Cauchy, Augustin Louis

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{{Infobox_Scientist
 
{{Infobox_Scientist
 
| name = Augustin Louis Cauchy
 
| name = Augustin Louis Cauchy
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| nationality = [[Image:Flag of France.svg|20px|]] [[France|French]]
 
| nationality = [[Image:Flag of France.svg|20px|]] [[France|French]]
 
| field = [[calculus]]
 
| field = [[calculus]]
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| work_institution = [[École Centrale du Panthéon]] </br>[[École Nationale des Ponts et Chaussées]] </br> [[École polytechnique]]
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| work_institution = [[École Centrale du Panthéon]] <br/>[[École Nationale des Ponts et Chaussées]] <br/> [[École polytechnique]]
 
| alma_mater = [[École Nationale des Ponts et Chaussées]]
 
| alma_mater = [[École Nationale des Ponts et Chaussées]]
 
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'''Augustin Louis Cauchy''' ([[August 21]], [[1789]] &ndash; [[May 23]],[[1857]]) was a [[France|French]] [[mathematician]]. He started the project of formulating and proving the theorems of [[calculus]] in a rigorous manner and was thus an early pioneer of [[mathematical analysis|analysis]]. He also gave several important theorems in [[complex analysis]] and initiated the study of [[permutation group]]s. A profound mathematician, Cauchy exercised by his perspicuous and rigorous methods a great influence over his contemporaries and successors. His writings cover the entire range of mathematics and [[mathematical physics]].
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'''Augustin Louis Cauchy''' (August 21, 1789 &ndash; May 23,1857) was a [[France|French]] [[mathematician]] who initiated the movement to introduce rigor into the theorems of the infinitesimal [[calculus]]. He also applied higher mathematics to the solution of problems in [[optics]] and [[mechanics]].  
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{{toc}}
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Cauchy was a devout [[Catholic]], and, toward the end of his life, dedicated as much of his time to charitable works as to his professional duties.
  
 
==Biography==
 
==Biography==
 +
===Early life===
  
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Having received his early education from his father [[Louis François Cauchy]] ([[1760]]&ndash;[[1848]]), who held several minor public appointments and counted [[Joseph Louis Lagrange|Lagrange]] and [[Pierre-Simon Laplace|Laplace]] among his friends, Cauchy entered the [[École Centrale du Panthéon]] in [[1802]], and proceeded to the [[École Polytechnique]] in [[1805]], and to the [[École Nationale des Ponts et Chaussées]] in [[1807]]. Having adopted the profession of an [[Engineering|engineer]], he left [[Paris]] for [[Cherbourg-Octeville|Cherbourg]] in [[1810]], but returned in [[1813]] on account of his health, whereupon Lagrange and Laplace persuaded him to renounce engineering and to devote himself to mathematics. He obtained an appointment at the École Polytechnique, which, however, he relinquished in [[1830]] on the accession of [[Louis-Philippe of France|Louis-Philippe]]. He did this because he found it impossible to take the necessary oaths to the new government as he remained loyal to the [[House of Bourbon]]. A short sojourn at [[Fribourg]] in [[Switzerland]] was followed by his appointment in [[1831]] to the newly-created chair of mathematical physics at the [[University of Turin]]. (Note: At that time, Turin was the capital of the Kingdom of Sardinia, which unified Italy later in 1871. Now Turin is just a city in northern Italy.)
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Cauchy was born a short time after the storming of the Bastille in 1789, the event that launched the French revolution. As a result, Cauchy's father, [[Louis François Cauchy]], who had been closely associated with the monarchy, was forced to flee with the family to [[Arcueil]]. Their life there was apparently hard, and Cauchy spoke of living on rice, bread, and crackers. This instilled in him a strong affinity for the monarchy and a disdain for the republican form of government.
  
