The fate of the manifold: Who is the winner?Recalling the major upheaval caused by the Poincaré Conjecture 20 years ago, its content and scientific significance——Based on the analysis and commentary of scientific history and scientific methodology
流形的命运：谁是胜者 追忆20年前庞加莱猜想引发的重大风波，它的内容和科学意义——基于科学史与科学方法论的分析和评论

摘要

本文主要分析讨论由庞加莱猜想破解引发的一场数学风波，其中包括中国数学界和物理学界在内，堪称国际数学界的一场江湖论剑，各路英雄纷纷登场，场面之宏大，情节之引人入胜，结果之离奇，真是难得一见，涉及各路英雄的故事，值得不同类型的、不同领域的、不同职业的各类读者阅读、思考。为什么20年后仍然需要讨论这些问题，主要是风波并没有平息，当时对这次风波的报道也很少，许多数学与物理学领域的科技人员甚至对此并不了解，也没有从中吸取教训。本文介绍和分析这个问题，主要目的是明确表达庞加莱猜想是俄罗斯数学家佩雷尔曼突破的。这已为国际数学界所确定，著名期刊《科学》对此做了详细报道，丘成桐、朱喜全和曹怀东也承认他们对庞加莱猜想的突破并没有做出实际性贡献。世界各大媒体，科学机构，科学家与众多群体关心、瞩目的庞加莱猜想破解之谜，出现了大喜大悲的场面，而且出现在中国大地上，让中国的科学界蒙羞，这始作俑者就是丘成桐，朱熹平和曹怀东等数学家，虽然世界科学群体宽容了这件事，但是，当事人应当做出深刻的反省，从中吸取教训。本文正是出于这一目的，对于在这次风波中出现的违反科研道德和科研规范的行为提是必要的批评。重新讨论这类问题是想引起众多科技群体的重视，不同观点的辩论，交流，甚至碰撞，交锋；以便促进并营造一个和谐、宽松、平等、自由讨论的创新环境时，要树立诚信待人、认真做事的人格。没有这一条件，就无法形成创新的环境、氛围和群体。文章重点分析了顶级里奇流专家的失误，张量分析的物理含义、里奇流的图示和佩雷尔曼的心理特征，等等；对于读者可以扩展视野，了解重大科技问题的复杂性以及最终结果的难于预测。作为前车之鉴，具有警示作用。

Abstract

This article mainly analyzes and discusses the mathematical controversy triggered by the resolution of the Poincaré Conjecture, which involved not only the Chinese mathematics and physics communities but also the international mathematics community. It can be described as a grand showdown among various heroes, with a grand scale, an intriguing plot, and an unexpected outcome, which is rarely seen. The stories of these heroes are worth reading and reflecting upon for readers of different types, fields, and occupations. Why do we still need to discuss these issues 20 years later? The main reason is that the controversy has not subsided. At that time, there were very few reports on this controversy, and many scientists in the fields of mathematics and physics were not even aware of it, nor did they learn any lessons from it. The purpose of this article is to clearly state that the Poincaré Conjecture was resolved by the Russian mathematician Grigori Perelman. This has been confirmed by the international mathematics community, and the renowned journal Science provided detailed coverage of it. Shing-Tung Yau, Xi-Ping Zhu, and Huai-Dong Cao also admitted that they did not make any substantive contributions to the resolution of the Poincaré Conjecture. The resolution of the Poincaré Conjecture, which attracted the attention of the world's major media, scientific institutions, scientists, and various groups, led to a scene of great joy and sorrow in China, bringing shame to the Chinese scientific community. The initiators of this were mathematicians Shing-Tung Yau, Xi-Ping Zhu, and Huai-Dong Cao. Although the global scientific community was tolerant of this incident, the parties involved should make a profound self-examination and learn from it. This article aims to criticize the violations of scientific research ethics and norms that occurred during this controversy. Re-discussing such issues is intended to draw the attention of various scientific communities. Different viewpoints should be debated, exchanged, and even collided and confronted to foster and create a harmonious, relaxed, equal, and free discussion environment for innovation. It is necessary to establish a personality of honesty and integrity and a serious attitude towards work. Without this condition, it is impossible to form an innovative environment, atmosphere, and community. The article focuses on analyzing the mistakes of top experts in Ricci flow, the physical meaning of tensor analysis, the illustration of Ricci flow, and Perelman's psychological characteristics, etc. For readers, it can broaden their horizons and help them understand the complexity of major scientific and technological issues and the difficulty in predicting the final outcome. As a warning, it serves as a cautionary tale.