学附属中学
指导老师： 徐恪、施一宁

研究的是什么问题？ 青光眼（glaucoma）是世界上第二大致盲性眼病，特点是视神经悄悄萎缩、视野慢慢缺损，等患者察觉症状时往往已经不可逆。早期筛查的关键是查"眼底"（视网膜），但传统眼底相机价格高昂、操作复杂，基层和发展中地区根本配不起。本论文要解决的就是：能不能用一部普通智能手机拍到的眼底彩色照片，让 AI 直接做出青光眼初筛？这种"低成本 AI 筛查"在公共卫生上的意义巨大。

用了什么方法？ 从题目和这类研究的典型范式推测：（1）数据采集——使用手机加一个简易的便携眼底镜（如 D-Eye 或同类硬件）对志愿者拍照，并配对收集真实诊断的"金标准"标签；（2）数据预处理——手机拍摄的图像质量远不如专业眼底相机，需要做光照归一化、模糊检测、视盘对中等预处理；（3）模型训练——通常用 ResNet、EfficientNet 或 Vision Transformer 这类成熟的图像分类网络，配合迁移学习（先在 ImageNet 上预训练，再在眼底数据上微调）；（4）模型解释性——通过 Grad-CAM 等可视化方法看模型究竟在看视盘（cup-to-disc ratio）还是看其他特征，确保它学到的是医学合理的特征而不是"短板"。

为什么评委青睐？ 评委看到的是一个"明确的现实痛点 + 切实可行的技术路径"。AI 眼底筛查在专业相机上已经做得很好（Google 与印度合作的 ARDA 项目就是典型），但要把这套技术下沉到手机端，挑战巨大——图像质量低、光照不可控、对焦不稳，这恰恰是技术与社会公益结合得最漂亮的应用。学生敢碰真实世界的"脏数据"问题，并交出可用的解决方案，比单纯"刷榜公开数据集"更受评委推崇。

对参赛者的启发： AI for healthcare 是高中生最适合切入的计算机方向之一——医学影像数据有大量公开数据集（如 EyePACS、MESSIDOR、ISIC），常见疾病的分类问题可以在普通 GPU 上训练，论文写作的标准也相对清晰（敏感性、特异性、AUC、混淆矩阵）。如果你能在此基础上加入"低成本部署"（手机端、可穿戴端、嵌入式端）这一维度，就能立刻把一个普通深度学习论文升级为有社会意义的工程项目。

2024 金奖 ·《LLM Mathematical Reasoning Grounded with Formal Verification》

学生 / 学校： 何坤朗（ALLEN HE），华润小径湾贝赛思国际学校
指导老师： 严骏驰（JunChi Yan）、Cody Kennedy

研究的是什么问题？ 大语言模型（LLM, 如 GPT、Claude）能写诗、写代码，但在做数学题时经常"信口开河"——推理一半时悄悄编一个错误的中间步骤，把答案推向错误。这种"幻觉"在数学场景中尤其致命，因为数学要求绝对的逻辑严密。本论文要解决的就是：能否给 LLM 配一个"形式化验证器"（formal verifier），让 LLM 提出推理步骤，验证器实时检查每一步是否符合形式逻辑——只有通过验证的步骤才被保留，没通过的则被丢弃或重新生成？这等于给"会瞎掰的天才学生"配了一位严谨的小学数学老师。

用了什么方法？ 从题目可推测的核心架构：（1）LLM 部分——使用 GPT-4 或开源的 Llama 等模型，让它生成数学推理的中间步骤；（2）形式化部分——把推理过程翻译到 Lean、Coq、Isabelle 等定理证明助手能识别的形式化语言（这一翻译过程本身就是研究热点）；（3）反馈循环——形式化系统验证某一步是否正确，把"通过/不通过"的信号反馈给 LLM；（4）评估部分——在 GSM8K、MATH 等标准数学推理数据集上对比"裸 LLM"和"LLM + 形式化验证"的准确率。这一思路与 2024 年 Google DeepMind 的 AlphaProof 项目高度同构，是当年 LLM + 数学方向最前沿的研究方向之一。

为什么评委青睐？ 这是一个让顶级 AI 研究者都觉得"非常时髦且重要"的方向。形式化方法（formal methods）与 LLM 的结合是 2024 年学术界最热的几个方向之一，能在高中阶段切入这种前沿，本身就说明学生站在了正确的浪潮上。指导老师严骏驰教授是上海交大 AI 领域的杰出年轻学者，论文的学术起点接近研究生水平。同时，"让 AI 不再瞎掰"是一个所有人都能理解的、有重大社会意义的目标，评委读完会觉得这是真正"有意义"的工作。

对参赛者的启发： 计算机方向想冲金奖，"踩中下一波技术热点"是关键。2024 年的热点是 LLM + 形式化推理，2025–2026 年的热点很可能是 LLM + 具身智能（机器人）、LLM + 多模态（视频生成、3D）、LLM + 科学发现。建议同学们至少订阅 1–2 个顶级 AI 实验室的博客或推特（OpenAI、DeepMind、Anthropic、上海 AI Lab 等），跟踪前沿方向的演进，再选择一个力所能及的小切入点做出自己的研究。

2025 金奖 ·《Beyond Reactive Assistance: PV-Care Using Low-Density EEG and AI to Provide Proactive, Context-Aware Help for MCI》

学生 / 学校： Simon Leonardo Liu，上海中学国际部
指导老师： 姚艳婕（Yanjie Yao）、陈智能（Zhineng Chen）

研究的是什么问题？ MCI（Mild Cognitive Impairment，轻度认知障碍）是介于"正常老化"和"阿尔茨海默症（AD）"之间的过渡状态，全球患者数以千万计。现有的辅助系统大多是"反应式"的——用户主动求助，系统才响应（比如喊"小爱同学，今天星期几"）。但 MCI 患者很多时候自己都意识不到需要帮助，等想起来求助时为时已晚。本论文设计了 PV-Care 系统，用"低密度脑电"（low-density EEG，只用 4–8 个电极的简易脑电帽）实时捕捉用户的认知状态，并由 AI 推断当前情境（context-aware），在用户出现混乱、走神、迷路等迹象之前就"主动"提供帮助。

用了什么方法？ 这是一个典型的"硬件 + 算法 + 应用场景"全栈系统。（1）硬件层——使用 OpenBCI、Muse 或同类消费级低密度 EEG 设备采集前额叶等关键区域的脑电；（2）信号处理层——对脑电做带通滤波、伪迹去除（眨眼、肌电干扰），提取功率谱特征（alpha、beta、theta 频段）；（3）模型层——训练分类器（CNN、Transformer 或 EEGNet）识别认知负荷、注意力下降、记忆混乱等状态；（4）应用层——结合用户当前情境（位置、时间、日程）做主动提示。整体设计非常贴近真实老年人居家场景的需求。

为什么评委青睐？ 这篇论文同时打到了三个评委敏感点：（1）"AI for aging" 是 2025 年全球公认的重大社会问题，中国老龄化进程使这一方向格外有意义；（2）"低密度 EEG + AI"是一个工程上可落地的方向——传统的医疗级 EEG 需要 32–128 个电极，根本无法在家用，本论文把它压缩到几个电极也能用，工程难度极高；（3）"从被动到主动"的设计理念有方法论上的创新，不是又一个普通的健康监测应用。

对参赛者的启发： 计算机系统类项目要拿大奖，关键是要"全栈"——硬件、算法、应用、人因（user study）都要交付出像样的结果。不要只做一个 demo 算法，要做一个"看上去能立刻给奶奶用"的完整系统。同时，老龄化、残障辅助、教育公平、心理健康是 2025–2030 年最有社会回声的几个方向，AI 与这些领域结合往往能拿到比"刷榜论文"更高的奖项。

（以上论文获奖信息均来自 yau-awards.com 官方公示页面，详见 ⁵）

奖项数量统计：2023 年共评出 金 1、银 1、铜 3、优胜 5；2024 年共评出 金 1、银 1、铜 3、优胜 5；2025 年共评出 金 1、银 1、铜 3、优胜 5、入围 4。

Python编程学习

首先，参与计算机类的课题，较为出色的编程能力属于该学生所需要具备的最基础的条件。学生根据自身经历的不同，可能会掌握Python，C，Java 等不同的语言，但对于丘成桐奖有关的课题，Python 由于其在机器学习方向广阔的应用以及简明的语法和大量的函数支持，应当成为编程语言学习的首选。

这里推荐使用Anaconda部署本地的Python环境，或者使用Kaggle，Colab这类的在线平台。本地和在线的运行各有优劣，需要学生灵活进行选择。在充分掌握Python的语法，基本数据结构等内容之后，学生还应了解并熟悉以下几类库的使用。

1. 数据分析类：NumPy、Pandas和SciPy （多维数据的处理运算、算法和相关数学工具）、MatplotLib和Seaborn（数据可视化，作图）

2. 机器学习类：Scikit-Learn （基础的机器学习工具包，包含大量成熟算法）、Pytorch和Tensorflow（深度学习的运算框架，大部分深度学习问题都可以利用其框架进行探究）、OpenCV和NLTK（对于计算机视觉问题和自然语言处理问题的常用库）

在这里必须要强调说明的是，学生不可能一次性完全了解这么多工具是如何进行使用的。但是，学生需要非常明确和熟悉相关代码可以实现哪些功能，以及在遇到问题时如何去搜索解决方法。对于 Python 语言和相关库的使用，其实本质上和语言学习类似，都是一个不断积累的过程。

微积分、统计、线性代数

其次，学生如果想明白机器学习的理论基础的话，应当具备足够的微积分、统计以及线性代数的知识。比如说，学生如果没有学过微积分的话，是很难明白梯度和回归相关问题的深层含义；学生如果没有学过统计学的话，对于机器学习模型验证的各种方法可能会一头雾水；学生如果没有学过线性代数的话，对于卷积神经网络的分层计算会丧失概念。

机器学习的核心其实还是数学问题，我们希望参加计算机比赛的学生有着良好的数学背景以及较强的学习能力，这样才能够很快的去掌握并理解新的概念与理论，这一点在计算机学科的比赛中非常重要。在这里，学生并不需要去理解或者掌握数学科目中较难题目的解法，这是和传统数学教学不太一样的。但是，学生需要充分明白一些数学概念在应用时背后的含义，这对于学生理解各种算法的本质帮助极大。

机器学习入门

最后，在掌握足够的编程和数学基础后，学生应当开始接触机器学习的各种内容。首先，学生应当考虑从算法上开始，这时学生应当开始涉足线性回归、逻辑回归、线性判别分析、朴素贝叶斯、KNN、随机森林等常用的算法，并掌握这些算法的应用场景和优缺点。然后，学生可以开始学习循环神经网络和卷积神经网络等有关知识，并能够理解在这些神经网络中例如反向传播、随机梯度下降、学习衰减率等有关概念。最后，学生可以开始考虑参照教程，来使用已有的深度学习库，对于一些实际问题进行探究。

在拥有以上的经历和基础后，学生将会很容易地加入到具体的科研课题中来。但是需要注意的是，上述的背景其实是具有传统意义上大学课程的难度，所以对于学生的学习能力和时间精力要求极强。如果不具备相关背景知识的话，学生也可以来参与有关的科研项目，但是其理解程度和体验将会大打折扣。

2021年全球计算机金奖/科学金奖

1.学生背景简述

Claire Wang和Yihao Huang为2021年丘成桐中学生科学奖计算机金奖以及科学金奖得主。两位学生均来自Phillips Academy Andover，全美最为顶尖的私立寄宿高中。除此之外，两位学生的项目来源于麻省理工学院颇具盛名的高中生科研项目，Program for Research in Mathematics, Engineering and Science for High School Students (简称PRIMES)，以及导师为Jessica Shi, MIT的2018年入学的计算机博士在读学生，同时论文致谢Julian Shun，MIT的在职教授以及Jessica的导师。

从背景来看，2021年计算机金奖和科学金奖的学生履历完美，无可挑剔。然而，这些优秀的背景并不能确保这两位高中生在高手如云的丘奖比赛中脱颖而出。究竟是什么原因使得这两位同学能够得到包括丘成桐在内的众多评委的青睐，我们下面将会具体解释。

2.论文概述

首先，我们来看论文大致讲了什么。这里我们看一下原文的题目以及摘要，然后我们看一下对应的翻译。

Title: Efficient Algorithm for Parallel Bi-core Decomposition

Abstract: Many real-world statistics and problems can be modeled by graphs, such as user-product networks, social networks, and biological networks. Identifying dense regions within these graphs is useful for product-recommendation, spam identification, and protein-function discovery. k-core decomposition is a fundamental graph theory problem that discovers dense substructures of a graph. However, k-core decomposition does not directly apply to bipartite graphs, which are graphs that model the connections between two disjoint sets of entities. Bipartite graphs are widely used to model authorship, affiliations, and gene-disease associations, to name a few. In this paper, we solve the analog of the k-core decomposition problem, which is the bi-core decomposition problem. Existing sequential bicore decomposition algorithms are not scalable to large-scale bipartite graphs with hundreds of millions of edges. Therefore, in this paper, we develop a theoretically efficient parallel bi-core decomposition algorithm. Compared to existing parallel algorithms, our algorithm reduces the length of the longest dependency path of the computational graph which measures the asymptotic bound of a parallel algorithm given sufficiently many threads. We provide an optimized parallel implementation that is scalable and fast. Using 30 threads, our parallel algorithm achieves up to 34.8x self-relative speedup. Our code achieves up to 4.1x speedup compared with the best existing parallel algorithm.