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In 1833 the deposed king [[Charles X of France]] summoned Cauchy to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impression which his investigations had made. Charles created him a baron in return for his services. Returning to Paris in 1838, Cauchy refused a proffered chair at the [[Collège de France]], but in 1848, the oath having been suspended, he resumed his post at the École Polytechnique, and when the oath was reinstituted after the coup d'état of 1851, Cauchy and [[François Arago]] were exempted from it. Subequently, Cauchy lived in the France ruled by the emperor [[Napoleon III]] until his death in 1857.
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In 1800, Cauchy's father became secretary of the senate under Napoleon. The elder Cauchy's position brought him into contact with many of the leaders of his age, including the mathematician [[Joseph Louis Lagrange]], who personally took an interest Cauchy's early education. Lagrange advised his father to educate Cauchy in the classics before exposing him to mathematical studies.
  
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Cauchy married Aloise de Bure in 1818. She was a close relative of a publisher who published most of Cauchy's works. Cauchy had two brothers: [[Alexandre Laurent Cauchy]] ([[1792]]&ndash;[[1857]]), who became a president of a division of the court of appeal in [[1847]], and a judge of the court of cassation in [[1849]]; and [[Eugène François Cauchy]] ([[1802]]&ndash;[[1877]]), a publicist who also wrote several mathematical works.
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Two of Cauchy's brothers would carve out reputations for themselves. [[Alexandre Laurent Cauchy]] became a president of a division of the court of appeal and a judge of the court of cassation. [[Eugène François Cauchy]] was a publicist who also wrote several mathematical works.
  
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Cauchy had two daughters.
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===University education===
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Cauchy entered the [[École Centrale du Panthéon]] in 1802, placing first in [[Latin]] and Greek verse and second in Latin composition. He left the school in 1804, and studied mathematics in preparation for the entrance examinations for the Ecole Polytechnique, in which he ranked second. He entered the Polytechnique in 1805, and the [[École Nationale des Ponts et Chaussées]] in 1807. Having adopted the profession of an [[Engineering|engineer]], he left [[Paris]] for a position at [[Cherbourg-Octeville|Cherbourg]] harbor in 1810, but returned in 1813, on account of his health, whereupon Lagrange and the eminent mathematical physicist [[Pierre-Simon Laplace]] persuaded him to renounce engineering and devote himself to mathematics.
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===Early work===
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The genius of Cauchy was perhaps first illustrated in his simple solution of the [[Apollonian gasket|problem of Apollonius]], that is, to describe a [[circle]] touching three given circles, which he discovered in 1805. In 1811, Cauchy added to this accomplishment through his generalization of [[Euler characteristic|Euler's formula]] on [[polyhedra]], and by the solutions to several other elegant problems.
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In 1815, Cauchy won the Grand Prix of the Institute of France for his solution to the problem of waves produced at the surface of a liquid of indefinite depth, beating out the esteemed mathematician [[Siméon Denis Poisson]]. The following year, he was admitted as a member of the French Academy of Sciences after the departure of Gaspard Monge and Lazare Carnot, two well respected members who lost their places because of strong ties with Napoleon's government, which had by then relinquished power to the bourbon monarchy. This generated tension between Cauchy and some members of the French scientific community.
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Cauchy became assistant professor of analysis at the École Polytechnique in 1815, and was promoted to full professor in 1816. In 1818, he married Aloise de Bure, with whom he had two daughters. His wife was a close relative of the publisher of most of Cauchy's works.
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In the 1820s, the Cauchy's teaching labors bore fruit through his publication of several major treatises. These included ''Cours d'analyse de l'[[École Polytechnique]]'' (1821); ''Le Calcul infinitésimal'' (1823); ''Leçons sur les applications de calcul infinitésimal''; ''La géométrie'' (1826&ndash;1828); and also in his ''Courses of Mechanics'' (for the École Polytechnique), ''Higher Algebra'' (for the [[Faculté des Sciences]]), and ''Mathematical Physics'' (for the Collège de France).
 +
 
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In 1826, he launched a periodical, ''Mathematical Exercises,'' devoted entirely to his own work. This publication continued, with intermittent interruptions, until Cauchy's death, and inspired many important investigations by later researchers.
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===Middle years===
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In 1830, on the accession of [[Louis-Philippe of France|Louis-Philippe]], Cauchy refused to take an oath of allegiance to the new government, and relinquished his position at the Polytechnique. A short sojourn at [[Fribourg]] in [[Switzerland]], was followed by his appointment in 1831, to the newly-created chair of mathematical physics at the [[University of Turin]].
 +
 
