Cauchy (1789— 1857) is a French mathematician, physicist and astronomer. /kloc-At the beginning of the 9th century, calculus has developed into a huge branch with rich contents and wide applications. At the same time, its weaknesses are increasingly exposed, and the theoretical basis of calculus is not strict. In order to solve new problems and clarify the concept of calculus, mathematicians have carried out rigorous work of mathematical analysis. In the foundation work of analytical foundation, Cauchy, a great mathematician, was the first to make outstanding contributions.
Cauchy was born in Paris on August 2 1789. My father is a lawyer who is proficient in classical literature and has close contacts with the great French mathematicians Lagrange and Laplace at that time. Cauchy's mathematical talent as a teenager was highly praised by two mathematicians, and he predicted that Cauchy would become a great man in the future. Lagrange suggested to his father to "give Cauchy a solid literary education as soon as possible" so that his hobbies would not lead him astray. Therefore, his father strengthened Cauchy's literary education and made him show great talent in poetry.
From 1807 to 18 10, Cauchy studied in the Institute of Technology and worked as a traffic road engineer. Due to poor health, he accepted the advice of Lagrange and Laplace, gave up the engineer and devoted himself to the study of pure mathematics. Cauchy's greatest contribution to mathematics is to introduce the concept of limit in calculus and establish a logical and clear analysis system based on limit. This is the essence of the development history of calculus and Cauchy's great contribution to the development of human science.
In 182 1, Cauchy put forward the method of limit definition, describing the limit process as inequality, which was improved by Weierstrass and became Cauchy limit definition or.
Definition. Now all calculus textbooks still (at least essentially) follow Cauchy's definitions of limit, continuity, derivative and convergence. His explanation of calculus was widely adopted by later generations. Cauchy has done the most systematic and pioneering work in definite integral, which he defined as the "limit" of sum. It is emphasized that the existence of integral must be established before definite integral operation. He first strictly proved the basic theorem of calculus by using the mean value theorem. Through the efforts of Cauchy and later Wilstrass, the basic concepts of mathematical analysis were strictly discussed. So as to end the ideological confusion of calculus in the past two hundred years, liberate calculus and its popularization from the complete dependence on geometric concepts, movements and intuitive understanding, and make calculus develop into the most basic and huge mathematical subject in modern mathematics.
The rigorous work of mathematical analysis has had a great influence from the beginning. Cauchy put forward the theory of series convergence at an academic conference. After the meeting, Laplace hurried home to check whether the series used in his masterpiece "Celestial Mechanics" all converged according to Cauchy's strict discriminant method.
Cauchy's research achievements in other fields are also very rich. He founded the calculus theory of complex variable function. He also made outstanding contributions in algebra, theoretical physics, optics and elasticity theory. Cauchy's mathematical achievements are not only brilliant, but also amazing in number. Cauchy, with 27 volumes and more than 800 works, is a prolific mathematician in the history of mathematics, second only to Euler. His glorious name is remembered by many textbooks today along with many theorems and standards.
As a scholar, he has quick thinking and outstanding achievements. From Cauchy's voluminous works and achievements, it is not difficult to imagine how he worked tirelessly all his life. But Cauchy is a complicated person. He is a loyal royalist, an enthusiastic Catholic and a lonely scholar. Especially as a prestigious master of science, he often ignores the creation of young scholars. For example, because Cauchy "lost" the pioneering manuscripts of the papers of talented young mathematicians Abel and Galois, it took about half a century for the group theory to come out.
1857 On May 23rd, Cauchy died in Paris. His last famous saying, "People will die, but achievements will last forever." It has struck the hearts of generations of students for a long time.
Cauchy's skill in pure mathematics and applied mathematics is quite profound. In mathematical writing, he is considered to be second only to Euler in number. He wrote 789 papers and published several books in his life, some of which were classics, but not all of his creations were of very high quality, so he was criticized as prolific and rash, contrary to the prince of mathematics. It is said that the French Academy of Sciences will publish. Because there are too many works by Cauchy, the Academy of Sciences has to bear a very large printing cost, which exceeds the budget of the Academy of Sciences. So later, the Academy of Sciences stipulated that the longest paper could only have four pages, so Cauchy's longer paper had to be submitted elsewhere.
When Cauchy was young, his father often took him to the office of the French Senate, where he instructed him in his studies, so he had the opportunity to meet two great mathematicians, Senator Laplace and Senator Lagrange. They appreciate his talent very much; Lagrange thought he would be a great mathematician in the future, but advised his father not to study mathematics before learning liberal arts well.