题目：并行双核分解的高效算法

摘要： 许多现实世界的统计和问题都可以用图来建模，如用户-产品网络、社交网络和生物网络。识别这些图中的密集区域对于产品推荐、垃圾邮件识别和蛋白质功能的发现是非常有用的。k-core分解是一个基本的图论问题，可以发现图的密集子结构。然而，k-core分解并不直接适用于双联图，双联图是模拟两个不相交的实体集合之间的联系的图。双联图被广泛用于模拟作者身份、隶属关系和基因-疾病关联，仅举几例。在本文中，我们解决了k-core分解问题的类似物，也就是双核分解问题。现有的顺序双核分解算法不能扩展到有数亿条边的大规模双子图。因此，在本文中，我们开发了一种理论上高效的并行双核分解算法。与现有的并行算法相比，我们的算法减少了计算图的最长依赖路径的长度，该路径衡量了给定足够多线程的并行算法的渐进约束。我们提供了一个优化的并行实现，它是可扩展和快速的。使用30个线程，我们的并行算法实现了高达34.8倍的自我相对加速。与现有的最佳并行算法相比，我们的代码实现了4.1倍的速度提升。

本文的具体研究方向为大规模双联图数据结构的高效并行计算，再通俗一点就是如何设计一个更快的算法，去对复杂的大规模数据进行分解。整篇文章的核心，包括Julian Shun的研究方向，都是在于并行计算上，这与大家所能明白的多线程工作比较相似。从传统来讲，计算机的处理方式是接收很多条命令，然后执行完一条后，紧接着执行下一条。然而，现代的计算机大多配备多核多线程的并行处理方式，这样能够极大程度的提升计算机运行速度，减少运算时间。同时对于特定问题而言，由于数据结构的关联性与逻辑性，并行运算的实现会极具挑战，于是如何更快的并行处理大规模数据也就成为计算机科学领域一个非常重要的课题。

3. 获奖点分析

• 选题: Claire Wang和Yihao Huang的选题可以看作是Jessica Shi和Julian Shun的科研课题的拓展。相比其他更易于高中生接受的深度学习建模及训练有关的命题，该题目明显更注重于计算机基础理论上的研究，这里基础理论包括并行算法和图网络这两个在当前计算机领域非常重要的课题。在计算机有关的科研中，能够提出理论算法上的创新和突破是非常难得的，这要比如何用编程代码去解决实际问题要困难的多。丘成桐的计算机评委在过往的比赛中也更为青睐从理论角度出发的科研论文，因为这些论文往往能够给人带来眼前一亮的感觉。但是，要去实现在计算机理论上的突破是极其困难的，这里与学生的学习能力精力，导师的背景等关系极为密切。同时过往也有优秀的理论方向论文使得评委产生真实性怀疑的案例。所以，我们希望能够学生可以用计算机理论有关的科研项目去进行丘成桐奖的评比，但是一定要保证对自己研究内容的充分理解和对于相关理论的清晰呈现。

• 论文: 整篇论文结构清晰，完美符合科研论文的写作思路和标准，专业性极强。论文从顺序性(Sequential)双核问题解释出发，一步步解释清自己的并行(Parallel)双核分解问题算法及相关优化，并最终在大量双联图结构数据中进行测试，得出相比于现有并行算法有着4.1倍速度提升的重要结论 。

  Contents
  1 Introduction
  2 Related Work
  3 Preliminaries
  4 Sequential Bi-core Decomposition
      4.1 Sequential Peeling
      4.2 Computation Sharing
      4.3 Analysis and Implementation Details
  5 Parallel bi-core Decomposition Algorithm
      5.1 Parallel Bucketing and Exponential Search
      5.2 Parallel Aggregated-Peeling
      5.3 Parallel Bi-core Decomposition
      5.4 Peeling Space Pruning Optimization
      5.5 Implementation and Other Optimizations
  6 Experiments
  7 Conclusion
  References

  这里，作者无论从理论基础，还是算法讲解，以及代码实现，都有着客观，细致且清晰的书写。能同时满足这些学术写作要求，对于高中生而言，是非常难能可贵的。同时，全文贯穿着大量清晰的图表，这些图表可以独立的去说明讲解很多有关的问题，这会极大程度的优化评委的阅读体验（参照 [section:reading] 学术论文阅读方法）。

  下面，我们从该文章中比较重要的几个细节方面来解释说明计算机论文中独具特色而且比较重要的地方。首先，该论文中使用了大量的伪代码来梳理核心编程逻辑。对于计算机领域的评委及专家而言，其大部分可能都会同意Linus Torvalds（Linux系统之父）的名言， “废话少说，放码过来。”（“Talk is cheap. Show me the code.”）尽管丘奖的评委可能不太乐意去研究参赛项目的源代码，但他们一定会希望能从伪代码的描述中来理解文章中编程有关的底层逻辑。同时，将复杂的程序凝练成简单易懂的伪代码也可以充分体现学生对于该项目的理解以及编程水平, 详见图31。

  

  除去伪代码部分，另一个文章的重要细节在于对整体算法部分的解释。文章中使用了清晰直观的方式，来讲解程序算法中每一步能够实现什么内容。同时，文章也花很多篇幅来对算法部分进行详细说明，确保读者能够明白这篇论文的精髓，详见图32。

  

  最后，我们可以来看一下论文中对于结果的展示。如何最清楚的将代码的结果进行清晰的呈现是每一篇论文都需要重点考虑的部分，在Claire和Yihao的文章中，两位作者用柱状图的形式将其创新优化后的算法与传统的算法进行了展示。从图中，我们可以很清晰的看到，优化后的算法对于运算时间有着巨大的提升（柱状图中黄颜色代表作者的算法，越短代表着所需运算越少也越优异），详见图33。

  

• 演讲: 由于整个丘成桐比赛的决赛现场并没有公开，我们在这一部分只能依靠现有的信息进行猜测。首先，由于丘成桐奖总决赛是全英文答辩，两位选手的顶级美高背景（有兴趣可以搜索Phillips Academy Andover的录取条件，该高中国内学生录取率低于哈佛耶鲁的录取率）能够确保其在语言上的巨大优势。其次，尽管总决赛的演示稿没有放出，我们还是能从麻省理工的网站上搜索到PRIMES相关课题的演示稿。两位选手的演示稿非常专业美观，几乎是我们搜集到的演示稿中最为优秀的。 图34, 图35为演示文稿中的两页节选，仅供参考。

  

  

2023–2025 年（第十六至第十八届）获奖趋势与代表性论文

经济金融建模学科 2023–2025 年的获奖论文围绕"宏观政策评估 / 平台经济 / 双碳与可持续金融 / AI 对劳动市场的冲击"四个主题展开。代表性论文包括：2023 年金奖《An Analysis of the Free-rider Problem Under Different Perspectives Based on Game Theory》（北京十一学校）、2024 年金奖《Importing for Producing: The Net Effect of Carbon Regulation on Emission Reduction》（上海美国学校浦西）、2025 年金奖《Firm-Level Impacts of Artificial Intelligence on Labor Demand: Evidence from Online Job Postings》（上海星河湾双语学校）。可以看出，评委倾向于具有"国家级政策抓手 + 干净的识别策略 + 现实数据"的实证经济学论文；理论与博弈类课题（如双碳与转移支付机制设计）也保持一席之地。

代表性获奖论文深度解读

2023 金奖 ·《An Analysis of the Free-rider Problem Under Different Perspectives Based on Game Theory》

学生 / 学校： 吴蕊杉，北京市十一学校
指导老师： 王潇

研究的是什么问题？ "搭便车问题"（free-rider problem）是经济学的核心概念之一——当一项物品具备"非排他性"和"非竞争性"（即典型的公共品，如国防、环保、疫苗接种）时，每个人都希望别人去出力提供，自己白白享用结果。结果就是大家都搭便车，公共品供给严重不足。本论文从博弈论视角出发，系统分析了不同视角下（个体理性、集体理性、长期重复博弈、信息不对称等）搭便车问题的表现形式与求解机制，并尝试给出现实政策启示。

用了什么方法？ 从博弈论研究的标准范式看，作者很可能涵盖了：（1）单期完全信息静态博弈——用经典囚徒困境或公共品博弈（public goods game）证明搭便车是占优策略；（2）无限重复博弈——引入"民间正义"（Folk Theorem），证明在足够长的时间维度下，合作可以作为纳什均衡持续存在；（3）机制设计视角——介绍 Vickrey–Clarke–Groves 机制等如何通过设计巧妙的支付规则，让说真话和贡献成为占优策略；（4）演化博弈视角——通过群体演化模拟分析"合作者"与"搭便车者"在演化压力下的比例变化。论文标题强调"under different perspectives"（多视角），意味着作者努力综合了上述各种博弈论分析框架。

为什么评委青睐？ 这是一个非常聪明的选题。搭便车问题是经济学经典议题之一，与碳减排、疫苗接种、知识产权、开源软件、社区治理几乎所有热点议题都密切相关。多视角研究展示了作者的理论功底——评委一看就知道作者真正读了博弈论的多本经典教材（如 Gibbons、Fudenberg-Tirole），而不是套用一两个简单模型。"经济金融建模"奖最看重的就是"建模"二字，而博弈论是经济学中最典型的建模工具之一。

对参赛者的启发： 经济金融建模奖里，理论建模类（博弈、机制设计、动态优化）一直比实证类更难，但只要做出来，金奖含金量极高。如果你对数学有兴趣、对社会现象有思考，博弈论是一个完美的切入点。建议同学们先把《博弈论与信息经济学》（张维迎）或 Gibbons 的《博弈论基础》通读一遍，然后挑一个具体现实问题（如疫情下的口罩供给、宿舍清洁责任、共享单车维护）做博弈建模。

2024 金奖 ·《Importing for Producing: The Net Effect of Carbon Regulation on Emission Reduction》

学生 / 学校： 李清璈（Sophia Li），上海美国学校浦西校区
指导老师： 陈仪（Yi Chen）

研究的是什么问题？ 中国实施碳排放交易（碳市场）的目的是让排放成本内化、倒逼企业减排。但是有一个隐患：企业可能会"曲线救国"——把高排放的中间品从国内生产改为从国外进口，把账面排放转移到出口国，自己看上去排放下降了，但全球总排放并没有真减。这种"碳泄漏"（carbon leakage）现象是国际气候谈判的核心难题之一（也是欧盟 CBAM 碳关税的动因）。本论文要回答的就是：在企业层面，中国的碳监管政策是否真的降低了排放？还是大部分减排只是把生产环节"进口"出去了？

用了什么方法？ 从题目"net effect"（净效应）的措辞推断，论文采用的是计量经济学的典型实证方法：（1）数据——使用中国工业企业数据库匹配海关进出口数据，能精确到企业级的中间品进口情况；（2）识别策略——很可能用 DID（双重差分）或合成控制法，把进入碳市场试点的企业与对照企业的排放、进口结构进行对比；（3）排放计算——直接排放（自己生产产生）与间接排放（进口品蕴含）分开统计，看碳监管下"自产→进口"的替代弹性有多大；（4）净效应估算——把"国内减排"减去"进口端排放增加"，得到真正的净减排效应。这套方法是 Yi Chen 教授等国内劳动与环境经济学家的标准研究范式。

为什么评委青睐？ 这是一个典型的"国家政策抓手 + 干净的识别策略 + 大型微观数据"的实证经济学论文。三点尤其突出：（1）选题极具政策意义——碳泄漏是双碳战略落地的关键障碍，回答这个问题对政策制定者有直接价值；（2）数据极为硬核——工业企业数据库 + 海关数据 + 排放数据的匹配本身就是研究生级别的工作量；（3）识别极为干净——使用 DID 等准实验方法控制内生性，结论可信度高。这种"真实证经济学"的论文是丘奖经济金融建模奖最青睐的类型。

对参赛者的启发： 经济金融建模奖的实证类金奖，套路其实可以总结成三句话：（1）选一个真实国家政策（碳市场、扶贫、退耕还林、家电下乡、新冠救助等）；（2）找一个被忽视的"传导机制"或"副作用"（如本论文的进口替代）；（3）用 DID/IV/RD 等准实验方法做出干净的因果识别。如果三个要素都齐备，再配合扎实的写作，几乎就锁定铜奖以上。

2025 铜奖 ·《Pension, Labor Supply and Moral Hazard: Evidence from China’s New Rural Pension Scheme》

学生 / 学校： 刘修齐（Xiuqi Liu）
指导老师： 何雅昕（Yaxin He）

研究的是什么问题？ 中国自 2009 年起推行"新型农村社会养老保险"（新农保），这是世界最大规模的农村养老金计划，覆盖数亿农村人口。但任何转移支付都有一个经济学家担心的"道德风险"问题——如果政府保证老了有钱拿，那么人们是不是就会减少自己工作的意愿（劳动供给下降）？甚至年轻人会减少对父母的赡养（家庭内转移减少）？本论文系统研究新农保对农村居民劳动供给的影响，并讨论其中的道德风险问题。

用了什么方法？ 从题目和这一研究领域的标准范式推测，作者采用了：（1）数据——使用 CHARLS（中国健康与养老追踪调查）或 CFPS（中国家庭追踪调查）等公开微观数据，覆盖大量农村老人个体数据；（2）识别策略——新农保是 2009 年开始分批试点的，作者很可能利用"政策推开时间的差异"做 DID 估计；或者利用 60 岁这一年龄阈值做 RDD（断点回归），比较 60 岁刚过领养老金的人与刚不到 60 岁不能领的人的劳动供给差异；（3）异质性分析——按性别、健康状况、子女数量等分组，看哪些群体的劳动供给最敏感；（4）机制讨论——区分纯收入效应（钱多了不愿工作）和真道德风险（有保障就不努力）。

为什么评委青睐？ 本论文学习了哈佛、芝大、北大顶级经济学家研究中国新农保的标准范式（Cheng–Liu–Zhao 等学者已发表多篇 AEJ 级别论文）。中学生能完整复现这套方法、并在中国数据上做出自己的实证结果，已经是相当过硬的工作。课题虽然不像"碳市场"或"AI 取代劳动力"那么炫，但农村养老金是中国最重要的社会保障议题之一，研究的现实意义不容小觑。

对参赛者的启发： 经济金融建模奖的实证论文不一定要选最热的话题——养老、医疗、教育、扶贫等"老话题"反而有更成熟的研究范式可以学习。建议同学们先选一两篇 American Economic Review 或 Journal of Public Economics 上研究中国某项政策的论文做完整精读，然后用同样的方法、同样的数据，问一个稍微不同的问题。这种"学经典论文写自己论文"的策略对高中生来说最容易出成果。

（以上论文获奖信息均来自 yau-awards.com 官方公示页面，详见 ⁶）

奖项数量统计：2023 年共评出 金 1、银 1、铜 3、优胜 5；2024 年共评出 金 1、银 1、铜 3、优胜 5；2025 年共评出 金 1、银 1、铜 3、优胜 5、入围 5。

学术基本素养

论文结构与规范、论文写作技法、经济学研究范式背景，通过这些来培养基本的问题意识。

研究技能

有针对性地掌握计量模型。因果推断是计量估计的基础，其中需要掌握一些基本常用的实证分析模型（静态面板模型、工具变量法、DID、RDD、PSM等），这些是讲问题转化为学术论文的关键，没有方法论，有很好的问题也没办法解决。

数据处理能力

数据清洗技能（缺失值处理、异常值处理等）、数据搜集（与研究问题相关的数据库使用能力：CSMAR/WRDS/CGSS等，这些数据库均出现在以往丘赛获奖论文中），数据是王道，对于数据的熟悉才能做好进一步的建模分析，没有数据，巧妇难为无米之炊。

统计学基础

其中包括回归模型（回归分析、分样本回归、分位数回归模型）；统计学常用方法（主成分分析、熵权等），这些对于实证设计与建模分析十分重要。

软件学习

Stata（一般情况下，Stata很强大足够解决很多问题)，Matlab（如果涉及空间计量模型，多推荐使用matlab），这些是前述方法的实现工具，需要熟练掌握，也是往年丘赛获奖论文中经常出现的工具。当然，往往掌握一种软件并熟练使用即可。 需要特别强调的是，方法的掌握更多的是在边做边学。由于计量和统计方法非常多，不可能把所有方法都学会，既不可能也没有必要因为并不是用到所有方法。因此，具体的方法和软件操作是在实证过程中学习和使用。

2023–2025 (16th–18th Editions): Award Trends and Representative Papers

From the 2023–2025 grand-final lists, mathematics topics, while keeping their traditional strength in pure mathematics (number theory, combinatorics, algebraic geometry, dynamical systems, etc.), have seen a clear rise in applied and interdisciplinary topics: the 2024 gold prize, Optimizing Dart Throwing Strategies for the Elderly Based on Markov Decision Process, applied Markov decision processes to elderly dart-throwing strategies, while the 2025 gold prize, Quasiconformal Normalization of Random Meromorphic Function (Trinity School), continued the high level of the pure-mathematics direction; the silver and bronze prizes included both classic algebraic directions such as the Temperley–Lieb algebra and the Hurwitz zeta function, and applied problems with a machine-learning background such as SDP relaxation, Markov decision, and neural networks. One can say the traditional pure-mathematics topic is still the surest path to gold, but papers that use modern mathematical tools to solve a concrete applied problem have grown markedly in the silver/bronze range.

