Augustin-Louis Cauchy: Biography from Answers.com

The French mathematician Augustin Louis Cauchy (1789-1857) provided the foundation for the modern period of rigor in analysis. He launched the theory of functions of a complex variable and was its authoritative pioneer developer.

Augustin Louis Cauchy was born in Paris on Aug. 21, 1789, 38 days after the fall of the Bastille. His father, Louis François, was a parliamentary lawyer, lieutenant of police, and ardent royalist. Sensing the political wind, he moved the family to his country cottage at Arcueil, where they lived for nearly 11 years. Here young Cauchy received a strict religious education from his mother and an elementary classical education from his father, who wrote his own textbooks in verse.

By 1800 the political situation had stabilized and the family moved back to Paris. At the age of 16 Cauchy entered the École Polytechnique, at that time the best school in the world for a budding mathematician. Originally designed to produce military engineers for the Revolutionary armies of France, the school developed as a revolutionary (in method) educational institution. Teaching was linked with research as the nation's finest mathematicians created pure mathematics in discussion with their students and showed them how mathematical theory and practice nourished one another at the very edge of invention.

As Lagrange and Laplace had predicted, Cauchy was a brilliant academic success. In the realm of personal relationships he was not so successful. The generally anticlerical polytechnicians simply could not believe that a brilliant student as aggressively pious and evangelically Catholic as Cauchy could exist. His imperturbability on the matter progressively amused, bewildered, irritated, and infuriated them. It was a pattern of responses that was to become typical in his social relationships. Many years later, after Cauchy had become the most influential mathematician in the world, the naive young genius Abel would conclude that Cauchy was insane. How else could a man of science be so bigoted in religious matters?

From Engineer to Mathematician

From the Polytechnique, Cauchy passed to the École des Ponts et Chaussées, where he studied engineering for 3 years. Upon graduation in 1810, he was sent to Cherbourg as a military engineer. But he could not stay away from pure mathematics. In his spare time he began to review all mathematics, "clearing up obscurities" and inventing new methods for the "simplification of proofs and the discovery of new propositions." He displayed the power and originality of these methods in a series of papers that impressed even the sophisticated mathematical community of Paris. Among these researches were two on polyhedrons, one on symmetric functions, and one on determinants. In the last paper Cauchy reorganized all that was then known about the subject and gave the word "determinant" its modern meaning. All this spare-time work had two results: it broke Cauchy's health, and he abandoned engineering to devote his life to mathematics.

If the mathematical community had been impressed by Cauchy the hobbyist mathematician, it was dazzled by Cauchy the fulltime professional. In 1815 he proved a Fermat conjecture on polygonal (figurate) numbers that had defeated some of the world's best mathematicians. In the following year he demonstrated his versatility by winning the grand prize of the Académie des Sciences with a mathematical treatment of wave propagation on the surface of a fluid. Meanwhile, he had obtained his first teaching position, at the Polytechnique. He was appointed professor there in 1816, and before long he was also lecturing at the Collége de France and the Sorbonne.

At the age of 27 Cauchy was elected to the Académie des Sciences-an unusual honor for so young a man. In his case, there were some who insisted that there was nothing honorable about it. The chair which Cauchy filled had belonged to Gaspard Monge, the father of descriptive geometry, first director of the École Polytechnique, and loyal follower of Napoleon I. The restored Bourbon regime demanded that Monge be expelled from the academy. The academicians complied and elected Cauchy in his place. Cauchy, as rigidly ultraroyalist in politics as he was ultra-Catholic in religion, could never see anything improper about the procedure.

In 1818, securely established as the outstanding mathematician of France, Cauchy married Aloise de Bure. They had two daughters.

Prolific Decade

Cauchy worked as if he expected his worth to be measured by the sheer weight of his publications. His ideas, touching upon nearly every branch of mathematics, pure and applied, seemed to materialize as fast as he could write them down. There were occasions when he would produce two full-length papers in one week.