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In 1833 the deposed king, [[Charles X of France]], summoned Cauchy to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel, and thereby become acquainted with the favorable impression which his investigations had made. Physicist Amedeo Avogadro assumed the Turin professorship vacated by Cauchy.
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Charles X conveyed to Cauchy the title and privileges of a baron in return for his services. Returning to Paris, in 1838, Cauchy refused a proffered chair at the [[Collège de France]] because an oath of allegiance to the throne was required. He was proposed for a post at the Bureau of Longitudes in 1839, but he likewise refused to take an oath, and, in spite of backing from friends and colleagues, lost the appointment. He still assumed responsibilities at the post, working there more or less illegally. In 1848, the oath having been suspended, he resumed his post at the École Polytechnique. In 1851, after the coup d'état of that year, Cauchy and [[François Arago]] were exempted from taking an oath. Subsequently, Cauchy lived in the France ruled by the emperor [[Napoleon III]] until his death.
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===Later life===
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Much of Cauchy's efforts in later years were devoted to religious and charitable works. When he was 53, he learned Hebrew in order to help his father with some religious researches. Toward the end of his life, Cauchy donated a large part of his income from the state to charitable purposes, and was engaged in other works of mercy. The mayor of Sceaux, where Cauchy made his home, said that Cauchy "had two distinct lives: The Christian and the scientific life, each so full, so complete, that it would have served to confer luster on any name" (Kelland 1858, 182). In 1856, when the mathematician [[Charles Hermite]] contracted [[smallpox]], it was Cauchy who nursed him back to health, and persuaded him to embrace the Catholic faith.
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In the field of mathematics, Cauchy was active until a few days before his death. In a paper published in 1855, he discussed some theorems, one of which is similar to the "Argument Principle" in many modern textbooks on complex analysis. In modern control theory textbooks, the [[Cauchy argument principle]] is quite frequently used to derive the [[Nyquist stability criterion]], which can be used to predict the stability of negative [[feedback amplifier]] and negative [[feedback]] control systems.
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 +
In May of 1857, he submitted a memoir to the academy on a technique for astronomical calculations. A week later, he attended a session of the academy, but was suffering from a cold. His symptoms became more severe, affecting his appearance and mobility. A cleric is said to have warned Cauchy to slow his work pace, so that the prayers of the faithful on his behalf would bare fruit. But he said in response: "Dear sir, men pass away, but their works remain. Pray for the work" (Kelland 1858, 182).
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Cauchy retreated to his residence at Sceaux, and remained there, continuing to work on the theory of series. As late as the May 21, he conversed with the archbishop of Paris, although in a considerably enfeebled condition. Two days later, on May 23, 1857, he awoke at three in the morning, only to expire half an hour later. His last words are said to have been a reference to the great figures of Catholic faith: [[Jesus]], [[Mary]], and [[Joseph]].
  
 
==Work==
 
==Work==
−
The genius of Cauchy was illustrated in his simple solution of the [[Apollonian gasket|problem of Apollonius]], i.e. to describe a [[circle]] touching three given circles, which he discovered in [[1805]], his generalization of [[Euler characteristic|Euler's formula]] on [[polyhedra]] in [[1811]], and in several other elegant problems. More important is his memoir on [[wave]] propagation, which obtained the Grand Prix of the Institut in [[1816]]. His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced. These are mainly embodied in his three great treatises, ''Cours d'analyse de l'[[École Polytechnique]]'' ([[1821]]); ''Le Calcul infinitésimal'' ([[1823]]); ''Leçons sur les applications de calcul infinitésimal''; ''La géométrie'' ([[1826]]&ndash;[[1828]]); and also in his ''Courses of mechanics'' (for the École Polytechnique), ''Higher algebra'' (for the [[Faculté des Sciences]]), and of ''Mathematical physics'' (for the Collège de France).
 
