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Source: Phoenix.com, Changping talks
The basic sciences are diverse, and the foundations in the basic sciences are mathematical sciences and theoretical physics. And mathematics is the basis of physics, but also the basis of all engineering theories!
In any strong, modern country, the achievement of mathematics must be at the top!
At present, Chinese mathematics is far from these old powers.
Chinese mathematics has not yet reached the level of the United States in the 40s of the 20th century.
Written by Oka Cheng Tung
There is no doubt that China must become a technological power. In the case of the Western dimension, we must grasp the roots of these technologies, which are what we call basic science.
There are many kinds of basic sciences, but the foundations in basic sciences are mathematical sciences and theoretical physics. And mathematics is the basis of physics, but also the basis of all engineering theories!
So in any strong modern country, the achievements in mathematics must be among the best!
Mathematics flourished in England with Isaac Newton (1643-1727), and after a period of about eighty years, it was revived in the nineteenth century until modern times.
法国数学始于费马(Pierre de Fermat, 1602-1665)、笛卡尔(René Descartes, 1596-1650)等人,历久不衰。
German mathematicians began with Gottfried Wilhelm Leibniz (1646-1716), and the masters were repeated, leading Western mathematics until the revival of the 1950s after the two world wars.
At present, Chinese mathematics is far from these old powers.
In order to develop mathematics, the United States began to send students to Europe in 1880, and in 1910, under the leadership of George David Birkhoff (1884-1944), they began to make a breakthrough, and they took advantage of the opportunity of the two world wars to absorb a large number of European mathematicians. By 1960, American mathematics was leading the world.
Chinese mathematics has not yet reached the level of the United States in the 40s of the 20th century.
The history of mathematics in Russia began in the 18th century from Leonhard Euler (1707-1783) to St. Petersburg, but it really took root in the middle of the 19th century, and by the middle of the 20th century, it was already able to compete with the United States.
After the collapse of the Soviet Union, the economy was sluggish, and a large number of scholars emigrated to the United States and Europe. Although it is not as big as before, the power is still not small.
The culture of Japan and the mainland is relatively close. During the Meiji Restoration, many scholars were sent to study in England, France, and Germany.
The most important scholar was Teiji Takagi (1875-1960), who went to the University of Göttingen in Germany at the end of the 19th century to study with David Hilbert (1862-1943), who returned to reform Japanese teaching methods.
In 1915, he made an extremely important breakthrough in the field of number theory, which greatly increased the confidence of Japanese scholars.
By the end of the 1940s, the Japanese had already made a name for themselves in the world of mathematics, and there were almost no mathematicians who influenced the world. Chinese mathematics has not yet reached this achievement.
It is important to note that the mathematicians developed in these countries represent most of the achievements of modern mathematics. The rise of mathematics in every country has an important leading scholar, whose work in mathematics can influence the academic world for a hundred years!
In China, such a scholar is, without a doubt, Shiing-Shen Chern (1911-2004). When Mr. Chen returned to China in 1946, he brought out a group of outstanding Chinese mathematicians. However, a few years later, all of them, including himself, went to the United States. Of course, he also brought out a group of Chinese mathematicians in the United States. It was not until the mid-80s of the last century that Mr. Chen fully returned to China. At that time, he was already in his seventies, and most of the good students he had cultivated studied abroad. It is very difficult to recreate the style of the 40s. Of course, the weak domestic economy at that time was also an important reason.
However, in today's situation in China, there are strong enemies waiting for them outside, unreasonable suppression, and science and technology being stuck; inside China there are still corrupt officials and corrupt officials, inferior gentry and strong people, and scholars who are looking at comfort and not thinking of danger.
Nowadays, the country has been peaceful for a long time, and most scholars only know how to seek personal interests from the government, and many officials dare not take responsibility and ignore the future of the country, just as Zhuge Liang said, "This sincerity is in danger of survival."
The real rise of mathematics in a country does not lie in the ability to follow the rules and follow the scholars of other countries to do some tinkering work, but in the fact that they have embarked on an important scientific research direction, and scholars from other countries will have a strong interest in following and learning. So far, China's level of mathematics has not reached the point where it is behind, but it has surpassed the level mentioned above. The next three years will be a critical moment in China's rise, and if we do not reach the forefront of the world, I am afraid that the scholars we have brought in will gradually leave and all their achievements will be wasted! This is not alarmism, because now capable scholars come to China in the hope of occupying a place on the world mathematical stage. If China does not have the means to provide such an academic environment, they may choose to leave.
