"Mathematics is a science of concepts, and the development of mathematics benefits from the innovation or transformation of concepts, and the qualitative change achieved by ChatGPT is limited. It may affect ordinary scientists, but it has not yet constituted a threat to the most cutting-edge scientists. In the short term It will not cause a huge change in the development of mathematics."

"There is no doubt that China must become a technological power. We must master the roots of these technologies, which is what we call basic science. There are many kinds of basic science, but the foundation of basic science is mathematical science and theoretical physics. .Mathematics is the foundation of physics and the foundation of all engineering theories.”

Yau Shing-tong, the guest speaker of the second phase of the "Pujiang Science Masters Forum". Image source: Fudan University

On April 7, the second session of the "Pujiang Science Masters Forum" was held in Xianghui Hall, Fudan University. The keynote speaker, Yau Shing-tong, made the above statement in his speech "The Present Situation and Future of Mathematics in China".

Qiu Chengtong, a tenured professor at Harvard University, the dean of Qiuzhen Academy of Tsinghua University, and the winner of the Fields Medal, the highest international mathematics award. Qiu Chengtong graduated with a Ph.D. at the age of 22, was hired as a professor at Stanford University in the United States at the age of 25, and conquered the world's mathematical problem "Calabi's conjecture" at the age of 27, which was upgraded to Calabi-Yau space, and won the Nobel Prize in mathematics at the age of 33 - Fields Medal. Since then, he has successively won the MacArthur Award, the Crawford Award, the Wolf Award, and the Marcel Grossman Award. He is the only mathematician who has won these five world science awards so far.

His influence was not limited to mathematics. Shing-Tung Yau was a professor in both the Department of Physics and the Department of Mathematics at Harvard University. The Calabi-Yau manifold named after him is the basic concept of string theory in physics.

What is the current situation of mathematics in modern China? What kind of math talents do we need? What kind of mathematician is a first-class mathematician? Qiu Chengtong has his own views on these issues.

The development of mathematical science does not lie in Xiao Guicao

What is the position of Chinese mathematics in the history of world mathematics? In Qiu Chengtong's view, from a historical perspective, Chinese mathematics had a prosperous period. Before the Wei, Jin, Southern and Northern Dynasties, Chinese mathematics was not bad in the world's ancient civilizations, and it was mainly applied. From the Sui and Tang Dynasties to the end of the Song Dynasty, Europe was in a dark age, and Chinese mathematics was more advanced than the West in some aspects. In the middle of the Ming Dynasty, the Western Renaissance, the development of world mathematics was unstoppable. "Chinese mathematics still has a long way to go to catch up."

Yau Shing-Tung gave a speech on the history of mathematics development in China and the world. Image source: Fudan University

One of the key points of catching up is "innovation". Qiu Chengtong once wrote in his autobiography "My Geometry Life": "The greatest progress in mathematics does not lie in solving difficult problems, because this will only end certain research fields, but in opening up new and various fields. Questions for exploration." The same is true for the development of mathematics in a country.

In Qiu Chengtong's view, for a country's mathematical ability to occupy a place in the world, the important thing is not to follow Xiao Guicao, but to go out of its own scientific research direction, "in this way, scholars from other countries will have a strong Come and learn if you are interested.”

One of the keys to stimulating innovation is to cultivate a good academic environment. For example, academic achievement should be the most important criterion for evaluating a scholar, so how to evaluate his academic achievement? Qiu Chengtong believes that modern mathematics is colorful and can be divided into dozens of categories. Correspondingly, the evaluation dimensions should also be diversified, and a fair evaluation system is needed. From the point of view of the reviewers, China needs to widely accommodate the opinions of experts from all over the world, always pay attention to the world's cutting-edge mathematics research, and know itself and the enemy. Secondly, in terms of the review dimension, the number of papers and the impact factor are the criteria for evaluating research results, but they are far from enough for frontier fields.

Under Qiu Chengtong's initiative, in July 2023, the first International Basic Science Conference will be held in Beijing. Qiu Chengtong introduced that the conference has set up basic science awards and best paper awards. During the selection process of the Best Paper Award, about 40 branch directions were divided, and five of the world's most active and authoritative scientists were found in each direction. A total of more than 100 world-leading scientists were invited to screen the shortlisted papers. At the same time, a re-examination committee composed of more than 30 scholars was established to review the papers again.

The reason why it is necessary to examine academic achievements in a multi-dimensional and comprehensive manner is because "the most important goal of being a scholar is knowledge itself, to find the mysteries of nature and to find all meaningful laws." Qiu Chengtong said. This is also what science and art have in common—sorting out order and laws from messy phenomena and presenting them to the public in a beautiful form.

cool passion

As the French writer Flaubert said: "Science and art part at the foot of the mountain and meet at the top of the mountain." Mr. Qiu Zhenying's Lectures on the History of Philosophy" and other books.

Influenced by his father, Qiu Chengtong was also interested in literature and other humanities. In his view, scientists who can ask good questions are always quite cultured. In an interview with the media on April 6, Qiu Chengtong said to The Paper: "Many goals of natural science and humanities are the same. For example, there are many interesting phenomena in nature. We will be moved when we see these phenomena, and literature and art directly express this. Scientists are responsible for carrying this emotion and studying the principles behind everything. Therefore, scientists need to have rich emotions. We are moved and excited by the small changes in nature, which drives us to continuously deepen the mechanism behind them. .So the starting point of the humanities and natural sciences is the same, and they are all driven by curiosity.”