  
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He wrote numerous treatises and made 789 contributions to scientific journals. These writings covered notable topics including the theory of series (where he developed with perspicuous skill the notion of convergency), the theory of numbers and complex quantities, the theory of groups and substitutions, and the theory of functions, differential equations and determinants. He clarified the principles of the calculus by developing them with the aid of limits and continuity, and was the first to prove [[Taylor's theorem]] rigorously, establishing his well-known form of the remainder. He also contributed significant research in [[mechanics]], substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. In [[optics]], he developed the wave theory, and his name is associated with the simple dispersion formula. In [[Elasticity (physics)|elasticity]], he originated the theory of [[stress (physics)|stress]], and his results are nearly as valuable as those of [[Simeon Poisson]].
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Cauchy made 789 contributions to scientific journals. These writings covered notable topics including the theory of series (where he developed with perspicuous skill the notion of [[convergency]]), the theory of numbers and complex quantities, the theory of groups and substitutions, and the theory of functions, differential equations, and determinants.
 +
 
 +
He clarified the principles of the [[calculus]] by developing them with the aid of limits and continuity, and was the first to prove rigorously [[Taylor's theorem]], which demonstrates the manner in which a function can be represented by an infinite series whose terms contain derivatives of the function at a point. In doing so, he laid down his well-known form of the remainder, the difference in value between the sums of a finite and an infinite number of terms of a series. He also contributed significant research in [[mechanics]]. In [[optics]], he developed the [[wave theory]], and his name is associated with the simple dispersion formula. In [[Elasticity (physics)|elasticity]], he originated the theory of [[stress (physics)|stress]], and his results are nearly as valuable as those of [[Simeon Poisson]].
  
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Other significant contributions include being the first to prove the [[Fermat polygonal number theorem]]. He created the [[residue theorem]] and used it to derive a whole host of most interesting series and integral formulas and was the first to define complex numbers as pairs of real numbers. He also discovered many of the basic formulas in the theory of [[q-series]]. His collected works, ''Œuvres complètes d'Augustin Cauchy'', have been published in 27 volumes.
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Other significant contributions include being the first to prove the [[Fermat polygonal number theorem]]. His collected works, ''Œuvres complètes d'Augustin Cauchy,'' have been published in 27 volumes.
  
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Although generally rigorous, he was way ahead of the rest of his field at the time, and thus one of his theorems was exposed to a "counter-example" by Abel, later fixed by the inclusion of uniform continuity.
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==Character and legacy==
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Cauchy was unusual in that he left not only a body of work of monumental proportions, but also the the example of a life devoted to good works. At the same time, he appears to have often been disputatious, sparing with fellow mathematicians, sometimes appearing to deny them credit for their work, and on occasion refusing to admit to the limitations of his own work.
  
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In a paper published in 1855, two years before his death, he discussed some theorems, one of which is similar to the "Argument Principle" in many modern textbooks on complex analysis. In modern control theory textbooks, the [[Cauchy argument principle]] is quite frequently used to derive the [[Nyquist stability criterion]], which can be used to predict the stability of negative [[feedback amplifier]] and negative [[feedback]] control systems. Thus Cauchy's work has strong impact on both pure mathematics and practical engineering.
+
Cauchy was a defender of royalism and hence refused to take oaths to any government after the overthrow of [[Charles X]]. This reveals him to have been a man of strong convictions and unbending principles.
  
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==Politics and religious beliefs==
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He was a devout Catholic and a member of the [[Society of Saint Vincent de Paul]]. He also had links to the [[Society of Jesus]] and defended them at the French Academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for the mathematician [[Charles Hermite]] and to have inspired him to plea on behalf of the Irish during the [[Potato Famine]].
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Augustin Louis Cauchy grew up in the house of a staunch royalist. This made his father flee with the family to [[Arcueil]] during the [[French Revolution]]. Their life there was apparently hard and Cauchy spoke of living on rice, bread, and crackers during the period. In any event he inherited his father's staunch royalism and hence refused to take oaths to any government after the overthrow of Charles X.
 
