Pafnuti Lvovich Chebyshev, formerly known as пант in Russian? тий Льво? виччебышёв, (1821May 26th-189465438+February 8th). He published more than 70 scientific papers in his life, covering number theory, probability theory, function approximation theory, integral calculus and so on. He proved beltran formula, prime number distribution theorem of natural sequence, general formula of law of large numbers and central limit theorem. He not only attaches importance to pure mathematics, but also attaches great importance to the application of mathematics. Chebyshev is the founder and leader of Petersburg School of Mathematics. During his 35 years of teaching in Petersburg University, Chebyshev has taught more than ten courses, such as number theory, advanced algebra, integral operation, elliptic function, finite difference, probability theory, analytical mechanics, Fourier series, function approximation theory and engineering mechanics. His lectures are very popular with the students. A.M. Liapunov (ляпунов) commented: "His courses are concise and to the point. He doesn't pay attention to the quantity of knowledge, but he is keen to explain some of the most important concepts to students. His explanation is vivid and attractive, and he is always full of wonderful comments on the importance of the problem and the scientific method. He trained generations of outstanding mathematicians Chebyshev for Russia. He has never been married, and his daily life is simple. All his savings are used to buy books and make machines. He also developed.

To Chebyshev inequality? 1856, Chebyshev was appointed as a member of the artillery Committee and actively participated in the work of innovating artillery equipment and technology. 1867, he proposed a formula for calculating the range of circular shells, which was quickly adopted by ballistics experts. His research on interpolation theory also partly comes from the need to analyze the landing point data. On the Method of Map Making (черченйегеорррчес) made by him at the joint meeting of professors at the University of Petersburg. At the 7th annual meeting of French Academy of Sciences, Chebyshev presented a paper entitled Surla Coupe des VTE-ments (1878), in which Chebyshev net became an important concept in surface theory.

Andrei Markov, Russian (1856-1922), doctor of physics and mathematics in Russia, academician of St. Petersburg Academy of Sciences, representative of St. Petersburg School of Mathematics, is famous for his work in number theory and probability theory. The main works are probability theory and so on. /kloc-0 won the gold medal in 878, and/kloc-0 won the title of meritorious professor in 905. Markov is a representative of the Petersburg School of Mathematics. He is famous for his work in number theory and probability theory. The main works are probability theory and so on. In number theory, he studied the theory of continued fraction and quadratic infinitive and solved many difficult problems. In probability theory, he developed the method of moments, which expanded the application scope of the law of large numbers and the central limit theorem. The most important work of Markov is that during the period of 1906 ~ 19 12, a general schema-Markov chain, which can be used to study natural processes by mathematical analysis, was proposed and studied. At the same time, it initiated the study of Markov, a stochastic process without aftereffect. After many observation experiments, Markov found that in the process of state transition of a system, the state obtained by the nth transition often depends on the result of the previous experiment ((n- 1)). After in-depth study, Markov pointed out that for a system, there is a transition probability in the process of transition from one state to another, which can be calculated according to its immediately preceding state, and has nothing to do with the original state of the system and the Markov process before this transition. At present, Markov chain theory and method have been widely used in natural science, engineering technology and public utilities.

Alexander mikhailovich Lyapunov (1857- 19 18) is a Russian mathematician and mechanic. /kloc-0 was born in yaroslavl on June 6th, 857; 1918165438+10 died in Odessa on October 3rd. 1876 when he graduated from middle school, he won a gold medal because of his excellent grades. In the same year, he was admitted to the Department of Physical Mathematics of St. Petersburg University. He was deeply attracted by the profound knowledge of the famous mathematician Chebyshev, so he transferred to Chebyshev's mathematics department to study. Under the influence of Chebyshev and Zolota Lev, he wrote an original paper in his fourth year of university and won the gold medal. 1880 Stay in school after graduation. 1892 received a doctorate and became a professor. 1893 has been a professor at kharkov university. 190 1 he was elected as a member of the communication department of St. Petersburg academy of sciences at the beginning of the year and concurrently served as the chairman of the department of applied mathematics. 1909 was elected as a foreign academician of the Italian National Piano Academy, and 19 16 was elected as a foreign academician of the Paris Academy of Sciences. He is an outstanding representative of the Petersburg School founded by Chebyshev and the founder of the theory of motion stability of ordinary differential equations with characteristic function method. Lyapunov's research on potential theory has opened up a new way for the development of mathematical physics methods. His paper "Some Studies on Dirichlet Problem" published in 1898 is also an important paper. In this paper, some basic properties of single-layer potential and double-layer potential are strictly discussed for the first time, and some problems are pointed out in the given range.

Nikolai Ivanovich Lobachevsky (никола? й Ива? нович Лобаче? вский, Nikolai Lobachevsky (1792121-1February 24th, 856), a world-renowned mathematician in Russia, was one of the early discoverers of non-Euclidean geometry. Lobachevsky, the founder of Roche Mathematics, was the president of Kazan University and the director of Kazan School District. When trying to prove the parallel axiom, he found that all previous proofs could not escape the error of circular argument. So, he made an assumption that a little beyond the straight line can make countless straight lines parallel to the known straight lines. If this assumption is denied, the parallel axiom is proved. However, he not only did not deny this proposition, but also used it to infer from other propositions unrelated to parallel axioms in Euclidean geometry, and got a new geometric system with logical rationality-non-Euclidean geometry. This is what people later called Roche mathematics. The establishment of Roche geometry has played a great role in the development of geometry and even the whole mathematics, but it was not paid attention to at first, and it was not until the death of Lobachevsky that 12 was gradually widely recognized?

1893, Kazan University established the world's first mathematician statue. Lobachevsky Lobachevsky, a great Russian scholar and an important founder of non-Euclidean geometry, was miserable in his later years. Although his son died blind in his later years, he still finished the paper "Non-Euclidean Geometry", a summary of the strict proof of geometric principles and parallel line theorems.