Why is Russian mathematics so awesome? Because the foundation is good

Speaking of the best universities in the world, everyone's first reaction should be Harvard University. There is a joke in Russia, "What is an American university? It is an American building, a Russian professor and a student in China. "

Russia was a relatively backward country in early modern history until Peter the Great succeeded to the throne. After dressing up in disguise, Peter I went to Germany, the Netherlands, Britain and other countries for a secret inspection and personally experienced the advanced science and technology culture of western European countries. After Peter I returned to China, he immediately pursued the Europeanization policy and carried out a series of economic, military, cultural and political reforms.

In terms of culture and education, Peter trained Russian technical talents from scratch, established arithmetic schools, shipbuilding schools, navigation schools, artillery schools, medical schools, engineering schools and mining schools, and sent a group of international students to study in Western Europe. Peter stipulated that aristocratic children must go to school, learn arithmetic and a foreign language. Otherwise, the nobility will be deprived of all privileges, and even those who do not graduate are not allowed to get married.

In the late period of Peter the Great, the National Academy of Sciences was established in 1724. During the reign of Peter the Great and his successor, Queen Catherine, the Academy of Sciences had sufficient funds and a large-scale comprehensive library, and only a few students were enrolled to reduce the teaching burden of professors. Give the professor enough time and freedom to explore scientific problems.

At this time, the bernhard brothers, who were badly run by family forces in continental Europe, came to Russia. The Bernoulli family enjoys great fame in the fields of mathematics, science, technology, engineering and even law, management, literature and art. The most incredible thing is that this family has produced eight outstanding mathematicians from17th century to18th century. They didn't deliberately choose mathematics as their career, but they were addicted to mathematics, just like drunkards who met hard liquor.

St. Petersburg school

John? Bernoulli first studied medicine and mathematics at the same time. John received his master's degree in medicine at 1690 and his doctorate at 1694. His thesis is about muscle contraction. Influenced by Leibniz, he soon fell in love with calculus. From 65438 to 0695, John was elected as a professor of mathematics in university of groningen, the Netherlands. 10 years later, John replaced his dead brother Jacob as a professor of mathematics in university of basel, and became a foreign academician of the Paris Academy of Sciences and a member of the Berlin Science Association. In 17 12, 1724 and 1725, John was also elected as a foreign academician of the Royal Society, the Bologna Academy of Sciences in Italy and the Petersburg Academy of Sciences respectively.

Another great achievement of John is to train a large number of outstanding mathematicians, including1Euler, the most famous mathematician in the 8th century (1707- 1783), the Swiss mathematician Clem (1704- 1752) and France.

Daniel? John's second son Bernoulli has a special interest in mathematics since he was a child. Daniel 13 entered the university to study philosophy and logic, and wanted to study mathematics. His father advised him that "mathematics can't make money" and suggested that he go into business. Daniel is persistent. While studying medicine, he secretly did math research without telling his father.

Daniel, who works in St. Petersburg Academy of Sciences, used to play with paper. He blew between two pieces of paper and found that the paper would not float outward, but would be squeezed together by a force. "In water or airflow, the speed is small and the pressure is high; When the speed is high, the pressure is small. " Later, people called it Bernoulli principle.

This little discovery made Daniel more famous, but Daniel was not very happy. This year, his brother Nicholas II died of appendicitis. Daniel is very sad. He thought of his good friend and father's student Euler and asked him to work in the Academy of Sciences in St. Petersburg, Russia.

1727 In May, Euler came to Petersburg. 1733, 26-year-old Euler became a professor of mathematics at the Academy of Sciences in Petersburg and Daniel's assistant. Daniel thinks it's great, because no matter what he thinks, Euler can grasp it at the first time. Euler stayed in St. Petersburg for 365,438+0 years, leaving a lot of precious wealth for the development of Russian mathematics.

It takes ten years to plant trees and a hundred years to educate people. It took several generations for St. Petersburg School to become the mainstream school. Although the starting point of Russian mathematics is not as good as that of old Europe, it has made great progress. Lobachevsky (1792- 1856) and Chebyshev (1821894) stand out.

Lobachevsky was the creator of non-Euclidean geometry and won the praise of "Copernicus in geometry". Chebyshev is the founder and representative of St. Petersburg School. Chebyshev's main research direction is analysis, and he has made great achievements in probability theory, number theory and function theory.

Chebyshev has two very famous students, Markov (1856- 1922) and Lyapunov (1857- 19 18). Markov is a pioneer of stochastic process theory. The fields he created influenced the development of science in many ways, and also made achievements in statistics and number theory. Lyapunov is one of the pioneers of stability theory of differential equations. He introduced the powerful tool of characteristic function and solved many problems concisely. Anyone who has studied automatic control theory should worship this fairy.

Moscow school

19 At the end of the 20th century, the strength of Moscow School, another major school of Russian mathematics, was still very weak, with yegorov as the representative. During his stay in Moscow University, yegorov often held mathematics discussion classes to encourage academic exchanges, which made outstanding contributions to promoting the transformation of mathematics from classical mathematics to modern mathematics.

The greatest achievement of the yegorov Seminar was the discovery of Luzin, a master of mathematics. Jin Lu was much younger than yegorov and later became a key figure of the Moscow School. Jin Lu is not only excellent in research, but also good at teaching. He wrote some classic textbooks and trained a large number of masters. For example, the famous André Andrey Kolmogorov, Alexander Love, one of the founders of topology in the 20th century. The Moscow School in the 1920s focused on the study of function theory, but the talented members of the school were not satisfied with just studying function theory. They began to study topology, differential equations, geometry and number theory.