One of Cauchy's major interests in these years was the attempt to repair the logical foundations of analysis in such a way that this branch of mathematics would have "all the rigor required in geometry." This was a problem of long standing. In his devastating criticism of the Newton-Leibniz calculus, Bishop Berkeley had suggested that the faulty reasoning of the calculus led to correct results because of compensating errors. Maclaurin and Lagrange accepted the criticism and both made heroic efforts to construct a logical justification for the methods of the differential calculus. Neither succeeded.

Cauchy did not quite succeed either. But he took a great step in the right direction when he made the concept of limit the basis for the whole development. His definition of continuity and the derivative in terms of limit was quite modern. But to say that Cauchy" gave the first genuinely mathematical definition of limit, and it has never required modification" is quite wrong.

Cauchy defines "limit" as follows: "When the values successively assigned to the same variable indefinitely approach a fixed value, so as to end by differing from it as little as desired, this fixed value is called the limit of all the others."

As a rough description of the limit idea, Cauchy's "definition" may have merit. But it is verbal, intuitive, crammed with undefined terms, and therefore absolutely nonmathematical in the modern sense. Strangely enough, Cauchy did give a precise mathematical definition of convergent series, and he went on to establish criteria for convergence. It is said that Laplace, after hearing Cauchy's first lectures on series, rushed home in a panic, barred his door, and laboriously tested all the series in his masterpiece, the Mécanique céleste, using Cauchy's criteria. This story, perhaps apocryphal, nevertheless indicates how Cauchy's methods began to set new standards of rigor in analysis.

Between 1825 and 1831 Cauchy published a series of papers which created a new branch of analysis, the theory of functions of a complex variable. It is the principal mathematical tool used in vast domains of physics.

A Matter of Principle

The Revolution of 1830 sent Charles X into exile. The new king, Louis Philippe, demanded oaths of allegiance from the professors of France. Cauchy refused. He had already sworn his oath to Charles. Stripped of all his positions, he exiled himself to Switzerland, leaving his family in Paris.

In 1831 Cauchy was appointed professor of mathematical physics at Turin. Two years later Charles summoned him to Prague to tutor Henri, his 13-year-old grandson. Cauchy, ever the faithful legitimist, agreed to supervise the education of the future pretender. His family joined him in Prague in 1834. Playing Aristotle to Henri's Alexander consumed most of Cauchy's waking hours and sharply curtailed his mathematical output. It never ceased entirely, however. Among the important papers of this period were a long memoir on the dispersion of light, and the first existence proofs for the solution to a system of differential equations.

In 1838 Cauchy and family returned to Paris. Charles had baroneted him, but the title was no help in getting a position, since Baron Cauchy still refused to take the oath. At last, after the Revolution of 1848, the oath was abolished, and Cauchy resumed his old professorship at the Polytechnique. Louis Napoleon reinstituted the oath in 1852, but Cauchy was specifically exempted.

Meanwhile Cauchy's rate of publication reached and even surpassed previous limits. Of special merit in the more than 500 papers that appeared after 1838 were treatises on the mechanics of continuous media, the first rigorous proof of Taylor's theorem, a remarkably modern representation of complex numbers in terms of polynomial congruences, and a collection of papers on the theory of substitutions.

Cauchy's Influence on Mathematics

If the worth of a mathematician were to be measured by the number of times his name appeared in modern college textbooks, Cauchy might be ranked as the greatest of them all. His long-standing influence and fame are due in part to the fact that he swamped the competition with the published word. He was the first mathematician to realize that the greatest material engine of mathematical progress was the printing press. He knew that the entire mathematical community, from professor to arithmetic teacher, took its cue from published papers and textbooks. He literally imprinted his ideas upon a generation.

This practice of rapid publication, together with Cauchy's rather flowery style, had its dangers. Abel, for one, had difficulty in understanding some of Cauchy's papers. "His works are excellent, but he writes in a very confusing manner." But Cauchy's style of writing was the least of the offenses he committed against Abel in particular and mathematics in general. The 15-year delay in the publication of Abel's masterpiece - from 1826 to 1841 - was largely due to Cauchy's cavalier treatment of it. Abel died in 1829, the same year in which Cauchy contributed to the suppression of young Galois's epochmaking discoveries. Galois died in 1832. It was this contemptuous attitude toward younger mathematicians, together with his religious and political bigotry, that made Cauchy unpopular with many of his colleagues. After all, it was difficult to overlook the fact that Galois had been a radical republican.

