Scientific Development Research

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.

Poincare conjecture; Ricci flow; Geometrization conjecture; Perelman; Fields medal