The lecture site was full of seats. Image source: Fudan University

However, mathematical science is a bit broader than natural science in the general sense, because mathematics studies certain laws, "We are curious about all laws." Qiu Chengtong said to The Paper reporter. "We want to understand many important laws of nature. Outside of nature, such as social science, we are also interested: the relationship between people, the changes in the stock market, the social relationship of 1.4 billion people... All changes can be understood from the perspective of mathematics. Therefore, there is a close relationship between mathematics and philosophy, and we all want to explore certain laws.”

Improving humanistic literacy is an indispensable part of cultivating mathematical talents. "This experience is not obtained in recent years. For hundreds of years, the most outstanding mathematicians in the West have high humanistic accomplishments," Qiu Chengtong said. "Newton, Gauss, Einstein... without exception. I haven't seen any learned scholar who has no literary and artistic accomplishment. Therefore, the cultivation of mathematics talents in China should not be limited to a certain field or skill." Such a concept It runs through the whole process of Qiu Chengtong's training of mathematics talents.

"We need a lot of top-notch math talent"

Throughout the history of the development of mathematics in the world, "we need to pay attention to the rise of mathematics in every country has an important leading scholar, whose work in mathematics can affect the academic world for a hundred years." Qiu Chengtong said.

In his lecture, he said that in his opinion, the Chinese mathematician with such great influence is Chern Shiingshen. Chern Shiing-shen is one of the greatest geometers of the 20th century, known as the "father of global differential geometry". He gave the intrinsic proof of the high-dimensional Gauss-Bonnet (Gauss-Bonnet) formula, which is commonly known as the Gauss-Bonnet-Chern (Gauss-Bonnet-Chen formula); Class)" has become a classic masterpiece. China now urgently needs such mathematicians.

In 2020, with the approval of the Ministry of Education, Tsinghua University established the Yau Mathematical Sciences Leading Talent Training Program ("Mathematics Leader Program"). On December 31, 2020, Tsinghua University announced the enrollment plan, saying that it will recruit students from all over the world, and the annual enrollment scale will not exceed 100. The eight-year mathematics and applied mathematics professional training mode is dedicated to cultivating future leading talents in mathematics and related fields.

On March 1, 2021, Tsinghua University issued the "Notice on the Establishment of Qiuzhen Academy of Tsinghua University". The notice said: In order to ensure the smooth development of Qiu Chengtong's mathematics science leading talent training plan, after discussion and approval at the 151st Standing Committee Meeting of the 14th Party Committee, it was decided to establish the Qiuzhen Academy of Tsinghua University, the English name is Qiuzhen College, Tsinghua University.

The motto of Qiuzhen Academy is "Looking for a happy place for heaven and people, and broadening our minds for eternity". College students not only learn mathematics knowledge, but also learn the history of mathematics. Qiu Chengtong told the media that this is one of the special courses, and the purpose of understanding the history of mathematics is to let students see how the trend of mathematics has developed in history. In addition, the academy also regularly holds scientist lectures and popular science activities, which not only attract college students, but also plant the seeds of science in the hearts of teenage middle school students.

Others wonder whether artificial intelligence such as ChatGPT will affect mathematicians. Qiu Chengtong believes that from the perspective of data processing, it can help mathematicians process a large amount of information quickly, but when it comes to bringing a major turning point to the development of mathematics, "I think it is still too early. Because mathematics is a science of concepts, the development of mathematics benefits The qualitative change achieved by ChatGPT is limited, it may affect ordinary scientists, but it has not yet constituted a threat to the most advanced scientists, and it will not cause great changes in the development of mathematics in the short term.”

In China, there are many scholars who study such popular applied disciplines, but not many are really creative. Qiu Chengtong believes that the reason is that Chinese applied mathematicians do not have a deep enough understanding of basic mathematics. First-class mathematicians start to develop at the level of basic mathematics. They discover many interesting phenomena and apply them instead of applying them for the sake of application. This has been the case since ancient times.

So in the future, "we need a large number of mathematicians, especially the most cutting-edge mathematicians, so as to break the industrial monopoly." Qiu Chengtong said. First-class mathematicians need to have an unquenchable enthusiasm for truth, just like the famous writer Stefan Zweig described the philosopher Nietzsche: "In their minds, truth is a wife, a solid property, they If you are closely connected with it, even when the god of death is approaching, you will not commit infidelity."

At the end of the speech, Yau Shing-Tung said: "The famous mathematician David Hilbert once said, 'If we seek the truth, we will know.' This is the basic spirit of science. I use a sentence I learned from "Chu To end today's speech with the words adapted from "Ci": You can know the truth, even if you die nine times, how can you regret it! I hope our young people will continue to work hard."

The "Pujiang Science Master Forum" was initiated and managed by the Shanghai Municipal People's Political Consultative Conference, co-sponsored by the Science and Technology and Education Committee of the Shanghai Municipal People's Political Consultative Conference, Fudan University, Shanghai Science and Technology Work Committee of the Communist Party of China, Shanghai Science and Technology Commission, and Shanghai Science and Technology Association. Top scientists in the world Co-organized by the association.