Cauchy died on May 23, 1857, after a short illness. His last words were, "Men die but their works endure."

Augustin-Louis Cauchy
Augustin-Louis Cauchy around 1840./ Lithography of Zéphirin Belliard after a painting by Jean Roller.
Born	21 August 1789(1789-08-21) Paris, France
Died	23 May 1857 (aged 67) Sceaux ^{[disambiguation needed]}, France
Residence	France
Nationality	French
Fields	Calculus Complex analysis
Institutions	École Centrale du Panthéon École Nationale des Ponts et Chaussées École polytechnique
Alma mater	École Nationale des Ponts et Chaussées
Doctoral students	Francesco Faa' di Bruno
Known for	Cauchy integral theorem
Religious stance	Catholic^[1]

Biography

Youth and education

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.^[2] The Cauchy family survived the revolution and the following Reign of Terror (1794) by escaping to Arcueil, where Cauchy received his first education, from his father. After the death of Robespierre (1794), it was safe for the family to return to Paris. There Louis-François Cauchy found himself a new bureaucratic job, and quickly moved up the ranks. When Napoleon Bonaparte came to power (1799), Louis-François Cauchy was further promoted, and became Secretary-General of the Senate, working directly under Laplace (who is now better known for his work on mathematical physics). The famous mathematician Lagrange was also no stranger in the Cauchy family.

On Lagrange's advice, Augustin-Louis was enrolled in the École Centrale du Panthéon, the best secondary school of Paris at that time, in the fall of 1802. Most of the curriculum consisted of classical languages; the young and ambitious Cauchy, being a brilliant student, won many prizes in Latin and Humanities. In spite of these successes, Augustin-Louis chose an engineering career, and prepared himself for the entrance examination to the École Polytechnique.

In 1805 he placed second out of 293 applicants on this exam, and he was 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 and 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.

Engineering days

After finishing school in 1810, Cauchy accepted a job as a junior engineer in Cherbourg, where Napoleon intended to build a naval base. Here Augustin-Louis stayed for three years, and although he had an extremely busy managerial job, he still found time to prepare three mathematical manuscripts, which he submitted to the Première Classe (First Class) of the Institut de France.^[3] Cauchy's first two manuscripts (on polyhedra) were accepted; the third one (on directrices of conic sections) was rejected.

In September 1812, now 23 years old, after becoming ill from overwork, Cauchy returned to Paris. 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. Although he formally kept his engineering position, he was transferred from the payroll of the Ministry of the Marine to the Ministry of the Interior. The next three years Augustin-Louis was mainly on unpaid sick leave, and spent his time quite fruitfully, working on mathematics (on the related topics of symmetric functions, the symmetric group and the theory of higher-order algebraic equations). He attempted admission to the First Class of the Institut de France, but failed on three different occasions between 1813 and 1815. In 1815 Napoleon was defeated at Waterloo, and the newly installed Bourbon king Louis XVIII (a brother of the beheaded Louis XVI) took the restoration in hand. The Académie des Sciences was re-established in March 1816; Lazare Carnot and Gaspard Monge were removed from this Academy for political reasons, and the king appointed Cauchy to take the place of one of them. The reaction by Cauchy's peers was harsh; they considered his acceptance of membership of the Academy an outrage, and Cauchy thereby created many enemies in scientific circles.

Professor at École Polytechnique

In November 1815, Louis Poinsot, who was an associate professor at the École Polytechnique, asked to be exempted from his teaching duties because of health reasons. Cauchy was by then a rising mathematical star, who certainly merited a professorship. One of his great successes at that time was the proof of Fermat's polygonal number theorem. However, the fact that Cauchy was known to be very loyal to the Bourbons, doubtless also helped him in becoming the successor of Poinsot. He finally quit his engineering job, and received a one-year contract for teaching mathematics to second-year students of the École Polytechnique. In 1816, this Bonapartist, non-religious school was reorganized, and several liberal professors were fired; the reactionary Cauchy was promoted to full professor.