  
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He was an equally staunch Catholic and a member of the [[Society of Saint Vincent de Paul]].[http://www.newadvent.org/cathen/03457a.htm] He also had links to the [[Society of Jesus]] and defended them at the Academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for [[Charles Hermite]] during his illness and leading Hermite to become a faithful Catholic. It also inspired Cauchy to plea on behalf of the Irish during the [[Potato Famine]].
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His royalism and religious zeal also made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. [[Niels Henrik Abel]] denounced his stubbornness but praised him as a mathematician. Many of Cauchy's views were widely unpopular among mathematicians, and when [[Guglielmo Libri Carucci dalla Sommaja]] was made chair in mathematics before him, he, and many others, felt his views were the cause. When Libri was accused of stealing books, he was replaced by [[Joseph Liouville]], which caused a rift between him and Cauchy. Another dispute concerned Jean Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by [[Jean-Victor Poncelet]], that he was in the wrong. Despite that, Cauchy refused to concede and nursed a bitterness on the whole issue.
  
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His royalism and religious zeal also made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. [[Niels Henrik Abel]] called him a "bigoted Catholic" and added he was "mad and there is nothing that can be done about him," but at the same time praised him as a mathematician. Cauchy's views were widely unpopular among mathematicians and when [[Guglielmo Libri Carucci dalla Sommaja]] was made chair in mathematics before him he, and many others, felt his views were the cause. When Libri was accused of stealing books he was replaced by [[Joseph Liouville]] which caused a rift between him and Cauchy. Another dispute concerned Jean Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by [[Jean-Victor Poncelet]], that he was in the wrong. Despite that Cauchy refused to concede this and nursed a bitterness on the whole issue.
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Still, Cauchy's great contributions to mathematics, and his devotion to teaching as reflected in his important treatises, render trivial the disputes with others he had during his lifetime.
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His daughter indicated his last moments brought him a certain calm and that his final words were "Jesus, Mary, and Joseph."
 
  
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(For corroboration of claims here see the link to [[MacTutor History of Mathematics archive]] for his and Hermite's biographies)
 
  
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==See also==
 
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<div style="-moz-column-count:3; column-count:3;">
 
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* [[Cauchy integral theorem]]
 
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* [[Cauchy's integral formula]]
 
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* [[Cauchy-Schwarz inequality]]
 
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* [[Cauchy's theorem (group theory)]]
 
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* [[Cauchy's theorem (geometry)]]
 
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* [[Cauchy distribution]]
 
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* [[Cauchy determinant]]
 
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* [[Cauchy formula for repeated integration]]
 
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* [[Cauchy sequence]]
 
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* [[Cauchy-Riemann equations]]
 
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* [[Cauchy-Frobenius lemma]]
 
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* [[Cauchy product]]
 
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* [[Cauchy principal value]]
 
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* [[Cauchy-Binet formula]]
 
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* [[Cauchy-Euler equation]]
 
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* [[Cauchy's equation]]
 
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* [[Cauchy problem]]
 
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* [[Cauchy horizon]]
 
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* [[Cauchy boundary condition]]
 
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* [[Cauchy surface]]
 
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* [[Cauchy-Kovalevskaya theorem]]
 
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* [[Maclaurin-Cauchy test]]
 
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* [[Cauchy's radical test]]
 
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* [[Cauchy (crater)]]
 
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* [[Cauchy functional equation]]
 
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* [[Cauchy-Peano theorem]]
 
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* [[Cauchy argument principle]]
 
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* [[Nyquist stability criterion]]
 
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</div>
 
  
 
==References==
 
==References==
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*{{1911}}
+
 
 +
* Royal Society (Great Britain). 1854. ''Proceedings of the Royal Society of London''. London: Taylor and Francis. 45-49.
 +
* Kelland. 1858. Notice of the life and writings of Baron Cauchy, in ''The Edinburgh New Philosophical Journal, Exhibiting a View of the Progressive Discoveries and Improvements in the Sciences and the Arts''. Edinburgh: A. and C. Black.
 +
* Nickles, Jerome. 1858. Obituary in ''American Journal of Science,'' 2d ser. 1846-70; New-Haven: Converse. 25:91-95.
 +
* Mitrinović, Dragoslav S. and Jovan D. Kečkić. 1984. ''The Cauchy Method of Residues: Theory and Applications''. Dordrecht: D. Reidel. 323-324.
  