An in-depth reading of representative winning papers

2023 Gold · Desargues' Involution at Action

Student / school: YU Hanzhang, Raffles Institution (Singapore)
Advisor: YU Sixia

What problem does it study? This paper studies a core object of classical projective geometry — the "involution." Intuitively, an involution is a transformation that "returns to the start when done twice": for example, mapping each point $x$ on the number line to $-x$, and doing it again returns to $x$. In projective geometry, the most famous involution theorem is the "involution theorem" discovered by the 19th-century French mathematician Desargues: when a line passes through the six edges of a complete quadrangle, its intersection points with those edges pair up to form an involution. The title's "at Action" hints that the author does not simply restate the theorem but applies this involution mechanism to a series of concrete geometric configurations, deriving new identities or simplifying proofs of classical configurations.

What method was used? Judging from the title and the common paths of projective-geometry research, the author most likely used: (1) the cross-ratio and perspective projection of projective geometry; (2) Desargues' involution theorem as a "wrench" to take apart configurations of conics, pencils, and quadrangles; (3) the moving-point method (letting a point slide along a line and studying how the involution changes in step) to find geometric invariants. This route — starting from a classic theorem and honing it into a "Swiss Army knife" applied to many settings — is one of the most favored paradigms in pure-mathematics competition papers.

Why did the judges favor it? Judges value not only a new result but the elegance of the method and the author's true command of classical geometry. Desargues' involution is a 19th-century theorem, but using it flexibly and freshly requires a systematic understanding of Euclidean geometry, projective geometry, and the theory of conics — extremely hard for a high-school student. The terminology in the abstract strictly follows the standard conventions of projective geometry, and the overall structure approaches that of a publishable paper — this is itself the "academic maturity" Yau judges highly value.

What entrants can learn: for students aiming at a mathematics gold prize, this paper offers a very clear paradigm — choose a classic geometry or algebra problem as a "mother theorem," master all its variants in depth, then use it to re-examine a set of modern problems or generalize the original configuration. You need not pursue a grand goal like "proving Goldbach"; using an old theorem "both deeply and broadly" can equally win gold.

2024 Bronze · Mathematical Modeling of Long-Wave for Interfacial Waves in Two-Layer Fluids Based on the Dirichlet-Neumann Operator

Student / school: RunBo Li, the Experimental High School Attached to Beijing Normal University
Advisor: Wang Cui, ZhenYu Guo

What problem does it study? Imagine a transparent glass container holding salt water (denser) below and fresh water (less dense) above; the boundary between the two layers is an invisible "interface." When you shake the container, this interface rises and falls, forming an "interfacial wave." The ocean is full of such waves — interfacial waves between thermoclines can be over a hundred meters high, with major effects on submarine navigation and ocean communication. This paper studies what simplified equation the interfacial wave between two fluid layers satisfies when the wavelength is far greater than the depth (the "long-wave approximation"), and constructs the equation using a tool called the Dirichlet–Neumann operator.

What method was used? From the title, the author's method is clear: (1) write down the full two-layer-fluid Euler equations; (2) introduce the Dirichlet–Neumann operator — an operator that translates "knowing the potential on the interface (Dirichlet condition)" into "knowing the normal velocity on the interface (Neumann condition)," a modern standard tool for analyzing water-wave problems, generalized by Craig–Sulem and others; (3) expand the Dirichlet–Neumann operator at the long-wave scale to obtain simplified equations of the Boussinesq, KdV, or Benjamin–Ono type. This approach is fully in line with the rigorous water-wave-equation research that the famous mathematician Walter Craig has driven since the 1990s.

Why did the judges favor it? For a second-year high-school student to command graduate-level tools such as partial differential equations, spectral analysis, and operator expansion is itself extremely rare. The judges also saw that the paper does not "force an application" but stands at the modern frontier of the Craig–Sulem method, giving a mathematical modeling framework for a real ocean-internal-wave problem. Even with only a bronze prize, the paper's technical content already approaches that of an undergraduate honors thesis.

What entrants can learn: applied mathematics is not a "second-class citizen." As long as you are willing to spend the time truly translating an engineering or physics problem (ocean internal waves, climate fluids, biomedicine) into rigorous mathematical language and then attacking it with modern analytical tools (operators, spectra, variational principles), your paper can be fully competitive. The key is not to stop at "I ran it in MATLAB" but to reach "I derived why this equation takes this form."

2025 Silver · Standard modules of the Temperley-Lieb algebra at zero

Student / school: Eddy Li, The Nueva School (California, USA)
Advisor: Kenta Suzuki

What problem does it study? The Temperley–Lieb algebra (TL algebra) is an important class of algebras that originated in statistical physics (the Potts model) in the 1970s and later played a central role in low-dimensional topology, knot theory (the Jones polynomial), and the representation theory of quantum groups. Its generators $e_1, e_2, \ldots, e_{n-1}$ satisfy specific relations $e_i e_{i\pm 1} e_i = e_i$ and $e_i^2 = \delta e_i$, where the parameter $\delta$ determines the algebra's properties. The paper studies the "standard modules" when this parameter $\delta = 0$ — a special but extremely important limiting case, corresponding to critical points in statistical physics and special parameters in topological field theory.

What method was used? From the title and the common paths of this field, the author most likely used: (1) explicitly constructing the "cell modules" or "standard modules" of the TL algebra at $\delta=0$; (2) analyzing the structure of these modules — whether irreducible, whether they have a composition series, what the Jordan–Hölder factors are; (3) comparing with the known results at $\delta \neq 0$ to reveal the special algebraic phenomena at the "degeneration point" $\delta=0$. This route belongs to the core research paradigm of modern representation theory.

Why did the judges favor it? At $\delta=0$, the TL algebra is known to exhibit a series of "bad behaviors" (non-semisimple, modules reducible but not completely reducible) — exactly the kind of "singularity" mathematicians care most about. For a high-school student to dare touch such an "algebraic singularity" and write a rigorous paper specifically classifying standard modules is very rare. The paper was supervised by an MIT graduate student (Kenta Suzuki, in combinatorial representation theory), which guarantees the rigor of the technical details.

What entrants can learn: if you are interested in pure algebra, you need not start by "proving a Fields-Medal-level conjecture." Many important algebras (the TL algebra, the Hecke algebra, the Brauer algebra) still have not-fully-classified modules at "special parameters" — exactly the kind of good problems for the transition from college to graduate study. Finding such a "concrete yet deep" problem often lets you write a structurally complete, technically solid winning paper.

(The award information for the papers above all comes from the official posting pages on yau-awards.com; see ¹.)

Prize counts: 2023 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2024 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2025 awarded 1 Gold, 1 Silver, 4 Bronze, 5 Merit, 5 Finalist.

Mathematics Course Foundations

The Yau Mathematics competition spans many branches — logic, number theory, algebra, geometry, algebraic geometry, mathematical analysis, topology, and so on. Students need a certain knowledge foundation, including:

Statistics: basic methods of data analysis — frequency, histograms, correlation coefficients, least-squares regression, sampling surveys, the normal distribution, hypothesis testing.

Calculus: elementary functions (power, exponential, logarithmic, trigonometric), limits, derivatives.

Usually the content of a competition topic is mostly advanced-mathematics knowledge. Before beginning research, a student may have almost zero of the foundation needed for the topic, so without guidance the student will not know where to start. Note that the courses above usually have no direct connection to the research topic, but whether the topic is pure mathematics, applied mathematics, or statistics, mastering the above is a great help in quickly getting research underway and understanding the related theory.

Programming Languages

For the Yau Mathematics competition, computation is an important part, mainly for the experimental verification of methods, especially for applied-mathematics topics. We therefore advise students to have some programming ability. A student should master any one of C/C++, Python, MATLAB, or Java, choosing freely according to interest and foundation. On a firm grasp of the language's basic syntax, variable types, and data structures, the student should master how to call basic library functions. Finally, the student must master how to implement algorithms (computational methods) in code. Note that the Yau competition emphasizes a work's originality. This means the student must, through programming at least one algorithm, master the basic process and methods of algorithm implementation, and then, after deriving the topic's theoretical method, implement the algorithm used in the topic by programming. Programming requires accumulated experience; for a high-school student, one must at least master the basics of algorithm-simulation programming and then slowly explore and practice in the course of the research.

This requires the student to learn to debug code. Debugging is the process of testing code and finding errors. The algorithm implementation in a research topic is a complex undertaking; one must continually debug while programming, completing the whole project step by step.

Paper Writing and Standardized Expression

Writing plays a vital role in presenting a competition entry. For the Yau Mathematics competition, we must not only give correct methods and results for the topic but also present our findings well. Looking across recent Yau Mathematics entries, excellent papers are usually written to the standard of a journal paper. Writing up research requires good organizational structure, and high-school students have usually never written this kind of article. So one must read a great deal of relevant literature and learn how to write a competent academic paper — especially in mathematics, which requires rigorous logic and correct expression and has even stricter demands on writing.

Mathematical expression is the key to writing a competition paper. Unlike literary writing, mathematical expression must, on one hand, make your content more professional and standardized, and, on the other, involves many variables, symbols, and formulas. Defining variables and formulas requires following certain conventions, making the paper look more standard and professional. Generally, in mathematical expression you can define any symbol to denote a variable, but you must also follow certain habits in the research context — for example, velocity is usually denoted v, σ denotes the standard deviation, Σ denotes the covariance matrix. You must also understand the ways of expressing different types of variables — scalar variables, vectors, matrices, sets — for example x, x, X are the same letter but, in different fonts and formats, denote a scalar variable, a vector, and a matrix respectively. Finally, mathematical problems involve a great many operations — summation, product, minimum, maximum, root-finding, and so on — corresponding to different operators.

In addition, one must learn to use professional tools to typeset mathematical formulas. Here we recommend using LaTeX to compile the paper.

2021 Mathematics Gold Prize

1. Brief background of the student

Max Liu was the 2021 mathematics gold-prize winner of the S.T. Yau High School Science Award. The student is from Shanghai High School International Division, a top public secondary school in China that in 2003 became Shanghai's only UNESCO Associated School. As the paper contains no information on topic selection, the project's origin is unknown to us. Notably, the advisor was Zuo Huaiqing of Tsinghua University, an associate professor and doctoral supervisor whose main research directions include the singularity theory of algebraic geometry. Zuo Huaiqing also collaborates with Shing-Tung Yau, and the student's research built on a paper jointly published by Zuo and Yau. We may thus surmise that the topic likely came from the advisor's research. From this background, the 2021 mathematics gold-prize student had a solid academic background, was fully able to complete the work under the advisor's guidance, and chose Yau's (Shing-Tung Yau's) geometric conjecture — a topic that fits the competition very well. Of course, what let the student excel was mainly the outstanding work and personal presentation ability. Below, drawing on the student's paper, we analyze why the student achieved such an excellent result among so many fine entries.

2. Overview of the paper

Here we analyze the paper's content. First, the title and abstract. Below we give the original title and abstract and their translation:

Title: On sharp upper estimate of lattice points: Yau geometric conjecture
Abstract: The simple problem of counting the number of lattice points in n-dimensional simplexes, in fact has a much greater significance in singularity theory and number theory. The number of lattice points is equal to the geometric genus of an isolated singularity of a weighted homogeneous polynomial. This paper estimates the number of lattice points in a seven-dimensional simplex, and proves the Yau Geometric Conjecture in seven dimensions, which gives an upper bound to the number. We do so by dividing the simplex to several layers of cross section sixth-dimensional simplexes and sums up the upper bound of lattice points in each layer. This proof provides potential insight to extend the upper bound estimate to the general n-dimensional case.

From the title and abstract, the content is very clear: to prove the Yau geometric conjecture in the seven-dimensional case, with the significance of the work noted. In pure-mathematics research there is much similar conjecture-proving work. Such conjectures are many, and many are unproven or not fully proven. For mathematics research, our aim is to do work of some academic value. For a high-school student, fully proving a conjecture is very hard, because such conjectures are themselves very complex and unproven. So many people's work proves part of a conjecture. For example, the famous Chinese mathematician Chen Jingrun was hailed as the foremost figure on "Goldbach's conjecture," and his published "1+2" was a milestone in the proof of Goldbach's conjecture.

3. Analysis of the winning points

1. Topic: Max Liu's topic extends the work of Shing-Tung Yau, Zuo Huaiqing, and others. From the title and content, the topic is a pure-mathematics theoretical derivation and proof. In mathematics research, originality of method more easily wins the judges' recognition. Proving mathematical theorems and conjectures requires rigorous logic and reasoning; this paper proved the Yau geometric conjecture in the seven-dimensional case. The work is an important supplement to the n-dimensional general case of the Yau geometric conjecture and has high theoretical value. The paper decomposed the whole proof into 7 different cases for discussion and gave a rigorous derivation — very important in pure-mathematics research. In mathematics research, innovation in method and theory is very hard, so in Yau Mathematics Award judging, derivation and innovation in mathematical methods and theory more easily win the judges' favor. From all past works advancing to the semi-final and final, we can see that most outstanding advancing works had a strong theoretical foundation and methodological innovation. Overall the paper ran to 54 pages; excluding the cover, contents, and so on, the derivation in the research alone took up as much as 43 pages, with the relevant theorems and proofs. This is very rare for a high-school student, because theoretical research requires great time and energy to understand the relevant background and the methods of derivation and proof. We therefore hope that, when studying a mathematics topic, entrants can fully learn the relevant basic methods and, combining the relevant knowledge, innovate on method at the difficult points of the topic.

2. Rigorous logic: the main body of this gold-prize paper fully follows the format of an SCI research-paper submission — structurally complete, logically clear, and well organized.

   A mathematics paper hinges on the rigor and clarity of its logic. On this point, the author showed an extremely high professional level in both mathematical expression and the arrangement of content. This, of course, is surely inseparable from the advisor's professional guidance.

   First, pure-theory mathematics research differs from applied research or topics in computer science, physics, biology, and so on, which need figures and tables to make the paper look more professional and rich. A pure-theory mathematics topic is more concise; its content is entirely the proof and derivation of a conjecture or theorem. So the paper contains only 5 parts: Introduction, Some Lemmas, Proof of Main Theorem, Conclusion, and References. The Introduction introduces the Yau geometric conjecture and the relevant background, including the mathematical definitions and basic properties of positive integral points and non-negative integral points, the GLY conjecture, the modified GLY conjecture, and so on. Some Lemmas introduces several lemmas needed later for the proof of the Yau conjecture. Part 3, Proof of Main Theorem, is the paper's main part, introducing in detail the proof and derivation of the Yau geometric conjecture in the seven-dimensional case. Part 4, Conclusion, summarizes the whole. Part 5, References, lists the cited works.

   For the research in the paper, Part 3 uses an overview-then-detail structure to introduce the overall idea of the work, as shown in Figure 2 below:

   

   At the start of Part 3, the author first introduces the idea of the subsequent proof: the seven-dimensional proof is discussed in 7 cases, each delimited by mathematical expression. The subsequent sections 3.1–3.7 then derive and prove each of the 7 cases.

3. Paper writing: among all the winning papers in recent years, this gold-prize paper is a rare long one, mainly because the derivation is relatively complex, covering 7 different cases with a rigorous, careful derivation. The student's advisor is himself an expert in the field with relevant publications. In writing, the author also showed an extremely high professional level, mainly in the following respects:

   (1) Definition of symbols. As noted above, in mathematics research there are conventions for defining variables and symbols. The author fully followed these in defining symbols, including those for positive integral points, non-negative integral points, the set of natural numbers, and primes.