When Cauchy was 28 years old, he was still living with his parents. His father found it high time for his son to marry; he found him a suitable bride, Aloïse de Bure, five years his junior. She was a close relative of the publisher who published most of Cauchy's works. They were married on April 4, 1818, with great Roman Catholic pomp and ceremony, in the Church of Saint-Sulpice. In 1819 the couple's first daughter, Marie Françoise Alicia, was born, and in 1823 the second and last daughter, Marie Mathilde.^[4] It appears that Cauchy did not give an important place to his family in his life, as his work had higher priority. Cauchy had two brothers: Alexandre Laurent Cauchy, 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, a publicist who also wrote several mathematical works.

The oppressive political climate that lasted until 1830 suited Cauchy perfectly. In 1824 Louis XVIII died, and was succeeded by his even more reactionary brother Charles X. During these years Cauchy was highly productive, and published one important mathematical treatise after another. He received cross appointments at the Collège de France, and the Faculté des Sciences of the University.

In exile

In July 1830 France underwent another revolution. Charles X fled the country, and was succeeded by the non-Bourbon king Louis-Philippe (of the House of Orléans). Riots, in which uniformed students of the École Polytechnique took an active part, raged close to Cauchy's home in Paris.

These events marked a turning point in Cauchy's life, and a break in his mathematical productivity. Cauchy, shaken by the fall of the government, and moved by a deep hatred of the liberals who were taking power, left Paris to go abroad, leaving his family behind. He spent a short time at Fribourg in Switzerland, where he had to decide whether he would swear a required oath of allegiance to the new regime. He refused to do this, and consequently lost all his positions in Paris, except his membership of the Academy, for which an oath was not required. In 1831 Cauchy went to the Italian city of Turin, and after some time there, he accepted an offer from the King of Sardinia (who ruled Turin and the surrounding Piedmont region) for a chair of theoretical physics, which was created especially for him. He taught in Turin during 1832-1833. In 1831, he had been elected a foreign member of the Royal Swedish Academy of Sciences.

In August 1833 Cauchy left Turin for Prague, to become the science tutor of the thirteen year old Duke of Bordeaux Henri d'Artois (1820-1883), the exiled Crown Prince and grandson of Charles X. As a professor of the École Polytechnique, Cauchy had been a notoriously bad lecturer, assuming levels of understanding that only a few of his best students could reach, and cramming his allotted time with much too much material. The young Duke had neither taste nor talent for either mathematics or science, so student and teacher were a perfect mismatch. Although Cauchy took his mission very seriously, he did this with great clumsiness, and with surprising lack of authority over the Duke.

During his civil engineering days, Cauchy once had been briefly in charge of repairing a few of the Parisian sewers, and he made the mistake of telling his pupil this; with great malice, the young Duke went about saying that Mister Cauchy started his career in the sewers of Paris. His role as tutor lasted until the Duke became eighteen years old, in September 1838. Cauchy did hardly any research during those five years, while the Duke acquired a life-long dislike of mathematics. The only good that came out of this episode was Cauchy's promotion to Baron, a title that Cauchy set great store by. In 1834, his wife and two daughters moved to Prague, and Cauchy was finally reunited with his family, after four years of exile.

Last years

Cauchy returned to Paris and his position at the Academy of Sciences late in 1838. He could not regain his teaching positions, because he still refused to swear an oath of allegiance. However, he desperately wanted to regain a formal position in Parisian science.

In August 1839 a vacancy appeared in the Bureau des Longitudes. This Bureau had some resemblance to the Academy; for instance, it had the right to co-opt its members. Further, it was believed that members of the Bureau could "forget" about the oath of allegiance, although formally, unlike the Academicians, they were obliged to take it. The Bureau des Longitudes was an organization founded in 1795 to solve the problem of determining position on sea - mainly the longitudinal coordinate, since latitude is easily determined from the position of the sun. Since it was thought that position on sea was best determined by astronomical observations, the Bureau had developed into an organization resembling an academy of astronomical sciences.

