Chebyshev's left foot was born disabled, and he often sat alone at home when he was a child, and developed the habit of thinking in loneliness. He has a sympathetic cousin who teaches him to sing, read French and do arithmetic while other children are playing in the manor. Until his death, Chebyshev kept his cousin's photo with him.
1832, the Chebyshev family moved to Moscow. For the education of their children, parents invited a very excellent tutor, погорелский), who was the most famous private teacher in Moscow at that time, and several popular elementary mathematics textbooks. Chebyshev learned a lot from his tutor and became interested in mathematics. He was deeply impressed by the proof that there was no maximum prime number in Euclid's Elements of Geometry. 1837, 16-year-old Chebyshev entered Moscow university and became a student majoring in physical mathematics under the philosophy department. At the university stage, Moravia-born mathematician H. Brashman had a great influence on him. 1On September 30th, 865, Chebyshev read a letter at the Moscow Mathematics Conference, in which he attributed his work of applying continued fraction theory to series expansion to Brashman's inspiration. In the last academic year of the university, Chebyshev submitted an article entitled Calculation of Equation Roots (вычислениекорней).
After graduating from university, Chebyshev worked as a teaching assistant at Moscow University while studying for a master's degree. Almost at the same time, their manor in Kaluga province went bankrupt because of famine. Chebyshev not only lost the financial support of his parents, but also had to pay part of the education expenses of his two underage brothers. 1843, Chebyshev passed the master's exam and published an article about multiple integrals in J. joseph liouville's Journal of Pure and Applied Mathematics. 1844 published an article on the convergence of Taylor series in L. Grelle's magazine of the same name, fü r die Reine and Angewante Mathematick. 1845, he completed his master's thesis "On the Basic Analysis of Probability Theory" (опытелементрное). His talent in mathematics soon won the admiration of B унковский (B Bernstein) and m·b· Ostrogradski (осй) who worked here. /kloc-in the spring of 0/847, in the topic "On using logarithmic integral" (обинтегри?внии) 1On May 27th, 849, his doctoral thesis "On congruence formula" (теорияс1088a внеий, 60. Chebyshev was promoted to associate professor at 1850 and professor at 1860. 1872, on the 25th anniversary of his teaching in Petersburg University, the university awarded him the title of meritorious professor. 1882, Chebyshev retired after 35 years of teaching at Petersburg University.
In the past 35 years, 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 explanations are vivid and attractive, and he is always full of wonderful comments on the importance of the problem and the scientific method. "
1853, Chebyshev was elected as alternate academician of Petersburg Academy of Sciences, and concurrently served as chairman of the Department of Applied Mathematics. 1856, became an associate academician. 1859 became an academician. Chebyshev has visited or conducted academic exchanges abroad for six times. He has a close relationship with the French mathematics community, and went to Paris three times to attend the annual meeting of the French Academy of Sciences. 1860, 187 1 and 1873 were elected as academicians of the School of Communication of the French Academy, the Royal Academy of Berlin and the Bologna Institute of Italy respectively, 1877, 1880 and1. At the same time, he is also an honorary member of all universities in Russia, a member of the All-Russian Secondary Education Reform Committee, and an honorary academician of the Petersburg Artillery Academy. He is also an enthusiastic supporter of the mathematical associations in Petersburg and Moscow. The all-Russian Congress of Natural Scientists and Doctors initiated by him has played a great role in mutual understanding between scientific circles and the influence of science on people. Chebyshev is the founder and leader of Petersburg School of Mathematics.
/kloc-Before the 9th century, Russian mathematics was quite backward. In the Academy of Sciences established in the year of Peter the Great's death, all the early mathematicians were foreigners, among whom Euler, Nicholas III Bernoulli, daniel bernoulli and Goldbach were famous. Russia does not have its own mathematicians, universities, or even a decent elementary mathematics textbook. Only in the first half of19th century did outstanding mathematicians like H. и lobachevsky (лобчевский), Bunyakovski and Ostrogradski appear in Russia. But except Lobachevsky, most of them were trained in foreign countries (especially French), and their achievements were not enough to attract the full attention of their counterparts in Western Europe at that time. Chebyshev engaged in his mathematical creation under this historical background. He is not only a native scholar, but also attracted a group of young Russian mathematicians with his outstanding talent and unique charm, and formed a distinctive school of mathematics, thus making Russian mathematics get rid of the backward situation and start to move towards the forefront of the world. Chebyshev is the founder and well-deserved leader of Petersburg School of Mathematics. His pioneering work in the fields of probability theory, analytic number theory and function approximation theory has fundamentally changed the views of mathematicians in France, Germany and other traditional mathematical powers on Russian mathematics.
Chebyshev engaged in the study of probability theory in the cold years. From the beginning, he grasped the basic problem in classical probability theory, that is, the law of large numbers, that is, the law of almost inevitable events. The first law of large numbers in history was put forward by Jacob I (Bernoulli), and later S-D.B. Poisson put forward a statement with wider conditions, but there was no progress in this respect. On the contrary, because some mathematicians overemphasized the role of probability theory in ethical science, and even tried to clarify the "hidden order of God", coupled with the lack of theoretical tools and the defects of the classical definition of probability itself, some orthodox mathematicians in Europe often excluded it from the precise science at that time.