 
==External links==
 
==External links==
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{{Wikiquote}}
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All links retrieved August 21, 2023.
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* {{MacTutor Biography|id=Cauchy}}
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* [http://planetmath.org/encyclopedia/CauchyCriterionForConvergence.html Cauchy criterion for convergence]
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* [http://www.archive.org/details/oeuvresdaugusti01caucrich ''Œuvres complètes d'Augustin Cauchy''] Académie des sciences (France). Ministère de l'éducation nationale.  
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* [http://www.archive.org/details/oeuvresdaugusti01caucrich ''Œuvres complètes d'Augustin Cauchy''] Académie des sciences (France). Ministère de l'éducation nationale.
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* [http://www-history.mcs.st-andrews.ac.uk/Biographies/Cauchy.html MacTutor biography].
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* [http://www-history.mcs.st-andrews.ac.uk/Biographies/Cauchy.html MacTutor biography]
 
  
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{{1911}}
  
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{{Persondata
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[[Category:Physical sciences]]
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|NAME= Cauchy, Augustin Louis
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[[Category:Biographies of Scientists and Mathematicians]]
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|ALTERNATIVE NAMES=
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[[Category:Biography]]
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|SHORT DESCRIPTION= [[calculus]]
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[[Category:Mathematics]]
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|DATE OF BIRTH= {{birth date|1789|8|21|df=y}}
 
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|PLACE OF BIRTH= [[Dijon]], [[France]]
 
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|DATE OF DEATH= {{death date|1857|5|23|df=y}}
 
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|PLACE OF DEATH= [[Paris]], [[France]]
 
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}}
 
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[[Category:1789 births|Cauchy, Augustin Louis]]
 
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[[Category:1857 deaths|Cauchy, Augustin Louis]]
 
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[[Category:19th century mathematicians|Cauchy, Augustin Louis]]
 
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[[Category:French mathematicians|Cauchy, Augustin Louis]]
 
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[[Category:Geometers|Cauchy, Augustin Louis]]
 
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[[Category:Mathematical analysts|Cauchy, Augustin Louis]]
 
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[[Category:Alumni of the École Polytechnique|Cauchy, Augustin Louis]]
 
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[[Category:French Roman Catholics|Cauchy]]
 
  
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Latest revision as of 19:07, 21 August 2023

Augustin Louis Cauchy

Augustin Louis Cauchy.JPG
Augustin Louis Cauchy
Born

August 21 1789(1789-08-21)
Dijon, France

Died 23 May 1857

Paris, France

Residence Flag of France.svg France
Nationality Flag of France.svg French
Field calculus
Institutions École Centrale du Panthéon
École Nationale des Ponts et Chaussées
École polytechnique
Alma mater École Nationale des Ponts et Chaussées
Known for Cauchy integral theorem
Religious stance Catholic

Augustin Louis Cauchy (August 21, 1789 – May 23,1857) was a French mathematician who initiated the movement to introduce rigor into the theorems of the infinitesimal calculus. He also applied higher mathematics to the solution of problems in optics and mechanics.

Cauchy was a devout Catholic, and, toward the end of his life, dedicated as much of his time to charitable works as to his professional duties.

Biography

Early life

Cauchy was born a short time after the storming of the Bastille in 1789, the event that launched the French revolution. As a result, Cauchy's father, Louis François Cauchy, who had been closely associated with the monarchy, was forced to flee with the family to Arcueil. Their life there was apparently hard, and Cauchy spoke of living on rice, bread, and crackers. This instilled in him a strong affinity for the monarchy and a disdain for the republican form of government.

In 1800, Cauchy's father became secretary of the senate under Napoleon. The elder Cauchy's position brought him into contact with many of the leaders of his age, including the mathematician Joseph Louis Lagrange, who personally took an interest Cauchy's early education. Lagrange advised his father to educate Cauchy in the classics before exposing him to mathematical studies.

Two of Cauchy's brothers would carve out reputations for themselves. Alexandre Laurent Cauchy became a president of a division of the court of appeal and a judge of the court of cassation. Eugène François Cauchy was a publicist who also wrote several mathematical works.

