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 Chinese student."

Russia has always been a relatively backward nation in the early and mid-modern history, until Peter the Great succeeded Bit. After Peter I disguised himself, he went to Germany, the Netherlands, the United Kingdom and other countries for secret inspections, and personally experienced the advanced technology and culture of Western European countries. After returning to China, Peter I immediately implemented the Europeanization policy and carried out a series of reforms in the economy, military, culture, and politics.

In terms of culture and education, Peter trained Russia's own technical talents from scratch, established arithmetic schools, shipbuilding schools, navigation schools, artillery schools, medical schools, engineering and technical schools, and mining schools, and also sent a Approval of international students to study in Western Europe. Peter stipulated that noble children must go to school and learn arithmetic and a foreign language. Otherwise, all privileges of the nobility will be deprived, and those who have not graduated will not be allowed to get married.

Late in Peter the Great’s life, the National Academy of Sciences was also established in 1724. During the reigns of Peter the Great and his successor, Empress Catherine, the Academy had ample funding and a large comprehensive library, and enrolled very few students to reduce the teaching burden on professors. Give professors sufficient time and freedom to explore scientific issues.

At this time, the Bernardin brothers, who were severely squeezed by family forces on the European continent, arrived in Russia. The Bernoulli family is famous in mathematics, science, technology, engineering and even law, management, literature, art, etc. The most incredible thing is that this family produced 8 outstanding mathematicians from the 17th to 18th centuries alone. They did not intentionally choose mathematics as a career, they just indulged in mathematics obsessively, just like an alcoholic who encounters strong liquor and cannot extricate himself.

St. Petersburg School

Johann Bernoulli initially studied medicine and mathematics at the same time. John received a master's degree in medicine in 1690 and a doctorate in 1694, with a thesis on muscle contraction. Influenced by Leibniz, he soon fell in love with calculus. In 1695, John was elected professor of mathematics at the University of Groningen in the Netherlands. Ten years later, John succeeded his deceased brother Jacob as professor of mathematics at the University of Basel, and became a foreign academician of the Paris Academy of Sciences and a member of the Berlin Science Association. In 1712, 1724 and 1725, John was also elected as a foreign academician of the Royal Society of England, the Italian Academy of Sciences of Bologna and the Academy of Sciences of Petersburg.

Another great achievement of John is to train a large number of outstanding mathematicians, including the most famous mathematician in the 18th century, Leonhard Euler (1707-1783), the Swiss mathematician Clem (G .Cramer,1704-1752), French mathematician G.F. L'Hopital (1661-1704), as well as his own son Daniel and nephew Nicholas II, etc.

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

Daniel, who works at the St. Petersburg Academy of Sciences, was bored and played with paper. He blew air between two pieces of paper and found that the paper would not float outward, but would be squeezed by a force. Pressed together "In water flow or air flow, if the speed is small, the pressure will be large; if the speed is large, the pressure will be small." Later generations called it "Bernoulli's principle".

This small discovery made Daniel more famous. However, Daniel was not very happy. In this year, his brother Nicholas II died of appendicitis. Daniel was very sad and thought of his good friend Euler, who was also his father's student, and asked him to come to work at the St. Petersburg Academy of Sciences in Russia.

Euler came to Petersburg on May 17, 1727. In 1733, at the age of 26, Euler became professor of mathematics at the Petersburg Academy of Sciences and Daniel's assistant.

Daniel felt great because no matter what thoughts he had, Euler could understand them immediately. Euler stayed in St. Petersburg for 31 years and left a lot of precious wealth for the development of Russian mathematics.

It takes ten years to educate trees and a hundred years to educate people. It took several generations for the St. Petersburg School to become a mainstream school. Although the starting point of Russian mathematics is not as good as that of old Europe, it has achieved great development. The first to stand out were Lobachevsky (1792-1856) and Chebyshev (1821-1894).

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

Chebyshev had two very famous students, Markov (1856-1922) and Lyaplov (1857-1918). Markov is the founder of stochastic process theory. The field he created has influenced the development of many aspects of science. He also made achievements in statistics and number theory. Lyaplov is one of the founders of the stability theory of differential equations. He introduced the powerful tool of characteristic functions and solved many problems concisely. Anyone who has studied automatic control theory should worship this god.

Moscow School

At the end of the 19th century and the beginning of the 20th century, another major school of Russian mathematics, the Moscow School, was still very weak, and its representative figure was Yegorov. During his time at Moscow State University, Yegorov often held mathematics seminars to encourage academic exchanges and made outstanding contributions to the transformation of mathematics from classical mathematics to modern mathematics.

The biggest achievement of Yegorov’s seminar was the discovery of the mathematics master Lu Jin. Rukin was much younger than Yegorov and later became a key figure in the Moscow School. Lu Jin is not only excellent in research, but also good at teaching. He has written some classic textbooks and trained a large number of masters. For example, the famous Kolmogorov and Alexander Love, one of the founders of topology in the 20th century. The Moscow School in the 1920s was mainly focused on the study of function theory, but the talented members of the school were no longer satisfied with just studying function theory. They began to move into topology, differential equations, geometry and number theory.

The emergence of Kolmogorov, a mathematical genius, made the name of the Soviet Union and Moscow University resound throughout the world. His research spans almost all areas of mathematics. I published 8 papers in my last year of college! Every paper has new concepts, new ideas, and new methods!