In November 1839 Cauchy was elected to the Bureau, and discovered immediately that the matter of the oath was not so easily dispensed with. Without his oath, the king refused to approve his election. For four years Cauchy was in the absurd position of being elected, but not being approved; hence, he was not a formal member of the Bureau, did not receive payment, could not participate in meetings, and could not submit papers. Still Cauchy refused to take any oaths; however, he did feel loyal enough to direct his research to celestial mechanics. In 1840, he presented a dozen papers on this topic to the Academy. The absurd membership of the Bureau lasted until the end of 1843, when Cauchy was finally replaced by Poinsot.

All through the nineteenth century the French educational system struggled with the separation of Church and State. The Catholic Church strived for freedom of education (that is, the right to establish Catholic schools); the Church found in Cauchy a staunch and illustrious ally in this struggle. He lent his prestige and knowledge to the École Normale Écclésiastique, a school in Paris run by Jesuits, for training teachers for their colleges. He also took part in the founding of the Institut Catholique. The purpose of this institute was to counter the effects of the absence of Catholic university education in France. These activities did not make Cauchy popular with his colleagues who, on the whole, supported the Enlightenment ideals of the French Revolution. When a chair of mathematics became vacant at the Collège de France in 1843, Cauchy applied for it, but got just three out of 45 votes.

The year 1848 was the year of revolution all over Europe; revolutions broke out in numerous countries, beginning in France. King Louis-Philippe, fearful of sharing the fate of Louis XVI, fled to England. The oath of allegiance was abolished, and the road to an academic appointment was finally clear for Cauchy. On March 1, 1849, he was reinstated at the Faculté de Sciences, as a professor of mathematical astronomy. After political turmoil all through 1848, France chose to become a Republic, under the Presidency of Louis Napoleon Bonaparte, nephew of Napoleon Bonaparte, and son of Napoleon's brother, who had been installed as the first king of Holland. Soon (early 1852) the President became the Emperor of France, and took the name Napoleon III.

Not unexpectedly, the idea came up in bureaucratic circles that it would be useful to require a loyalty oath from all state functionaries, including university professors. Not always does history repeat itself, however, because this time a cabinet minister was able to convince the Emperor to exempt Cauchy from the oath. Cauchy remained a professor at the University until his death at the age of 67. He received the Last Sacraments and died at 4 a.m. during the night of May 23, 1857.

Work

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. More important is his memoir on wave propagation, which obtained the Grand Prix of the French Academy of Sciences in 1816. Cauchy's writings covered notable topics including: the theory of series, where he developed the notion of convergence and discovered many of the basic formulas for q-series. The theory of numbers and complex quantities; he was the first to define complex numbers as pairs of real numbers. The theory of groups and substitutions; and the theory of functions, differential equations, and determinants.

In the theory of light he worked on Fresnel's wave theory and on the dispersion and polarization of light. He also contributed significant research in mechanics, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. He wrote on the equilibrium of rods and elastic membranes and on waves in elastic media. He introduced^[5] a 3 × 3 symmetric matrix of numbers that is now known as the Cauchy stress tensor. 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.

However, Cauchy is most famous for his single-handed development of complex function theory. The first pivotal theorem proved by Cauchy, now known as Cauchy's integral theorem, was the following:

$\oint_C f(z)dz = 0,$

where f(z) is a complex-valued function analytic on and within the non-self-intersecting closed curve C (contour) lying in the complex plane. The contour integral is taken along the contour C. The rudiments of this theorem can already be found in a paper that the twenty-four year old Cauchy presented to the Académie des Sciences (then still called "First Class of the Institute") on August 11, 1814. In full form^[6] the theorem was given in 1825. The 1825 paper is seen by many as Cauchy's most important contribution to mathematics.

In 1826^[7] Cauchy gave a formal definition of a residue of a function. This concept regards functions that have poles—isolated singularities, i.e., points where a function goes to infinity. If the complex-valued function f(z) can be expanded in the neighborhood of a singularity a as

$f(z) = \phi(z) + \frac{B_1}{z-a} + \frac{B_2}{(z-a)^2} + \cdots \frac{B_n}{(z-a)^n},\quad B_i, z,a \in \mathbb{C},$

where φ(z) is analytic (i.e., well-behaved without singularities), then f is said to have a pole of order n in the point a. If n = 1, the pole is called simple. The coefficient B₁ is called by Cauchy the residue of function f at a. If f is non-singular at a then the residue of f is zero at a. Clearly the residue is in the case of a simple pole equal to,

$\underset{z=a}{\mathrm{Res}} f(z) = \lim_{z \rightarrow a} (z-a) f(z),$

where we replaced B₁ by the modern notation of the residue.

