A story about a mathematician in urgent need

Mathematical wizard and father of computers - von Neumann

The 20th century is about to pass, and the 21st century is coming. When we stand at the threshold of the turn of the century and look back on the glorious development of science and technology in the 20th century, we cannot but mention von Neumann, one of the most outstanding mathematicians of the 20th century. As we all know, the electronic computer invented in 1946 has greatly promoted the progress of science and technology and social life. In view of the key role von Neumann played in the invention of electronic computers, he is hailed by Westerners as the "Father of Computers".

John von Neumann (John Von Nouma, 1903-1957), a Hungarian American, was born in Budapest, Hungary on December 28, 1903. His father was a banker and his family was wealthy. Pay attention to the education of your children. Von Neumann was extremely smart since he was a child, had a wide range of interests, and had a photographic memory of what he read. It is said that when he was 6 years old, he could chat with his father in ancient Greek and mastered seven languages ??in his life. He is the best at German, but when he is thinking about various ideas in German, he can also translate them into English at the speed of reading. He is familiar with the books and papers he has read. Able to retell the content quickly and accurately, and can still do so years later. From 1911 to 1921, while studying at the Luceren High School in Budapest, von Neumann emerged and was highly valued by his teacher. Under the individual guidance of Mr. Feicht and in cooperation with him, he published his first mathematical paper. At this time, von Neumann was less than 18 years old. From 1921 to 1923, he studied at the University of Zurich. Soon he obtained a doctorate in mathematics from the University of Budapest with honors in 1926. At this time, von Neumann was only 22 years old. From 1927 to 1929, von Neumann served as a mathematics lecturer at the University of Berlin and the University of Hamburg.

In 1930, he accepted the position of visiting professor at Princeton University and traveled west to the United States. In 1931, he became a tenured professor of the school. In 1933, he transferred to the Institute of Advanced Studies of the school and became one of the first six professors, and worked there all his life. Von Neumann is an honorary doctorate from Princeton University, the University of Pennsylvania, Harvard University, the University of Istanbul, the University of Maryland, Columbia University and the Higher Technical School of Munich. He is a fellow of the National Academy of Sciences of the United States, the National Academy of Natural Sciences of Peru and the National Academy of Forestry in Italy. In 1954, he served as a member of the United States Atomic Energy Commission; from 1951 to 1953, he served as president of the American Mathematical Society.

In the summer of 1954, von Neumann was diagnosed with cancer. He died in Washington on February 8, 1957, at the age of 54.

Von Neumann conducted pioneering work in many fields of mathematics and made significant contributions. Before World War II, he was mainly engaged in research on operator theory, nose theory, set theory, etc. The 1923 paper on transfinite ordinal numbers in set theory showed von Neumann's unique way and style of dealing with set theory problems. He axiomatized the assembly theory, and his axiomatic system laid the foundation of axiomatic set theory. Starting from axioms, he used algebraic methods to derive many important concepts, basic operations, and important theorems in set theory. Especially in a paper in 1925, von Neumann pointed out that there are undecidable propositions in any axiomatic system.

In 1933, von Neumann solved Hilbert's fifth problem, which proved that the local Euclidean compact group is a Lie group. In 1934, he unified the theory of compact groups with Bohr's theory of nearly periodic functions. He also had a profound understanding of the structure of general topological groups and found out that its algebraic structure and topological structure are consistent with the real numbers. He conducted pioneering work on its subalgebra and determined its theoretical basis, thereby establishing a new branch of mathematics called operator algebra. This branch is called von Neumann algebra in contemporary relevant mathematical literature. This is a natural generalization of matrix algebra in finite dimensional spaces. Von Neumann also founded game theory, another important branch of modern mathematics. In 1944, he published the foundational and important paper "Game Theory and Economic Behavior". The paper contains a purely mathematical explanation of game theory and a detailed description of practical game applications. The article also contains teaching ideas such as statistical theory. Von Neumann has done important work in the fields of lattice theory, continuous geometry, theoretical physics, dynamics, continuum mechanics, meteorological calculations, atomic energy and economics.

Von Neumann's greatest contribution to mankind is his pioneering work in computer science, computer technology and numerical analysis.

