Ladies and gentlemen: About one hundred years ago, the first international congress of mathematicians was held in Zurich in 1897 and in Switzerland in 1932. At that meeting, the Fields Medal was established as your grand prize, which is equivalent to the Nobel Prize. This is the third time that China has hosted your conference. No other country has enjoyed this honor given by your scientific group. I believe "Lord Huang Cheng" also appreciates your sincerity and wishes your meeting success. I personally feel very honored to attend the opening ceremony of the conference. This is a rare opportunity to entertain world mathematicians and participate in their two-year scientific discussion. Not long ago, UNESCO launched the initiative of "World Mathematics Year 2000" in Rio de Janeiro. The International Mathematical Union (IMU) takes this opportunity to define a view on mathematics, which focuses on the relationship between science and society. Rio de Janeiro Declaration pointed out: "Pure mathematics and applied mathematics are one of the main keys to understanding the world and its development." I'm sure society needs these keys. But because I'm not myself. I don't know which doors these keys can open or where they lead. I want to ask you what mathematicians think of their role in society. In order to think about the relationship between science and society, I asked three questions to a dozen of the most famous mathematicians in the world. I am grateful for all the answers I received. The first two problems are caused by the difference between pure mathematics and applied mathematics mentioned in Rio de Janeiro Declaration. The first question involves pure mathematics. It seems that pure mathematics only works in a completely independent kingdom, so its purpose is not whether it is useful to society, but whether it is truth. The clarity of these truths embodies a kind of beauty, so pure mathematics is sublimated into an art, but unlike the harp's use of music to please people, a pure mathematician can't make his art accepted by the wider public. Therefore, Beno ekman said: Mathematics "sets the standard for every objective thinking". Friedrich Hirzebruch believes that "without mathematics, there will be no organized logical thinking". Raoul Bott replied: "The treasure (pursued by mathematicians) is the core of everything ... the accurate exploration of the world, and such research must be the most concerned by any advanced country." I agree and believe that as a basic part of the modern world, it is necessary to have mathematical thinking. Historically, mathematics was the key to the Enlightenment. Today, pure mathematics can still be regarded as the guardian of the holy disk of logical thinking. But Roland Bresch wrote: "Mathematics is a hidden culture". Jü rgen Mo Ze further said: "Teaching cannot be accepted as the appreciation of the general audience." If this pure mathematical culture is both hidden and unacceptable, how to show its practical use and prove its elusive conclusion? Armand Borel declared: "Mathematics is like an iceberg: submerged in the water is a pure mathematical field that is not seen by the public. The visible top floating on the water is called applied mathematics. " Phillip Griffiths believes that "one of the most mysterious miracles in life is that the best pure mathematics always insists on its own unobtrusive and unpredictable way." You Ergen Mo Ze also said,' The difficulty in winning praise for this letter is that it often takes a long time to understand the importance of mathematical discovery, and it must take 20 years or more. Unfortunately, politicians always want to see very short-term results. "Absolutely not just politicians, but the whole society. Nowadays, what we are pursuing is that the turnover period of everything in life is getting shorter and shorter. We hope to recover our investment immediately and get timely information. The life of technology is getting shorter and shorter. Efficiency and speed have become the basic criteria for judging any human activity. However, this is dangerous because our vision is too short-sighted. In this environment, it is very important to continue to recognize that knowledge itself is a manifestation of value. The development of mathematics, philosophy or any basic research depends on this basic principle. This is an important part of our civilization. Once we forget it, we destroy the source of our progress. The future is unpredictable. We can't use this as a basis to judge the value of knowledge immediately. For example, Vaughan Jones's work links the three-dimensional knot theory with functional analysis because of its intrinsic value. At the last Kyoto meeting, he was awarded the Fields Medal. Later, his theory was used by physicists in statistical mechanics. Biologists also use it to explain the structure of DNA. Therefore, only through the above understanding and supporting basic research can the whole society maintain the sustained progress and all-round development of science. We turned to applied mathematics. Today, applied mathematics has become the basis of all other sciences, and has had a great influence in modern social life. Applied mathematics has been highly connected with society; And very useful, but lost innocence. However, unlike the responsibility debate of nuclear physics or genetic engineering, I seem to feel that there are few ethical discussions about the role of mathematics in society. So, my second question is: Is there no such discussion in mathematics? Some mathematicians believe that mathematics is morally neutral. For example, rene Toum said in his letter to me, "Mathematics itself is ethically neutral." However, Sir Michael attiya reminded me in his reply: "The atomic bomb was built after a lot of mathematical calculations." Jü rgen Mo Ze also pointed out that "famous mathematicians Wol Neumann and Ulan" played an important role in this project. "armand borell asked:" Should people regard the fact that mathematics is the basis of artillery or air-to-air missiles as an ethical issue? "Yes, I think so. . Friedrich Hirzebruch wrote: It is true that "most mathematicians don't care about the application prospect. Nockemann went further, saying, "Mathematics itself has nothing to do with these (political and ethical) discussions." ... as a purely intellectual activity, it cannot be influenced by this discussion. Of course, people engaged in applied mathematics have to face (this kind of) discussion. "However, I don't think that drawing a line between abstract theory and practical application can eliminate ethical problems at once. The progress of our society is too much due to mathematicians. We should not only acknowledge their achievements, but also remind them of their responsibilities. . Raoul Bott once expressed his "irrational" view to me: "For all of us, the age of innocence has passed. "I firmly believe that this is true not only for science but also for most human activities. Today, relying on science, our society has developed a powerful force to control nature. This power enables us to grasp ourselves. It also forces us to take responsibility for it. If the era of innocence has passed, then we must admit that it has been replaced by the era of responsibility. . Philip Griffith was very generous with his theme, and he replied, "All should be given to mathematical scientists. "gerd faltings also said: Nine seats were given to math, but he loves music. He saved a seat for the harpist, sir. Michal attiya. Friedrich Hirzebruch and Jürgen Moser asked for four or five math seats. This is almost the average of all the answers. In fact, today, only one out of every 20 seats in Switzerland is for mathematics. Surprisingly, some answers only emphasize the needs of natural science. However, when we consider the complexity of the social problems we are facing, I am convinced that the solution of the problems needs the close cooperation of natural sciences and the support and contribution of social and humanities. Today, scientific research is very important. You don't have to convince me, the minister of science, but let's convince the public, Congress and taxpayers together. When there is a huge deficit in the national budget, this is an arduous task.