At the beginning of the 20th century, headed by Hilbert, Gottingen School developed for more than 100 years, which led the development of mathematics in the 20th and 20th centuries, and Gottingen became a holy land for all mathematicians. But at the beginning of the 20th century, besides the Gottingen School, there was also the little-known Moscow School, which was detached from the world and obsessed with self-exploration and became the main school to compete with the Gottingen School. Even in the 265,438+0 century, after 65,438+000 years of changes, despite the massive brain drain in Europe and the United States, the Moscow School continued to develop tenaciously and created remarkable achievements. Before Peter I, Russian basic science was very weak and almost a wasteland. After Peter I succeeded to the throne, he thought that science should be developed vigorously. 1724 65438+ 10, in October, Peter I issued a decree, decided to establish a Russian scientific research institution, named it Academy of Sciences, and drew up its statutes. 1725 was formally established. When Peter I was preparing for the Academy of Sciences, he was fully integrated with the Paris Academy of Sciences and adopted the opinions of the German philosopher Leibniz when formulating the articles of association. After the establishment of the Academy of Sciences in Petersburg, Peter I recruited talented people, and the first-class scientists at that time all received the invitation of Peter I. Finally, Eiler, a scholar, Bernoulli, a mathematician, Gomez, a German naturalist, and Euler, a mathematician from Wang Zhiyi, all worked in the Academy of Sciences in Petersburg. Their arrival sowed the seeds of knowledge in the scientific wasteland of Russia, promoted the development of basic education in Russia, spread advanced scientific knowledge in Europe and America, and trained a large number of talents for Russia. After about 100 years of development, Lobachevsky, a leader who can lead the development of Russian mathematics, finally appeared in Russia. At that time, Euclidean geometry was still regarded as the Bible in the West, and algebra was not completely independent from Euclidean geometry. When studying Euclid's fifth postulate, Lobachevsky creatively put forward non-Euclid geometry. The fifth postulate involves parallel lines. What it says is: If a straight line intersects with two straight lines and the sum of two internal angles on the same side is less than two right angles, then extending these two straight lines, they will intersect at one side of those two internal angles. Since 2000, countless mathematicians have failed to study the fifth postulate. During the research, Lobachevsky used the opposite assertion: at least two straight lines can be drawn parallel to the known straight lines through a point outside the straight line. As a hypothesis, combine it with other postulates of Euclid geometry, and then make this assertion an axiom. If this assumption is incompatible with other postulates, it will be proved by the fifth postulate. From this, a series of theorems of new geometry are logically deduced, forming a logically possible and non-contradictory theory, thus creating non-Euclidean geometry. The appearance of Lobachevsky promoted the great progress of Russian mathematics. After more than one hundred years' development, until the late 9th century, the Petersburg School of Mathematics centered on Chebyshev appeared, including a large number of scientists such as Markov, Bernstein, krylov and vinogradov, mainly focusing on analytic numbers. The emergence of Petersburg School of Mathematics laid the foundation of Moscow School of Mathematics. Chebyshev's student is also a representative of Lyapunov's Petersburg School. He obtained a concise proof of the central limit theorem in probability theory and was widely used. His greatest contribution is to lay the foundation of the stability theory of ordinary differential equations and put forward many new methods. The development of this direction will become a major feature of Russian mathematics in the future. At the beginning of the 20th century, mathematicians Ye Golov and Mlodeshevski set up a research society together. At first, differential geometry derived from classical analysis was the theme. However, the analytic application of geometric problems prompted people to further clarify the basic concept of real analysis, so at that time, they began a preliminary study of real analysis, and thus formed the Moscow School. It can be said that Russian mathematician Yeh Golov created the Moscow School of Mathematics by inheriting and developing the theories and traditions of the Petersburg School. However, it is essentially different from the Petersburg school, and the Moscow school of mathematics mainly focuses on pure mathematics. Jin Lu, a student from yegorov, further developed the Moscow School, and Jin Lu trained a large number of students, such as Mensov, Qin Xin, Aleksandrov, Orisson, Su Shilin, Novikov and Liu Tiernik. They all started from the solid core of real analysis and made their own achievements in function theory, further extending and laying the foundation for a series of new fields of modern mathematics. This school is often divided into two schools with different professional directions, namely, the functional school and the topological school. The former was founded by Ye Golov and Luzin, and carried forward by Colmo Gallov and others. The latter is represented by π C Alec Sandrov, Urison, Pontryagin and others. The development of Russian mathematics school was actually isolated from the mainstream mathematics circles in Europe and America because of the different social nature at that time, but this did not affect the development of Russian mathematics school. In the forties and fifties of the 20th century, despite the western blockade, the Moscow School did not suffer heavy losses, but reached its peak. It made great progress in many frontier branches such as probability theory, stochastic