   (2) Mathematical expression. As noted above, in a mathematics paper the expression must be standard, objective, concise, and logical — as can be seen from the introduction to the Yau geometric conjecture. In academic writing, the prose must be objective and scientific — what we call academic expression — whereas an ordinary student writing such a paper inevitably tends toward plain colloquial language.

   

   (3) Typesetting of formulas and symbols. The author used professional editing software to typeset the symbols, variables, and formulas. As noted above, in mathematics even the same character in different fonts denotes different things, so we must be especially careful when writing, studying the literature to learn. The typesetting and definition of formula symbols is a matter of expressive convention, with no dedicated reference. So whether a paper is professional and up to standard can be glimpsed from the writing itself.

   (4) Citation of references. The paper involves a great many theorems and lemmas; the author marked every place needing a citation and provided abundant references, giving the work a solid foundation.

   

2023–2025 (16th–18th Editions): Award Trends and Representative Papers

The 2023–2025 winning physics topics continued the mainstream of "mechanics + fluids + acoustics + experimental apparatus" — for example, the 2024 gold prize Number Recognition by Listening used acoustic features plus machine learning to count the balls in a black box, and the 2025 gold prize "Phase Transition" in a Mechanical System studied spontaneous symmetry breaking and the hysteresis loop in a mechanical system — showing that the judges' preference for mechanics/fluid/acoustics topics from everyday life is very stable. At the same time, the 2024 silver prize The Inseparable "Paper Vice" and the 2025 silver prize Development of a High-Efficiency Objective-Prism Stellar Spectrograph embody the winning paradigm of "self-built apparatus + phenomenon analysis + model construction." Topics needing heavy experimental equipment, such as astrophysics and condensed matter, were still few in 2023–2025, but the 2024 bronze prize Investigating Physical Conditions and Critical Factors across the Center of the Galaxy M82 shows that if a student can obtain professional-grade telescope data and complete the statistical analysis with an advisor's help, the astronomy direction can also win.

An in-depth reading of representative winning papers

2023 Silver · Dynamics and Abnormal Sway Precession of Euler's Magnetic Pendulum

Student / school: Zhou Houxi, the High School Affiliated to Renmin University of China
Advisor: Zhang Yongping, Ma Yuhan

What problem does it study? Imagine a small magnet hung by a string with several fixed strong magnets below; release the small magnet and let it swing — its motion becomes extremely complex, now circling this magnet, now that, seemingly random yet following deterministic physical laws. This is the famous "magnetic pendulum," a classic experimental device of nonlinear dynamics and chaos theory. The Euler magnetic pendulum is one special variant, and researchers are usually interested in its "precession" — the slow rotation of the swing plane about the central axis. This paper focuses on an "abnormal" precession mode: under certain initial conditions, the direction, speed, and even the stability of the precession exhibit counter-intuitive behavior.

What method was used? From the title, the author used a parallel "theory + experiment" approach: theoretically, writing down the Lagrangian with the magnetic-dipole interaction, deriving the pendulum's equations of motion, and doing a small-amplitude linearization to predict the precession frequency; experimentally, recording the pendulum's trajectory by high-speed camera or position sensor and analyzing its phase-space structure (Poincaré sections, Lyapunov exponents, and the like are standard tools here). The "abnormal precession" likely arises from the nonlinearity of the magnetic force plus the non-conservative effects of out-of-plane coupling.

Why did the judges favor it? This is a standard "Yau-flavored" topic — the topic comes from a simple tabletop device, but behind the phenomenon lies deep nonlinear dynamics. The judges were drawn not by the magnetic pendulum itself but by the author's daring to ask "why is the precession abnormal" and by the quantitative analysis offered. This route — starting from a concrete phenomenon and drawing in the intersection of mechanics, electromagnetism, and chaos theory — is exactly the paradigm Yau physics most favors.

What entrants can learn: physics gold and silver prizes rarely go to topics needing big equipment, such as condensed matter or quantum computing; more often they go to experiments "doable on your own desk" but with mathematical depth. A magnetic pendulum, a toothpick, a glass of water — all can become objects of deep study. The key is to: (1) choose a "counter-intuitive" phenomenon; (2) capture high-quality data; (3) explain it quantitatively with mechanics/fluid equations; (4) derive a universal law by varying parameters.

2024 Gold · Number Recognition by Listening — Traditional Acoustic Feature Analysis and Machine Learning Method for Estimating the Number of Balls in a Black Box

Student / school: Zixuan Peng, Xiaoxi Zhou, Jifan Zhang, Nanjing Foreign Language School
Advisor: Dong Zhang

What problem does it study? Given an opaque sealed box holding several balls, shaking it makes the balls collide with each other and the walls, producing sound. From this sound alone, can you count how many balls are inside? It sounds like a magic trick, but behind it is a highly practical inverse problem: inferring a system's physical state from acoustic signals. Industrial "fault diagnosis by sound" (bearing diagnosis, pipe-leak detection) and medical "acoustic imaging" are of the same kind.

What method was used? The paper used a dual "traditional acoustic features + machine learning" method. Traditional acoustic features include: (1) the energy envelope — the more collisions among more balls, the larger the energy integral of the sound; (2) the spectral centroid and bandwidth — the more balls, the wider the distribution of collision frequencies; (3) impact-event density — detecting peaks via a short-time energy threshold and counting impact events per unit time. The machine-learning part then takes these features as input and trains a regression or classification model (likely an SVM, random forest, or shallow neural network) to predict the number of balls. The title's emphasis on "Traditional Acoustic Feature Analysis" shows the author did not simply throw the sound into a black-box network but first did careful physical feature engineering — the key technical highlight that won gold.

Why did the judges favor it? This topic perfectly fits the three elements of Yau physics — "everyday phenomenon + serious physics + modern tools": shaking a box is something almost everyone has done; but accurately recovering the number of balls from the shaking sound requires multiple disciplines — rigid-body collision dynamics, Hertzian contact mechanics, acoustic propagation, signal processing, and machine learning. The paper does not "force physics with machine learning" but first builds physical intuition and then lets machine learning refine the prediction — a restrained, rigorous methodology that judges greatly admire. The three-author team also shows the topic's openness and workload.

What entrants can learn: when you want to use machine learning for a physics topic, avoid the temptation of "end-to-end deep learning" — throwing raw sound into a neural network does produce a result, but lacks physical insight, and judges will feel "this is a computer-science topic, not a physics topic." The right posture is: first do physically meaningful feature engineering (energy, spectrum, phase), then use machine learning for the last-mile fit. This shows both physical depth and command of modern tools.

2025 Gold · "Phase Transition" in a Mechanical System: Rotation-Induced Spontaneous Symmetry Breaking and Hysteresis Loop

Student / school: Tianhao Mu, Haiyi Luo, Chongqing Yucai Secondary School
Advisor: Chengxin Zhang

What problem does it study? "Phase transitions" usually appear in statistical-physics textbooks — water freezing, a magnet losing its magnetization. But this paper studies a purely mechanical system that, above a certain rotation-speed threshold, undergoes "spontaneous symmetry breaking": the originally symmetric equilibrium suddenly tilts to one side, and when you slowly lower the speed and then slowly raise it again, the system's position does not return along the same path but forms a "hysteresis loop," just like a magnet's magnetization curve. This means a seemingly trivial mechanical device exhibits behavior fully isomorphic to phase transitions in statistical physics.

What method was used? From the title, the author used: (1) theoretical modeling — writing the system's total potential-energy function in the rotating frame and analyzing how its minima evolve with rotation speed (the typical theory of pitchfork or saddle-node bifurcations); (2) experimental verification — building a device with precisely controllable rotation speed (likely a weighted rotating arm or centrifugal structure) and recording position versus speed with a position sensor or high-speed camera; (3) hysteresis-loop measurement — slowly increasing and decreasing the speed and recording the difference between the "up" and "down" curves as a criterion for distinguishing second-order from first-order phase transitions.

Why did the judges favor it? The paper's most elegant feature is "translating" high-level concepts of statistical physics (spontaneous symmetry breaking, the order parameter, the hysteresis loop, second-order phase transitions) into a mechanical device a high-school student can build by hand. It told the judges: the author not only understands the mathematical essence of phase transitions but can also recognize in which non-traditional systems they reappear. This "cross-domain analogy" is one of the core abilities of a top physicist. The judges also appreciated the author bringing the spirit of Landau's phenomenological theory into classical mechanics — a very elegant cross-scale demonstration of physics teaching.

What entrants can learn: a gold-prize physics topic often lies not in how expensive the equipment or how big the data, but in whether you can build a bridge between two seemingly unrelated fields. If you understand both classical mechanics and a little about phase transitions, you have a chance to find this kind of "big physics in a small machine." We advise students to read the first few chapters of Landau's Statistical Physics and to use "phase transition" as a thinking framework for re-examining everyday mechanics and fluid phenomena.

(The award information for the papers above all comes from the official posting pages on yau-awards.com; see ².)

Prize counts: 2023 awarded 0 Gold, 2 Silver, 3 Bronze, 5 Merit; 2024 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2025 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit, 5 Finalist.

Theory: Mechanics, Fluid Mechanics, Calculus, and More

On a grasp of basic high-school mechanics, the student must also deepen study in other areas. The mechanics analysis in the Yau Award is basically at the scope and difficulty of third-year-undergraduate classical mechanics. Beyond traditional Newtonian vector mechanics, many topics use the methods of analytical mechanics such as Lagrangian mechanics; this requires a strong background in mathematical calculus and is therefore quite hard for a high-school student. But the methods of analytical mechanics are usually more elegant and professional and more readily win the judges' favor.

Another branch of mechanics is fluid mechanics, which has its own system and knowledge structure; its problem-solving methods require computer simulation involving much numerical computation, such as the common finite-element analysis. So for fluid-mechanics problems there is a great deal of new material to learn. When choosing a topic in this direction, the student must prepare to study thoroughly. The experiments here also place certain demands on equipment; many factors must be considered to ensure the experiment goes smoothly.

Beyond physics knowledge, the Yau physics award also requires much mathematics, most commonly calculus — for example, solving partial differential equations. On one hand this consolidates the student's in-school study (such as AP Calculus); on the other it fully trains thinking and computational ability. So although most of this theoretical content is not traditional high-school exam material, studying it helps the student's progress to higher education across the board.

Experimental Design

For high-school students, experiments are usually a series of required steps completed from an existing lab manual. But in the Yau competition, students must devise their own experiments for the topic studied, which places high demands on students and their advisors. How to design scientific, rigorous experimental steps, how to eliminate various errors and the influence of objective factors, how to ensure the results fully reflect the intended conclusion — these directly determine whether the work is competitive.

Experimental design can basically be understood as the core assessment point of the Yau physics award; whether the student is interested and gifted at it actually reflects whether the student can do future research in physics, engineering, and the like, so for students entering the physics competition this is also an angle from which to plan their lives.

Simulation Software: MATLAB, Mathematica, Python, and More

For current physics research, computer simulation and computation are quite important. For many physics problems, we can find the answer by theoretical simulation, bypassing experiment. We can also cross-validate simulation results against experimental results for a comprehensive discussion. In current physics research, many problems can be solved by simulation and computation in MATLAB and Mathematica and data analysis in Python. So in the Yau Award, many topics study and verify their problems by computer simulation, and the importance of this has gradually risen in recent years' competitions.

MATLAB and Mathematica are both very powerful simulation and computation software; if a high-school student can begin learning them through the Yau competition, it greatly helps both later coursework and the convenience of research. For example, many mathematical problems can be verified and visualized in Mathematica. In addition, Python plays a large role in physics research, and students can learn a great deal of programming while solving physics problems — of great significance to their later development.

2020 Global Physics Gold Prize

1. Brief background of the students

That year's winning group was three students from Nanjing Foreign Language School, all of whom achieved good results in the National High School Physics Olympiad, the British Physics Olympiad, the Physics Bowl, and other competitions, with a solid foundation and good talent in physics. Besides school teachers, their advisors included Professor Wang Sihui of Nanjing University, so the paper had a very high starting point, and both its overall structure and the completion of the experiments showed excellent logic and completeness.

2. Overview of the paper

For the paper, we first look at the title and abstract to get a rough idea of the whole.

The paper specifically studies the physical mechanism of the spontaneous knotting of string — an everyday phenomenon (earphone cords, data cables, water hoses, and so on), yet few people stop to ask why such cords knot the moment one is not careful. The paper mainly studies the effects of vibration and rotation on knotting, considering many factors such as amplitude, frequency, length, and material, to explain spontaneous knotting from several angles. The whole article's theme is one that even a person who has never studied physics can fully understand, yet why this phenomenon arises has had no good explanation.

3. Analysis of the winning points

• Topic: undoubtedly, the topic should be the most important factor in this work's gold prize. First, spontaneous knotting is extremely common in daily life, causing everyone various vexations to a greater or lesser degree. But what exactly causes it might be hard even for a physics professor to explain clearly. So a topic that resonates strongly yet whose mechanism is little known more readily wins the judges' favor. Second, the topic does not involve much advanced physics; from the whole paper, only high-school-level physics is involved, plus basic calculus and statistics. Using basic knowledge to solve a complex real problem is something the Yau physics direction greatly admires. Third, the topic can be tested with little equipment, using no complex apparatus, which makes it more approachable. Finally, the topic can connect with other physics content — the spontaneity of the second law of thermodynamics, materials physics, and so on — giving it profound research significance.

  Problems like the spontaneous knotting of string are very common in real life, which calls on students and advisors to watch for such problems and think deeply about how to solve them with the simplest, most direct methods. Such problems in human society are countless, but most of the time people ignore them or passively accept them; the Yau physics award offered its own view and solution for this phenomenon.

• Paper:

  From the table of contents, we can see the author's research approach. We can see the author studied and experimented on the problem from many angles. Exploring the same problem from multiple dimensions is of great significance for cultivating the logic and dialectic of a student's thinking, and accords with the important place of critical thinking in foreign education; the comprehensiveness of the research object is also an important reason this work won high praise.

  

  Besides the table of contents, let us look at this article's merits from a few angles. First, the theoretical part is clearly written, starting from high-school physics and applying it to a real problem, as shown in Figure 8. We can see the paper needs no advanced physics background, yet the overall derivation is extremely neat and logical and very easy for the reader to understand.

  

  

  In addition, for the experimental part the student chose very common everyday materials, all extremely easy to obtain. Yet with this very simple equipment the student could explore the knotting problem from many angles — a very rare thing.

  

  Finally, this group of students fully summarized the whole experiment, systematically combining theory and experiment to explain the whole problem in detail — embodying the scientific rigor and completeness of physics research, and perfectly fitting the way of acquiring a posteriori knowledge in Kant's Critique of Pure Reason.

2023–2025 (16th–18th Editions): Award Trends and Representative Papers

In 2023–2025, chemistry continued to show the features of "experiment-led, synthesis and electrochemistry both emphasized, closely tied to dual-carbon and biomedical hot spots." The 2023 gold prize CRISPR-enabled signal amplification for visual antigen detection (Shanghai Soong Ching Ling School) used CRISPR signal amplification for visual antigen detection; the 2024 gold prize Improving Intracellular Synthesis Efficiency of GFP Catenane through Directed Evolution used directed evolution to raise the intracellular synthesis efficiency of a GFP catenane; the 2025 gold prize Fabrication of an NTO/Ag/g-C3N4 Self-Supporting Membrane focused on photocatalytic hydrogen production from seawater. These topics share common features: the topics are closely tied to environmental/energy/biomedical hot spots, the methods are mainly experimental synthesis, supplemented by systematic physicochemical characterization.