The ENIAC machine is now generally considered to be the world's first electronic computer. It was developed by American scientists and started operating in Philadelphia on February 14, 1946. In fact, the "Colosas" computer developed by British scientists such as Tommy and Flowers preceded the advent of the ENIAC machine by more than two years. It began operation at Bletchley Park on January 10, 1944. The ENIAC machine proves that electronic vacuum technology can greatly improve computing technology. However, the ENIAC machine itself has two major shortcomings: (1) It has no memory; (2) It uses a wiring board for control, and even needs to be connected to the sky, and the calculation speed is also very slow. It was offset by this work. Mowgli and Eckert of the ENIAC machine development team obviously felt this, and they also wanted to start developing another computer as soon as possible for improvement.

After von Neumann was introduced to the ENIAC machine development team by Lieutenant Goldstin of the ENIAC machine development team, he led this group of innovative young scientific and technological personnel to march towards higher goals. ． In 1945, based on discussions with colleagues, they published a brand new "stored program universal electronic computer solution" - EDVAC (the abbreviation of Electronic Discrete Variable Automatic Computer). In the process, von Neumann showed his strong basic knowledge of mathematics and gave full play to his

His advisory role and ability to explore problems and comprehensively analyze.

The EDVAC plan clearly established that the new machine is composed of five parts, including: arithmetic unit, logic control device, memory, input and output equipment, and described the functions and interrelationships of these five parts. The EDVAC machine also has two very important improvements, namely: (1) It uses binary, not only the data is in binary, but the instructions are also in binary; (2) A stored program is established, and the instructions and data can be placed together in the memory and processed. The same process was used to simplify the structure of the computer and greatly improve the speed of the computer. In July and August 1946, von Neumann, Goldstine, and Bocks developed a new computer for Princeton University based on the EDVAC program. When the institute developed the IAS computer, it also proposed a more complete design report, "A Preliminary Study on the Logic Design of Electronic Computers." The above two documents, which contained both theory and specific design, set off a "computer craze" around the world for the first time. Their comprehensive design idea is the famous "Von Neumann machine", the center of which is the stored program principle - instructions and data are stored together. This concept is known as 'the history of computer development. "A milestone". It marks the true beginning of the electronic computer era and guides future computer design. Naturally, everything is always developing. With the advancement of science and technology, people today realize that "Von Neumann" Due to the shortcomings of "machine", which hindered the further improvement of computer speed, the idea of ??"non-Von Neumann machine" was proposed. Von Neumann also actively participated in the promotion of applied computers, and had a lot of knowledge on how to program and do He made outstanding contributions to numerical calculations. Von Neumann won the Potzer Prize of the American Mathematical Society in 1937; the U.S. President’s Medal of Merit and the U.S. Navy’s Outstanding Citizen Service Award in 1947; and the U.S. President’s Medal of Freedom in 1956. and the Einstein Memorial Prize and the Fermi Prize.

After von Neumann's death, the unfinished manuscript was published under the title "Computers and the Human Brain". His major works are collected in. Six volumes of "The Complete Works of von Neumann", published in 1961.

Mathematical Wizard - Galois Top of Page

On the morning of May 30, 1832, in Paris There was an unconscious young man lying near Lake Glassell. The passing farmers judged from the gunshot wounds that he had been seriously injured after a duel, so they carried the unknown young man to the hospital at ten o'clock the next morning. Passed away. The youngest and most creative mind in the history of mathematics stopped thinking. It is said that his death delayed the development of mathematics for several decades. This young man was under 21 years old.

Galois was born in a small town not far from Paris. His father was a school principal and had been the mayor for many years. The influence of his family made Galois move forward courageously and fearlessly. In 1823, Galois was 12 years old. Hua left his parents to study in Paris. He was not satisfied with the rigid classroom indoctrination and went to study the most difficult original mathematics books on his own. Some teachers also gave him great help, saying that he "should only study in the cutting-edge fields of mathematics." Work".

