Augustin-Louis Cauchy

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  • Topic: Calculus, Complex analysis, Mathematics
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  • Published : April 28, 2009
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Cauchy was born on August 21, 1789 and grew up in Paris as a young child [6, p.1]. Life was difficult because it was during the time of the French Revolution. Cauchy’s family moved to Arcueil, fearing the dangers of life in Paris [6, p.1]. Nevertheless, they soon returned to Paris and Cauchy began his education. Most of Cauchy’s early education was from his father, Louis Francois Cauchy. The family was often visited by mathematicians, such as Lagrange and Laplace. Lagrange took a deep interest in Cauchy’s education, suggesting that Cauchy receive a good education in languages prior to studying mathematics [2, p.1]. In 1802, Cauchy entered Ecole Centrale du Pantheon studying classical languages. Two years later, Cauchy began studying mathematics and entered Ecole Polytechnique, placing second in his class. He attended classes taught by Lacroix, de Prony, and Hachette and his analysis tutor was Ampere. In 1807, he graduated and enrolled at Ecole des Ponts et Chaussees to study engineering. Cauchy excelled at practical work in his studies and, in 1810, got an engineering job in Cherbourg working on port facilities for Napoleon’s English invasion fleet [1, p.40]. He brought a copy of two of Lagrange’s books, Mechanique Celeste and Theorie de Fonctions, which he studied copiously [6, p.3]. Cauchy began his mathematical career a year later by solving a problem set introduced by Lagrange, which was that the angles of a convex polyhedron are determined by its faces. His solution is still considered a clever and intelligent piece of classic mathematics [1, p.142]. In beginning his work with mathematics, Cauchy found his strong Catholic beliefs to be in conflict with his work. Cauchy’s devotion he had to mathematics caused him to become isolated from his religious community [6, p.2]. Cauchy felt that in order to be an established mathematician he had to return to Paris; however, in 1813, he became ill, possibly due to depression, and was forced to return to Paris. In Paris, Lagrange and Laplace convinced Cauchy to devote himself solely to mathematics [2, p.1]. Cauchy began investigating symmetric functions and, in November 1812, he submitted a memoir to be published in the Journal of the Ecole Polytechnique [1, p.145]. Once Cauchy recovered from illness, he realized the job in Cherbourg was not what he wanted to pursue. Instead, he asked de Prony for a professorship at Ecole des Ponts et Chausses and was turned down. He returned to an engineering job on the Ourcq Canal [6, p.5]. Cauchy hoped to pursue an academic career rather than engineering. He applied for a job in Bureau des Longitudes and did not get the job. At the time, political events in France prevented Cauchy from working on the Ourcq Canal, so he focused his attention on research [6, p.4]. Cauchy eventually attained a job at Ecole Polytechnique as assistant professor of analysis. In 1816, he won the Gran Prix of the French Academy of Science for work he had done on waves [1, p.142]. He also wrote a paper to the Institute solving one of Fermat’s claims on polygonal numbers. Cauchy, with the help of politics, was admitted to the Academy of Sciences [6, p.4]. At the Academy of Science, Cauchy lectured on methods of integration, which he discovered, but had not published. Cauchy was the first to use a rigorous study of the conditions for convergence of infinite series in addition to his rigorous definition of an integral [1, p.143]. He taught from his text Cours d’analysein 1821. Five years later, he began to study the calculus of residues with Sur un nouvea genre de calculus analogue au calculus infinitesimal. In 1829, he defined for the first time a complex function and complex variable in Lecons sur le Calculus Differential [6, p.3].

By 1830, the political events in Paris had left Cauchy tired and strained. After the revolution of July, he decided to take a break at Freiburg, Switzerland. Here, he helped try to set up the Academie Helvatique, which failed because of...
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