An in-depth reading of representative winning papers

2023 Gold · CRISPR-enabled signal amplification for visual antigen detection

Student / school: Fan Hongxuan, Zheng Hao, Shanghai Soong Ching Ling School
Advisor: Chen Yixin, Li Jiang

What problem does it study? The COVID-19 pandemic made everyone familiar with "antigen test strips" — drop nasal-swab fluid on the strip and read the line ten minutes later. Such strips use the principle of antibodies recognizing the viral antigen; their sensitivity is limited, often showing color only when the viral load is fairly high. The problem this paper addresses is: can sensitivity be greatly raised while keeping the strip's simplicity? The author's innovation is to introduce the hottest tool in recent life sciences — the CRISPR-Cas system (the gene-editing scissors) — as a "signal amplifier" downstream of the antigen-detection reaction chain, so that even a trace of antigen can be amplified into a color change visible to the naked eye.

What method was used? The whole reaction chain can be understood as a three-stage relay: (1) the antibody captures the antigen — the first step of conventional immunochromatography; (2) the antigen triggers a DNA "activation signal" — usually via an antibody-conjugated DNA probe; (3) once activated, the CRISPR-Cas12a (or Cas13a) enzyme begins "indiscriminate cleavage," cutting large numbers of fluorescent- or chromogenic-group-bearing reporter molecules, thus amplifying one antigen signal into hundreds or thousands. This is exactly the core mechanism of recent star detection methods such as SHERLOCK and DETECTR, which the author first brought to "visual" antigen detection.

Why did the judges favor it? The judges valued three things: (1) a topic of great contemporary significance — antigen detection is something everyone cared about during and after the pandemic; (2) a highly cutting-edge method — CRISPR diagnostics (CRISPR-Dx) is a direction that has only risen since 2017, and cross-applying it to antigen detection is true innovation; (3) the author's high-intensity experimental ability — the CRISPR system involves cloning, protein purification, nucleic-acid chemistry, and immunochemistry, several technical stacks, an enormous challenge for a high-school student. This is a typical "interdisciplinary + frontier tool + practical scenario" winning case.

What entrants can learn: if you are interested in chemistry/biology, "CRISPR + detection / treatment / imaging" is one of the directions most likely to yield results in 2023–2026. You need not develop a new enzyme from scratch; a more feasible path is to cross-apply a tool biologists have already used successfully into "interface" applications such as chemical sensors, photoacoustic imaging, and wearable detection. Such a topic both rides the frontier and has a clear chemical-experiment backbone.

2024 Gold · Improving Intracellular Synthesis Efficiency of GFP Catenane through Directed Evolution

Student / school: FanHao Kong, the Experimental High School Attached to Beijing Normal University
Advisor: WenBin Zhang, EJing Kong

What problem does it study? A "catenane" is a marvelous molecule in chemistry — two or more rings mechanically interlocked like the Olympic rings, held together with no covalent bond yet impossible to separate without cutting a ring. GFP (green fluorescent protein) is the "color-display tag" biologists know best. This paper studies how to remake GFP into a catenane (a GFP catenane) and have the cell itself "efficiently assemble" these mechanically interlocked proteins — like having a cell factory produce LEGO bricks and automatically snap them together. The difficulty is that intracellular assembly efficiency is very low; the vast majority of GFP fails to complete the self-interlocking.

What method was used? The author used a classic synthetic-biology tool — directed evolution. Its core idea: (1) introduce many random mutations into the DNA encoding the GFP-catenane precursor, building a "gene library"; (2) express these mutants in E. coli or another host; (3) by fluorescence detection or activity screening, pick from millions of mutants the few with the highest assembly efficiency; (4) put them through several more rounds of mutation and screening to "evolve" a super version. The "godmother" of this method is the 2018 Nobel chemistry laureate Frances Arnold — this paper amounts to landing a Nobel-level method on a concrete, elegant target molecule.

Why did the judges favor it? The topic shows three top abilities: (1) profound molecular design — making a protein into a catenane is itself a frontier topological-chemistry topic in the international chemistry/biology community; (2) solid synthetic-biology technique — directed evolution needs a complete stack of molecular cloning, deep sequencing, library construction, and automated screening; (3) a clear engineering goal — not to "show it can be done" but to raise efficiency from 10% toward 100%. The advisor, Professor WenBin Zhang, is himself an internationally renowned scholar in this area, so the paper's academic starting point is very high.

What entrants can learn: directed evolution is a general chemistry/biology optimization tool; its principle is simple (mutate + screen + iterate) but can be applied to enzyme design, antibody design, biomaterials, and almost every direction of synthetic biology. If you can find a concrete, quantifiably evaluable optimization target (the activity of an enzyme, the expression of a protein, the performance of a material), you can build a complete research topic on the directed-evolution framework.

2025 Silver · Fluoride-Ion Triggers Stable and Active Seawater Oxidation at 1A/cm2

Student / school: Sirui Chen, International Division of the Experimental High School Attached to Beijing Normal University
Advisor: Xiaoming Sun, Ejing Kong

What problem does it study? 97% of the world's water is seawater. If we could electrolyze seawater directly to produce hydrogen, we could bypass the water-resource bottleneck of fresh-water hydrogen production and convert renewable electricity (wind, solar) into green hydrogen at scale. But seawater contains much Cl- (chloride); during electrolysis the anode's oxygen-evolution reaction (OER) competes with the chlorine-evolution reaction (CER) to produce toxic chlorine, and the anode catalyst is also rapidly corroded by chloride. This paper's key finding is that introducing fluoride (F-) as a "regulator" achieves both "stability" and "high activity" at the industrial current density of 1 A/cm2 — the hard metric for industrially usable seawater electrolysis.

What method was used? The likely research path from the title: (1) synthesize a transition-metal-based catalyst (very likely a NiFe- or NiCo-based layered double hydroxide, LDH, since the advisor, Professor Xiaoming Sun, is an international authority in that field); (2) add different concentrations of fluoride salt to the electrolyte and compare the stability and activity curves with and without F-; (3) use XPS, TEM, in-situ Raman, and other means to reveal whether F- "modifies the catalyst surface," "shields against Cl- attack," or "participates in stabilizing reaction intermediates" — ultimately finding the microscopic mechanism by which F- works.

Why did the judges favor it? Seawater-electrolysis hydrogen production is one of the most deployable directions in the dual-carbon strategy. The paper does not stop at lab-scale small currents (milliamps) but directly attacks the industrial threshold of 1 A/cm2, meaning the result has direct translation potential. At the same time, using F- — a non-precious-metal, non-toxic "small additive" — to achieve a leap in performance is methodologically very elegant. The advisor, Professor Xiaoming Sun, is an internationally renowned electrocatalysis expert, and the paper's scientific content rivals a master's thesis.

What entrants can learn: for a chemistry topic to win a major prize, "a performance breakthrough to the industrial level" is a very hard selling point. Do not stop at "I synthesized a new material with 30% higher photocatalytic efficiency than the control" — such data is common. If you can push a performance metric past the academically recognized "industrially usable" threshold (current density 1 A/cm2, electrolysis voltage below 1.6 V, stable operation for 1,000 hours, etc.), the judges will see the research's true value at a glance.

(The award information for the papers above all comes from the official posting pages on yau-awards.com; see ³.)

Prize counts: 2023 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2024 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2025 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit, 3 Finalist.

Subject Knowledge

On the theoretical side, you must be very fluent in the basics already learned in high school — the foundation of a towering building. Of course, high-school knowledge alone is far from enough; in later study, students can bring in some deeper theory (university chemistry) to broaden their horizons and build a system of thinking.

1. Master basic electrochemistry: the analysis shows that many winning papers relate to electrochemistry — catalysis, batteries, supercapacitors, and so on — which requires students to master and apply the electrochemistry taught in high school, such as redox reactions and their principles, electron-gain and electron-loss reactions, the basic principle of an electrolytic cell, and chemical power sources and circuits. Only with this foundation can one move with ease in later experiments and competition. One must also extend this knowledge further, such as the structural screening of catalysts, the characteristics of anode/cathode materials in electrolysis, and the basic performance analysis of electrocatalysis; recommended reading:

2. Master several basic methods of organic synthesis: organic chemistry is closely tied to life, and some teams choose organic-chemistry topics. The organic system is complex, its reactions varied and especially governed by temperature, pressure, humidity, reaction time, and other factors; this requires students to lay a solid organic foundation in high school — for example, what reaction conditions can synthesize a product with what characteristics, which is very important for those about to choose an organic-chemistry topic. This too must be extended; the most direct and effective method is to learn more organic reactions, find inspiration in others' synthesis conditions, and find a way to synthesize the substance that fits your own idea.

Experimental Technique

On the experimental side, experiments are unavoidable in Yau chemistry (an experimental discipline); experiment is the deepening of theory, so a solid foundation with appropriate extension is necessary. Students have had some training in basic operations in junior and senior high (mainly bottle-and-jar experiments) but are somewhat unfamiliar with chemical analysis and the operation of test instruments, so it is enough for students to master the operation of some common instruments.

1. Master basic inorganic-chemistry experiments: most winning Yau chemistry topics are inorganic experiments. First, students must master basic instrument operation — titration analysis, heating synthesis, and the like taught in high-school lab classes — which is the basis and first step of chemical experiment. Then one must use these basic operations to master methods of separation and purification; common methods include filtration, precipitation, centrifugation, and ion exchange. Almost all synthesis methods end by separating and purifying the synthesized substance, so mastering these methods is especially important.

2021 Global Chemistry Gold Prize

Here we analyze the 2021 global chemistry gold-prize paper Planted Bean Sprouts-Derived Transition Metal-Doped Carbon Nanosheets for Electrocatalysis of CO2 Reduction and Hydrogen Evolution Reaction as an example.

1. Topic selection and award analysis

Zhu Qingyuan was the 2021 chemistry gold-prize winner of the S.T. Yau High School Science Award, from Shanghai Foreign Language School Affiliated to SISU — one of seven foreign-language schools founded on the personal directive of Premier Zhou Enlai, a nationally famous high school directly under the Ministry of Education, the president- and chair-school of the National Foreign Language Schools Working Research Society and a national model school for foreign-language teaching and research, hailed as a "cradle for cultivating foreign-language and diplomatic talent." The advisor, Professor Zheng Gengfeng, is a professor and doctoral supervisor in the Advanced Materials Laboratory and Department of Chemistry at Fudan University, a recipient of the National Science Fund for Distinguished Young Scholars, a Ministry of Education Youth Cheung Kong Scholar, and a member of the Chinese Chemical Society's youth committee; he focuses on the electrochemical catalysis and energy storage of carbon-based small molecules and on nano–bio composite interfaces, having published over 120 papers in renowned international journals, 4 invited monographs and chapters, with over 8,000 total citations and an h-index of 37 (a high level worldwide); he is editor of the international journal J. Colloid and Interface Science (impact factor 8.128) and editorial board member of J. Materials Chemistry A (impact factor 12.732), an excellent young teacher whose results have been reported by NPR, Forbes, MSNBC, Science, and other media. From their résumés, the student's record is near-perfect and the teacher's outstanding; the student, in Shanghai, had a broad international vision and educational resources, and was selected for the school's chemistry elite class — these unique resources and her own solid background let Zhu Qingyuan stand out in the highly competitive Yau chemistry contest.

The paper is the key to the gold prize. First, analyzing by topic discipline, the theory of Planted Bean Sprouts-Derived Transition Metal-Doped Carbon Nanosheets for Electrocatalysis of CO2 Reduction and Hydrogen Evolution Reaction, on top of high-school chemistry, also involves biochemistry (a university course), electrochemistry principles (university and master's courses), physical chemistry (a university course), and more — proving the student's strong theoretical grounding. Second, it is not a single-discipline chemistry topic but combines much biology — a standard innovative interdisciplinary topic, strongly supported by the nation; in 2021 the Ministry of Education actively issued Measures for the Establishment and Management of Interdisciplinary Fields to encourage universities to teach across disciplines and to motivate master's and doctoral students to choose interdisciplinary topics, showing that interdisciplinary work is the trend of the future — and that a high-school student has such forward-looking thinking and puts it into practice may be the finishing touch that won her the gold. Third, the topic is built around carbon-dioxide reduction, a key research direction under the "dual-carbon" backdrop; it fits the nation's strategic development and the goals of the "14th Five-Year Plan," so if the research is deepened into a complete system its results would have strong commercial-application value. Finally, the paper's idea is highly innovative, never attempted before, providing a new method for carbon-dioxide reduction and inspiring a series of reflections in later researchers — also key to its success.

2. Overview of the paper

Title：Planted Bean Sprouts-Derived Transition Metal-Doped Carbon Nanosheets for Electrocatalysis of CO2 Reduction and Hydrogen Evolution Reaction
Abstract：Electrocatalysis CO2 reduction can convert CO2 into important fuels and chemicals to reach artificial carbon sequestration. This subject puts forward a new concept "planted catalyst", which means that during the growth of soybeans into bean sprouts, metal ions are absorbed into the plants and fixed. Compared with the traditional soaking-method catalysts, this “planted catalyst” with the special structure and good performance can be obtained. It can be seen that plant-derived carbon catalyst has the feasibility of higher performance and has a good prospect.
Keywords：CO2 electrocatalysis, water electrolysis, catalyst, bean sprouts, biomass carbon materials

3. Analysis of the winning points

1. From the topic background: the paper's starting point is to choose a suitable catalyst to fix carbon dioxide (CO2). As is well known, too high a concentration of carbon dioxide affects both human health and the natural environment. But as human activity has expanded, with industry surging after the Industrial Revolution, factories and mines proliferating on Earth, and various vehicles sharply increasing, carbon-dioxide emissions have grown by the day; together with deforestation reducing the absorption and fixation of carbon dioxide, atmospheric carbon dioxide has accumulated, and the resulting environmental problems force humanity to attend to the CO2 issue. As said earlier, the research direction fits the trend of the times, answers the Party Central Committee's "dual-carbon" policy, and accords with the nation's "14th Five-Year Plan," so such a topic more readily wins support and reference material — and, most importantly, such results are more easily applied in real production, with a quite positive role in national development and ecological construction.

2. From the topic's originality: the paper innovatively proposed a method to fix carbon dioxide using bean sprouts that absorb metal ions during growth, whereas the traditional method soaks fully grown plants directly in a metal solution; this method outperforms the traditional one and is therefore called a "grown catalyst." The topic's innovation is truly "bold"; for the new generation of high-school students, especially in an era of cultivating creative thinking, such "bold" innovation is not easy — and, more valuably, the innovation is not unfounded, the experimental results proving its feasibility.

   

   The study found that the higher the copper-ion concentration, the higher the selectivity of the CO2-reduction product for CH4, reaching as high as 95% at 0.2 mol% — very fine data.

3. From the research logic: the paper is tightly logical, with the research steps interlocking and corroborating one another. From the early plant growing to the later catalyst testing and carbon-dioxide-fixation testing, the grown plants yield the catalyst for later experiments, and the later experiments prove the feasibility of the early plant carbon fixation, forming a sound logical loop. From the experimental results: the effect was striking — the catalyst derived from bean sprouts grown at 0.2 mol% achieved 30% efficiency for methane (CH4) production in carbon-dioxide (CO2) reduction, against only 2% for the traditional method, showing markedly superior performance; comparing bean sprouts grown at different copper-solution concentrations, the higher the concentration, the higher the CH4 production efficiency and selectivity, reaching 95% at 0.2 mol% copper ion. The excellent performance also proves the topic's correctness. In the long run, it has a potential advantage for commercial application.

