“祝贺你，孙理察！”

10月25日，2025世界顶尖科学家论坛开幕式暨2025世界顶尖科学家协会奖颁奖典礼在上海举行。斯坦福大学名誉讲席教授孙理察（Richard Schoen）获颁“智能科学或数学奖”。菲尔兹奖得主、上海数学与交叉学科研究院理事长丘成桐为孙理察进行颁奖并致颁奖词。以下是致辞原文：

女士们、先生们，早上好。

非常荣幸和欣慰能够将世界顶尖科学家协会数学奖授予孙理察（Richard Schoen）教授。孙理察不仅是位卓越的数学家，更是我昔日的学生、长期的合作者与挚友。过去五十年间，我有幸见证他从一位思想丰沛、沉静坚定的青年学者，成长为一位这个时代真正伟大的几何学家之一。

上世纪七十年代孙理察来到斯坦福与我共事时，几何分析领域初现雏形。在那个几何学与分析法分庭抗礼的年代，他率先洞察到这两个领域不仅能相互对话，更能交融催生全新范式。他清晰的思维、精湛的技艺与深邃的直觉，使其成为这一现代视角的开拓者。

我们关于广义相对论中正质量定理的合作尤为难忘。这个自爱因斯坦时代便困扰着无数物理学家与数学家的难题，让我们耗费了无数个日夜。至今仍记得黑板前的漫漫长夜，我们的讨论常持续至破晓，而孙理察始终以沉静而执着的专注，将分析的严谨与几何的深邃编织成完整的论证。当证明最终完成时，这不仅是数学的胜利，更揭示了数学洞察自然本质的伟力。

此后孙理察独立取得了多项里程碑式的成就——解决山边问题、证明微分球面定理、对调和映射与极小曲面理论的深远贡献。每项突破都为后辈数学家开辟了新航向。他构建起贯通几何、分析与物理的完整框架，将几何分析塑造为现代数学的支柱。

然而最令我动容的不仅是他的才智，更是他的人格魅力。他谦逊而严谨，慎思明辨；平日沉静寡言，但每言必中。他的学生与合作者从他身上学到的不仅是数学知识，更是做学问的方式——严谨、耐心与真诚。

作为他的导师，今日我既自豪又谦卑。得见学生超越所有期待，以如此优雅的姿态重塑整个学科，实属师者至幸。他的研究持续影响着几何学、物理学、拓扑学，乃至我们理解空间与曲率的哲学思辨。

我谨代表世界顶尖科学家协会，怀着由衷的欣喜，将2025年世界顶尖科学家协会数学奖授予孙理察教授——以表彰他在几何分析与微分几何领域的开创性贡献，和他以毕生心血重塑我们对数学及其与物理世界关联的认知。

祝贺你，孙理察。

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Good morning, ladies and gentlemen.

It is a great honor and personal satisfaction for me to present the World Laureate Association Prize in Mathematics to Professor Richard Schoen.

Richard is not only a mathematician of the highest caliber; he is also my former student, my long-time collaborator, and a dear friend. Over the past five decades, I have had the privilege of watching him grow from a young scholar filled with ideas and quiet determination into one of the truly great geometers of our time.

When Richard came to work with me at Stanford in the 1970s, geometric analysis was only beginning to take shape as a field. It was a time when geometry and analysis were often seen as separate worlds. Richard was among the first to see that these worlds could not only talk to each other, but could produce something entirely new when brought together. His clarity of thought, technical mastery, and deep intuition made him a pioneer of this modern viewpoint.

One of our most memorable collaborations was on the Positive Mass Theorem in general relativity. This was a problem that had challenged physicists and mathematicians alike since the time of Einstein. We spent many intense months trying to understand how geometry could capture the idea that the total energy of an isolated physical system should never be negative. I still remember the long nights at the blackboard, our discussions stretching until dawn, and Richard’s calm yet relentless focus as he pieced together the analytical and geometric components of the argument. When the proof finally came together, it was not just a mathematical victory—it was a moment of truth about how mathematics can reveal the structure of nature itself.

Richard went on to achieve remarkable results on his own—the resolution of the Yamabe problem, the Differentiable Sphere Theorem, and profound contributions to the theory of harmonic maps and minimal surfaces. Each of these achievements opened new paths for generations of mathematicians. He built an entire framework that united geometry, analysis, and physics, shaping what we now call geometric analysis into a central pillar of modern mathematics.

What has always struck me about Richard, however, is not only his brilliance but also his character. He is modest, precise, and deeply thoughtful. He listens more than he speaks, but when he does speak, every word counts. His students and collaborators have learned not just mathematics from him, but a way of doing mathematics—with rigor, patience, and integrity.

Today, as his former advisor, I feel both proud and humbled. It is rare for a teacher to see a student surpass every expectation, to make discoveries that redefine a field, and to do it all with such grace. Richard’s work continues to influence not only geometry but also physics, topology, and the philosophy of how we understand space and curvature.

On behalf of the World Laureate Association, and with great personal joy, I present the 2025 WLA Prize in Mathematics to Professor Richard Schoen—for his pioneering contributions to geometric analysis and differential geometry, and for a lifetime of work that has transformed our understanding of mathematics and its connection to the physical world.

Congratulations, Richard.