How to know the content of mathematics in a school and a country must have a fair evaluation system. After all, we must know that if we want to be on an equal footing with our international counterparts, a very important part is to know ourselves and our opponents, but until now, the Chinese mathematical community has not understood where our country's mathematics level is at the forefront of the world.
Generally speaking, China does not seek the opinions of international experts when evaluating awards and promotions, and most of the opinions are decided by some domestic peers. But modern mathematics is so colorful that it can be divided into dozens of different directions. However, most of the important scholars in Chinese mathematics are older and tend to stick to the old ways, and their understanding of the development of modern mathematics is not comprehensive, and their assessment of some emerging disciplines is not accurate enough.
In this context, young scholars will continue to stick to the old ways, have no ability or interest to follow their own path, and gradually derail from the development of the world's frontier.
Even in international evaluations, many schools make decisions based on the number of papers, the level of impact factor, and so on. This method is reliable for general learning, but it is far from enough for cutting-edge learning.
Ten years ago, I saw a news that Taiwan's engineering program at National Chiao Tung University was ranked No. 1 in the world, and in recent years, I have heard that Tsinghua University's engineering program has also been ranked No. 1 in the world. Everyone is very happy, but everyone knows in their hearts that the engineering departments of the Massachusetts Institute of Technology, Stanford University, the University of California, Berkeley and other famous universities are stronger than these two universities, and they continue to publish world-leading papers and develop the most cutting-edge technologies in the industry, while our famous Chinese universities have not yet made such breakthrough scientific research.
From this point of view, we know that these methods used to evaluate whether a discipline is world-class through machine search for impact factors are not objective and cannot achieve the goal of evaluation! Prestigious universities in the United States, such as Harvard University, Massachusetts Institute of Technology, Stanford University, Princeton University, University of California, Berkeley, etc., all have world-class scholars, and they have a deep understanding of cutting-edge learning, coupled with peer review, they are very clear about their own level.
In general, they do not make their opinions public. However, Chinese universities lack the most cutting-edge scientists and rarely solicit the opinions of global experts, and even if they do, they are mostly limited to Chinese scholars, which is not comprehensive.
Now let me talk about how I judge the achievements of Chinese mathematics. From 1979, when I set foot in Beijing, until now, I have been to China every year, whether it is the mainland, Taiwan or Hong Kong, on average, the total time is always a few months, and there are many students and visiting scholars who study in the place where I teach in the United States every year. In the past ten years, there have been many of my disciples who have returned to China, including two far-reaching academicians. So far, I have established more than eight mathematics research institutes for China. My own studies also span basic mathematics, applied mathematics and theoretical physics, so I still have a certain understanding of the situation in Chinese mathematics.
But even so, I didn't know much about Chinese mathematics until last year.
In 2022, the leaders of the China Association for Science and Technology came to Tsinghua University to meet with me, hoping that I would lead Chinese mathematics to find its own way in the world.
With the support of Beijing, my colleagues from the Center for Mathematical Sciences at Tsinghua University and the Yanxi Lake Institute of Applied Mathematics in Beijing organized the International Conference on Basic Sciences last year, inviting scholars from all over the world who have made important contributions to mathematics, theoretical physics and engineering to gather in Beijing to discuss cutting-edge academic research.
At the same time, we have established an extremely important international award, called the Best Paper Award, which is planned to be presented at the International Basic Sciences Congress.
We divide the main directions of mathematics, theoretical physics, and engineering into about forty sub-directions. Find five of the most active experts in the field in each direction: European, American, Russian, Israeli, Japanese, and Indian.
Among the judges we invited were five Fields Medal winners, two Nobel Prize winners, two Turing Award winners, as well as a number of other international award-winning experts and more than 60 academicians of academies around the world, all about 160 university scholars.
These scholars evaluate together to select the best papers published in the past five years. These papers should be able to accurately represent the direction of mathematics development, and the winners are well deserved.
