Augustin-Louis Cauchy: Difference between revisions
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On Lagrange's advice Augustin-Louis was enrolled in the École Central du Panthéon in the fall of 1802. This was the best secondary school of Paris at that time. Most of the curriculum consisted of classical languages and the young ambitious Cauchy, being a brilliant student, won many prizes in Latin and Humanities. In spite of these successes, Augustin-Louis decided for an engineering | On Lagrange's advice Augustin-Louis was enrolled in the École Central du Panthéon in the fall of 1802. This was the best secondary school of Paris at that time. Most of the curriculum consisted of classical languages and the young ambitious Cauchy, being a brilliant student, won many prizes in Latin and Humanities. In spite of these successes, Augustin-Louis decided for an engineering | ||
career and prepared himself for the entrance examination to the École Polytechnique. | career and prepared himself for the entrance examination to the École Polytechnique. | ||
In 1805 he became second out of 293 applicants on this | In 1805 he became second out of 293 applicants on this exam, and was, of course, admitted. | ||
One of the main purposes of this school was to give future civil and military engineers a high-level scientific and mathematical education. The school functioned under military discipline, which caused the young pious Cauchy some problems in adapting. Nevertheless, he finished the Polytechnique in 1807 at the age of 18 and went on to the École des Ponts et Chaussées (School for Bridges and Highways). He graduated in civil engineering with the highest honors in 1810 and accepted a job as junior engineer in Cherbourg, where Napoleon intended to build a naval port. Here Augustin-Louis stayed three years and although he had an extremely busy managerial type job, he still found time to prepare three mathematical manuscripts, which he submitted to the ''Première Classe'' of the [[Institut de France]]. (In the revolutionary years the French ''Académie des sciences'' was known as the "First Class of the Institut"). Cauchy's first two manuscripts (on [[regular polyhedron|polyhedra]]) were accepted, the third one (on directrixes of conic sections) was rejected. | |||
In September 1812 Cauchy returned to Paris after becoming ill by being overworked. Another reason | |||
for his return to the capital was that he was losing his interest in his engineering job, being more and more attracted to abstract beauty of mathematics. In Paris he would have a much better chance to find a mathematics related position. Formally he remained an engineering position, although he was transfered from the pay role of the Ministry of the Marine to the Ministry of the Interior. The next three years Augustin-Louis was mainly on sick leave from his engineering job, but spend his time quit fruitfully on mathematics (on the related topics of [[symmetric functions]], the [[symmetric group]] and the theory of higer-order equations). He tried to be admitted to the First Class of the Institut and failed three times between 1813 and 1815. | |||
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Back in Paris Cauchy investigated symmetric functions and submitted a memoir on this topic in November 1812. This was published in the Journal of the École Polytechnique in 1815. However he was supposed to return to Cherbourg in February 1813 when he had recovered his health and this did not fit with his mathematical ambitions. His request to de Prony for an associate professorship at the École des Ponts et Chaussées was turned down but he was allowed to continue as an engineer on the Ourcq Canal project rather than return to Cherbourg. Pierre Girard was clearly pleased with his previous work on this project and supported the move. | |||
An academic career was what Cauchy wanted and he applied for a post in the Bureau des Longitudes. He failed to obtain this post, Legendre being appointed. He also failed to be appointed to the geometry section of the Institute, the position going to Poinsot. Cauchy obtained further sick leave, having unpaid leave for nine months, then political events prevented work on the Ourcq Canal so Cauchy was able to devote himself entirely to research for a couple of years. | |||
Other posts became vacant but one in 1814 went to Ampère and a mechanics vacancy at the Institute, which had occurred when Napoleon Bonaparte resigned, went to Molard. In this last election Cauchy did not receive a single one of the 53 votes cast. His mathematical output remained strong and in 1814 he published the memoir on definite integrals that later became the basis of his theory of complex functions. | |||
In 1815 Cauchy lost out to Binet for a mechanics chair at the École Polytechnique, but then was appointed assistant professor of analysis there. He was responsible for the second year course. In 1816 he won the Grand Prix of the French Academy of Sciences for a work on waves. He achieved real fame however when he submitted a paper to the Institute solving one of Fermat's claims on polygonal numbers made to Mersenne. Politics now helped Cauchy into the Academy of Sciences when Carnot and Monge fell from political favour and were dismissed and Cauchy filled one of the two places. | |||
In 1817 when Biot left Paris for an expedition to the Shetland Islands in Scotland Cauchy filled his post at the Collège de France. | |||
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'''(To be continued)''' | '''(To be continued)''' | ||
Revision as of 07:53, 31 October 2007
Augustin-Louis Cauchy (Paris, August 21 1789 – Sceaux, May 23, 1857) was one of the most prominent mathematicians of the first half of the 19th century. He was the first to give a rigorous basis to the concept of limits. He established a convergence criterion for sequences of the type that are now called Cauchy sequences. The Cauchy condition for the convergence of series can be found in any present-day textbook on calculus. Probably Cauchy is most famous for his singlehanded development of complex function theory, with Cauchy's residue theorem as the fundamental result.
