Born Augustin Louis Cauchy Augustin Louis Cauchy 21 August 1789 Paris, France 23 May 1857 (aged 67)Sceaux, France France French CalculusComplex analysis École Centrale du PanthéonÉcole Nationale des Ponts et ChausséesÉcole polytechnique École Nationale des Ponts et Chaussées Cauchy integral theorem Catholic

Augustin Louis Cauchy (August 21, 1789May 23, 1857; pronounced [o. Events 1192 - Minamoto Yoritomo becomes Seii Tai Shōgun and the De facto ruler of Japan. Year 1789 ( MDCCLXXXIX) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Common Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city This article is about the country For a topic outline on this subject see List of basic France topics. Events 1430 - Siege of Compiègne: Joan of Arc is captured by the Burgundians while leading an army to relieve Compiègne Click here for Indian Rebellion of 1857 Year 1857 ( MDCCCLVII) was a Common year starting on Thursday (link will display the This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of Mathematics investigating functions of Complex The École nationale des ponts et chaussées (ENPC ("National school of Bridges and Roads" often referred to as les Ponts, is the world's oldest civil For other Écoles Polytechniques see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval The École nationale des ponts et chaussées (ENPC ("National school of Bridges and Roads" often referred to as les Ponts, is the world's oldest civil In Mathematics, the Cauchy integral theorem in Complex analysis, named after Augustin Louis Cauchy, is an important statement about Line integrals Catholic is an Adjective derived from the Greek adjective '' / 'katholikos' meaning "whole" or "complete". Events 1192 - Minamoto Yoritomo becomes Seii Tai Shōgun and the De facto ruler of Japan. Year 1789 ( MDCCLXXXIX) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Common Events 1430 - Siege of Compiègne: Joan of Arc is captured by the Burgundians while leading an army to relieve Compiègne Click here for Indian Rebellion of 1857 Year 1857 ( MDCCCLVII) was a Common year starting on Thursday (link will display the gysˈtɛ̃  lwi koˈʃi]) was a French mathematician. This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. He started the project of formulating and proving the theorems of calculus in a rigorous manner and was thus an early pioneer of analysis. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Analysis has its beginnings in the rigorous formulation of Calculus. He also gave several important theorems in complex analysis and initiated the study of permutation groups. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of Mathematics investigating functions of Complex In Mathematics, a permutation group is a group G whose elements are Permutations of a given set M, and whose group operation 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. Mathematical physics is the scientific discipline concerned with the interface of Mathematics and Physics.

## Biography

Cauchy received his early education from his father Louis François Cauchy (1760–1848), who held several minor public appointments and counted Lagrange and Laplace among his friends. Louis François Cauchy (1760-1848 was a senior French government official and the father of the Mathematician Augustin Louis Cauchy. Cauchy entered l'École Centrale du Panthéon in 1802, proceeded to the École Polytechnique in 1805, and to l'École Nationale des Ponts et Chaussées in 1807, afterwards adopting the profession of an engineer. For other Écoles Polytechniques see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and He left Paris for 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. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city He obtained an appointment at the École Polytechnique, which, however, he relinquished in 1830 on the accession of Louis-Philippe after Charles X of France of the House of Bourbon was ousted. Louis Philippe ( 6 October 1773 &ndash 26 August 1850) was King of the French from 1830 to 1848 in what was known as the Charles X (9 October 1757 – 6 November 1836 ruled as King of France and Navarre from 20 May 1824 until the French Revolution of 1830, when he abdicated The House of Bourbon is an important European Royal house, a branch of the Capetian dynasty. He did this because he found it impossible to take the necessary oaths to the new government because he remained loyal to the House of Bourbon. The House of Bourbon is an important European Royal house, a branch of the Capetian dynasty. 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. Fribourg ( French) (Freiburg or de Freiburg im [[Üechtland]], often Fribourg) is the capital of the Swiss canton of Switzerland (English pronunciation; Schweiz Swiss German: Schwyz or Schwiiz Suisse Svizzera Svizra officially the Swiss Confederation The University of Turin ( Italian Università degli Studi di Torino, UNITO is a University in the city of Turin in the Piedmont region (Note: At that time, Turin was the capital of the Kingdom of Sardinia, which unified Italy later in 1871. Turin is now a city in northern Italy. )

In 1833, the deposed king Charles X of France summoned Cauchy to be a tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impressions that his investigations made. Charles X (9 October 1757 – 6 November 1836 ruled as King of France and Navarre from 20 May 1824 until the French Revolution of 1830, when he abdicated Charles made 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. The Collège de France is a higher education and research establishment ( Grand établissement) located in Paris, France, in the 5th arrondissement François Jean Dominique Arago ( Francesc Joan Dominic Aragó; 26 February 1786 2 October 1853 was a French Catalan Mathematician, Subsequently, Cauchy lived in the France ruled by the emperor Napoleon III until his death in 1857. Napoléon III, also known as Louis-Napoléon Bonaparte (full name Charles Louis Napoléon Bonaparte) (20 April 1808 9 January 1873 was the first President

Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), 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 (1802–1877), a publicist who also wrote several mathematical works.

Cauchy had two daughters.