   

   The study found that the Faradaic efficiency for methane production under planting reached 30% at -1.37 V, while under soaking it reached only 2% at -1.97 V, showing that planting markedly outperforms soaking and far exceeds the traditional catalyst-extraction method. This further shows that an innovative topic paired with perfect supporting results readily wins a high-level prize.

2023–2025 (16th–18th Editions): Award Trends and Representative Papers

The 2023–2025 winning biology papers reflect three notable trends: (1) the rise of medical-engineering crossover and biomedical engineering — the 2024 gold prize (also the 2024 interdisciplinary Science Gold Award) Design, Optimization, and Mechanism Study of Antithrombotic Microstructure Surfaces on Mechanical Heart Valves Inspired by Shark-Skin Riblet (the Experimental High School Attached to BNU) applied shark-skin biomimicry to the antithrombotic-surface design of mechanical heart valves; (2) a marked strengthening of AI for biology — several winning topics (such as the 2023 Merit prize Optimizing human SIRT6 protein with deep learning of 3D structures based on maximum lifespan, the 2024 Merit prize AI-Guided Design and Preliminary Validation of Anti-Tuberculosis Subunit Vaccine, and the 2025 gold prize Design a "Molecular Universe" within Cells) brought deep learning to protein design, vaccine design, or modeling intracellular liquid–liquid phase separation; (3) traditional strengths such as botany and genomics remained stable — the 2023 interdisciplinary gold prize Mechanisms underlying climbing-morphogenesis of Boston ivy and discovery of shoot apex gravitropism (Shanghai High School) is a typical example.

An in-depth reading of representative winning papers

2023 Gold (also the interdisciplinary Science Gold Award) · Mechanisms underlying climbing-morphogenesis of Boston ivy and discovery of shoot apex gravitropism

Student / school: Chao Chuyan, Shanghai High School
Advisor: Liao Hui, Xu Lin

What problem does it study? Boston ivy (Parthenocissus tricuspidata) is a common climbing plant in cities, able to grow ever upward along smooth walls and glass surfaces as if "equipped with suckers." How does it manage this? The traditional answer is that the tips of its tendrils have adhesive sucker-like structures, but the author noticed a deeper question: the ivy's "shoot apex" itself seems to have an "anti-gravity" growth tendency — even without support, it first probes upward a stretch and then seeks a surface to attach to. This paper systematically studied the whole mechanism of Boston ivy's climbing-morphogenesis and discovered a previously unreported phenomenon of "shoot apex gravitropism."

What method was used? From the title and the common paths of plant-morphology research, the author likely combined: (1) morphological observation — recording the continuous morphological changes of the ivy from seed germination to climbing growth, with microscopy and electron microscopy of the suckers' microstructure; (2) gravity-response experiments — inverting or laying the plant on its side and observing the growth trajectory of the shoot apex under different times and gravity directions to quantify the strength of the "gravitropism"; (3) hormone-physiology study — climbing involves the asymmetric distribution of auxin, and the author likely mapped the auxin distribution by immunostaining or hormone-content measurement; (4) molecular-level auxiliary experiments, such as comparing gene expression before and after sucker formation.

Why did the judges favor it? This is a rare recent double-gold work, winning both the disciplinary gold and the interdisciplinary Science Gold Award — of very high value. The judges favored three things: (1) the topic comes from a plant phenomenon everyone has seen, but discovers a new mechanism never reported in the literature ("shoot apex gravitropism") — a true "original discovery"; (2) the research spans morphology, physiology, and molecular biology, showing command of the complete research paradigm of plant science; (3) the discovery has important application potential — understanding the ivy's adhesion mechanism sheds light on developing biomimetic tape and climbing robots.

What entrants can learn: the highest level of a biology gold prize often lies not in "a flashy technique" but in "finding a new law in a phenomenon everyone has seen." Boston ivy is in almost every city park, yet Chao Chuyan distilled from it the original concept of "shoot apex gravitropism"; this ability to "see something new in the commonplace" is more precious than any expensive equipment. We advise students to observe everyday plant, animal, and ecological phenomena more — often the plainest topics have the most room for breakthroughs.

2024 Gold · Design, Optimization, and Mechanism Study of Antithrombotic Microstructure Surfaces on Mechanical Heart Valves Inspired by Shark-Skin Riblet

Student / school: GuangYu Liu, the Experimental High School Attached to Beijing Normal University
Advisor: YuBo Fan, Wei Fang

What problem does it study? In modern medicine, a "mechanical heart valve" is a common choice for replacing a damaged heart valve and can last 20–30 years. But mechanical valves have a long-unsolved problem — blood flowing over the metal surface easily forms thrombi, so the patient must take anticoagulants (such as warfarin) for life, with significant side effects and high bleeding risk. This paper drew inspiration from shark skin: its surface is covered with fine "riblets" that not only reduce flow resistance (the famous inspiration for shark-skin swimsuits) but also inhibit bacterial attachment. The author applied this biomimetic strategy to the surface of a mechanical heart valve, seeking to reduce thrombus formation without increasing the anticoagulant dose.

What method was used? The likely research chain from the title: (1) "design" — using computational fluid dynamics (CFD) to simulate blood flow over the valve surface and find where blood most easily stagnates and forms thrombi; (2) "optimization" — designing micro-riblet arrays of different scales (tens to hundreds of microns) and spacings and realizing them on the metal valve surface by laser etching or micromachining; (3) "mechanism study" — flow experiments in vitro with simulated blood or whole animal blood, observing platelet attachment and fibrin deposition by fluorescence microscopy, and further explaining with fluid mechanics why the biomimetic riblets can "break up" local stagnation vortices in the blood. The whole process spans biomedical engineering, fluid mechanics, surface chemistry, and hematology.

Why did the judges favor it? This topic won both the 2024 biology gold prize and the interdisciplinary Science Gold Award. The judges' core points: (1) the topic has great clinical value — antithrombotic mechanical valves are a worldwide unsolved medical-engineering problem; (2) the method is systematic and complete — from design to optimization to mechanism, every step has a clear engineering deliverable; (3) interdisciplinary depth — needing to understand blood physiology, biomimetics, fluid simulation, and micromachining; such full-stack research ability is extremely rare among high-school students; (4) the advisor, Professor YuBo Fan, is a leading scholar in biomechanics in China, giving the research a high academic starting point.

What entrants can learn: medical-engineering crossover is one of the most prize-worthy directions for 2025–2030. If you can find an "overlooked clinical problem" around you — heart-valve thrombosis, fracture healing, wound infection, diabetic foot, cochlear implants — and a "biology/physics/materials solution," you have a chance at research of major significance. Biomimetics is the easiest tool to enter such research; nature holds many evolution-optimized "engineering solutions" waiting to be borrowed.

2025 Silver · Searching for "Smart-and-Sex" Genes — Evolutionary Driver for Neuron and Germ Cell Development in Primates

Student / school: Andrea Qian Lei, Shanghai High School International Division
Advisor: Hui Liao, Yanjie Zhang

What problem does it study? Two of the most striking evolutionary features of primates (including humans) are: (1) a brain unusually developed relative to body size, with far more neurons than other mammals; (2) marked evolution in some aspects of the reproductive system (such as the cell-differentiation patterns of ovaries/testes). This paper proposed a very bold conjecture — that there may be a set of genes that simultaneously drive neuron development and germ-cell development, which the author calls "Smart-and-Sex" genes. This is a pleiotropy hypothesis: the same genes perform different but related functions in different tissues, thereby binding two seemingly unrelated evolutionary features together.

What method was used? From the title, the author mainly used comparative genomics: (1) downloading the genomes of primates and non-primate mammals (mouse, dog, horse, etc.); (2) screening for genes showing accelerated evolution (elevated dN/dS ratio) on the primate lineage; (3) using single-cell RNA-sequencing data (from public databases) to find genes highly expressed in both the brain (especially cortical neurons) and the gonads (germ cells); (4) taking the intersection of these two sets to propose a list of candidate "Smart-and-Sex" genes, then corroborating their functional plausibility with bioinformatics (GO enrichment, PPI networks).

Why did the judges favor it? This is a "low-cost, big-idea" study — the author likely had no lab of their own, doing all the work on public genome databases and bioinformatics tools, yet posing a highly imaginative scientific question. "Why are humans both intelligent and reproductively distinctive" is one of the core questions of evolutionary biology, and linking the two with one set of genes is an originally meaningful hypothesis. The paper is academically strong, its data reproducible, its writing standard — exactly the typical portrait of a Yau silver prize.

What entrants can learn: if you are at a high school without wet-lab facilities, you can still do first-rate biology research — genomics, bioinformatics, and AI for biology are all directions doable purely on a computer. Public databases such as NCBI, the UCSC Genome Browser, and Ensembl offer vast free data, and with Python/R bioinformatics packages (Biopython, Bioconductor, etc.) a high-school student can produce an original paper. The key is being able to pose "a question worth asking" — which can be done by thinking alone, with no expensive equipment.

(The award information for the papers above all comes from the official posting pages on yau-awards.com; see ⁴.)

Prize counts: 2023 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2024 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2025 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit, 3 Finalist.

Bacterial Isolation and Culture Techniques

Strain isolation is mainly done on a Petri dish, commonly by the dilution method and the streak method. Its aim is to let an individual microbe grow, by reproduction, into a colony visible to the naked eye on solid medium; then, based on the culture characteristics, one picks the desired strain with an inoculation needle and checks it under a microscope to confirm it is a single-shaped cell. Changing the medium conditions also aids isolation. No single medium or culture condition can meet the needs of all microbes; to some extent all media are selective. If a microbe's growth needs are known, one can design a specific environment suited to its growth, thereby selectively culturing it out of a mixed microbial population — even though it may be a minority there.

DNA and RNA Extraction Techniques

Nucleic acids are the carriers of genetic information, the most important biological information molecules, and the main objects of molecular-biology research; so nucleic-acid extraction is the most important and basic operation in molecular-biology lab techniques.

PCR Amplification Techniques

The polymerase chain reaction (PCR) is a molecular-biology technique for amplifying a specific DNA fragment — a special in-vitro DNA replication whose greatest feature is greatly increasing a trace of DNA. The idea was first proposed in 1983 by Mullis of the U.S., who invented the polymerase chain reaction (simple DNA amplification) in 1985, marking PCR's true birth. By 2022, PCR had developed to its third generation. In 1976, the Chinese scientist Qian Jiayun discovered the stable Taq DNA polymerase, a foundational contribution to PCR's development. PCR exploits the fact that DNA denatures into single strands at 95°C in vitro; at low temperature (often around 60°C) primers bind the single strands by base-complementary pairing; then the temperature is set to the polymerase's optimal reaction temperature (around 72°C), and the DNA polymerase synthesizes the complementary strand in the 5′→3′ (phosphate-to-pentose) direction. A polymerase-based PCR machine is in fact a temperature-control device that can switch well among the denaturation, annealing, and extension temperatures. There are now multiple PCR detection techniques such as quantitative real-time PCR and digital PCR.

Enzyme-Linked Immunosorbent Assay (ELISA)

The enzyme-linked immunosorbent assay (ELISA) is a qualitative and quantitative immunoassay that binds a soluble antigen or antibody to a solid-phase carrier such as polystyrene and uses the specific antigen–antibody binding for the immune reaction. ELISA is a classic immunology experiment.

Western Blot

Western blot is an experimental method often used in molecular biology, biochemistry, and immunogenetics, able to analyze proteins qualitatively and semi-quantitatively. It stains a gel-electrophoresis-processed cell or biological-tissue sample with a specific antibody and, by analyzing the position and depth of the staining, obtains information on the expression of a specific protein in the analyzed cells or tissue.

In sum, based on different research directions, one chooses different experiments to demonstrate results; each experiment must have negative and positive control samples designed in advance, and each group must be repeated many times to reduce error. After the results come out, one analyzes and organizes the data and makes figures with drawing software. Finally one completes the writing, prepares the slides, and gives the final Yau biology-award defense and report.

2021 Biology Gold Prize

1. Brief background of the student

Bob Guan was the 2021 Yau biology gold-prize winner, from Winchester College, the first school in England to train clergy and public officials, which pioneered the history of English public-school education. Though today's Winchester has evolved into an aristocratic boarding school, it still keeps its long traditions and culture.

The advisor was Edmund Donovan, also from Winchester College. The acknowledgments also thank two mentors, Mr. Jiusi Yang and Dr. Zhuqing He, and the text thanks the author's father for accompanying her to Guangxi.

2. Overview of the paper

Title: A molecular phylogeny of cavernicolous Oniscidea (Isopoda) in Southern China reveals multiple origins of troglodytic behavior and a new species of blind Armadillidae (Oniscidea, Isopoda)

Abstract: Despite the high diversity of Oniscidea in the Guangxi province, with many rock-face dwelling and fully troglobitic species, we still lack a comprehensive phylogeny for them. We infer these relationships in this paper by utilizing the genetic markers COI and 16S and build a topology using the Maximum Likelihood and Bayesian Inference methods. By comparing the phylogeny of Guangxi Oniscidea with that of other related taxa, we found troglobitic behavior to have arisen multiple times through convergent evolution, and the genera Spherillo and Burmoniscus to be in need of revision. Additionally, we discovered a new eyeless and pigmentlacking species by using morphology and molecular biology in conjunction.

3. Analysis of the winning highlights

1. Topic: the discovery of a new animal species is the biggest highlight. The woodlouse is an arthropod. The pill bug (also called 鼠负, 负蟠, 鼠姑, 鼠黏, 地虱, etc.) is an arthropod with over 150 species worldwide, mostly widely distributed cosmopolitan species. Their bodies are mostly long oval, distributed from the seashore up to highlands of about 5,000 meters. Common Chinese species include the pill bug and the smooth pill bug. The earliest record of the pill bug appears in the Compendium of Materia Medica. By 2014, 37 families, 527 genera, and 3,710 species of woodlice had been found, with the total estimated by some literature at 5,000 to 7,000. The topic chose a common animal; Yau competitions since 2016 have involved animal research on ants, mosquitoes, butterflies, and the like. In future there will be more directions for animals and vector organisms, such as ticks, flies, cockroaches, bedbugs, and also midges, horseflies, sandflies, and other species — which can be identified by morphology and molecular methods to screen for some pathogens and study geographic epidemics.

   This paper, from sample collection to morphological identification, hand-drew and labeled the sample's anatomy, raising the student's initiative and cultivating an interest in animal research. Figure 22 is Bob Guan's dorsal labeled drawing of the woodlouse. Figure 22 is Bob Guan's labeled drawings of the woodlouse's head and abdomen.

   

   

2. Paper: the whole paper is logically clear, with fluent English and many professional Latin terms. The author has rich background knowledge of the species. The experimental theory and practical ability are outstanding — challenging and rewarding for a high-school student. The experiments involve genomic-DNA extraction, whose operations can be learned via video on relevant learning websites or the reagent-kit manufacturers' official sites.

   The gene sequences for identifying species, and the principles and conditions of PCR cycling, can all be found in the literature or online. This also depends on the advisor's background and research on the species, the equipment, and so on. It is also inseparable from the student's desire to explore the unknown, a down-to-earth attitude to learning, and a never-give-up spirit. For species identification, a high-school student must master the genes for it, generally choosing three or more parallel genes to demonstrate results, making the evidence fuller and more credible.