1845, Chebyshev made a detailed analysis and strict proof of Jacob Bernoulli's law of large numbers with the help of a very elementary tool-maclaurin expansion of ln (1+x). A year later, he published the article "Dé demention è lè mentaire d 'une proposition gé nerale de Lathé orie des probabilité s, 1846" in Greer's magazine, and then he gave a proof of the law of large numbers in Poisson form. 1866, Chebyshev published On Average (o·среднихвеличинх). 1887, he published two important theorems about probability (O двухтеорем a хотнн)
A series of concepts and research topics introduced by Chebyshev were inherited and developed by Russian and later Soviet mathematicians. A.A. Markov (мрков) supplemented the "moment method" and successfully solved the condition problem of normal convergence of the sum of random variables. Lyapunov developed the characteristic function method, which led to the transformation of the central limit theorem research to the modernization direction. Marked by the axiom system of probability theory established by André Andrey Kolmogorov (колмогоров) in 1930s, the Soviet Union has gained an undisputed leading position in this field. The research of modern limit theory-the law of infinite separable distribution has been studied by C.H. Bernstein (бернштейн), a.g лн Qin Xin (н Andrey Kolmogorov, a famous mathematician in the Soviet Union, wrote in The Development of Russian Probability Science (рольсускойнуккккккккккккк It is also different from Jakob Bernoulli's proof of his limit theorem with detailed arithmetic precision), but the main significance of Chebyshev's work lies in him. In addition, Chebyshev was the first person to clearly foresee the value of concepts such as' random variable' and its' expected (average) value' and apply them. These concepts existed before him and can be derived from basic concepts such as' event' and' probability', but random variables and their expected values are topics that can bring more suitable and flexible algorithms. "
Chebyshev's research on analytic number theory focused on his first four years as a teacher at Petersburg University, when he was a lecturer in advanced algebra and number theory and an editor of the number theory part of Euler's collected works. The latter appointment was recommended by Bunyakovski to the Academy of Sciences in Petersburg. 1849, the number theory part of L. Euler Comment-Iones Arithmetic AE Collection (1849) was officially published in Petersburg. Chebyshev made great efforts to this end, and at the same time realized the charm of combining profound thoughts and flexible skills from Euler's works, especially the ξ function introduced by Euler and its wonderful proof of the ancient proposition of infinite prime numbers, which attracted him to further explore the distribution law of prime numbers.
Integrating theory with practice is a remarkable feature of Chebyshev's scientific work. He was interested in machinery since he was a child, and he took mechanical engineering as an elective in college. Just before his first visit to western Europe, he was a lecturer in the department of applied knowledge (quasi-engineering department) of Petersburg University. Shortly after his return from this visit, he was elected as the chairman of the Department of Applied Mathematics of the Chinese Academy of Sciences, a position that he did not take over until the death of Lyapunov. By applying the theory and algorithm of function approximation theory to machine design, Chebyshev has made many beneficial achievements, including the theory of direct motion, the theory of continuous motion and variable pulse motion, the principle of the simplest parallelogram, the conditions for the hinged bar system to become a machine, the motion theorem of three-hinged four-bar mechanism, the principle of centrifugal controller and so on. He also designs and manufactures machines himself. According to statistics, he designed more than 40 kinds of machines in his life, including more than 80 kinds of these machines, including walking machines that can imitate animals, rowing machines that can automatically change the angle of oars entering and leaving the water, curve gauges that can measure the curvature of large arcs and actually draw them, as well as presses, screening machines, seed selectors, automatic chairs and different types of hand-cranked computers. Many of his new inventions were exhibited at the Paris Expo in 1878 and the Chicago Expo in 1893. Some of the exhibits are still preserved in the Institute of Mathematics of the Soviet Academy of Sciences, the Moscow Museum of History and the Paris Art Institute.
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.
Chebyshev never married, and his daily life was very simple. All his savings have been used to buy books and make machines. On holidays, he is also happy to relax with his nephew and children, but his greatest pleasure is to discuss math problems with young people. 1894165438+1At the end of October, his leg disease suddenly worsened, and then his thinking also appeared obstacles. But he still insisted on inviting graduate students to discuss the problem. This student is ддрве Glave (гжве), who later became a pioneer of Russian algebra. 1894 65438+At 9: 00 on February 8, this respectable scholar died suddenly at his desk. He had neither children nor money, but he left a priceless legacy to mankind-a glorious school.
Petersburg Mathematics School grew up with Chebyshev's decades of hard study. It is deeply rooted in the fertile soil of the university. Most of its members attach importance to basic theory and practical application, and are good at using classical problems as a breakthrough and using elementary tools to establish profound achievements. /kloc-In the second half of the 9th century, Russian mathematics, mainly under Chebyshev's leadership, first made breakthroughs in probability theory, analytic number theory and function approximation theory. Colding, Zolotarev, B. Sokhotski (сохоцкий), K.A. boxer (посе). B.A. steklov (стеклов) and others have made great achievements in complex variable functions, differential equations, algebra, group theory, number geometry, function construction, mathematical physics and other fields. At the end of 19, Russian mathematics kept up with the world advanced trend.
Today, Russia is a developed country in mathematics, and the leaders of Russian mathematics circles are still proud of being called the descendants of Chebyshev and Petersburg School.