In 1828, the 17-year-old Galois began to study equation theory, created the concept and method of "permutation groups", and solved equations that had caused headaches for hundreds of years to solve problems. Galois's most important achievement was to propose the concept of "group" and use group theory to change the entire face of mathematics. In May 1829, Galois wrote his results into a paper and submitted it to the French Academy of Sciences. However, this masterpiece was accompanied by a series of blows and misfortunes. First, his father committed suicide because he could not bear the slander from the priests. Then, because his answers were both simple and profound, which dissatisfied the examiners, he failed to enter the famous Ecole Polytechnique in Paris. As for his paper, it was first considered to have too many new concepts and was too simple and required rewriting; the second manuscript with detailed derivation was missing due to the death of the reviewer; the third paper submitted in January 1831 was also rejected due to review issues. People cannot understand everything and are denied.

On the one hand, the young Galois pursued the true knowledge of mathematics, and on the other hand, he devoted himself to the cause of pursuing social justice.

During the "July Revolution" in France in 1831, as a freshman at the Ecole Normale Supérieure, Galois led the masses to take to the streets to protest against the king's autocratic rule, but was unfortunately arrested. While in prison, he contracted cholera. Even under such harsh conditions, Galois continued his mathematical research and wrote a paper to be published after he was released from prison. Not long after he was released from prison, he died in a duel because he was involved in a boring "love" entanglement.

It was 16 years after Galois's death that his 60 pages of surviving manuscripts were published, and his name spread throughout the scientific community.

"God of Mathematics" - Archimedes Top

Archimedes was born in 287 BC in Syracuse, Sicily, at the southern tip of the Italian peninsula. His father is a mathematician and astronomer. Archimedes had a good family upbringing since he was a child. At the age of 11, he was sent to Alexandria, the cultural center of Greece at that time, to study. In this famous city known as the "City of Wisdom", Archimedes read widely and absorbed a lot of knowledge. He also became a disciple of Euclid's students Eratoses and Canon, and studied "Elements of Geometry" .

Later, Archimedes became a great scholar who was both a mathematician and a mechanics scientist, and he was known as the "Father of Mechanics". The reason is that he discovered the lever principle through a large number of experiments, and used geometric evolution methods to derive many lever propositions and give strict proofs. Among them is the famous "Archimedes' Principle". He also has extremely brilliant achievements in mathematics. Although there are only about a dozen of Archimedes' works that have been handed down to this day, most of them are geometric works, which played a decisive role in promoting the development of mathematics.

"Sand Calculation" is a book dedicated to calculation methods and calculation theory. Archimedes wanted to calculate the number of sand grains filling the large sphere of the universe. He used a very strange imagination, established a new magnitude counting method, determined new units, and proposed a model to express any large quantity. This is consistent with logarithms. Operations are closely related.

"Measurement of a Circle" uses the circumscribed and inscribed 96 polygons of a circle to calculate the pi value: ＜π＜. This is the earliest π value in the history of mathematics that clearly points out the error limit. He also proved that the area of ??a circle is equal to the area of ??an equilateral triangle with the circumference as the base and the radius as the height; using the exhaustive method.

"Sphere and Cylinder" skillfully uses the exhaustion method to prove that the surface area of ??a sphere is equal to four times the area of ??the great circle of the sphere; the volume of the sphere is four times the volume of a cone, and the base of the cone is equal to the great circle of the sphere. , the height is equal to the radius of the ball. Archimedes also pointed out that if there is an inscribed sphere in an equilateral cylinder, the total area of ??the cylinder and its volume are respectively the surface area and volume of the sphere. In this work, he also proposed the famous "Archimedes' Axiom".

"Parabolic Quadrature Method" studied the problem of quadrature of curved figures, and used the exhaustion method to establish this conclusion: "Any arc (that is, a parabola) surrounded by a straight line and a right-angled cone section , its area is one-third of the area of ??a triangle with the same base and the same height." He also used the mechanical weight method to verify this conclusion again, successfully combining mathematics and mechanics.

"On Spirals" is Archimedes' outstanding contribution to mathematics. He clarified the definition of a spiral and how to calculate its area. In the same work, Archimedes also derived geometric methods for the summation of geometric and arithmetic series.

"The Balance of the Plane" is the earliest scientific treatise on mechanics. It talks about the problem of determining the center of gravity of plane figures and three-dimensional figures.

"Floating Bodies" is the first monograph on hydrostatics. Archimedes successfully applied mathematical reasoning to analyze the balance of floating bodies, and used mathematical formulas to express the laws of floating body balance.