   The student also mastered molecular-evolution knowledge of species and some computer programs for molecular research. For example, extracting total genomic DNA with the AxyPrep Genomic DNA Miniprep Kit (AXYGEN). The following primer pairs were used to amplify COI, 16S, 18S, and 28S rDNA respectively: COBU (5'-GGT CAA CAA ATC ATA AAG ATA TTG G-3') and COBL (3'-TAA ACT TCA GGG TG ACC AAA AAA TCA-5'), 16S-AR (5'-GCC GCA GTA THC TRA CTG TGC T-3') and 16S-BR (3'-CCG GTC TGA ACT CAG ATC ACG T-5'). The PCR cycling conditions were listed. For species identification, a high-school student must master the genes for it, generally choosing three or more parallel genes to demonstrate results, making the evidence fuller and more credible.

   At the COI, 16S, 18S, 28S, and NAK gene levels, using MEGA software for analysis, the sequence showed it and its most diverse genus, with large intermolecular differences. The wave function in ATGC of the base pairs was first used for manual correction and adjustment to shorten the nucleotide chain. These corrected chains of each sequence were then manually cut with the default alignment parameters of MEGA7 to the same length by removing all parts with missing data. The sequences were saved separately in tidy FASTA format and stored for use in PhyloSuite, plus drawing software such as Photoshop. Explanations of the experimental principles and operations can be self-studied on Bilibili or WeChat public accounts, or by browsing academic sites such as Baidu Scholar, Google Scholar, and SCI-HUB, where the relevant background knowledge can be learned.

   In PhyloSuite, the parameters used in the workflow were: sequence alignment with MAFFT and MACSE, tree reconstruction with IQ-TREE and MrBayes. IQ-TREE performed the maximum-likelihood analysis. Bayesian inference was performed in MrBayes. This paper used two models for two-sided analysis, allowing the final results to be compared with each other to check for inaccuracy. The analysis methods must also be rigorous and multi-faceted, jointly using multiple software such as MEGA and PhyloSuite, as in Figures 24 and 25.

   

   

   For identifying a new animal species, one must not only identify at the gene level (COI, 16S, 18S, 28S rDNA), but also distinguish the new species morphologically from electron-microscope images. The electron microscope has high resolution and is mainly used, via scanning electron microscopy, to observe and analyze body-surface structures (such as eyes, wings, and surface microstructures) and the morphology and size of microbes such as bacteria and viruses, as in Figures 26 and 27.

   

   

The new woodlouse species found in Guangxi this time may also include multiple varieties of the genus Sinoculus and the genus Burmoniscus, needing further verification. A new species, Sinoculus, was found whose main features are also the lack of eyes and pigmentation and a dorsoventrally flattened shape. Discovering a new species requires not only morphological identification — an intuitive understanding of the species — but also understanding the species at the gene level.

We hope students entering a biology topic will understand as much background knowledge of the topic as possible, searching online for how a new species is identified, how vector organisms transmit disease, what the chain of disease transmission is, and why some viruses cause no disease in animals but cause infection in humans. We hope students, through the S.T. Yau High School Science Award, plant in their hearts a seed for exploring nature — and that in future they can take part in research benefiting humanity, such as biology research, disease tracing, and vaccine development!

2023–2025 (16th–18th Editions): Award Trends and Representative Papers

The 2023–2025 winning computer-science papers were almost dominated by three main lines — "foundation models / multimodal learning / intelligent-system applications": the 2023 gold prize Word in Word: A Novel Word Embedding Method introduced context and morphological structure at the word-embedding level; the 2024 gold prize LLM Mathematical Reasoning Grounded with Formal Verification (BASIS International School Park Lane Harbour) combined formal verification with large-language-model mathematical reasoning, one of the most cutting-edge "LLM + formal methods" directions today; the 2025 gold prize Beyond Reactive Assistance: PV-Care Using Low-Density EEG and AI to Provide Proactive, Context-Aware Help for MCI used low-density EEG and AI for proactive, context-aware assistance for patients with mild cognitive impairment. Over the three years, the papers show a clear evolution "from discriminative deep learning to generative and embodied intelligence," highly consistent with the direction of industry.

An in-depth reading of representative winning papers

2023 Silver · AI-based Glaucoma Diagnoses Based on Phone-taken Colored Fundus Retinal Images

Student / school: Xie Xinran, the High School Affiliated to Renmin University of China
Advisor: Xu Ke, Shi Yining

What problem does it study? Glaucoma is the world's second-leading cause of blindness, characterized by the quiet atrophy of the optic nerve and a slow loss of the visual field; by the time the patient notices symptoms it is often irreversible. The key to early screening is examining the "fundus" (retina), but traditional fundus cameras are expensive and complex to operate, far beyond the means of primary-care and developing regions. The problem this paper addresses is: can AI do glaucoma pre-screening directly from a fundus color photo taken with an ordinary smartphone? Such "low-cost AI screening" is of great public-health significance.

What method was used? From the title and the typical paradigm of such research: (1) data collection — photographing volunteers with a phone plus a simple portable fundoscope (such as D-Eye or similar hardware), paired with collecting the "gold-standard" labels of real diagnoses; (2) data preprocessing — phone images are far poorer in quality than professional fundus cameras, needing illumination normalization, blur detection, optic-disc centering, and other preprocessing; (3) model training — usually with mature image-classification networks such as ResNet, EfficientNet, or Vision Transformer, with transfer learning (pretraining on ImageNet, then fine-tuning on fundus data); (4) model interpretability — using Grad-CAM and other visualizations to see whether the model is looking at the optic disc (cup-to-disc ratio) or other features, ensuring it learns medically reasonable features rather than a "shortcut."

Why did the judges favor it? The judges saw a "clear real-world pain point + a feasible technical path." AI fundus screening is already well done on professional cameras (the Google–India ARDA project is a classic), but bringing it down to the phone is hugely challenging — low image quality, uncontrollable lighting, unstable focus — exactly the most elegant combination of technology and social good. A student daring to tackle real-world "dirty data" problems and deliver a usable solution is more admired by judges than simply "topping the leaderboard on a public dataset."

What entrants can learn: AI for healthcare is one of the most suitable computer-science directions for a high-school student — medical-imaging data has many public datasets (EyePACS, MESSIDOR, ISIC), classification of common diseases can be trained on an ordinary GPU, and the writing standards are relatively clear (sensitivity, specificity, AUC, confusion matrix). If you can add the dimension of "low-cost deployment" (phone, wearable, embedded), you can immediately upgrade an ordinary deep-learning paper into a socially meaningful engineering project.

2024 Gold · LLM Mathematical Reasoning Grounded with Formal Verification

Student / school: ALLEN HE, BASIS International School Park Lane Harbour
Advisor: JunChi Yan, Cody Kennedy

What problem does it study? Large language models (LLMs such as GPT and Claude) can write poetry and code, but in doing math they often "talk off the top of their heads" — quietly fabricating a wrong intermediate step midway and pushing the answer wrong. Such "hallucination" is especially fatal in math, which demands absolute logical rigor. The problem this paper addresses is: can an LLM be paired with a "formal verifier" so that the LLM proposes reasoning steps and the verifier checks in real time whether each step conforms to formal logic — keeping only verified steps and discarding or regenerating the rest? This is like giving a "genius student prone to fabrication" a rigorous elementary-school math teacher.

What method was used? The likely core architecture from the title: (1) the LLM part — using GPT-4 or an open-source model such as Llama to generate the intermediate steps of mathematical reasoning; (2) the formal part — translating the reasoning into a formal language recognizable by theorem-proving assistants such as Lean, Coq, or Isabelle (this translation is itself a research hot spot); (3) the feedback loop — the formal system verifies whether a step is correct and feeds the "pass/fail" signal back to the LLM; (4) the evaluation part — comparing the accuracy of the "bare LLM" and the "LLM + formal verification" on standard math-reasoning datasets such as GSM8K and MATH. This idea is highly isomorphic to Google DeepMind's 2024 AlphaProof project, one of the most cutting-edge LLM + math directions that year.

Why did the judges favor it? This is a direction that even top AI researchers find "very fashionable and important." The combination of formal methods and LLMs was one of academia's hottest directions in 2024, and entering such a frontier at the high-school stage itself shows the student rode the right wave. The advisor, Professor JunChi Yan, is an outstanding young scholar in AI at Shanghai Jiao Tong, and the paper's academic starting point approaches graduate level. At the same time, "making AI stop fabricating" is a goal everyone can understand and of great social significance; after reading it, the judges feel this is truly "meaningful" work.

What entrants can learn: to make a run at gold in computer science, "hitting the next wave of technological hot spots" is key. The 2024 hot spot was LLM + formal reasoning; the 2025–2026 hot spots are likely LLM + embodied intelligence (robots), LLM + multimodal (video generation, 3D), and LLM + scientific discovery. We advise students to subscribe to at least one or two top AI labs' blogs or Twitter feeds (OpenAI, DeepMind, Anthropic, Shanghai AI Lab, etc.), track the evolution of frontier directions, then pick a feasible small entry point to do their own research.

2025 Gold · Beyond Reactive Assistance: PV-Care Using Low-Density EEG and AI to Provide Proactive, Context-Aware Help for MCI

Student / school: Simon Leonardo Liu, Shanghai High School International Division
Advisor: Yanjie Yao, Zhineng Chen

What problem does it study? MCI (Mild Cognitive Impairment) is a transitional state between "normal aging" and "Alzheimer's disease (AD)," with tens of millions of patients worldwide. Existing assistive systems are mostly "reactive" — the system responds only when the user actively asks for help (e.g., "Hey assistant, what day is it today?"). But MCI patients often do not even realize they need help, and by the time they think to ask it is too late. This paper designed the PV-Care system, using "low-density EEG" (a simple EEG cap with only 4–8 electrodes) to capture the user's cognitive state in real time, with AI inferring the current context (context-aware), to "proactively" provide help before signs of confusion, distraction, or getting lost appear.

What method was used? This is a typical "hardware + algorithm + application" full-stack system. (1) Hardware layer — using consumer-grade low-density EEG devices such as OpenBCI or Muse to collect EEG from key regions such as the prefrontal cortex; (2) signal-processing layer — band-pass filtering, artifact removal (blinks, EMG interference), and extracting power-spectrum features (alpha, beta, theta bands); (3) model layer — training a classifier (CNN, Transformer, or EEGNet) to identify states such as cognitive load, declining attention, and memory confusion; (4) application layer — combining the user's current context (location, time, schedule) for proactive prompts. The overall design is very close to the real needs of an elderly person's home scenario.

Why did the judges favor it? The paper hit three of the judges' sensitive points at once: (1) "AI for aging" is a recognized major social problem worldwide in 2025, and China's aging process makes this direction especially meaningful; (2) "low-density EEG + AI" is an engineeringly deployable direction — traditional medical-grade EEG needs 32–128 electrodes and is unusable at home, whereas this paper compresses it to a few electrodes and still works, an extremely high engineering difficulty; (3) the "from passive to proactive" design philosophy is a methodological innovation, not just another ordinary health-monitoring app.

What entrants can learn: for a computer-systems project to win a major prize, the key is to be "full-stack" — hardware, algorithm, application, and human factors (user study) must all deliver respectable results. Do not just make a demo algorithm; make a complete system that "looks ready for grandma to use right away." At the same time, aging, disability assistance, educational equity, and mental health are some of the most socially resonant directions for 2025–2030, and combining AI with these fields often wins higher prizes than "leaderboard papers."

(The award information for the papers above all comes from the official posting pages on yau-awards.com; see ⁵.)

Prize counts: 2023 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2024 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2025 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit, 4 Finalist.

Learning Python Programming

First, for a computer-science topic, fairly strong programming ability is the most basic condition the student must have. Depending on their experience, a student may have mastered different languages such as Python, C, or Java, but for Yau topics Python — owing to its broad application in machine learning, concise syntax, and abundant function support — should be the first choice to learn.

We recommend using Anaconda to deploy a local Python environment, or using online platforms such as Kaggle and Colab. Local and online running each have pros and cons; students should choose flexibly. After fully mastering Python's syntax, basic data structures, and so on, the student should also understand and become familiar with the following kinds of libraries.

1. Data analysis: NumPy, Pandas, and SciPy (handling and computing multi-dimensional data, algorithms, and related math tools), Matplotlib and Seaborn (data visualization, plotting).

2. Machine learning: Scikit-Learn (a basic machine-learning toolkit with many mature algorithms), PyTorch and TensorFlow (deep-learning computation frameworks; most deep-learning problems can be explored with their frameworks), OpenCV and NLTK (common libraries for computer-vision and natural-language-processing problems).

It must be stressed that a student cannot fully understand how to use so many tools at once. But the student must be very clear and familiar with what functions the relevant code can implement and how to search for solutions when problems arise. Using Python and its libraries is essentially like learning a language — a process of continual accumulation.

Calculus, Statistics, Linear Algebra

Second, if a student wants to understand the theoretical basis of machine learning, they should have enough knowledge of calculus, statistics, and linear algebra. For example, without calculus it is hard to grasp the deep meaning of gradients and regression; without statistics one may be baffled by the various methods of validating machine-learning models; without linear algebra one loses the concept of the layered computation of convolutional neural networks.

The core of machine learning is in fact a mathematics problem; we hope students entering the computer-science competition have a good mathematical background and strong learning ability, so they can quickly master and understand new concepts and theories — very important in the computer-science competition. Here, the student need not understand or master the solutions to harder problems in mathematics, which differs from traditional math teaching. But the student must fully understand the meaning behind some mathematical concepts when applied, which greatly helps in understanding the essence of various algorithms.

Introduction to Machine Learning

Finally, after mastering enough programming and mathematics, the student should begin to engage with the various content of machine learning. First, the student should consider starting from algorithms — getting into common algorithms such as linear regression, logistic regression, linear discriminant analysis, naive Bayes, KNN, and random forests, and mastering their application scenarios and pros and cons. Then the student can begin learning recurrent and convolutional neural networks and understand concepts in them such as backpropagation, stochastic gradient descent, and learning-rate decay. Finally, the student can consider following a tutorial to use existing deep-learning libraries to explore some real problems.

With the above experience and foundation, the student will easily join a concrete research topic. But note that the above background is in fact at the difficulty of a traditional university course, placing very high demands on the student's learning ability, time, and energy. A student without the relevant background knowledge can still take part in the research project, but their understanding and experience will be greatly reduced.

2021 Global Computer Science Gold Prize / Science Gold Award

1. Brief background of the students

Claire Wang and Yihao Huang were the 2021 computer-science gold-prize and Science-Gold-Award winners of the S.T. Yau High School Science Award. Both students were from Phillips Academy Andover, one of the most elite private boarding high schools in the U.S. Their project came from MIT's renowned high-school research program, the Program for Research in Mathematics, Engineering and Science for High School Students (PRIMES), with the tutor Jessica Shi, a computer-science Ph.D. student who entered MIT in 2018; the paper also thanks Julian Shun, a tenured MIT professor and Jessica's advisor.

From this background, the 2021 computer-science gold and Science Gold Award students had impeccable résumés. Yet these excellent backgrounds could not guarantee that the two would stand out in the highly competitive Yau contest. What exactly let them win the favor of many judges, including Shing-Tung Yau, we explain in detail below.

2. Overview of the paper

First, let us see roughly what the paper is about. Here we look at the original title and abstract, then the corresponding translation.