After more than a month of round-the-clock discussions, the more than 160 judges we invited selected 110 of the most outstanding papers in mathematics in the past five years. In the interest of objectivity and fairness, we set up a review committee composed of more than 30 distinguished scholars, and finally selected 85 of the best papers. The entire judging process is rigorously participated by the most authoritative experts in the world, and it is the most credible judging process I have ever seen!
I was very surprised by the results of the review! Of the 85 papers, only six were the work of domestic university professors, while there were more than 70 papers written by American university professors!
All of our meetings and discussions related to the selection are convened by Chinese university professors, and it is unlikely that we will discriminate against Chinese scholars. Therefore, the results of the Best Paper Award can be used as an indicator of the comparison between Chinese mathematics and the world's frontiers, which convincingly reflects the real level of mathematics in China.
Combined with the results of our awards, and comparing the results of many important awards in China, it can be clearly seen that the existing evaluations in China do not "really" show the level of Chinese scholars. For example, many scholars who have won important awards in China have not been selected, which means that their research results have not entered the forefront of mathematics in the world and have not been widely recognized by international peers.
The first thing worth discussing is that in the past decade, China's economic rise, although personal wealth is not as good as that of the United States, the salary and housing funding of outstanding scholars in China have exceeded that of most American professors, and Shenzhen, Shanghai, Hangzhou and other places have extremely rich awards.
I heard that Zhejiang Province has a "Kunpeng Action" program that provides an astronomical sum of 60 million yuan! Several mathematicians have benefited from this.
Unfortunately, the winners of these awards are not the authors of the five winning papers.
Another question is why it is difficult for Chinese American scholars to make cutting-edge scholarship at prestigious American universities, but it is difficult for them to do so at prestigious Chinese universities.
However, even among overseas Chinese scholars, the work of the past 40 years, apart from the famous work of Zhang Yitang, is incomparable to the important work of Chern and Wei-Liang Chow (1911-1995) in algebraic geometry.
It cannot be said that the ambitions of overseas Chinese mathematicians must be simple, but they are not surrounded by Chinese "hats" and lured by the glory of Chinese academicians, and they are still willing to strive for the middle and upper reaches. But it is difficult to compare with the work of Mr. Chern!
I have thought about this question for a long time, and I have come to the conclusion that the Chinese method of inducing scholars to do scholarship is too focused on material rewards and does not take into account the achievement of the content of the scholarship itself.
We have a large number of excellent young people, young people, outstanding young people and other reward methods, many colleges and universities stipulate that they only provide these scholars with "hats" with generous salaries and housing allowances, so all young scholars are desperate for "hats"!
Due to the lack of evaluation by particularly prominent international experts, the achievements in learning and science are either exaggerated or incomprehensible!
Young people don't dare to do the most cutting-edge knowledge, because some judges don't understand these cutting-edge knowledge, and they are also selfish, they are afraid that after the cutting-edge knowledge is popular in China, they themselves will not have a place!
Universities and young people are encouraged to establish clear goals, with at least ten universities aspiring to become world-class universities. And the ambition of young people must be improved, and at least a small group of young students have the ambition to become world-class scholars, do breakthrough work, and be able to lead the way in the academic world and influence the development of mathematics in the coming decades!
We can't let our young people's lifelong ambition be to take the "hat" issued by the government, become academicians, or even win the Nobel Prize. The goal of learning is to find the mysteries of nature and find all meaningful laws!
This article is compiled from the lecture given by Mr. Chengtong Yau at Huazhong University of Science and Technology on "The Current Situation and Future of Chinese Mathematics" on April 30, 2024.
Chengtong Yau is an academician of the American Academy of Sciences, an academician of the American Academy of Arts and Sciences, a foreign academician of the Chinese Academy of Sciences, a foreign academician of the Russian Academy of Sciences, a tenured professor of mathematics and physics at Harvard University, a chair professor of Tsinghua University, the director of the Chengtong Yau Center for Mathematical Sciences, the dean of Qiuzhen College, and the dean of the Beijing Yanqi Lake Institute of Applied Mathematics. He has won the Fields Medal, MacArthur, Crafoord, Wolf, Marcel Grossmann, and Shaw.