"On Cones and Spheres" talks about determining the volume of a cone formed by rotating a parabola and a hyperbola around its axis, and the rotation of an ellipse around its major and minor axes. The volume of the spherical body.

The Danish mathematics historian Heiberg discovered in 1906 copies of Archimedes' letter to Eratosthe and some other works of Archimedes. Through research, it was found that these letters and manuscripts contained the idea of ??calculus. What he lacked was the concept of limits, but the essence of his thoughts extended to the field of infinitesimal analysis that became mature in the 17th century, foretelling the development of calculus. Birth.

Because of his outstanding contributions, the American E.T. Bell commented on Archimedes in "Mathematical Figures": Any list of the three greatest mathematicians in history is Among them, Archimedes must be included, and the other two are usually Newton and Gauss. However, comparing their magnificent achievements and the background of the times, or comparing their profound and long-lasting influence on contemporary and future generations, Archimedes should be the first to be mentioned.

The Story of Mathematician - Zu Chongzhi Top of Page

Zu Chongzhi (429-500 AD) was a native of Laiyuan County, Hebei Province during the Southern and Northern Dynasties of my country. He read many books on astronomy and mathematics since he was a child. He was diligent, studious and practiced hard, which finally made him an outstanding mathematician and astronomer in ancient my country.

Zu Chongzhi’s outstanding achievement in mathematics was the calculation of pi. Before the Qin and Han Dynasties, people used "three days per week" as the pi rate, which was the "ancient pi rate". Later, it was discovered that the error of the ancient rate was too large. The pi should be "the diameter of a circle is one and the diameter of three is more than three." However, there are different opinions on how much there is. It was not until the Three Kingdoms period that Liu Hui proposed a scientific method for calculating pi - "circle cutting", which uses the circumference of a regular polygon inscribed in a circle to approximate the circumference of a circle. Liu Hui calculated that the circle is inscribed in 96 polygons and obtained π=3.14. He also pointed out that the more sides the inscribed regular polygon has, the more accurate the π value obtained. Based on the achievements of his predecessors, Zu Chongzhi worked hard and calculated repeatedly, and found that π is between 3.1415926 and 3.1415927. And the approximate value of π in the form of a fraction is obtained, which is taken as the approximate ratio and taken as the density. Taking six decimal places is 3.141929, which is the fraction closest to the value of π within 1000 in the numerator and denominator. Exactly what method Zu Chongzhi used to arrive at this result cannot be investigated now. If he were to calculate according to Liu Hui's "circle cutting" method, he would have to calculate that the circle is inscribed with 16,384 polygons. How much time and tremendous labor this would take! This shows that his tenacious perseverance and intelligence in scholarship are admirable. It was more than a thousand years later that foreign mathematicians obtained the same density calculated by Zu Chongzhi. In order to commemorate Zu Chongzhi's outstanding contribution, some foreign mathematics historians suggested calling π= "Zu rate".

Zu Chongzhi read the famous classics of the time and insisted on seeking truth from facts. He compared and analyzed a large amount of data from personal measurements and calculations, and found serious errors in the past calendars. He had the courage to improve them, and successfully compiled them when he was thirty-three years old. The "Da Ming Calendar" opened up a new era in the history of calendars.

Zu Chongzhi also used an ingenious method to solve the calculation of the volume of a sphere together with his son Zu Xun (also a famous mathematician in my country). A principle they adopted at the time was: "Since the power potentials are the same, the products are indifferent." That is to say, two solids located between two parallel planes are intercepted by any plane parallel to the two planes. If the two If the areas of the cross sections are always equal, then the volumes of the two solids are equal. This principle is called Cavalieri's principle in Spanish, but it was discovered by Cavalieri more than a thousand years after Zu. In order to commemorate the great contribution of Zu and his son in discovering this principle, everyone also calls this principle "Zu Xun's Principle".

The Story of a Mathematician - Su Buqing Top of Page

Su Buqing was born in September 1902 in a mountain village in Pingyang County, Zhejiang Province. Although his family was poor, his parents lived frugally and worked hard to support his education. When he was in junior high school, he was not interested in mathematics. He felt that mathematics was too simple and he could understand it as soon as he learned it. It can be estimated that a later mathematics class affected the path of his life.