Cauchy was a prolific writer, he wrote more than 800 research articles and five complete textbooks. He was a devout Roman Catholic, strict (Bourbon) royalist, and a close associate of the Jesuit order.
Biography
Cauchy's father (Louis-François Cauchy) was a high official in the Parisian Police of the Old Régime. He lost his position because of the French Revolution (July 14, 1789) that broke out one month before Augustin-Louis was born. This fact is sometimes seen as the cause of the deep hatred of the French Revolution that Cauchy felt all through his life. The Cauchy family survived the revolution and the following Reign of Terror (1794) by escaping to Arcueil, where Cauchy jr. got his first education from his father. After the death of Robespierre (1794) it was safe for the family to return to Paris, where Cauchy sr. found himself a new bureaucratic job and where he quickly moved up the ranks. When Napoleon Bonaparte came to power (1799) Cauchy sr. made further promotion to Secretary-General of the Senate working directly under Laplace, who is now better known for his work on mathematical physics. Also the famous mathematician Lagrange was no stranger to the Cauchy family.
On Lagrange's advice Augustin-Louis was enrolled in the École Central du Panthéon in the fall of 1802. This was the best secondary school of Paris at that time. Most of the curriculum consisted of classical languages and the young ambitious Cauchy, being a brilliant student, won many prizes in Latin and Humanities. In spite of these successes, Augustin-Louis decided for an engineering career and prepared himself for the entrance examination to the École Polytechnique. In 1805 he became second out of 293 applicants on this exam, and was, of course, admitted. One of the main purposes of this school was to give future civil and military engineers a high-level scientific and mathematical education. The school functioned under military discipline, which caused the young pious Cauchy some problems in adapting. Nevertheless, he finished the Polytechnique in 1807 at the age of 18 and went on to the École des Ponts et Chaussées (School for Bridges and Highways). He graduated in civil engineering with the highest honors in 1810 and accepted a job as junior engineer in Cherbourg, where Napoleon intended to build a naval port. Here Augustin-Louis stayed three years and although he had an extremely busy managerial type job, he still found time to prepare three mathematical manuscripts, which he submitted to the Première Classe of the Institut de France. (In the revolutionary years the French Académie des sciences was known as the "First Class of the Institut"). Cauchy's first two manuscripts (on polyhedra) were accepted, the third one (on directrixes of conic sections) was rejected.
In September 1812 Cauchy returned to Paris after becoming ill by being overworked. Another reason for his return to the capital was that he was losing his interest in his engineering job, being more and more attracted to abstract beauty of mathematics. In Paris he would have a much better chance to find a mathematics related position. Formally he remained an engineering position, although he was transfered from the pay role of the Ministry of the Marine to the Ministry of the Interior. The next three years Augustin-Louis was mainly on sick leave from his engineering job, but spend his time quit fruitfully on mathematics (on the related topics of symmetric functions, the symmetric group and the theory of higer-order equations). He tried to be admitted to the First Class of the Institut and failed three times between 1813 and 1815.
(To be continued)
Reference
Bruno Belhoste, Augustin-Louis Cauchy: a biography, translated from the French by F. Ragland, Springer, New York (1991). ISBN 0-387-97220-X
External links
- Biography at MacTutor History of Mathematics, John J. O'Connor and Edmund F. Robertson, School of Mathematics and Statistics, University of St Andrews, Scotland.