University education

Cauchy entered the École Centrale du Panthéon in 1802, placing first in Latin and Greek verse and second in Latin composition. He left the school in 1804, and studied mathematics in preparation for the entrance examinations for the Ecole Polytechnique, in which he ranked second. He entered the Polytechnique in 1805, and the École Nationale des Ponts et Chaussées in 1807. Having adopted the profession of an engineer, he left Paris for a position at Cherbourg harbor in 1810, but returned in 1813, on account of his health, whereupon Lagrange and the eminent mathematical physicist Pierre-Simon Laplace persuaded him to renounce engineering and devote himself to mathematics.

Early work

The genius of Cauchy was perhaps first illustrated in his simple solution of the problem of Apollonius, that is, to describe a circle touching three given circles, which he discovered in 1805. In 1811, Cauchy added to this accomplishment through his generalization of Euler's formula on polyhedra, and by the solutions to several other elegant problems.

In 1815, Cauchy won the Grand Prix of the Institute of France for his solution to the problem of waves produced at the surface of a liquid of indefinite depth, beating out the esteemed mathematician Siméon Denis Poisson. The following year, he was admitted as a member of the French Academy of Sciences after the departure of Gaspard Monge and Lazare Carnot, two well respected members who lost their places because of strong ties with Napoleon's government, which had by then relinquished power to the bourbon monarchy. This generated tension between Cauchy and some members of the French scientific community.

Cauchy became assistant professor of analysis at the École Polytechnique in 1815, and was promoted to full professor in 1816. In 1818, he married Aloise de Bure, with whom he had two daughters. His wife was a close relative of the publisher of most of Cauchy's works.

In the 1820s, the Cauchy's teaching labors bore fruit through his publication of several major treatises. These included Cours d'analyse de l'École Polytechnique (1821); Le Calcul infinitésimal (1823); Leçons sur les applications de calcul infinitésimal; La géométrie (1826–1828); and also in his Courses of Mechanics (for the École Polytechnique), Higher Algebra (for the Faculté des Sciences), and Mathematical Physics (for the Collège de France).

In 1826, he launched a periodical, Mathematical Exercises, devoted entirely to his own work. This publication continued, with intermittent interruptions, until Cauchy's death, and inspired many important investigations by later researchers.

Middle years

In 1830, on the accession of Louis-Philippe, Cauchy refused to take an oath of allegiance to the new government, and relinquished his position at the Polytechnique. A short sojourn at Fribourg in Switzerland, was followed by his appointment in 1831, to the newly-created chair of mathematical physics at the University of Turin.

In 1833 the deposed king, Charles X of France, summoned Cauchy to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel, and thereby become acquainted with the favorable impression which his investigations had made. Physicist Amedeo Avogadro assumed the Turin professorship vacated by Cauchy.

Charles X conveyed to Cauchy the title and privileges of a baron in return for his services. Returning to Paris, in 1838, Cauchy refused a proffered chair at the Collège de France because an oath of allegiance to the throne was required. He was proposed for a post at the Bureau of Longitudes in 1839, but he likewise refused to take an oath, and, in spite of backing from friends and colleagues, lost the appointment. He still assumed responsibilities at the post, working there more or less illegally. In 1848, the oath having been suspended, he resumed his post at the École Polytechnique. In 1851, after the coup d'état of that year, Cauchy and François Arago were exempted from taking an oath. Subsequently, Cauchy lived in the France ruled by the emperor Napoleon III until his death.

Later life

Much of Cauchy's efforts in later years were devoted to religious and charitable works. When he was 53, he learned Hebrew in order to help his father with some religious researches. Toward the end of his life, Cauchy donated a large part of his income from the state to charitable purposes, and was engaged in other works of mercy. The mayor of Sceaux, where Cauchy made his home, said that Cauchy "had two distinct lives: The Christian and the scientific life, each so full, so complete, that it would have served to confer luster on any name" (Kelland 1858, 182). In 1856, when the mathematician Charles Hermite contracted smallpox, it was Cauchy who nursed him back to health, and persuaded him to embrace the Catholic faith.

In the field of mathematics, Cauchy was active until a few days before his death. In a paper published in 1855, he discussed some theorems, one of which is similar to the "Argument Principle" in many modern textbooks on complex analysis. In modern control theory textbooks, the Cauchy argument principle is quite frequently used to derive the Nyquist stability criterion, which can be used to predict the stability of negative feedback amplifier and negative feedback control systems.