That was when Su Buqing was in the third grade of junior high school. He was studying in the No. 60 Middle School of Zhejiang Province, and there came a teacher Yang who had just returned from studying in Tokyo and taught mathematics. In the first class, Teacher Yang did not teach mathematics, but told stories. He said: "In today's world, the weak prey on the strong, and the world's major powers rely on their ships and cannons to carve up China. The danger of China's national subjugation and annihilation is imminent. Revitalize science, develop industry, and save the nation in one fell swoop. 'Every man is responsible for the rise and fall of the world.' , every student here has a responsibility." He quoted from many sources and talked about the huge role of mathematics in the development of modern science and technology. The last sentence of this class is: "In order to save the nation and survive, we must revitalize science. Mathematics is the pioneer of science. In order to develop science, we must learn mathematics well." Su Buqing had listened to many classes in his life, but this class made him unforgettable. .

Teacher Yang’s class deeply moved him and injected new stimulants into his mind. Reading is not only to get rid of personal difficulties, but to save the vast number of suffering people in China; reading is not only to find a way out for individuals, but to seek new life for the Chinese nation. That night, Su Buqing tossed and turned and couldn't sleep all night. Under the influence of Teacher Yang, Su Buqing's interest shifted from literature to mathematics, and from then on he established the motto of "Reading without forgetting to save the country, and saving the country without forgetting reading". Once he fell in love with mathematics, Su Buqing only knew how to read, think, solve problems, and calculate, no matter it was scorching summer or winter, frosty morning or snowy night. In 4 years, he calculated tens of thousands of mathematical problems. Now Wenzhou No. 1 Middle School (i.e. the Provincial No. 10 Middle School at that time) still treasures Su Buqing's geometry exercise book, written with a brush, and his workmanship is neat. When he graduated from middle school, Su Buqing scored above 90 points in all subjects.

At the age of 17, Su Buqing went to Japan to study and was admitted to the Tokyo Advanced Technical School with first place, where he studied eagerly. The belief of winning glory for the country drove Su Buqing to enter the field of mathematics research early. While completing his studies, he wrote more than 30 papers, achieved remarkable results in differential geometry, and received a doctorate in science in 1931. Before receiving his Ph.D., Su Buqing had been a lecturer in the Department of Mathematics at the Imperial University of Japan. Just when a Japanese university was preparing to hire him as an associate professor with a well-paid salary, Su Buqing decided to return to his country and teach in his ancestors who raised him. Su Buqing, who returned to Zhejiang University as a professor, lived a very difficult life. Faced with the dilemma, Su Buqing's answer was, "It doesn't matter if I endure hardship. I am willing to do so because I have chosen the right path. This is a patriotic and bright path!"

This is the mathematics of the older generation. The patriotic heart of a family

The Father of Mathematics - Salles Top of Page

Salles was born in 624 BC and was the first world-famous ancient Greek. great mathematician. He was originally a very shrewd businessman. After accumulating considerable wealth by selling olive oil, Salles concentrated on scientific research and travel. He is diligent and studious, but at the same time he is not superstitious about the ancients. He has the courage to explore, create and think actively about problems. His hometown is not too far from Egypt, so he often travels to Egypt. There, Salles was introduced to the vast mathematical knowledge that the ancient Egyptians had accumulated over thousands of years. When he traveled to Egypt, he used an ingenious method to calculate the height of the pyramid, which made the ancient Egyptian King Amesses envious.

Salles’ method is both ingenious and simple: choose a sunny day, erect a small stick next to the pyramid, and then observe the change in the length of the stick’s shadow until the length of the shadow is exactly equal to the length of the stick. At this moment, quickly measure the length of the shadow of the pyramid, because at this moment, the height of the pyramid happens to be equal to the length of the shadow. Some people also say that Salles calculated the height of the pyramid by using the ratio of the length of the stick's shadow to the tower's shadow, which is equal to the ratio of the height of the stick to the height of the tower. If this is the case, we need to use the mathematical theorem that the corresponding sides of a triangle are proportional. Salles boasted that he taught this method to the ancient Egyptians, but the truth may be exactly the opposite. It should be that the Egyptians had known similar methods for a long time, but they were only satisfied with knowing how to calculate without thinking about why. This way you can get the correct answer.