In 1831, while in Turin, Cauchy submitted two papers to the Academy of Sciences of Turin. In the first^[8] he proposed the formula now known as Cauchy's integral formula,

$f(a) = \frac{1}{2\pi i} \oint_C \frac{f(z)}{z-a} dz,$

where f(z) is analytic on C and within the region bounded by the contour C and the complex number a is somewhere in this region. The contour integral is taken counter-clockwise. Clearly, the integrand has a simple pole at z = a. In the second paper^[9] he presented the residue theorem,

$\frac{1}{2\pi i} \oint_C f(z) dz = \sum_{k=1}^n \underset{z=a_k}{\mathrm{Res}} f(z),$

where the sum is over all the n poles of f(z) on and within the contour C. These results of Cauchy's still form the core of complex function theory as it is taught today to physicists and electrical engineers. For quite some time, contemporaries of Cauchy ignored his theory, believing it to be too complicated. Only in the 1840s the theory started to get response, with Pierre-Alphonse Laurent being the first mathematician, besides Cauchy, making a substantial contribution (his Laurent series published in 1843).

The title page of a textbook by Cauchy.

In addition to his work on complex functions, Cauchy was the first to stress the importance of rigor in analysis; 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 wrote a textbook^[10] (see the illustration) for his students at the École Polytechnique in which he developed the basic theorems of mathematical analysis as rigorously as possible. In this book he gave the necessary and sufficient condition for the existence of a limit in the form that is still taught. Also Cauchy's well-known test for absolute convergence stems from this book: Cauchy condensation test. In 1829 he defined for the first time a complex function of a complex variable in another textbook.^[11] In spite of these, Cauchy's own research papers often used intuitive, not rigorous, methods;^[12] thus one of his theorems was exposed to a "counter-example" by Abel, later fixed by the introduction of the notion 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 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 a strong impact on both pure mathematics and practical engineering.

Cauchy was very productive, in number of papers second only to Leonhard Euler. It took almost a century to collect all his writings into 27 large volumes:

Oeuvres complètes d'Augustin Cauchy publiées sous la direction scientifique de l'Académie des sciences et sous les auspices de M. le ministre de l'Instruction publique (27 volumes) (Paris : Gauthier-Villars et fils, 1882-1974)

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 royale polytechnique (1821)
Le Calcul infinitésimal (1823)
Leçons sur les applications de calcul infinitésimal; La géométrie (1826–1828)

His other works include:

Exercices d'analyse et de physique mathematique (Volume 1)
Exercices d'analyse et de physique mathematique (Volume 2)
Exercices d'analyse et de physique mathematique (Volume 3)
Exercices d'analyse et de physique mathematique (Volume 4) (Paris: Bachelier, 1840-1847)
Analyse algèbrique (Imprimerie Royale, 1821)
Nouveaux exercices de mathématiques (Paris : Gauthier-Villars, 1895)
Courses of mechanics (for the École Polytechnique)
Higher algebra (for the Faculté des Sciences)
Mathematical physics (for the Collège de France).

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. Their life there was apparently hard and Lois-François Cauchy spoke of living on rice, bread, and crackers during the period. A paragraph from an undated letter from Louis-François to his mother in Rouen, cited by C A Valson in Vie et les Travaux du baron Cauchy (Volume 1, Pg 13) says:

We never had more than a half pound of bread — and sometimes not even that. This we supplement with little supply of hard crackers and rice that we are allotted. Otherwise, we are getting along quite well, which is the important thing and goes to show that human beings can get by with little. I should tell you that for my children's pap I still have a bit of fine flour, made from wheat that I grew on my own land. I had three bushels, and I also have a few pounds of potato starch. It is as white as snow and very good, too, especially for very young children. It, too, was grown on my own land (9).^[13]

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.^[14] 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 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. 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.