## Work

Classical mechanics
$\vec{F} = \frac{\mathrm{d}}{\mathrm{d}t}(m \vec{v})$
Newton's Second Law
History of ...
Scientists
Galileo · Kepler · Newton
Laplace · Hamilton · d'Alembert
Cauchy · Lagrange · Euler
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The genius of Cauchy was illustrated in his simple solution of the problem of Apollonius—describing a circle touching three given circles—which he discovered in 1805, his generalization of Euler's formula on polyhedra in 1811, and in several other elegant problems. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Early Ideas on Motion The Greek philosophers, and Aristotle in particular were the first to propose that there are abstract principles governing nature Galileo Galilei (15 February 1564 &ndash 8 January 1642 was a Tuscan ( Italian) Physicist, Mathematician, Astronomer, and Philosopher Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Sir William Rowan Hamilton (4 August 1805 &ndash 2 September 1865 was an Irish Mathematician, Physicist, and Astronomer who In Euclidean plane geometry, Apollonius' problem is to construct Circles that are tangent to three given circles in a plane (Figure 1 two Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the Year 1805 ( MDCCCV) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or In Mathematics, and more specifically in Algebraic topology and Polyhedral combinatorics, the Euler characteristic is a Topological invariant Year 1811 ( MDCCCXI) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common year More important is his memoir on wave propagation, which obtained the Grand Prix of the Institut in 1816. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Year 1816 ( MDCCCXVI) was a Leap year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Leap year 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 (18261828); 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). For other Écoles Polytechniques see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. Year 1821 ( MDCCCXXI) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common year Year 1823 ( MDCCCXXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian Calendar (or a Common For the game see 1826 (board game. Year 1826 ( MDCCCXXVI) was a Common year starting on Sunday (link will display The year 1828 ( MDCCCXXVIII) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian Calendar (or a Leap

Cauchy 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 convergence; 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. In Calculus, Taylor's theorem gives a sequence of approximations of a Differentiable function around a given point by Polynomials (the Taylor He also contributed significant research in mechanics, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements 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. A material is said to be elastic if it deforms under stress (e Stress is a measure of the average amount of Force exerted per unit Area. Siméon-Denis Poisson (21 June 1781 &ndash 25 April 1840 was a French Mathematician, Geometer, and Physicist.

Other significant contributions include being the first to prove the Fermat polygonal number theorem. In Mathematics, the Fermat polygonal number theorem states every positive integer is a sum of at most n n- Polygonal numbers That is every Cauchy created the residue theorem, used it to derive a whole host of interesting series and integral formulas, and was the first to define complex numbers as pairs of real numbers. The residue theorem in Complex analysis is a powerful tool to evaluate Line integrals of Analytic functions over closed curves and can often be used to compute He also discovered many of the basic formulas in the theory of q-series. In Mathematics, in the area of Combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a Q-analog of the common Pochhammer His collected works, Œuvres complètes d'Augustin Cauchy, are published in 27 volumes.

Although generally rigorous, Cauchy 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.

In a paper published in 1855, two years before Cauchy's death, he discussed some theorems, one of which is similar to the "Argument Principle" in many modern textbooks on complex analysis. In Complex analysis, the Argument principle (or Cauchy's argument principle) states that if f ( z) is a Meromorphic function inside 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 Complex analysis, the Argument principle (or Cauchy's argument principle) states that if f ( z) is a Meromorphic function inside The Nyquist stability criterion, named after Harry Nyquist, provides a simple test for Stability of a Closed-loop Control system by examining When a fraction of the output of an amplifier is combined with the input Feedback exists if the feedback opposes the original signal it is negative feedback and if it increases Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input. Thus Cauchy's work has a strong impact on both pure mathematics and practical engineering.

## Politics and religious beliefs

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. Arcueil is a commune in the Val-de-Marne department located in what can be considered as the southern suburbs of Paris The French Revolution (1789–1799 was a period of political and social upheaval in the History of France, during which the French governmental structure previously an 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.

He was an equally staunch Catholic and a member of the Society of Saint Vincent de Paul. The Society of Saint Vincent de Paul is an international organization of Roman Catholic lay men and women of all ages whose primary mission is to help the poor and less [1] He also had links to the Society of Jesus and defended them at the Academy when it was politically unwise to do so. The Society of Jesus ( Latin: Societas Iesu, SJ and SI or SJ, SI) is a Catholic religious order 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. Charles Hermite (ʃaʁl ɛʁˈmit ( December 24, 1822 &ndash January 14, 1901) was a French Mathematician who did It also inspired Cauchy to plead 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 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. Niels Henrik Abel (August 5 1802 &ndash April 6 1829 was a noted Norwegian Mathematician who proved the impossibility of solving the Quintic equation 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. Count Guglielmo Libri Carucci dalla Sommaja (born January 1, 1803 in Florence, Italy; died September 28, 1869 When Libri was accused of stealing books he was replaced by Joseph Liouville which caused a rift between him and Cauchy. Joseph Liouville ( March 24 1809 &ndash September 8 1882) was a French Mathematician. 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. Jean-Victor Poncelet ( July 1, 1788 &ndash December 22, 1867) was a French Engineer and Mathematician who served Despite that Cauchy refused to concede this and nursed a bitterness on the whole issue.

His daughter indicated his last moments brought him a certain calm and that his final words were "Jesus, Mary, and Joseph. "

(For corroboration of claims here see the link to MacTutor History of Mathematics archive for his and Hermite's biographies)

## References

• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain. The Encyclopædia Britannica Eleventh Edition (1910–1911 is a 29-volume reference work that marked the beginning of the Encyclopædia Britannica The public domain is a range of abstract materials &ndash commonly referred to as Intellectual property &ndash which are not owned or controlled by anyone