-Introduction to the Development of Modern Mathematics, Zhang Guangyuan Chongqing Publishing House 199 1. 12.
Modern Knowledge Base-20th Century Mathematics History Knowledge Publishing House 1984.2 Shanghai
Note 1: This is a saying in the history of mathematics in the 20th century.
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The highest prize in international mathematics? Fields Prize and International Congress of Mathematicians
Why is there no math prize for the Nobel Prize? There have been various speculations and discussions about this. The annual Nobel Prize in Physics, Chemistry, Physiology and Medicine has attracted worldwide attention, commending the great achievements of these disciplines and rewarding scientific elites. If there is no math prize, wouldn't it be a missed opportunity to evaluate the great achievements and outstanding talents in the world for this important basic discipline?
In fact, there is also a worldwide award in the field of mathematics, that is, the Fields Prize, which is awarded every four years. In the eyes of mathematicians all over the world, the honor brought by the Fields Prize can be compared with the Nobel Prize.
The Fields Prize is evaluated by the International Mathematical Union (IMU) and awarded only at the International Congress of Mathematicians (ICM) held every four years. Part of the authority of the Fields Medal comes from this. So, here is a brief introduction to "Alliance" and "Congress".
Since19th century, mathematics has made great progress. New ideas, new concepts, new methods and new achievements emerge one after another. Faced with a dazzling array of new documents, even first-class mathematicians feel the need for international communication. They are eager to communicate directly in order to grasp the development trend as soon as possible. The first International Congress of Mathematicians was held in Zurich under this circumstance. Then, in 1900, the second meeting was held in Paris. At the intersection of the two centuries, the German mathematician Hilbert put forward 23 mathematical problems connecting the past and the future, making this conference a veritable conference to welcome the new century.
Since 1900, the general assembly has been held every four years. It was only because of the influence of the world war that it was interrupted between 19 16 and 1940 ~ 1950. The first congress after World War II was held in the United States on 1950. On the eve of this meeting, the International Mathematical Union was established. This alliance has contacted almost all the major mathematicians in the world. Its main task is to promote the development of mathematics and international exchanges, organize the international congress of mathematicians and other professional international conferences every four years, and award the Fields Prize. Since then, the meeting has been held relatively normally. Since 1897, the General Assembly has held nineteen congresses, nine of which were held from 1950 to 1983.
The daily affairs of the Alliance are led by the Executive Committee for a term of four years. In recent years, this committee has a chairman, two vice-chairmen, a secretary-general and five general members, all of whom are famous mathematicians with influence in the international digital field. The agenda of each meeting shall be drawn up by a nine-member advisory committee nominated by the Executive Committee. The winner of the Fields Prize was selected by an eight-member evaluation committee nominated by the Executive Committee. The chairman of the jury is also the chairman of the executive Committee, which shows the importance attached to this award. This jury was first nominated by everyone, focusing on nearly 40 candidates worthy of serious consideration, then fully discussing and listening to the opinions of mathematicians from all over the world, and finally voting within the jury to decide the winner of this year's Fields Prize.
Now, the International Congress of Mathematicians is the most important academic exchange activity for mathematicians all over the world. Since 1950, more than 2,000 people have participated in each time, and more than 3,000 people have participated in the last two sessions. With so many participants and countless new achievements in the past four years, how can we communicate well? In recent years, several conferences have adopted the method of three-level speech. Take 1978 as an example, about 700 people volunteered to give a 10-minute speech in various professional groups, and then the advisory Committee decided on the list of about 200 people who were invited to give a 45-minute speech in various professional groups, and selected 17 people to give a 1 hour summary report to the plenary session. It is a great honor to be assigned to give a lecture for an hour. Lecturers are the most active mathematicians today, and many of them are past or future Fields Prize winners.
The announcement and award of the Fields Medal is the main content of the opening ceremony. When the chairman of the Executive Committee (the chairman of the jury) announced the winners, the audience applauded. Then an important person from the host country (the local mayor, the president of the National Academy of Sciences, even the king and president) or the chairman of the jury will award a gold medal, plus a bonus of 500 dollars. Finally, some authoritative mathematicians introduced the outstanding works of the winners and concluded the opening ceremony.
The Fields Medal was awarded to the late Canadian mathematician John? Charles. Fields named it.
1May, 86314th, Fields was born in Ottawa, Canada. His father died at the age of eleven and lost his loving mother at the age of eighteen. His family is not very good. Fields/Kloc-entered the University of Toronto at the age of 0/7 and specialized in mathematics. 1887, 24-year-old Fields received his doctorate from Johns Hopkins University. Two years later, he became a professor at Allegheny University.
At that time, the center of world mathematics was in Europe. Almost all mathematicians in North America will study and work in Europe for some time. 1892, Fields crossed the ocean and studied in Paris and Berlin for ten years. In Europe, he had close contacts with famous mathematicians forsyth and Fraubenius. This experience greatly broadened Fields' horizons.
As a mathematician, Fields' work interests focus on algebraic functions, and his achievements are not outstanding, but as an organizer and manager of mathematics, Fields has made outstanding achievements.
Fields realized the importance of postgraduate education very early. He was the first person in Canada to promote postgraduate education. Now people all know that the postgraduate training in a country is a reliable indicator to measure the scientific level of this country. It was really valuable to have such an understanding at that time.
Fields has some outstanding views on the importance of international exchange of mathematics and the promotion of the development of mathematics in North America. In order to catch up with Europe in mathematics in North America, Fields made every effort to host and prepare the Toronto International Congress of Mathematicians in 1924 (this was the first conference held outside Europe). The meeting exhausted him and his health never improved, but the meeting had a far-reaching impact on the growth of mathematics level in North America.