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

Notes

^ "Cauchy biography". History.mcs.st-and.ac.uk. http://www-history.mcs.st-and.ac.uk/Biographies/Cauchy.html. Retrieved 2009-06-19.
^ His father's dismissal is sometimes seen as the cause of the deep hatred of the French Revolution that Cauchy felt all through his life.
^ In the revolutionary years the French Académie des Sciences was known as the "First Class" of the Institut de France.
^ Belhoste, Bruno (1991). Augustin-Louis Cauchy: A Biography. Ann Arbor, Michigan: Springer-Verlag New York Inc.. p. 134. ISBN 3-540-97220-x.. http://www.amazon.com/Augustin-Louis-Studies-Mathematics-Physical-Sciences/dp/354097220X/ref=sr_11_1?ie=UTF8&qid=1238792211&sr=11-1.
^ Cauchy, De la pression ou tension dans un corps solide, [On the pressure or tension in a solid body], Exercices de Mathématiques, vol. 2, p. 42 (1827)
^ Cauchy, Mémoire sur les intégrales définies prises entre des limites imaginaires [Memorandum on definite integrals taken between imaginary limits], submitted to the Académie des Sciences on February 28, 1825
^ Cauchy, Sur un nouveau genre de calcul analogue au calcul infinitésimal [On a new type of calculus analogous to the infinitesimal calculus], Exercices de Mathématique, vol. 1, p. 11 (1826)
^ Cauchy, Sur la mécanique céleste et sur un nouveau calcul qui s'applique à un grande nombre de questions diverses [On the celestial mechanics and on a new calculus that can be appplied to a great number of diverse questions], presented to the Academy of Sciences of Turin, October 11, 1831.
^ Cauchy, Mémoire sur les rapports qui existent entre le calcul des Résidus et le calcul des Limites, et sur les avantages qu'offrent ces deux calculs dans la résolution des équations algébriques ou transcendantes Memorandum on the connections that exist between the residue calculus and the limit calculus, and on the advantages that these two calculi offer in solving algebraic and transcendental equations], presented to the Academy of Sciences of Turin, November 27, 1831.
^ Cauchy, Course d'Analyse de l'École Royale Polytechnique, I.^re partie, Analyse Algébrique, Paris (1821)
^ Cauchy, Leçons sur le Calcul Différentiel, Paris (1829)
^ Morris Kline, Mathematics: The Loss of Certainty, ISBN 0-19-503085-0, p. 176
^ Belhoste, Bruno (1991). Augustin-Louis Cauchy: A Biography. Ann Arbor, Michigan: Springer-Verlag New York Inc.. p. 3. ISBN 3-540-97220-x.. http://www.amazon.com/Augustin-Louis-Studies-Mathematics-Physical-Sciences/dp/354097220X/ref=sr_11_1?ie=UTF8&qid=1238792211&sr=11-1.
^ "CATHOLIC ENCYCLOPEDIA: Augustin-Louis Cauchy". Newadvent.org. 1908-11-01. http://www.newadvent.org/cathen/03457a.htm. Retrieved 2009-06-19.

References

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External links

Wikiquote has a collection of quotations related to: Augustin-Louis Cauchy

O'Connor, John J.; Robertson, Edmund F., "Augustin-Louis Cauchy", MacTutor History of Mathematics archive .
Cauchy criterion for convergence
Œuvres complètes d'Augustin Cauchy Académie des sciences (France). Ministère de l'éducation nationale.
Augustin-Louis Cauchy at the Mathematics Genealogy Project
Augustin-Louis Cauchy - Cauchy's Life by Robin Hartshorne

Persondata
NAME	Cauchy, Augustin Louis
ALTERNATIVE NAMES
SHORT DESCRIPTION	calculus
DATE OF BIRTH	21 August 1789(1789-08-21)
PLACE OF BIRTH	Dijon, France
DATE OF DEATH	23 May 1857
PLACE OF DEATH	Paris, France

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Augustin-Louis Cauchy

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