Before Salles, when people understood nature, they were only satisfied with what kind of explanations they could put forward for various things. But the greatness of Salles was that he was not only able to make explanations explanation, and also added a scientific question mark as to why. The mathematical knowledge accumulated by the ancient Eastern people mainly consists of some calculation formulas summed up from experience. Salles believes that the calculation formulas obtained in this way may be correct when used in one problem, but not necessarily correct in another problem. Only after they are theoretically proved to be universally correct can they be widely used. They solve real problems. In the early stages of the development of human culture, it is commendable that Salles consciously put forward such a point of view. It gives mathematics a special scientific significance and is a huge leap in the history of mathematics development. So Salles is known as the father of mathematics, and this is why. Salles first proved the following theorem:

1. A circle is bisected by any diameter.

2. The two base angles of an isosceles triangle are equal.

3. When two straight lines intersect, their opposite vertex angles are equal.

4. The inscribed triangle of a semicircle must be a right triangle.

5. If two triangles have one side and two angles on this side are equal, then the two triangles are congruent. This theorem was also first discovered and proved by Salles, and later generations often call it Salles' theorem. According to legend, Salles was so happy after proving this theorem that he killed a bull and offered it to the gods. Later, he also used this theorem to calculate the distance between ships at sea and land.

Salles also made pioneering contributions to ancient Greek philosophy and astronomy. Historians definitely say that Salles should be regarded as the first astronomer. He often lay on his back to observe the constellations in the sky and explore the mysteries of the universe. His maid often joked that Salles wanted to know the distant sky, but ignored what was in front of him. Beauty. The historian of mathematics Herodotus has learned from various researches that day suddenly turned into night (actually a solar eclipse) after the battle of Hals, and before the battle, Seles predicted this to Delians. There is an inscription on Salles's tombstone:

"The tomb of this king of astronomers is somewhat small, but his glory in the field of stars is quite great.

Mathematician's epitaph top page

Some mathematicians devoted themselves to mathematics during their lifetime, and after their death, symbols representing their life achievements were engraved on their tombstones.

After the ancient Greek scholar Archimedes died at the hands of Roman enemies attacking Sicily (before his death, he said: "Don't break my circle."), people inscribed on his tombstone to commemorate him. The figure of the upper sphere inscribed in the cylinder commemorates his discovery that the volume and surface area of ??the sphere are two-thirds of the volume and surface area of ??the circumscribed cylinder. The German mathematician Gauss discovered the rule of the regular heptadagon during his research. After doing this, he gave up his original intention to study literature and devoted himself to mathematics, and even made many significant contributions in mathematics. In his will, he even proposed to build a tombstone for him with a regular heptagonal prism as the base.

Rudolf, a German mathematician in the 16th century, spent his whole life calculating pi to 35 decimal places. Later generations called it Rudolf's number. After his death, others engraved this number on his tombstone. The Swiss mathematician Jacques Bernoulli studied spirals (known as the line of life) during his lifetime. After his death, a logarithmic spiral was engraved on his tombstone, and the inscription also read: "Although I Changed, but the same as before." This is a pun that not only depicts the nature of the spiral but also symbolizes his love for mathematics

The highest award in the international mathematics community - the Fields Medal and International Mathematics Home Conference Top

Why is there no mathematics prize among the Nobel prizes? There have been various speculations and discussions about this. The annual Nobel Prize in Physics, Chemistry, Physiology and Medicine honors these. The major achievements in this discipline have rewarded scientific elites and attracted worldwide attention.

If there is no mathematics award, wouldn't this important basic subject lose an opportunity to evaluate major achievements and outstanding talents around the world? In fact, there is also a worldwide award in the field of mathematics, which is the Fields Medal awarded every four years. In the eyes of mathematicians from all over the world, the honor brought by the Fields Medal is comparable to the Nobel Prize.

The Fields Medal is assessed by the International Mathematical Union (IMU) and is only awarded at the International Congress of Mathematicians (ICM) held every four years. The authority of the Fields Medal partly comes from this. Therefore, here is a brief introduction to "alliance" and "conference".