In May of 1857, he submitted a memoir to the academy on a technique for astronomical calculations. A week later, he attended a session of the academy, but was suffering from a cold. His symptoms became more severe, affecting his appearance and mobility. A cleric is said to have warned Cauchy to slow his work pace, so that the prayers of the faithful on his behalf would bare fruit. But he said in response: "Dear sir, men pass away, but their works remain. Pray for the work" (Kelland 1858, 182).

Cauchy retreated to his residence at Sceaux, and remained there, continuing to work on the theory of series. As late as the May 21, he conversed with the archbishop of Paris, although in a considerably enfeebled condition. Two days later, on May 23, 1857, he awoke at three in the morning, only to expire half an hour later. His last words are said to have been a reference to the great figures of Catholic faith: Jesus, Mary, and Joseph.

Work

Cauchy made 789 contributions to scientific journals. These writings covered notable topics including the theory of series (where he developed with perspicuous skill the notion of convergency), the theory of numbers and complex quantities, the theory of groups and substitutions, and the theory of functions, differential equations, and determinants.

He clarified the principles of the calculus by developing them with the aid of limits and continuity, and was the first to prove rigorously Taylor's theorem, which demonstrates the manner in which a function can be represented by an infinite series whose terms contain derivatives of the function at a point. In doing so, he laid down his well-known form of the remainder, the difference in value between the sums of a finite and an infinite number of terms of a series. He also contributed significant research in mechanics. In optics, he developed the wave theory, and his name is associated with the simple dispersion formula. In elasticity, he originated the theory of stress, and his results are nearly as valuable as those of Simeon Poisson.

Other significant contributions include being the first to prove the Fermat polygonal number theorem. His collected works, Œuvres complètes d'Augustin Cauchy, have been published in 27 volumes.

Character and legacy

Cauchy was unusual in that he left not only a body of work of monumental proportions, but also the the example of a life devoted to good works. At the same time, he appears to have often been disputatious, sparing with fellow mathematicians, sometimes appearing to deny them credit for their work, and on occasion refusing to admit to the limitations of his own work.

Cauchy was a defender of royalism and hence refused to take oaths to any government after the overthrow of Charles X. This reveals him to have been a man of strong convictions and unbending principles.

He was a devout Catholic and a member of the Society of Saint Vincent de Paul. He also had links to the Society of Jesus and defended them at the French Academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for the mathematician Charles Hermite and to have inspired him to plea on behalf of the Irish during the Potato Famine.

His royalism and religious zeal also made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. Niels Henrik Abel denounced his stubbornness but praised him as a mathematician. Many of Cauchy's views were widely unpopular among mathematicians, and when Guglielmo Libri Carucci dalla Sommaja was made chair in mathematics before him, he, and many others, felt his views were the cause. When Libri was accused of stealing books, he was replaced by Joseph Liouville, which caused a rift between him and Cauchy. Another dispute concerned Jean Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by Jean-Victor Poncelet, that he was in the wrong. Despite that, Cauchy refused to concede and nursed a bitterness on the whole issue.

Still, Cauchy's great contributions to mathematics, and his devotion to teaching as reflected in his important treatises, render trivial the disputes with others he had during his lifetime.


References
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  • Royal Society (Great Britain). 1854. Proceedings of the Royal Society of London. London: Taylor and Francis. 45-49.
  • Kelland. 1858. Notice of the life and writings of Baron Cauchy, in The Edinburgh New Philosophical Journal, Exhibiting a View of the Progressive Discoveries and Improvements in the Sciences and the Arts. Edinburgh: A. and C. Black.
  • Nickles, Jerome. 1858. Obituary in American Journal of Science, 2d ser. 1846-70; New-Haven: Converse. 25:91-95.
  • Mitrinović, Dragoslav S. and Jovan D. Kečkić. 1984. The Cauchy Method of Residues: Theory and Applications. Dordrecht: D. Reidel. 323-324.

External links

All links retrieved August 21, 2023.

This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.

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