1924, the conference did not invite mathematicians from Germany and other countries that lost the first world war. Prior to this, the meeting of 1920 was held in Strasbourg, France (Germany before the war), and Germany refused to participate (the Bologna meeting of 1928 was also attended because of Hilbert's insistence. )。 These things probably triggered Fields' idea of launching an international prize, because Fields strongly advocated that the development of mathematics should be international. When Fields learned that there were surplus funds for the 1924 conference, he suggested setting up such a fund. Fields went to Europe and America for support and wanted to join in? 1932, the Zurich parliament personally put forward a formal proposal, but he died before the opening ceremony. It was Sidney of the Department of Mathematics of the University of Toronto who submitted this proposal and a large sum of money (including the balance of the 1924 conference and Fields' legacy) to the Zurich conference, and the conference immediately accepted this proposal.
According to Fields, this award should be called an international award and should not be named after any national institution or individual. However, the International Congress of Mathematicians decided to name it the Fields Prize. Mathematicians hope to express their commemoration and praise of the field in this way. He used his foresight, organizational ability and hard work to promote the cause of mathematics in this century, rather than his own research work.
The first Fields Medal was awarded in 1936. Soon, the international situation deteriorated sharply. The meeting scheduled for 1940 in the United States was unsuccessful. The second Fields Medal was awarded in the first Congress after the war, namely 1950. Since then, this agenda has been successfully implemented at every meeting. ? Generally, there are two winners in each session. However, in 1966, 1970 and 1978, there were four winners. It is said that the bonus can be temporarily increased to 4 pounds because of an anonymous donor. The Warsaw meeting of 1982 was postponed to1August 983 for some reason, and three winners were awarded. A total of 27 mathematicians won the Fields Prize.
In 1936? At the three congresses in 1950 and 1954, a mathematician introduced the work of all the winners. 1936, Carla Kiu Dolly also told a little about the life of the winner. 1950 Bohr, the chairman of the jury, only briefly described the work in clear rather than professional language. 1954, introduced by a famous mathematician in this century, Wall praised the two winners for "reaching heights they never dreamed of" in his concluding remarks. "I have never seen such stars rise brilliantly in the mathematical sky". He said, "The mathematical community is proud of the work you two have done. It shows that the old tree full of knots in mathematics is still full of juice and vitality. How do you start, how do you continue! "
Since 1958, each winner has been introduced by a mathematician. The content of the introduction is relatively limited to the works, and rarely involves the personal situation of the winners. This practice continued until the recent Congress.
The Fields Medal is only a gold medal, which is really insignificant compared with the Nobel Prize of100000 dollars. Why is the status of the Fields Medal equal to the Nobel Prize in people's minds?
There seem to be many reasons. The Fields Medal was selected by the International Mathematical Union, an international academic group in the field of mathematics, from the top mathematicians in the world. In terms of authority and internationality, no other award can be compared with it. The Fields Prize is awarded only once every four years, and there are at most four winners each time, so the chances of winning the prize are much smaller than the Nobel Prize. But the main reason should be that the winners so far have proved that the Fields Prize is the most important international mathematics prize with their outstanding work. The situation is this: on the surface, a reward brings great honor to the winner; In fact, on the contrary, it is the level of the winning works that lays the academic status of this award.
The Fields Prize is first of all a work award (the same as the Nobel Prize), that is, the reason for awarding can only be "achievements already made", but not other reasons such as excellent service and positive activities. However, the Fields Medal is only awarded to mathematicians under the age of 40 (at first it was a tacit understanding, and later it became an unwritten rule), so it is also a bit encouraging. The question is, what is the status of the Fields Medal if it is placed within the scope of the whole mathematician?
Let's give a small example. 1978, a famous mathematician of the older generation and one of the founders of Bourbaki School published a paper entitled "On the Trend of Current Pure Mathematics", which comprehensively summarized the frontiers of various branches of pure mathematics in the past twenty years. In the article, he listed thirteen branches of mathematics that are currently in the mainstream. Some important work in 12 branch was done by the winners of Fields Prize. This clearly shows the status of the Fields Medal.
People have to admit that the influence of mathematics on real life is increasing. Many subjects are quietly going through a mathematical process, sooner or later. Now, no field can resist the infiltration of mathematical methods.
Mathematics itself is also developing rapidly. Thousands of mathematicians all over the world work hard in dozens of branches and hundreds of professional directions. They put forward about 200 thousand new theorems every year! The number of important papers, such as abstracts of Mathematical Review, will double every eight to ten years. The explosion of literature and the rapid updating of method concepts make it a little difficult for mathematicians working in different directions to even speak, let alone non-mathematics majors.
This has created a sharp contradiction. On the one hand, the public needs mathematics very much and is eager to know it! Another one? On the other hand, modern mathematics is too abstruse, too huge and more and more difficult to understand.
Therefore, popularizing mathematics, especially modern mathematics, so that the work of mathematics and mathematicians can have a positive impact on real life has become a topic of increasing concern.
The dawn of 2 1 century is about to shine all over the world, so it is not easy to summarize the development of mathematics in the 20th century. As far as pure mathematics is concerned, we think there are two themes that can be used as an outline: one is the proposal, solution and development of Hilbert's 23 problems, and the other is the winners of Fields Prize and their works.
As a reward for the achievement of pure mathematics, the Fields Prize certainly cannot reflect all the contents of modern mathematics. As far as the awards themselves are concerned, there are also various shortcomings. However, no matter from which aspect, the winners of Fields Prize can be regarded as representatives of contemporary mathematicians, and their fields generally cover the forefront of the mainstream branch of pure mathematics. In this way, the Fields Medal has become a good "window" to peep at the face of modern mathematics.