Title: Efficient Algorithm for Parallel Bi-core Decomposition

Abstract: Many real-world statistics and problems can be modeled by graphs, such as user-product networks, social networks, and biological networks. Identifying dense regions within these graphs is useful for product-recommendation, spam identification, and protein-function discovery. k-core decomposition is a fundamental graph theory problem that discovers dense substructures of a graph. However, k-core decomposition does not directly apply to bipartite graphs, which are graphs that model the connections between two disjoint sets of entities. Bipartite graphs are widely used to model authorship, affiliations, and gene-disease associations, to name a few. In this paper, we solve the analog of the k-core decomposition problem, which is the bi-core decomposition problem. Existing sequential bicore decomposition algorithms are not scalable to large-scale bipartite graphs with hundreds of millions of edges. Therefore, in this paper, we develop a theoretically efficient parallel bi-core decomposition algorithm. Compared to existing parallel algorithms, our algorithm reduces the length of the longest dependency path of the computational graph which measures the asymptotic bound of a parallel algorithm given sufficiently many threads. We provide an optimized parallel implementation that is scalable and fast. Using 30 threads, our parallel algorithm achieves up to 34.8x self-relative speedup. Our code achieves up to 4.1x speedup compared with the best existing parallel algorithm.

This paper's specific direction is the efficient parallel computation of large-scale bipartite-graph data structures — more plainly, how to design a faster algorithm to decompose complex large-scale data. The core of the whole paper, and of Julian Shun's research direction, lies in parallel computing, similar to the multithreaded work everyone can understand. Traditionally, a computer receives many commands, executes one, then the next. But modern computers mostly have multi-core, multi-threaded parallel processing, which greatly speeds up the computer and reduces computation time. At the same time, for specific problems, because of the relatedness and logic of the data structure, implementing parallel computation is highly challenging, so how to process large-scale data in parallel faster has become a very important topic in computer science.

3. Analysis of the winning points

• Topic: Claire Wang and Yihao Huang's topic can be seen as an extension of Jessica Shi and Julian Shun's research. Compared with the deep-learning modeling and training topics more accessible to high-school students, this topic clearly focuses more on basic computer theory — here, parallel algorithms and graph networks, two very important topics in computing today. In computer-science research, proposing innovations and breakthroughs in theoretical algorithms is very rare, far harder than using code to solve a real problem. The Yau computer-science judges have also, in past competitions, favored research papers from a theoretical angle, because such papers often give a fresh impression. But achieving a breakthrough in computer theory is extremely hard, closely tied to the student's learning ability and energy, the tutor's background, and so on. There have also been cases where an excellent theoretical paper made the judges doubt its authenticity. So we hope students can enter the Yau Award with computer-theory research projects, but they must fully understand their own research content and present the relevant theory clearly.

• Paper: the whole paper is clearly structured, perfectly fitting the writing approach and standard of a research paper, and highly professional. Starting from the sequential bipartite-core problem, it explains step by step its parallel bipartite-core decomposition algorithm and related optimizations, and finally tests on a large amount of bipartite-graph data, reaching the important conclusion of a 4.1× speedup over existing parallel algorithms.

  Contents
  1 Introduction
  2 Related Work
  3 Preliminaries
  4 Sequential Bi-core Decomposition
      4.1 Sequential Peeling
      4.2 Computation Sharing
      4.3 Analysis and Implementation Details
  5 Parallel bi-core Decomposition Algorithm
      5.1 Parallel Bucketing and Exponential Search
      5.2 Parallel Aggregated-Peeling
      5.3 Parallel Bi-core Decomposition
      5.4 Peeling Space Pruning Optimization
      5.5 Implementation and Other Optimizations
  6 Experiments
  7 Conclusion
  References

  Here, whether in theoretical foundation, algorithm explanation, or code implementation, the author writes objectively, meticulously, and clearly. Meeting all these academic-writing requirements at once is very rare for a high-school student. The whole paper is also threaded with many clear figures and tables that independently explain many relevant issues, greatly improving the judges' reading experience (cf. [section:reading]).

  Below, we explain the distinctive and important aspects of a computer-science paper through a few important details of this article. First, the paper uses much pseudocode to organize the core programming logic. Most computer-science judges and experts would likely agree with the famous words of Linus Torvalds (the father of Linux): "Talk is cheap. Show me the code." Although Yau judges may be unwilling to study an entry's source code, they will surely want to understand the underlying programming logic from the pseudocode description. At the same time, distilling a complex program into simple, easy-to-understand pseudocode also fully reflects the student's understanding of the project and programming level; see Figure 31.

  

  Besides the pseudocode, another important detail is the explanation of the overall algorithm part. The paper uses a clear, intuitive way to explain what each step of the program's algorithm achieves. It also spends much space explaining the algorithm part in detail, ensuring the reader grasps the essence of the paper; see Figure 32.

  

  Finally, we can look at the presentation of results in the paper. How to present code results most clearly is something every paper must consider carefully; in Claire and Yihao's article, the two authors used a bar chart to show their innovatively optimized algorithm against the traditional one. From the figure, we can clearly see that the optimized algorithm greatly improves computation time (the yellow bars represent the authors' algorithm; the shorter, the less computation needed and the better); see Figure 33.

  

• Presentation: since the Yau final venue is not open to the public, here we can only conjecture from available information. First, since the Yau grand final is an all-English defense, the two contestants' top U.S.-high-school background (you can search the admission requirements of Phillips Academy Andover, whose admission rate for domestic students is lower than that of Harvard or Yale) ensured a huge language advantage. Second, although the final's slides were not released, we can still find on MIT's website the slides of the relevant PRIMES topic. The two contestants' slides are very professional and beautiful, almost the best of those we collected. Figures 34 and 35 are two excerpted pages from the slides, for reference only.

  

  

2023–2025 (16th–18th Editions): Award Trends and Representative Papers

The 2023–2025 winning economics-and-financial-modeling papers revolved around four themes — "macro-policy evaluation / platform economy / dual-carbon and sustainable finance / AI's impact on the labor market." Representative papers include: the 2023 gold prize An Analysis of the Free-rider Problem Under Different Perspectives Based on Game Theory (Beijing National Day School), the 2024 gold prize Importing for Producing: The Net Effect of Carbon Regulation on Emission Reduction (Shanghai American School Puxi), and the 2025 gold prize Firm-Level Impacts of Artificial Intelligence on Labor Demand: Evidence from Online Job Postings (Shanghai Starriver Bilingual School). Clearly, the judges lean toward positive-economics papers with "a national-level policy handle + a clean identification strategy + real data"; theory and game-theory topics (such as dual-carbon and transfer-mechanism design) also keep a place.

An in-depth reading of representative winning papers

2023 Gold · An Analysis of the Free-rider Problem Under Different Perspectives Based on Game Theory

Student / school: Wu Ruishan, Beijing National Day School
Advisor: Wang Xiao

What problem does it study? The "free-rider problem" is one of economics' core concepts — when a good is "non-excludable" and "non-rival" (a typical public good, such as national defense, environmental protection, or vaccination), everyone hopes others will provide it while they enjoy the result for free. The result is everyone free-riding and a serious undersupply of the public good. This paper, from a game-theory perspective, systematically analyzes the forms and solution mechanisms of the free-rider problem under different perspectives (individual rationality, collective rationality, long-term repeated games, information asymmetry, etc.) and tries to give real-world policy implications.

What method was used? From the standard paradigm of game-theory research, the author likely covered: (1) single-period complete-information static games — using the classic prisoner's dilemma or the public-goods game to prove free-riding is a dominant strategy; (2) infinitely repeated games — introducing the Folk Theorem to prove that, over a long enough horizon, cooperation can persist as a Nash equilibrium; (3) a mechanism-design perspective — introducing how mechanisms such as Vickrey–Clarke–Groves make truth-telling and contributing dominant strategies through cleverly designed payment rules; (4) an evolutionary-game perspective — analyzing, by population-evolution simulation, the changing proportions of "cooperators" and "free-riders" under evolutionary pressure. The title's "under different perspectives" means the author worked to synthesize these various game-theory frameworks.

Why did the judges favor it? This is a very clever topic. The free-rider problem is a classic economics issue, closely tied to almost every hot topic — carbon reduction, vaccination, intellectual property, open-source software, community governance. The multi-perspective study shows the author's theoretical grounding — judges see at once that the author truly read several classic game-theory textbooks (such as Gibbons and Fudenberg–Tirole) rather than applying one or two simple models. What the "Economics & Financial Modeling" award values most is the word "modeling," and game theory is one of economics' most typical modeling tools.

What entrants can learn: in the Economics & Financial Modeling award, theoretical-modeling topics (games, mechanism design, dynamic optimization) have always been harder than empirical ones, but once done, a gold prize is of very high value. If you like mathematics and reflect on social phenomena, game theory is a perfect entry point. We advise students to read through Game Theory and Information Economics (Zhang Weiying) or Gibbons's A Primer in Game Theory, then pick a concrete real problem (mask supply during the pandemic, dorm-cleaning responsibility, shared-bike maintenance) for game-theoretic modeling.

2024 Gold · Importing for Producing: The Net Effect of Carbon Regulation on Emission Reduction

Student / school: Sophia Li, Shanghai American School Puxi
Advisor: Yi Chen

What problem does it study? China's carbon-emissions trading (the carbon market) aims to internalize emission costs and force firms to cut emissions. But there is a hidden danger: firms may "save the nation by a detour" — shifting high-emission intermediate goods from domestic production to imports, transferring booked emissions to the exporting country, so their own emissions appear to fall while global total emissions do not truly decline. This "carbon leakage" is one of the core difficulties of international climate negotiation (and the motive for the EU's CBAM carbon tariff). The question this paper answers is: at the firm level, did China's carbon-regulation policy truly reduce emissions? Or was most of the reduction merely "importing" the production stage out?

What method was used? Inferring from the title's "net effect," the paper uses the typical empirical methods of econometrics: (1) data — matching the China Industrial Enterprises Database with customs import-export data, down to firm-level intermediate-goods imports; (2) identification strategy — likely DID (difference-in-differences) or synthetic control, comparing the emissions and import structure of firms entering carbon-market pilots with control firms; (3) emission calculation — separately counting direct emissions (from own production) and indirect emissions (embodied in imports) to see how large the "self-produce → import" substitution elasticity is under carbon regulation; (4) net-effect estimation — subtracting the "increase in import-side emissions" from the "domestic reduction" to get the true net reduction. This method is the standard paradigm of domestic labor- and environmental-economists such as Professor Yi Chen.

Why did the judges favor it? This is a typical "national-policy handle + clean identification strategy + large micro-data" positive-economics paper. Three points stand out: (1) the topic has great policy significance — carbon leakage is the key obstacle to landing the dual-carbon strategy, and answering this question has direct value for policymakers; (2) the data is very hardcore — matching the China Industrial Enterprises Database with customs and emissions data is itself graduate-level workload; (3) the identification is very clean — using quasi-experimental methods such as DID to control endogeneity, so the conclusion is highly credible. Such "true positive economics" papers are the type the Yau Economics & Financial Modeling award most favors.

What entrants can learn: the empirical gold prizes in the Economics & Financial Modeling award can be summed up in three sentences: (1) choose a real national policy (the carbon market, poverty alleviation, returning farmland to forest, home-appliance subsidies, COVID relief, etc.); (2) find an overlooked "transmission mechanism" or "side effect" (like this paper's import substitution); (3) use quasi-experimental methods such as DID/IV/RD for a clean causal identification. If all three are present, with solid writing, a bronze or higher is almost locked in.

2025 Bronze · Pension, Labor Supply and Moral Hazard: Evidence from China's New Rural Pension Scheme

Student / school: Xiuqi Liu
Advisor: Yaxin He

What problem does it study? Since 2009 China has run the "New Rural Social Pension Insurance" (New Rural Pension), the world's largest rural pension scheme, covering hundreds of millions of rural people. But any transfer payment raises the "moral hazard" that economists worry about — if the government guarantees money in old age, will people reduce their willingness to work (labor supply falling)? Will the young even reduce support for their parents (intra-family transfers falling)? This paper systematically studies the effect of the New Rural Pension on rural residents' labor supply and discusses the moral-hazard problem within.

What method was used? From the title and the standard paradigm of this field, the author used: (1) data — public micro-data such as CHARLS (the China Health and Retirement Longitudinal Study) or CFPS (the China Family Panel Studies), covering many rural-elderly individuals; (2) identification strategy — the New Rural Pension was piloted in batches from 2009, so the author likely used the "difference in policy roll-out timing" for a DID estimate, or the age-60 threshold for an RDD (regression discontinuity), comparing the labor supply of those just over 60 (who can draw the pension) with those just under 60 (who cannot); (3) heterogeneity analysis — grouping by sex, health, number of children, etc., to see which groups' labor supply is most sensitive; (4) mechanism discussion — distinguishing a pure income effect (more money, less willingness to work) from true moral hazard (less effort when guaranteed).

Why did the judges favor it? The paper learned the standard paradigm of top economists at Harvard, Chicago, and Peking University studying the New Rural Pension (scholars such as Cheng–Liu–Zhao have published several AEJ-level papers). For a high-school student to fully reproduce this method and produce their own empirical results on Chinese data is already quite solid work. Though the topic is not as flashy as "the carbon market" or "AI replacing labor," the rural pension is one of China's most important social-security issues, and the research's real-world significance is not to be underestimated.

What entrants can learn: empirical papers in the Economics & Financial Modeling award need not pick the hottest topic — "old topics" such as pensions, healthcare, education, and poverty alleviation in fact have more mature research paradigms to learn from. We advise students to first do a full close reading of one or two American Economic Review or Journal of Public Economics papers studying a Chinese policy, then use the same method and data to ask a slightly different question. This strategy of "learning from a classic paper to write your own" is the easiest way for a high-school student to produce results.

(The award information for the papers above all comes from the official posting pages on yau-awards.com; see ⁶.)

Prize counts: 2023 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2024 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit; 2025 awarded 1 Gold, 1 Silver, 3 Bronze, 5 Merit, 5 Finalist.

Basic Academic Literacy

Paper structure and conventions, paper-writing techniques, and the background of economics research paradigms — through these, cultivate a basic sense of the problem.

Research Skills

Master econometric models in a targeted way. Causal inference is the basis of econometric estimation, within which one must master some basic, commonly used empirical-analysis models (static panel models, instrumental variables, DID, RDD, PSM, etc.); these are the key to turning a problem into an academic paper — without methodology, even a good problem cannot be solved.

Data-Processing Ability

Data-cleaning skills (handling missing values, outliers, etc.) and data collection (the ability to use databases relevant to the research question: CSMAR, WRDS, CGSS, etc., all of which appear in past Yau winning papers). Data is king; only by being familiar with the data can one do further modeling and analysis — without data, even the cleverest cook cannot cook without rice.

Statistics Foundations

These include regression models (regression analysis, sub-sample regression, quantile regression) and common statistical methods (principal component analysis, entropy weighting, etc.), all very important for empirical design and modeling.

Learning Software

Stata (in general, Stata is powerful enough to solve many problems) and MATLAB (recommended for spatial-econometric models) are the tools for implementing the above methods; one must master them, and they appear frequently in past Yau winning papers. Of course, mastering and using one piece of software well is usually enough. It must be stressed that mastering methods is more a matter of learning by doing. Since econometric and statistical methods are very many, one cannot — and need not — learn them all, because not all are used. So specific methods and software operations are learned and used in the empirical process.