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Augustin-Louis Cauchy pioneered the study of analysis and the theory of permutation groups. He also researched in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.
Cauchy stated as a military engineer and in 1810 went to Cherbourg to work on Napoleon's English invasion fleet. In 1813 he returned to Paris and, after persuasion from Lagrange and Laplace, devoted himself to mathematics.
He held various posts in Paris at Faculté des Sciences, the Collège de France and the École Polytechnique. In 1816 he won the Grand Prix of the French Academy of Science.
He pioneered the study of analysis and the theory of substitution groups (now called permutation groups). Cauchy proved in 1811 that the angles of a convex polyhedron are determined by its faces. In 1814 he published the memoir on definite integrals that became the basis of the theory of complex functions.
His other contributions include researches in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.
Numerous terms in mathematics bear his name:- the Cauchy integral theorem, in the theory of complex functions, the Cauchy-Kovalevskaya existence theorem for the solution of partial differential equations, the Cauchy-Riemann equations and Cauchy sequences.
Cauchy was the first to make a rigorous study of the conditions for convergence of infinite series and he also gave a rigorous definition of an integral. His text Cours d'analyse in 1821 was designed for students at École Polytechnique and was concerned with developing the basic theorems of the calculus as rigorously as possible. The 4-volume text Exercises d'analyse et de physique mathematique published between 1840 and 1847 proved extremely important.
He produced 789 mathematics papers but was disliked by most of his colleagues. He displayed self-righteous obstinacy and an aggressive religious bigotry. An ardent royalist he spent some time in Italy after refusing to take an oath of allegiance. He left Paris after the revolution of 1830 and after a short time in Switzerland he accepted an offer from the King of Piedmont of a chair in Turin where he taught from 1832. In 1833 Cauchy went from Turin to Prague in order to follow Charles X and to tutor his son.
Cauchy returned to Paris in 1838 and regained his position at the Academy but not his teaching position because he refused to take an oath of allegiance. When Louis Philippe was overthrown in 1848 Cauchy regained his chair at the Sorbonne. He held this post until his death.
References elsewhere in this archive:
Tell me about Cauchy's theorem in Complex analysis
Tell me about Cauchy's part in the rise of calculus
Tell me about his work on Fermat's last theorem
Tell me about Cauchy's part in the life of Évariste Galois
Tell me about his part in the development of group theory and abstract linear spaces
Tell me about Cauchy's work on matrices and determinants and on the fundamental theorem of algebra
References:
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