Augustin Louis Cauchy
Augustin Louis Cauchy
Augustin Louis Cauchy
August 21 1789
|23 May 1857
|École Centrale du Panthéon
École Nationale des Ponts et Chaussées
|École Nationale des Ponts et Chaussées
|Cauchy integral theorem
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.
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.
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.
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.
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.
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.
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.
ReferencesISBN links support NWE through referral fees
- 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.
All links retrieved August 21, 2023.
- Œuvres complètes d'Augustin Cauchy Académie des sciences (France). Ministère de l'éducation nationale.
- MacTutor biography.
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