Mathematics has made tremendous progress since the 19th century. New ideas, new concepts, new methods, and new results emerge one after another. Faced with a dazzling array of new literature, even first-class mathematicians feel the need for international exchanges. They are eager to communicate directly in order to grasp the development trend as soon as possible. It was under such circumstances that the first International Congress of Mathematicians was held in Zurich. Immediately afterwards, the second conference was held in Paris in 1900. At the junction of two centuries, the German mathematician Hilbert proposed twenty-three mathematical problems that connected the past with the future, making this conference worthy of its name. meeting to welcome the new century.

Since 1900, the conference has generally been held every four years. It was only because of the impact of the world war that it was suspended between 1916 and 1940-1950. The first conference after World War II was held in the United States in 1950. On the eve of this conference, the International Mathematical Union was established. This alliance has contacted almost all major mathematicians in the world. Its main mission is to promote the development and international exchange of mathematics, organize the quadrennial International Congress of Mathematicians and other professional international conferences, and award the Fields Medal. Since then, the conference has been held relatively normally. Since 1897, the Communist Party of China has held nineteen congresses, nine of which were held between 1950 and 1983.

The daily affairs of the alliance are led by an executive committee with a four-year term. In recent years, this committee has one chairman, two vice-chairmen, one secretary-general, and five ordinary members, all of whom are composed of international figures. A famous and influential mathematician in the world. The agenda of each conference is compiled by a nine-member advisory committee nominated by the Executive Committee. The Fields Medal winners are 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 is first nominated by each person and puts forward nearly forty candidates worthy of serious consideration. Then it conducts full discussions and listens to the opinions of mathematicians from all over the world. Finally, it votes within the evaluation committee to decide on the winner of this year's Fields Medal. Award winner.

Now, the International Congress of Mathematicians is the most important academic exchange event for mathematicians around the world. Since 1950, the number of participants has exceeded 2,000 each time, and the number of participants in the last two conferences has exceeded 3,000. With so many participants and countless new achievements in the past four years, what method can be used to communicate well? In recent conferences, lectures have been divided into three levels. Taking 1978 as an example, about 700 people applied to give ten-minute speeches in various professional groups. Then the advisory committee determined the list of about 200 people who gave 45-minute invited speeches in each professional group. , and 17 candidates to give a one-hour summary report to the plenary session. It is a privilege to be assigned to give one-hour lectures by some of the most active mathematicians working today, many of whom are past or future Fields Medalists.

The announcement and awarding of the Fields Medal is the main content of the opening ceremony. When the chairman of the executive committee (i.e. the chairman of the jury) announced the list of winners this year, the audience burst into applause. Then, an important person in the host country (the local mayor, the president of the National Academy of Sciences, or even the king or president) or the chairman of the jury will award a gold medal, plus a bonus of US$500. Finally, some authoritative mathematicians will introduce the outstanding work of the winners, and this will end the opening ceremony.

The Fields Medal is named after the late Canadian mathematician John Charles Fields.

On May 14, 1863, Fields gave birth to a son in Ottawa, Canada. His father passed away when he was eleven years old, and he lost his loving mother when he was eighteen years old. His family situation was not very good. At the age of seventeen, Fields entered the University of Toronto to major in mathematics. In 1887, when Fields was twenty-four years old, he was living in the United States under John. Hopkins received his Ph.D. Two years later, he became a professor at Allegheny University in the United States.

At that time, the center of world mathematics was in Europe. Almost all North American mathematicians go to Europe to study and work for a period of time. In 1892, Fields traveled across the ocean and studied in Paris and Berlin for ten years. In Europe, he had close contacts with famous mathematicians such as Vouchers and Fraubenius. This experience greatly broadened Fields' horizons. As a mathematician, Fields' work interests focus on algebraic functions, and his achievements are not outstanding. However, as an organizer and manager of mathematics, Fields has outstanding achievements.

Fields realized the importance of graduate education very early and was the first person to promote graduate education in Canada. Now everyone knows that a country’s postgraduate training is a reliable index to measure the country’s scientific level. At that time, it was really rare to have such an understanding. Fields had some outstanding insights into the importance of international exchanges of mathematics and in promoting the development of mathematics in North America. In order to quickly catch up with European mathematics in North America, Fields did his best to preside over the preparations for the 1924 International Congress of Mathematicians in Toronto (the first congress held outside Europe). The conference left him exhausted and his health never improved, but the conference had a profound impact on the growth of mathematics in North America