process, complex variable function, mathematical logic, functional, number theory, differential equation and topology, and a large number of famous mathematicians and more mathematical educators emerged, such as Qin Xin, Menzoff, Schmidt and Orisson. The prosperity of Moscow School is inseparable from the efforts of Andre Andrey Kolmogorov, a famous mathematician and mathematical educator. Colmo Golov has been a professor at Moscow University since 193 1 under Jin Lu, who took over the mantle of Jin Lu. 1933 director, institute of mathematical mechanics, Moscow university. It can be said that he is the leader and soul of Moscow School. Andre Andrey Kolmogorov can be said to be an all-rounder in mathematics. His research covers a wide range: from basic mathematics, mathematical logic, theory of real variable functions, differential equations, probability theory, mathematical statistics, information theory, functional analytical mechanics, topology … to mathematics in the fields of fluid, physics, chemistry, geology and metallurgy. He is also considered to have created some new branches of mathematics-information algorithm theory, probability algorithm theory and language statistics. Since 1930s, he has been guiding students' mathematical Olympic activities in the whole Soviet Union, compiling counseling books, giving lectures to students in person, and cultivating a large number of outstanding middle school students. . André Andrey Kolmogorov directed nearly 70 graduate students in his life, most of whom became world-class mathematicians, and 14 of them became academicians of the Soviet Academy of Sciences. Colmo Golov has trained a large number of mathematics talents for the whole Russian mathematics field, and also promoted the development of Moscow School. What's more, with André Andrey Kolmogorov as the driving center, Moscow School also extended the tentacles of mathematics to basic mathematics, mathematical philosophy, mathematical logic, mathematical history, cybernetics, biological mathematical calculation theory, applied mathematics and so on. And did a lot of innovative things. At that time, during the Cold War, it was difficult for Russian mathematics schools to acquire the knowledge of mathematics in Europe and America, so their textbooks were all compiled by themselves, such as "Mathematical Analysis Problem Set" by Jimidovich, "Linear Algebra Problem Set" by ProSchooler Cove and "Higher Algebra Problem Set" by Deyev. The development of Moscow mathematics school can be said to provide the strongest guarantee for the rise of the former Soviet Union. Russian journalist Gerson believes that mathematics is Stalin's greatest secret weapon in the former Soviet Union in his book Perfect Computing: A Genius and the Discovery of Century Mathematics. 194 1 year, only three weeks after Nazi Germany attacked the Soviet Union, the Soviet air force was wiped out. Stalin tried to rebuild the air force by transforming civilian aircraft into bombers. The speed of civil aircraft is too slow to predict and control the time required to attack the target. At that time, Andrei André Andrey Kolmogorov and other Soviet mathematicians reformulated all the bombing calculation systems of the Soviet army, eliminating Stalin's troubles. The former Soviet Union has made advanced achievements in the fields of aviation, aerospace, ballistic missiles, new fighters and nuclear weapons upgrading. These are the achievements of knowledge transformation technology that mathematicians of Moscow School have worked hard to study. Mathematicians from Moscow Institute of Mathematics enjoyed the most preferential treatment in the former Soviet Union. They don't have to worry about the burden of livelihood, thoughts, interpersonal relationships, lectures and papers. They can study mathematics wholeheartedly. Their achievements in mathematics are so high that they can't be ignored even during the cold war. C π Novikov and margulies won the Fields Prize of 1970 and 1978 respectively. Novikov, a representative of the Moscow School of Topology, proved that the rational Pontryagin characteristic class of a simply connected manifold is topologically invariant (Note: Pontryagin characteristic class is not topologically invariant! ), differential homeomorphisms are also classified into 5-dimensional and 5-dimensional simple connected smooth manifolds. He introduced higher-order sign difference and put forward Novikov conjecture, which promoted the development of topology later. Gregory perelman, a Russian mathematician we are familiar with, belongs to the Moscow School of Mathematics. He successfully solved the problem of "Poincare conjecture" in mathematics for 100 years. Poincare conjecture is a topological problem put forward by French mathematician Henri Poincare in 1904, which provides clues for calculating the shape and size of the universe. However, in the 1990s, the former Soviet Union disintegrated and the Moscow Institute of Mathematics suffered heavy losses. Many Moscow mathematicians, including Gregory perelman, fled to Europe and America. However, the Moscow School has not fallen, but is still developing tenaciously. The Department of Mathematical Mechanics and the Department of Computational Mathematics and Automatic Control in Moscow are still in the leading position in the world. The development of Moscow School can be said to have witnessed the ups and downs of Russia's development in the 20th century. They didn't follow the Gottingen school step by step. Facing the western blockade, they didn't lose their way. But they kept exploring and finally gave birth to the world-famous mathematics school! Cultivate a large number of world-class scientists! There is only a first in science, and there is no second. ",China in the field of basic science, if you don't have your own school, don't have your own thoughts, basically follow the Europeans and Americans, then you will never get the first place, then you will be holding hands and there is no way to make leading and pioneering achievements.