In the 1930s, Kolmogorov worked on probability theory, projective geometry, mathematical statistics, real variable function theory, topology, approximation theory, differential equations, mathematical logic, biomathematics, philosophy, and history of mathematics. He has published more than 80 papers on mathematical methodology and other aspects. An average of 8 articles per year, and they are in different fields! In the 1940s, this guy went back to turbulence theory. In 1941, he published three articles in one breath, establishing his status as a great master in the field of fluid mechanics. People in the world call it the K41 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 was to determine whether Kolmogorov was a person or a research institution."

After that, mathematicians such as Bondryagin, Kantorovich, Arnold, Novikov, and Manning appeared one by one, making the Soviet Union the world's number one hegemon in mathematics at that time, and Moscow The number and quality of outstanding mathematicians emerging from universities is so large that, except for the University of G?ttingen at the end of the 19th century and the beginning of the 20th century, even the famous Princeton University would not dare to call itself a brother to Moscow University.

After the United States and the Soviet Union entered the Cold War, the Soviet Union knew that competition in science and technology was first and foremost a competition in basic science. Therefore, the Soviet Union elevated education to the level 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’s definition of a mathematical elite is this: first of all, he should solve a big problem that many famous mathematicians cannot solve (that is, prove the Great Theorem) when he is about 22 years old, and publish the results publicly come out.

How big this problem/theorem is will determine how big his future achievements will be. At the age of 30-35, establish your own theories based on previous solutions to various practical problems and be accepted by peers. At the age of 40-45, he established his own school of thought in the international academic community and had a considerable number of followers.

The Soviet Union did not offer any Mathematical Olympiad classes. Mathematics professors from various universities gave lectures and reports on mathematics to students. The Mathematics Summer Camp of Moscow State University is the most popular, and it is overcrowded with people who sign up every year. Everyone hopes to see the majestic masters of mathematics, listen to lectures and give reports by the masters of mathematics. Under Kolmogorov's proposal, starting in the 1970s, most of the famous universities in the Soviet Union established scientific middle schools, the most famous of which is undoubtedly the Kolmogorov Scientific Middle School of Moscow State University. This school recruits students with talents in mathematics and physics from all over the country, and it is completely free.

Having first-class students may not necessarily produce first-class mathematicians, but a rigorous academic style is also required. Mo Da's regulations are quite strict. There are compulsory courses. If you fail one course, you will be repeated a grade. If you fail two courses, you will be expelled. Mo Da's examination method is very special, it is entirely an oral examination. For main courses such as mathematical analysis or modern geometry, physics, and theoretical mechanics, you need to pass the test 7-8 times in one semester. For example, mathematical analysis needs to be tested 7-8 times.

Mathematics majors in China often involve teachers filling the entire classroom with lectures, while students listen. The worst case scenario is that some teachers read from the text and become repeaters. Teachers at Moda basically don’t teach according to the syllabus, and there are no fixed teaching materials. They designate several books as teaching materials, but they are actually used as reference books! Most courses at MUST have corresponding discussion classes, and the ratio of discussion classes to lectures in each course is at least 1:1.

The Russians have a saying: "As long as the Department of Mathematics in Moscow remains, even if Russia becomes ruins, Russia will definitely be able to rise again." It can be seen that Russia has great achievements in basic sciences, especially mathematics. The level of educational methods is extremely high.

Most of the mathematics books we use at Tsinghua and Peking University are compiled by Russians. Although China has not learned the essence of Big Brother, it produces millions of qualified engineers every year by copying jobs, which is a big headache for the West. This system of the Soviet Union trained a large number of talents in basic disciplines for Russia, allowing the former Soviet Union to compete with the United States for so many years, accounting for less than 60% of the GDP of the United States. The Department of Mathematics and Physics at Moscow State University has nurtured a group of top talents in military science fields such as aviation, missiles, new fighters, and nuclear weapons upgrades for Soviet Russia, which makes the old and the United States covetous.

With the disintegration of the Soviet Union, Russia's economic development began to slow down. Many high-level mathematics talents were attracted by the generous salaries in Europe and the United States, and they flocked to developed countries such as Europe and the United States. With the loss of talent, Russia, once a strong country in mathematics, has begun to decline in the field of mathematics.

Today’s Russian mathematics is not as good as before, and in many cases it is still resting on its laurels. The Russian Academy of Sciences, which was founded by Peter the Great and has produced 20 Nobel Prize winners, has also had major layoffs in the past few years. Frankly speaking, even if Russia rests on its roots in mathematics, it is still better than China in mathematics. The former Soviet Union had a complete system to cultivate and select talents, forming a complete ecosystem. China's mathematics education and physics education are out of touch in the industry-university-research link. Genius children cannot have access to cutting-edge science, and awesome PhD supervisors and professors do not teach at all. No matter how deep mathematics and physics are, Chinese manufacturing can reach the corresponding height...such as the combustion model in a turbofan engine, such as an aircraft. The design of some aerodynamics, etc., the vapor deposition process of the chip, etc., are all mathematical problems in the end, and they remain the same.

Whether it is the G?ttingen school or the Soviet school (St. Petersburg/Moscow), basic science has gone from backward to unparalleled in the world. It has experienced the inheritance and development of one generation after another. Education has rejuvenated the country and passed down the fire from generation to generation.