The appearance of Andrei Andrey Kolmogorov, a mathematical genius, made the names of the Soviet Union and Moscow University resound around the world. His research covers almost all fields of mathematics. Eight papers were published in the last year of college graduation! Every paper has new concepts, new ideas and new methods!

From 65438 to 0930, Andre Andrey Kolmogorov published more than 80 papers, covering probability theory, projective geometry, mathematical statistics, real variable function theory, topology, approximation theory, differential equations, mathematical logic, biological mathematics, philosophy, mathematical history and mathematical methodology. Eight articles a year on average, and they are in different fields! 1940s This guy has gone to theoretical turbulence again. 194 1 year, he published three articles in one breath, which established his position as a master of fluid mechanics. Jianghu people call it K4 1 theory. This theory is the basis of aerodynamics (aircraft design) and submarine design. American statistician Wolfowitz once said, "A special purpose of my coming to the Soviet Union is to determine whether André Andrey Kolmogorov is a person or a research institution." .

Later, mathematicians such as Bandari Yakin, Kantrovich, Arnold, Novikov and Manning appeared one after another, making the Soviet Union the first mathematician in the world at that time. However, the number and quality of outstanding mathematicians emerging from Moscow University are so high that even the famous Princeton University is afraid to be brothers with Moscow University, except for the University of Gottingen at the end of 19 and the beginning of the 20th century.

After the United States and the Soviet Union entered the Cold War, the Soviet Union knew that the competition of science and technology was first and foremost the competition of basic science. Therefore, the Soviet Union put education at the height of national security strategy, and invested a large proportion of government funds in STEM subjects (that is, science, technology, engineering and mathematics) in schools.

The Soviet Union, a mathematical elite, defined it this way. First, around the age of 22, he will solve a big problem that many famous mathematicians can't solve (that is, prove the last theorem) and publish the results publicly. How big this problem/theorem is, to what extent it determines his future achievements. At the age of 30-35, he established his own theory on the basis of solving various practical problems and was accepted by his peers. At the age of 40-45, he was unique in international academic circles and had quite a few followers.

There is no course of Olympic Mathematics in the Soviet Union. Mathematics professors from various universities give lectures to students and give lectures and reports on mathematics. The summer math camp of Moscow University is the most popular. People who sign up every year are overcrowded. Everyone wants to see the elegant demeanour of mathematics masters, listen to their lectures and make reports. At the suggestion of Kolmogorov, since 1970s, most famous universities in the Soviet Union have set up science middle schools, the most famous of which is Kolmogorov Science Middle School of Moscow University. This school recruits talented students in mathematics and physics for the whole country, and it is completely free.

First-class students may not be able to train first-class mathematicians, but they must also have a rigorous style of study. The big rules are quite strict, compulsory courses, failing once, failing twice and being expelled. The examination method of MoDa is very special, which is completely oral. Main courses, such as mathematical analysis or modern geometry, physics, theoretical mechanics and so on, should be tested well once a semester, such as mathematical analysis, 7-8 times.

China's mathematics major is often full of teachers, and students are listening below. The worst thing is that some teachers read from the book and become repeat students. Most teachers don't teach according to the syllabus, and there are no fixed textbooks. They designated several books as teaching materials, but they were all reference books! Most courses have corresponding discussion classes, and the ratio of discussion classes to lectures in each course is at least 1: 1.

Russians have a saying: "As long as the mathematics department in Moscow exists, even if Russia becomes a ruin, it will definitely rise again." This shows that Russia has a high level of educational methods in basic science, especially mathematics.

Most of the math books used by Tsinghua Peking University were compiled by Russians. China didn't learn the essence of Big Brother, but by copying his homework, he trained millions of qualified engineers every year, which made the west suffer the brunt. This system of the Soviet Union has trained a large number of talents in basic disciplines for Russia in batches, making the former Soviet Union compete with the United States for less than 60% of GDP for so many years. The Department of Mathematics and the Department of Physics of Moscow State University have trained a group of top talents in military science fields such as aviation, missiles, new fighters and nuclear weapons upgrading for Soviet Russia, which has made the United States greedy.

With the disintegration of the Soviet Union, Russia's economic development began to slow down, and many senior talents in mathematics were attracted by the generous treatment in Europe and the United States and flocked to developed countries such as Europe and the United States. With the brain drain, Russia, once a powerful mathematical country, began to decline in the field of mathematics.

Today's Russian mathematics is not as good as it used to be, and many times it is still eating the old money. The Russian Academy of Sciences, founded by Peter the Great, has trained 20 Nobel Prize winners and laid off a large number of employees a few years ago. Frankly speaking, even if Russia eats the roots of mathematics, it is still better than China's mathematics. The former Soviet Union has a complete system of training and selecting talents, forming a perfect ecology. Mathematics education and physics education in China are out of touch in Industry-University-Research. Gifted children are not exposed to cutting-edge science, and arrogant doctoral tutors and professors don't teach at all. How advanced mathematics and physics are, China can stand at a corresponding height ... such as the internal combustion model of turbofan engine, such as the aerodynamic design of aircraft design, the vapor deposition process of chips, etc. In the end, it's all math, and it will never change.

Both Gottingen School and Russian School (St. Petersburg/Moscow) have experienced the inheritance and development from generation to generation, and education has been passed down from generation to generation.