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 have a lot of common sense about his talents; Lagrange thought he would be a great mathematician in the future, but advised his father not to study mathematics before learning liberal arts well.
Cauchy entered middle school on 1802. In middle school, he got excellent grades in Latin and Greek and won many competitions. Math scores are also highly praised by teachers. 1805 was admitted to a comprehensive engineering school, mainly studying mathematics and mechanics. 1807 was admitted to Daqiao Highway School, 18 10 graduated with honors and went to Cherbourg to participate in the harbor construction project.
Cauchy went to Cherbourg with Lagrange's analytic function theory and Laplace's celestial mechanics, and later received some math books sent from Paris or borrowed from the local area. In his spare time, he carefully studied books in various branches of mathematics, from number theory to astronomy. According to Lagrange's suggestion, he studied polyhedron and submitted two papers to the Academy of Sciences at181and 18 12. The main results are as follows:
(1) It is proved that there are only five kinds of convex regular polyhedrons (the number of faces is 4, 6, 8, l 2 and 20 respectively) and four kinds of star regular polyhedrons (the number of faces is l2, and one face is 20).
(2) Another proof about the Euler relation of the number of vertices, faces and edges of polyhedron is obtained and generalized.
(3) It is proved that a polyhedron with a fixed surface must be fixed, from which a theorem of Euclid that has never been proved can be derived.
These two papers have had a great influence in mathematics. Cauchy fell ill at work in Cherbourg and returned to her parents' home in Paris on 18 12.
Cauchy was appointed as the engineer of the Paris Canal Project at 18l3. During his rest and work as an engineer in Paris, he continued to devote himself to studying mathematics and participating in academic activities. His main contributions during this period are:
(1) has studied substitution theory and published basic papers on substitution theory and group theory in history.
(2) Prove Fermat's conjecture about polygon number, that is, any positive integer is the sum of angles. This speculation has been put forward for more than a hundred years at that time, and it has not been solved after many mathematicians' research. The above two studies began when Cauchy was in Cherbourg.
(3) Calculating the real integral with the integral of complex variable function is the starting point of Cauchy's integral theorem in the theory of complex variable function.
(4) Studied the propagation of liquid surface waves, obtained some classical results in fluid mechanics, and won the 18 15 mathematics prize of French Academy of Sciences.
The publication of the above outstanding achievements brought Cauchy a high reputation, and he became an internationally famous young mathematician at that time.
Napoleon failed in France, Bourbon was restored, and Louis Stanislas Xavier became king of France. On 18 16, Cauchy was hired as an academician of French Academy of Sciences and a professor of comprehensive engineering. 182 1 was appointed as a professor of mechanics at the University of Paris and also taught at the French Academy. His main contributions during this period are:
(1) Teaching analysis courses in comprehensive engineering schools, establishing the basic limit theory of calculus and expounding the limit theory. Before that, the concepts of calculus and series were vague. Because Cauchy's speech was different from the traditional way, the teachers and students of the school put forward many criticisms to him at that time.
Cauchy's works published in this period include Algebraic Analysis Course, Infinitesimal Analysis Course Outline and Application Course of Calculus in Geometry. These works laid the foundation of calculus, promoted the development of mathematics and became a model of mathematics curriculum.
(2) Cauchy studied continuum mechanics again after being a professor of mechanics at the University of Paris. In a paper from 65438 to 0822, he established the foundation of elasticity theory.
(3) Continue to study the calculation of integrals and residues on the complex plane, and apply related results to study partial differential equations in mathematical physics.
A large number of his papers have been published in the Journal of French Academy of Sciences and his own periodical Mathematical Exercises.
1830, the revolution that overthrew the Bourbon dynasty broke out in France. King Charles of France fled hastily, and Louis Philippe, Duke of Orleans, succeeded him. At that time, it was stipulated that he must swear allegiance to the new king when he held public office in France. Because Cauchy belonged to the orthodox school that supported the Bourbon dynasty, he refused to swear allegiance and left France by himself. I went to Switzerland first, and then worked as a professor of mathematical physics at the University of Turin in Italy on 1832- 1833, and participated in the academic activities of the local academy of sciences. At that time, he studied the series expansion of complex variable function and differential equation (strong series method), and made important contributions to this.
From 1833 to 1838, Cauchy first worked in Prague, then worked as a teacher of the Bourbon Crown Prince and the Duke of Bordeaux in Golz, and was finally awarded the title of Baron. During this period, his research work was less.
Cauchy returned to Paris on 1838. Because he didn't swear allegiance to the king of France, he could only participate in academic activities of the Academy of Sciences, but could not engage in teaching. He published a large number of important papers on complex variable function, celestial mechanics, elasticity and so on in the report of French Academy of Sciences "and his own periodic analysis and mathematical physics exercises".
1848, the French revolution broke out again, Louis Philippe fell, the Republic was re-established, and the oath of allegiance of public officials to the French king was abolished. Cauchy became a professor of mathematical astronomy at the University of Paris in 1848, and resumed his teaching work in French institutions of higher learning, which was interrupted in 18.
1852, Napoleon staged a coup for the third time, and France changed from a republic to an imperial system, restoring public officials to swear allegiance to the new regime. Cauchy immediately resigned from the University of Paris. Later, Napoleon granted a third exemption from the oath of loyalty of himself and physicist arago. So Cauchy was able to continue his teaching work until/kloc-0 died in the suburbs of Paris in 857. Cauchy continued to participate in academic activities and published scientific papers until his death.